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Problem 8101

Triangles $J K L$ and $P Q R$ are congruent, where $J$ corresponds to $P$ , and $K$ corresponds to $Q$ . The measure of angle $J$ is $45^{\circ}$ , the measure of angle $K$ is $10^{\circ}$ , and the measure of angle $L$ is $125^{\circ}$ . What is the measure, in degrees, of angle $P$ ? (Disregard the degree symbol when entering your answer.) $\square$ Answer Preview:

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Problem 8102

iClicker Student - Login HW9.7 - PHYS 112 | PrairieLe 1 Inbox (1,047) - rhea.umraniac gordon ramsay thaw black se prairielearn.ok.ubc.ca/pl/course_instance/58/instance_question/2435307/ irieLearn PHYS 112, 2024WT1S2 Assessments Gradebook HW9
HW9.7. Rotational Displacement of Tires
A van accelerates from rest at $t=0$ such that its tires undergo a constant rotational acceleration of $\alpha=$ $8.51 \mathrm{rad} / \mathrm{s}^{2}$ .
Compute the rotational displacement of each tire at $t=13.5 \mathrm{~s}$ . $\Delta \theta$ number (rtol $=0.05$ , atol $=1 \mathrm{e}-08$ )
Problem is licensed under the CC-BY-NC-SA 4.0 license. (c) $\mathrm{CH}_{\mathrm{BY}}^{\mathrm{NC}}$ (5) () Save \& Grade 4 attempts left Save only Additional attempts available with new variants -

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Problem 8103

Suppose the weights of seventh-graders at a certain school vary according to a Normal distribution, with a mean of 100 poun and a standard deviation of 7.5 pounds. A researcher believes the average weight has decreased since the implementation of a new breakfast and lunch program at the school. She finds, in a random sample of 35 students, an average weight of 98 pounds.
What is the $P$ -value for an appropriate hypothesis test of the researcher's claim? $-1.578$ 0.115 0.943 0.057

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Problem 8104

A real estate company offers a series of three webinars. 2,000 people attended the first webinar $65 \%$ of the people who attended the first webinar attended the second webinar, and $44 \%$ of the people who attended both the first and second webinar attended the third webinar. Of those who attended the first but did not attend the second webinar, $31 \%$ attended the third webinar. How many people attended both the first and third webinars but did not attend the second webinar?
Answer Preview:

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Problem 8105

HW9.5. Frictional Force between Tires and the Road
A racecar of mass $m$ is driving around a horizontal circular track of radius $R$ at constant speed $v$ . The frictional force between the tires of the racecar and the road is at its maximum value.
Write the expression to find the value of the coefficient of friction between the tires and the road in terms of the mass $m$ , velocity $v$ , radius $R$ , and the acceleration of free-fall $g$ .
Note that it may not be necessary to use every variable. Use the following table as a reference for each variable: For Use m m $v \mathrm{v}$ $R$ R $g \quad \mathrm{~g}$

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Problem 8106

A random sample of 40 students has a mean annual earnings of $\$ 3120$ and assume that the population standard deviation is $\$ 677$ . Construct the confidence interval for the population mean, $\mu$ if $\mathrm{c}=0.95$ . A. $(\$ 4812, \$ 5342)$ B. $(\$ 210, \$ 110)$ C. $(\$ 1987, \$ 2346)$ D. $(\$ 2910, \$ 3330)$

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Problem 8107

18. Two friends can paddle a canoe at a rate of $6 \mathrm{~km} / \mathrm{h}$ in still water. It takes them 1 h to paddle 2 km up a river and back again. Find the speed of the current.

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Problem 8108

Write down, but do not solve, an equation that correctly states the following relationship. Use $x$ to represent the unknown quantity.
The sum of the distance driven on Wednesday and 234 is 579. $\square$

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Problem 8109

prombe, possinge
Determine the monthly principal and interest payment for a 20 -year mortgage when the amount financed is $\$ 285,000$ and the annual percentage rate (APR) is $4.5 \%$ . Click here for table of Monthly Payments
The monthly principal and interest payment is $\$$ $\square$ (Round to the nearest cent as needed.) Monthly Principal and Interest Payment per \1000 of Mortgage \begin{tabular}{|cccccc|} \hline \multicolumn{5}{c|}{ Number of Years } \\ Rate \% & 10 & 15 & \mathbf{2 0} & \mathbf{2 5} & \mathbf{3 0} \\ 4.0 & \ $10.12451$ & $\$ 7.39688$ & $\$ 6.05980$ & $\$ 5.27837$ & $\$ 4.77415$ \\ 4.5 & $\$ 10.36384$ & $\$ 7.64993$ & $\$ 6.32649$ & $\$ 5.55832$ & $\$ 5.06685$ \\ 5.0 & $\$ 10.60655$ & $\$ 7.90794$ & $\$ 6.59956$ & $\$ 5.84590$ & $\$ 5.36822$ \\ 5.5 & $\$ 10.85263$ & $\$ 8.17083$ & $\$ 6.87887$ & $\$ 6.14087$ & $\$ 5.67789$ \\ 6.0 & $\$ 11.10205$ & $\$ 8.43857$ & $\$ 7.16431$ & $\$ 6.44301$ & $\$ 5.99551$ \\ 6.5 & $\$ 11.35480$ & $\$ 8.71107$ & $\$ 7.45573$ & $\$ 6.75207$ & $\$ 6.32068$ \\ 7.0 & $\$ 11.61085$ & $\$ 8.98828$ & $\$ 7.75299$ & $\$ 7.06779$ & $\$ 6.65302$ \\ 7.5 & $\$ 11.87018$ & $\$ 9.27012$ & $\$ 8.05593$ & $\$ 7.38991$ & $\$ 6.99215$ \\ 8.0 & $\$ 12.13276$ & $\$ 9.55652$ & $\$ 8.36440$ & $\$ 7.71816$ & $\$ 7.33765$ \\ 8.5 & $\$ 12.39857$ & $\$ 9.84740$ & $\$ 8.67823$ & $\$ 8.05227$ & $\$ 7.68913$ \\ 9.0 & $\$ 12.66758$ & $\$ 10.14267$ & $\$ 8.99726$ & $\$ 8.39196$ & $\$ 8.04623$ \\ 9.5 & $\$ 12.93976$ & $\$ 10.44225$ & $\$ 9.32131$ & $\$ 8.73697$ & $\$ 8.40854$ \\ \hline \end{tabular}

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Problem 8110

```latex Is there a doctor in the house? A market research firm reported the mean annual earnings of all family practitioners in the United States was random sample of 47 family practitioners in Los Angeles had mean earnings of $\bar{x}=\$192,890$ with a standard deviation of $\$43,117$ . Do the data significance and the $P$ -value method with the TI-84 Plus calculator.
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. ```

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Problem 8111

An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region $A$ is less than the wind speed in Region $B$ . To test the regions, the average wind speed is calculated for 90 days in each region. The mean wind speed in Region A is 14.1 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.3 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At $\alpha=0.05$ , can the company support the researcher's claim? Complete parts (a) through (d) below. D. The wind speed in Region A is less than the wind speed in Region B.
Let Region $A$ be sample 1 and let Region $B$ be sample 2. Identify $H_{0}$ and $H_{a}$ . $\begin{array}{l} H_{0}: \mu_{1} \geq \mu_{2} \\ H_{a}: \mu_{1}<\mu_{2} \end{array}$ (b) Find the critical value(s) and identify the rejection region.
The critical value(s) is/are $z_{0}=$ $\square$ (Round to two decimal places as needed. Use a comma to separate answers as needed.)

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Problem 8112

Question 25 Points: 1
A house cleaning service claims that it can clean a four-bedroom house in less than 2 hours. A sample of $n=16$ houses is taken, and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours.
Write the interpretation base on the decision. A. There is enough evidence to reject the claim B. There is not enough evidence to support the claim C. There is enough evidence to support the claim D. There is not enough evidence to reject the claim

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Problem 8113

Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2. A. $(56.12,78.34)$ B. $(77.29,85.71)$ C. $(66.35,69.89)$ D. $(87.12,98.32)$

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Problem 8114

www-awualeks.com Content Aleks Blackboard Content Session Clo... Content Jonathan $\mathrm{V}_{\text {-. }}$ Timed Out knicks - Go... NFL Footba... Homework * 5: 9(1,3,4,5) 14(1,2) Question 10 of 30 (1 point) I Question Attempt: 1 of 3
Spam: A researcher reported that $71.8 \%$ of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be $77 \%$ . He examines a random sample of 500 emails received at an email server, and finds that 364 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from $77 \%$ ? Use both $\alpha=0.01$ and $\alpha=0.05$ levels of significance and the $P$ -value method with the TI-84 Plus calculator.
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypotheses test is a left-tailed $\quad \nabla$ test.
Correct Answer: $\begin{array}{l} H_{0}: p=0.77 \\ H_{1}: p \neq 0.77 \end{array}$
This hypotheses test is a two-tailed test.
Part: $1 / 5$
Part 2 of 5 (b) Compute the value of the test statistic. Round the answer to at least two decimal places. $z=\square$

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Problem 8115

\text{A researcher reported that } 71.8\% \text{ of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be } 77\%. \text{ He examines a random sample of 500 emails received at an email server, and finds that 364 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from } 77\%? \text{ Use both } \alpha=0.01 \text{ and } \alpha=0.05 \text{ levels of significance and the } P\text{-value method with the TI-84 Plus calculator.}
\text{Part 1 of 5}
(a) \text{ State the appropriate null and alternate hypotheses.}
$\begin{array}{l} H_{0}: \square^{\otimes} \\ H_{1}: \square^{\otimes} \end{array}$
\text{This hypotheses test is a left-tailed} \square \text{ test.}
\text{Correct Answer:}
$\begin{array}{l} H_{0}: p=0.77 \\ H_{1}: p \neq 0.77 \end{array}$
\text{This hypotheses test is a two-tailed test.}
\text{Part 2 of 5}
(b) \text{ Compute the value of the test statistic. Round the answer to at least two decimal places.}
$z=2.23$
\text{Correct Answer:}
$z=-2.23$
\text{Part: } 2/5
\text{Part 3 of 5}
(c) \text{ Compute the } P\text{-value. Round the answer to at least four decimal places,}
$P \text{-value }=$

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Problem 8116

$Q$ is a point on segment $\overline{P R}$ . If $P Q=4 x+3, Q R=3 x+8$ , and $P R=18$ , what is $P Q$ ? Simplify your answer and write it as a proper fraction, mixed number, or integer.

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Problem 8117

Problem 1. Professor Naehrig is running on a circular track in a uniform circular motion. Her position can be described through the parametric equations $x=10+100 \cos \left(\frac{2}{3} \pi t+\frac{\pi}{4}\right) \text { and } y=100 \sin \left(\frac{2}{3} \pi t+\frac{\pi}{4}\right) \text {, }$ where $t$ is measured in minutes, the angle is measured in radians, and lengths are measured in meters.
1. What are the circle center coordinates?
2. Explain the meaning of $\frac{2}{3} \pi$ in the parametric equations.
3. Explain the meaning of $\frac{\pi}{4}$ in the parametric equations.
4. What is the radius of the circular track?
5. In coordinate system, sketch the circular track and Professor Naehrig's position at $t=0, t=0.5, t=1.5, t=3$ minutes.
6. Find the first 3 times when Professor Naehrig's $x$ -coordinate is $50 \sqrt{3}+10$ .
7. At the first time you found in the previous part, how far is she from the point $(20,30)$ ?
8. Find the first 3 times when Professor Naehrig's $y$ -coordinate is $50 \sqrt{2}$ . What is her $x$ -position at those respective times?

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Problem 8118

```latex \text{Homework } \mathbf{f} \, 5: 9(1,3,4,5) \, 14(1,2) \\ \text{Question 10 of 30 (1 point) I Question Attempt: 1 of 3} \\ \text{Jonathan} \\ 6 \\ 7 \\ 8 \\ \checkmark 9 \\ 10 \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ \text{Españ} \\ 17 \\
\text{Spam: A researcher reported that } 71.8\% \text{ of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be } 77\%. \text{ He examines a random sample of 500 emails received at an email server, and finds that 364 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from } 77\% \text{? Use both } \alpha=0.01 \text{ and } \alpha=0.05 \text{ levels of significance and the } P\text{-value method with the TI-84 Plus calculator.}
\text{Part 1 of 5} \\ \text{(a) State the appropriate null and alternate hypotheses.} \\ H_{0}: \square^{\infty} \\
\text{Part 3 of 5} \\ \text{(c) Compute the } P\text{-value. Round the answer to at least four decimal places.} \\ P\text{-value }=0.05^{\otimes} \\
\text{Correct Answer:} \\ P\text{-value }=0.0256 \\
\text{Part 4 of 5} \\ \text{(d) Determine whether to reject } H_{0}. \\
\text{At the } \alpha=0.01 \text{ level, do not reject } \nabla \text{ the null hypothesis } H_{0}. \\ \text{At the } \alpha=0.05 \text{ level, reject } \quad \boldsymbol{r} \text{ the null hypothesis } H_{0}. \\
\text{Part: } 4 / 5 \\
\text{Part 5 of 5} \\ \text{(e) State a conclusion.} \\
\text{At the } \alpha=0.01 \text{ level of significance, there } \square \text{ enough evidence to conclude that the percentage of emails that are spam differs from } 77\%. \\ \text{At the } \alpha=0.05 \text{ level of significance, there } \square \text{ (Choose one) enough evidence to conclude that the percentage of emails that are spam differs from } 77\%. \\ \text{Skip Part} \\ \text{Check} \\ \text{Save For Later} \\ \text{Submit Assignment}

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Problem 8119

Homework $/ 5: 9(1,3,4,5) 14(1,2)$ Question 11 of 30 (1 point) I Question Attempt 1 of 3 Jonathan 06 6 07 $\checkmark 9$ 10 11 12 13 14 15 Español 16 17
Confidence in banks: A poll conducted asked a random sample of 1358 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults said that they had a great deal of confidence. An economist claims that less than $13 \%$ of $\mathrm{U} . \mathrm{S}$ . adults have a great deal of confidence in banks. Can you conclude that the economist's claim is true? Use both $\alpha=0.10$ and $\alpha=0.01$ levels of significance and the $P$ -value method with the TI-84 Plus calculator.
Part: $0 / 5$
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypothesis test is a (Choose one) $\boldsymbol{\nabla}$ test. Skip Part Check Save For Later O 2024 MaGrow HIIILC. All Rights Resened

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Problem 8120

In a survey of 200 females who recently completed high school, $76 \%$ were enrolled in college. In a survey of 150 males who recently completed high school, $68 \%$ were enrolled in college. At $\alpha=0.07$ , can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). (a) Identify the claim and state $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$ .
The claim is "the proportion of female college enrollees is $\square$ the proportion of male college enrollees."

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Problem 8121

A musician charges $C(x)=64 x+30,000$ where $x$ is the total number of attendees at the concert. The venue charges $\$ 84$ per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?
The venue breaks even after $\square$ tickets are sold for a total value of $\$$ $\square$

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Problem 8122

Homework $\boldsymbol{0}$ 5: $9(1,3,4,5) 14(1,2)$ Question 11 of 30 (1 point) I Question Attempt: 1 of 3 Jonath
Confidence in banks: A poll conducted asked a random sample of 1358 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults sald that they had a great deal of confidence. An economist claims that less than 13\% of U.S. adults have a great deal of confidence in banks. Can you conclude that the economist's claim is true? Use both $\alpha=0.10$ and $\alpha=0.01$ levels of significance and the $P$ -value method with the TI-84 Plus calculator.
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: 0.10 \\ H_{1}: 0.01 \end{array}$
This hypothesis test is a right-tailed $\boldsymbol{\nabla}$ test.
Correct Answer: $\begin{array}{l} H_{0}: p=0.13 \\ H_{1}: p<0.13 \end{array}$
This hypothesis test is a left-tailed test.
Part: $1 / 5$
Part 2 of 5 (b) Compute the value of the test statistic. Round the answer to at least two decimal places. $z=\square$ Skip Part Check Save For Later Submit Assign - 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use I Pivacy Center I Ace

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Problem 8123

A Jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 9 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 292.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.
The Jeep was traveling at $\square$ mph and the BMW was traveling at $\square$ mph.

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Problem 8124

22. (II) A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75 . What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

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Problem 8125

23. (II) In Fig. 5-36 the coefficient of static friction between mass $m_{\mathrm{A}}$ and the table is 0.40 , whereas the coefficient of kinetic friction is 0.30 . (a) What minimum value of $m_{\mathrm{A}}$ will keep the system from starting to move? (b) What value(s) of $m_{\mathrm{A}}$ will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.]

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Problem 8126

24. (II) A $68-\mathrm{kg}$ snowboarder has an initial velocity of $5.0 \mathrm{~m} / \mathrm{s}$ at the top of a $28^{\circ}$ incline (Fig. 5-37). After sliding down the $110-\mathrm{m}$ -long incline (assume a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.18$ ), the snowboarder has attained a velocity $v$ . The snowboarder then slides along a flat surface (on which $\left.\mu_{\mathrm{k}}=0.15\right)$ and comes to rest after a distance $x$ . Use Newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface. Then use these accelerations to determine $x$ . Ignore air resistance.

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Problem 8127

25. (II) A package of mass $m$ is dropped vertically onto a horizontal conveyor belt whose speed is $v=1.5 \mathrm{~m} / \mathrm{s}$ , and the coefficient of kinetic friction between the package and the belt is $\mu_{\mathrm{k}}=0.70$ . (a) For how much time does the package slide on the belt (until it is at rest relative to the belt)? (b) How far does the package move during this time?

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Problem 8128

FIGURE 5-38 Problem 26. (II) A child slides down a slide with a $28^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

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Problem 8129

28. (II) (a) Suppose the coefficient of kinetic friction between $m_{\mathrm{A}}$ and the ramp in Fig. $5-39$ is $\mu_{\mathrm{k}}=0.15$ , and that $m_{\mathrm{A}}=m_{\mathrm{B}}=2.7 \mathrm{~kg}$ . As $m_{\mathrm{B}}$ moves down, determine the magnitude of the acceleration of $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$ , given $\theta=34^{\circ}$ . (b) What smallest value of $\mu_{\mathrm{k}}$ will keep the system from accelerating? [Ignore masses of cord and (frictionless) pulley.]
FIGURE 5-39 Problem 28. Problems 139

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Problem 8130

30. (III) For two blocks, connected by a cord and sliding down the incline shown in Fig. 5-40 (see Problem 29), describe the motion $(a)$ if $\mu_{\mathrm{A}}<\mu_{\mathrm{B}}$ , and $(b)$ if $\mu_{\mathrm{A}}>\mu_{\mathrm{B}}$ . (c) Determine a formula for the acceleration of each block and the tension $F_{\mathrm{T}}$ in the cord in terms of $m_{\mathrm{A}}, m_{\mathrm{B}}$ , and $\theta$ ; interpret your results in light of your answers to $(a)$ and $(b)$

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Problem 8131

Content Aleks Blactboard Content Content Session Cla... Timed Out knicks - -0 NFL Footba. (6) Kaicena Honswoik $\neq 5,9(3,4,5) 4(2)$ Question 16 of 30 (1 point) ; Question Attempt: 1 of 3 Jonathan
10 12 13 14 15 $\equiv 16$ 17 18 19 Espar
A random sample of size 13 from a normal distribution has standard deviation $s=51$ . Test $H_{0}: \sigma=46$ versus $H_{1}: \sigma>46$ . Use the $\alpha=0.01$ level of significance. Part 1 of 5
The hypotheses are provided above. This hypothesis test is a $\square$ right-tailed test.
Part: $1 / 5$
Part 2 of 5
Find the critical value. Critical value $=$ $\square$ Skip Part Check Save For Later Submit Assignmen

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Problem 8132

31. (III) A $2.5-\mathrm{kg}$ block is placed on a table as shown in Fig. 5-41. The coefficient of kinetic friction between the block and the table is 0.35 . The block is connected by massless ropes over pulleys (whose mass and friction can be ignored) to a $5.0-\mathrm{kg}$ block on the right, and a $3.0-\mathrm{kg}$ block on the left, as shown in Fig. 5-41. Find the acceleration of the block on the table if it is moving to the right.
FIGURE 5-41 Problem 31.

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Problem 8133

www-awu_aleks.com - Nor... Content A Aleks Blackboard Content Content Timed Out Homework $=5: 9(1,3,4,5) 14(1,2)$ Question 16 of 30 (1 point) I Question Attempt: 1 of 3 ( 10 11 12 13 14 15 17 $=16$ 18 19 Jona
A random sample of size 13 from a normal distribution has standard deviation $s=51$ . Test $H_{0}: \sigma=46$ versus $H_{1}: \sigma>46$ . Use the $\alpha=0.01$ level of significance. Part 1 of 5
The hypotheses are provided above. This hypothesis test is a right-tailed $\square$ test. Part 2 of 5
Find the critical value. Critical value $=$ 26.217 $\square$
Part: $2 / 5$
Part 3 of 5
Compute the test statistic. Round the answer to three decimal places as needed. $\chi^{2}=$ $\square$ Skip Part Check

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Problem 8134

Use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram. $\begin{array}{l} n(A)=30 \\ n(B)=50 \\ n(A \cup B)=70 \\ n(U)=200 \end{array}$ a. $n\left(A \cap B^{\prime}\right)=$ $\square$

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Problem 8135

32. (III) A $3.0-\mathrm{kg}$ block sits on top of a $5.0-\mathrm{kg}$ block which is on a horizontal surface. The blocks are connected (Fig. 5-42) by a cord over a pulley (ignore mass and friction). The $5.0-\mathrm{kg}$ block is pulled to the right with a force $\overrightarrow{\mathbf{F}}$ . The coefficient of static friction between all surfaces is 0.60 and the kinetic coefficient is 0.40 . (a) What is the minimum value of $F$ needed to move the two blocks? (b) If the force is $10 \%$ greater than your answer for $(a)$ , what is the acceleration of each block?
FIGURE 5-42 Problem 32.

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Problem 8136

33. (III) A $4.0-\mathrm{kg}$ block is stacked on top of a $12.0-\mathrm{kg}$ block, which is accelerating along a horizontal table at $a=5.2 \mathrm{~m} / \mathrm{s}^{2}$ (Fig. 5-43). Let $\mu_{\mathrm{k}}=\mu_{\mathrm{s}}=\mu$ . (a) What minimum coefficient of friction $\mu$ between the twó blocks will prevent the $4.0-\mathrm{kg}$ block from sliding offर्थ( $(b)$ If $\mu$ is only half this minimum value, what is the acceleration of the $4.0-\mathrm{kg}$ block with respect to the
FIGURE 5-43 Problem 33.

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Problem 8137

34. (III) A small block of mass $m$ rests on the rough, sloping side of a triangular block of mass $M$ which itself rests on a horizontal frictionless table as shown in Fig. 5-44. If the coefficient of static friction is $\mu$ , determine the minimum horizontal force $F$ applied to $M$ that will cause the small block $m$ to start moving up the incline.
FIGURE 5-44 Problem 34.

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Problem 8138

5. (I) What is the maximum speed with which a $1200-\mathrm{kg}$ car can round a turn of radius 90.0 m on a flat road if the coefficient of static friction between tires and road is 0.65 ? Is this result independent of the mass of the car?

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Problem 8139

(I) A child sitting 1.40 m from the center of a merry-go-round moves with a speed of $1.30 \mathrm{~m} / \mathrm{s}$ . Calculate $(a)$ the centripetal acceleration of the child and $(b)$ the net horizontal force exerted on the child (mass $=22.5 \mathrm{~kg}$ ).

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Problem 8140

(I) A horizontal force of 310 N is exerted on a $2.0-\mathrm{kg}$ ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m . Calculate the speed of the ball.

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Problem 8141

(I) A jet plane traveling $1890 \mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 4.80 km . What is the plane's acceleration in $g$ 's?

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Problem 8142

39. (II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of $95 \mathrm{~km} / \mathrm{h}$ ?

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Problem 8143

40. (II) A $0.45-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?

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Problem 8144

41. (II) On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s . If we assume their arms are each 0.80 m long and their individual masses are 55.0 kg , how hard are they pulling on one another?

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Problem 8145

42. (II) How fast (in rpm) must a centrifuge rotate if a particle 8.00 cm from the axis of rotation is to experience an acceleration of $125,000 \mathrm{~g}^{\prime} \mathrm{s}$ ?

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Problem 8146

43. (II) A car drives in a spiral path of gradually decreasing radius in a large empty parking lot. The speed is held constant at $10.0 \mathrm{~m} / \mathrm{s}$ , and the car starts at a distance of 50.0 m from the center of the spiral. If the coefficient of static friction is 0.80 , how far is the car from the center when it first starts to skid?

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Problem 8147

46. (II) Is it possible to whirl a bucket of water fast enough in a vertical circle so that the water won't fall out? If so, what is the minimum speed? Define all quantities needed.

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Problem 8148

7. (II) At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5-45) do not fall out? Assume a radius of curvature of 7.6 m .
FIGURE 5-45 Problem 47.

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Problem 8149

48. (II) A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m . At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N . (a) Find the speed of the bucket. (b) How fast must the bucket move at the top of the circle so that the rope does not go slack?

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Problem 8150

(II) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 125 m . At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

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Problem 8151

Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $(-1,1) \text { and }(5,6)$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is $\square$ (Simplify your answer.) B. The slope is undefined.
Indicate whether the line through the points rises, falls, is horizontal, or is vertical. A. The line is vertical. B. The line falls from left to right. C. The line is horizontal. D. The line rises from left to right.

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Problem 8152

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. $\text { Slope }=-\frac{1}{4}, \text { passing through }(9,-1)$
Write an equation for the line in point-slope form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

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Problem 8153

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through $(-3,-2)$ and $(2,3)$
What is the equation of the line in point-slope form? $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the equation of the line in slope-intercept form? $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

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Problem 8154

Question 1 (2 points) Saved
A brand of potato chips has an average weight of 300 g . A random sample of 56 potato chip bags has an average weight of 310 g and a standard deviation of 5 g . Is there enough evidence, at the 0.02 level of significance to say that the mean weight of the potato chips is not equal to 300 g ?
Select the correct null and alternative hypothesis.
Two-tail: $H_{0}: \mu=300$ grams, and $H_{1}: \mu \neq 300$ grams
Left-tail $H_{0}: \mu \geq 300$ grams, and $H_{1}: \mu<300$ grams
Right-tail $H_{0}: \mu \leq 300$ grams, and $H_{1}: \mu>300$ grams

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Problem 8155

In Butt welding, Chamfer is applied for metal pieces that are less than 3 mm thick.
Select one: True False

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Problem 8156

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through $(9,-6)$ and perpendicular to the line whose equation is $y=\frac{1}{5} x+5$
Write an equation for the line in point-slope form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

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Problem 8157

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through $(-6,1)$ and parallel to the line whose equation is $5 x-2 y-3=0$
The equation of the line in point-slope form is $\square$ (Type an equation. Use integers or fractions for any numbers in the equation.) The equation of the line in general form is $\square$ $=0$ . (Type an expression using $x$ and $y$ as the variables. Simplify your answer. Use integers or fractions for

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Problem 8158

Question 13 Mharianne K
Keiko is on vacation at a tropical bay that has three islands. She rents a boat on Island A and plans to navigate to Island C, which is 14 miles away. Based on the figure below, at what angle $\theta$ should she navigate to go to Island $C$ ?
Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a degree.

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Problem 8159

A kite is flying 86 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is $46^{\circ}$ . Find the length of the string. Round your answer to the nearest tenth. $\square$ ft

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Problem 8160

2 A tin of soup has the following information on the label. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{} \\ \hline 200 grams of soup contains \\ \hline Protein & Carbohydrate & Fat \\ \hline $4 . \mathrm{g}$ & 8.7 g & 5.8 g \\ \hline \end{tabular} (a) What fraction of the soup is Protein? Give your answer in its simplest form. $\frac{4}{200} \Rightarrow \frac{1}{50}$ (b) What percentage of the soup is Carbohydrate? $4.305 \frac{8-7}{200} \times 100 \quad \text { Answer(b) ......................................... \% [1] }$

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Problem 8161

Write the standard form of the equation of the circle with the given center and radius. Center $(-5,7), r=8$
Type the standard form of the equation of the circle. (Simplify your answer.)

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Problem 8162

The equation of an ellipse with center $(2,3)$ that passes through the points $(6,3)$ and $(2,5)$ has the form $f(x, y)=1$ . Find $f(x, 0)$ .

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Problem 8163

A 5.0-gram ice cube at - 2.0 degrees Celsius is dropped into 60 grams of liquid water at 12 degrees Celsius. If the ice and water are isolated from the environment, what is the final temperature of the combined liquid water when all of the ice has melted and the mixture reaches thermal equilibrium? $\square$ A $\quad$ degrees Celsius $\square$ Hide hint for Question 1 Report your result to 2 significant figures.

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Problem 8164

Direction: Solve all of the problems in this section a
1. Convert the following units: A. 0.2 g to microgram [ 5 pts $]$ B. 0.86 mcg to gram [ 5 pts $]$ C. 280 lb to kilogram [5 pts]
Give the correct amount of tablets Do All
2. A patient has been prescribed 850 mg TDD in 4 divided doses. The stock tablets you have are 250 mg . How many tablets do you give the patient for a single dose? [9.37 pts]
3. A patient has been prescribed 300 mg every 4 hours. The stock tablets you have are 150 mg . How many tablets do you give the patient in a day? [9.37 pts]
Give the correct amount for iniection Do Any Two (2)
4. The patient needs 350 mcg of Drug $X$ . You have 1 mg in 1 ml . How many ml do you give? $[9.37 \mathrm{pts}]$
5. 0.6 mg of drug $X$ is required. Stock is 0.4 mg in 2 ml . What volume do you give? 19.37 $\mathrm{pts} \mid$
6. 0.1 ml is given; it should have been 0.01 ml . How many times too much is this? 19.37 $\mathrm{pts}]$
Body Weight Calculations (Single dose) Do Any Twa (2)
7. A male patient weighs 90 kg and has been prescribed, $1.5 \mathrm{mg} / \mathrm{kg}$ dose of drug X . How many mg will he need for a single dose? [9.37 pts]
8. A female patient has been prescribed Chloramphenicol, 40 mg kgldose. She weighs 78 kg . How many grams of the drug does she require for each dose? $[9.37 \mathrm{pts}]$
9. A patient who is 5 years old and weighs 20 kg has been prescribed 5 mog per kilogrth body weight of Digoxin elixir. The digoxin elixir is available as 50 mcg per ml . 19.37 $\mathrm{pts}]$ a). How many mog does the patient require pet single does? b). What volume will you give the patient at each does? What is his total daily dose? $[9.37 \mathrm{pts}]$
11. A patient has been prescribed Cephalothin. $20 \mathrm{mg} \mathrm{kg} T[\mathrm{Ds}$ . She weigts 67 kg , whit will be her total daily dose in grams? [9.37 pts]

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Problem 8165

The minimum hourly wage, $y$ (in dollars per hour), in a country can be approximated by the equation $y=0.16 x+2.63$ . In this equation, $x$ represents the number of years since 1970 ( $x=0$ represents 1970, $x=5$ represents 1975, and so on).
Federal Minimum Hourly Wage by Year
Part 1 of 4 (a) Use the equation to approximate the minimum wage in the year 1975.
The minimum wage in 1975 was approximately $\$ 3.43$ . $\square$
Part 2 of 4 (b) Use the equation to estimate the minimum wage in the year 1995.
The minimum wage in 1995 was approximately $\$ 6.63$ .
Part: $2 / 4$
Part 3 of 4 (c) Determine the $y$ -intercept. Interpret the meaning of the $y$ -intercept in the context of this problem.
The $y$ -intercept is $\square$ $\square$ . In the year $\square$ the minimum wage was approximately $\$$ $\square$ per hour.

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Problem 8166

Government agencies keep data about the income distribution of the population. The Wood family and Butler family live in a county with 11,000 families. The Wood family's income is at the $14^{\text {th }}$ percentile. The Butler family's income is at the $59^{\text {th }}$ percentile. (a) Which of the following must be true about the Wood family's and the Butler family's incomes? The Butler family earns more than the Wood family. Both the Wood family and the Butler family earn more than the median income. The Butler family earns $\$ 45,000$ more than the Wood family.
The Wood family and the Butler family both have incomes in the bottom half of incomes in their county. (b) Which of the following must be true about the Wood family's income? The Wood family earns more than about $86 \%$ of families in their county. About $86 \%$ of the families in their county earn more than the Wood family. The wood family earns about $14 \%$ of the highest income in their county. The wood family earns about $86 \%$ of the highest income in their county.

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Problem 8167

D. negotiate for a higher than market wage hike every year through collective bargaining. b. Suppose that the objective of a union is to maximize the total dues paid to the union by its membership. If union dues are paid as a flat amount per union member employed, the union's strate will be to A. negotiate for the wage level that is consistent with perfectly elastic demand for labor. B. negotiate for the maximum wage rate the employer is willing to pay for the number of workers belonging to the union. C. negotiate for the wage level that is consistent with unit elastic demand for labor. D. negotiate for limiting the entry of new workers over time. Clear all Check answer

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Problem 8168

Draw a line that has the indicated slope and $y$ -intercept. slope $=\frac{3}{2}$ and $y$ -intercept $(0,-5)$
Use the graphing tool on the right to draw the line.
Click to enlarge graph

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Problem 8169

Q. 3 ( 5 marks): Sands Corporation processes sugar beets that it purchases from farmers. Sugar beets are processed in batches, A batch of sugar beets costs \ $50 to buy from farmers and \$15 to crush in the company's plant. Two intermediate products, beet fiber and beet juice, emerge from the crushing process. The beet fiber can be sold as is for$ \ $20$ or processed further for $\$ 19$ to make the end product industrial fiber that is sold for $\$ 58$ . The beet juice can be sold as is for $\$ 41$ or processed further for $\$ 23$ to make the end product refined sugar that is sold for $\$ 58$ . Required: 1)- Which of the intermediate products should be processed further? 2)- How much profit (loss) does the company make by processing one batch of sugar beets into the end products industrial fiber and refined sugar?

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Problem 8170

Your answer is incorrect.
A bank offers an investment account with an annual interest rate of $1.51 \%$ compounded annually. Ahmad invests $\$ 3900$ into the account for 5 years. list of financial formulas. (a) Assuming no withdrawals are made, how much money is in Ahmad's account after 5 years? $\$ 4201.86$ (b) How much interest is earned on Ahmad's investment after 5 years? $\$ 301.86$

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Problem 8171

Your roommate, Gianna, offered to buy groceries for you and your other roommate. The total bill was $\$ 77.80$ . She forgot to save the individual receipts but remembered that your groceries were $\$ 0.05$ cheaper than half of her groceries, and that your other roommate's groceries were $\$ 1.90$ more than your groceries. How much was each of your share of the groceries?

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Problem 8172

The circumference of a circular field is 216 yards. What is the radius of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. yards

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Problem 8173

The circumference of a circular field is 200 yards. What is the diameter of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. $\square$ yards

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Problem 8174

The circumference of a circular lot is 204 yards. What is the diameter of the lot? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. $\square$ yards

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Problem 8175

Geomety Circumference and area of a cincle
The diameter of a circle is 8 ft . Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference and area of the circle. Write your answers in terms of $\pi$ .
Exact circumference: $\square$ Exact area: $\square$ $\mathrm{ft}^{2}$ $\mathrm{ft}^{3}$ (b) Approximate the circumference and area of the circle. To do the approximations, use the $\pi$ button on the ALEKS calculator and round your answers to the nearest hundredth.
Approximate circumference: $\square$ Approximate area: $\square$

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Problem 8176

Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69.2 bpm . For a random sample of 175 adult males, the mean pulse rate is 69.5 bpm and the standard deviation is 10.8 bpm . Complete parts (a) and (b) below. a. Express the original claim in symbolic form. $\square$ $\square$ $\square$ bpm (Type an integer or a decimal. Do not round.) b. Identify the null and alternative hypotheses. $\mathrm{H}_{0}$ : $\square$ $\square$ $\square$ bpm $\mathrm{H}_{1}$ : $\square$ $\square$ bpm (Type integers or decimals. Do not round.)

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Problem 8177

Claim: Fewer than $97 \%$ of adults have a cell phone. In a reputable poll of 1091 adults, $92 \%$ said that they have a cell phone. Find the value of the test statistic.
The value of the test statistic is $\square$ (Round to two decimal places as needed.)

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Problem 8178

C Knowledge Check Question 17
A hardware salesman measures the mass of a box containing 1000 washers. The mass is 0.3932 kg . What is the mass of a single washer in milligrams? Write your answer as a decimal. $\square$ mg

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Problem 8179

\text{How much heat is produced when 74 grams of Al react in the following reaction?} \\ 2 \mathrm{Al}(s) + \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \rightarrow 2 \mathrm{Fe}(s) + \mathrm{Al}_{2} \mathrm{O}_{3}(s) \\ \text{Heat of reaction} = -851.5 \, \mathrm{kJ} \\

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Problem 8180

Mary's TV uses a perpetual inventory system. The following are three recent merchandising transactions: Mar. 6 Purchased eight TVs from Whosa Industries on account. Invoice price, $\$ 350$ per unit, for a total of $\$ \mathbf{2 , 8 0 0}$ . The terms of purchase were $\mathbf{2 / 1 0 , ~} \mathbf{n} / \mathbf{3 0}$ . Mar. 11 Sold two of these televisions for $\mathbf{\$ 6 0 0}$ cash. Mar. 16 Paid the account payable to Whosa Industries within the discount period. Instructions a. Prepare journal entries to record these transactions assuming that Mary's records purchases of merchandise at:
1. Net cost
2. Gross invoice price b. Assume that Mary's did not pay Whosa Industries within the discount period but instead paid the full invoice price on April 6. Prepare journal entries to record this payment assuming that the original liability had been recorded at:
1. Net cost
2. Gross invoice price c. Assume that you are evaluating the efficiency of Mary's bill-paying procedures. Which accounting method-net cost or gross invoice priceprovides you with the most useful information? Explain.

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Problem 8181

3- A biology department is conducting an experiment and needs to select 7 plants from a group of 10 plants for testing. How many different groups of plants can the researchers select, if: (3 marks) a- the arrangement is important (permutation): b- the arrangement is not important (combination):
4- A factory produces 5 batches of items daily, and the probability that any batch contains defective items is $\mathbf{0 . 2 0}$ . (binominal) (4 marks)
1. What is the probability that none of the batches are defective today?
2. What is the probability that exactly 2 batches are defective today? And what does it mean?
3. Find the mean.
4. Calculate the variance

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Problem 8182

Use table and graph to find the solution accurate to one decimal place to the equation below $2^{x}=33$ $\square$ Question Help: Video

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Problem 8183

where $m_{E}$ and $d_{E}$ are the mass of the Earth and its distance appraximation of uniform circular motion, determine:
1. The acceleration due to gravity $g_{M}$ at the surface of Mars.
2. The orbital period $T_{M}$ of Mars around the Sun in Earth years.
3. The velocity of a satellite to remain in orbit around Mars at an altitude $h=300 \mathrm{~km}$ . Given: $m_{E}=5.97 \times 10^{24} \mathrm{~kg}, R_{E}=6371 \mathrm{~km}, R_{M}=3396 \mathrm{~km}$ , and $G=6.67 \times 10^{-11} \mathrm{SI}$ . - Exercise 3.5
Alcomsat-1 is an Algerian telecommunications satellite of mass $m=92 \mathrm{~kg}$ , launched on December 10, 2017. The satellite was placed in a geostationary orbit considered to be circular with a radius $r$ .
1. Asuming that the only force acting on the satellite is the gravitational force exerted by the Earth, what are the other forces neglected in this case?
2. Recalling the expression for the vector of the Earth's gravitational force acting on the satellite as a function of its altitude $h$ , show that the motion is uniform (specify the chosen reference frame).
3. Deduce the velocity expression of the satellite and calculate it for $h=300 \mathrm{~km}$ .
4. Find the expression of the angular momentum $\vec{L}_{0}$ of the satellite with respect to the center $O$ of the Earth in the cylindrical coordinate system $\left(\vec{u}_{r}, \vec{u}_{\theta}, \vec{u}_{z}\right)$ . Show that the vector $\vec{L}_{0}$ is constant during the motion. Given: Mass of the Earth $M_{E}=5.97 \times 10^{24} \mathrm{~kg}$ , radius of the Earth $R_{E}=6380 \mathrm{~km}, G=6.67 \times$ $10^{-11} S I$ . e Exercise 3.6 Gravimetry is concerned with the measurement of the gravitational field intensity at a given point. Through gravimetry, the presence of underground cavities can be detected.
1. At the Earth's surface, calculate the gravitational field $g_{0}$ of the Earth without any cavity and the gravitational field $g_{1}$ above a spherical cavity of radius $R_{C}$ with its center located at a depth $d \geq R_{C}$ .
2. Assuming that we can measure the gravitational field with a precision $\delta=\frac{90-91}{90}=10^{-6}$ and we want to detect a cavity just below the ground surface (i.e., $R_{C}=d$ ). What is the radius of the smallest cavity that can be detected? (Radius of the Earth $R_{T}=6370 \mathrm{~km}$ ).
Exercise 3.7

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Problem 8184

1 The mass, $m$ kilograms, of a horse is 429 kg , correct to the nearest kilogram. Complete this statement about the value of $m$ . $\leqslant m<$

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Problem 8185

In England, people use mile per hour as a unit of speed on roads. In Egypt, we use kilometer per hour on roads. In physics class, students tried to compare the speeds indicated 20 MPH in these signs with the SI unit of speed. Which of students' attempts is correct?
A $-20 \mathrm{~km} / \mathrm{h}>20 \mathrm{MPH}>20 \mathrm{~m} / \mathrm{s}$ B- $20 \mathrm{MPH}>20 \mathrm{~km} / \mathrm{h}>20 \mathrm{~m} / \mathrm{s}$ C. $20 \mathrm{~m} / \mathrm{s}>20 \mathrm{~km} / \mathrm{h}>20 \mathrm{MPH}$
D- $20 \mathrm{~m} / \mathrm{s}>20 \mathrm{MPH}>20 \mathrm{~km} / \mathrm{h}$

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Problem 8186

Question 67 Point $P(-1,2)$ is the midpoint of segment $A B$ . Co-ordinates of $A$ are $(-2, y)$ and $B$ are $(x, 3)$ . What is the value of $x$ ? Marks:1.0 Negative Marks:0.25

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Problem 8187

Question 55 Twelve years ago, the combined ages of all members of a small village council of nine people totalled 360 years. Five years later, two members retired at the ages of 65 and 70 , respectively, and two new members, aged 30 and 35 , joined the council that same year. Four years after that, another member retired at the age of 68 , and a new member aged 39 joined the council. What is the current average age of the council member? Marks 1.0 Negative Marks 025

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Problem 8188

11. Three vectors are given by $\vec{P}=3 i-3 j-2 \hat{K}, \vec{Q}-i-j i+2 \mathrm{~K}$ and $\vec{S}=2 \mathrm{i}+2 \mathrm{j}+\mathrm{K}$ . Then get $2 \vec{P} \cdot(3 Q+\vec{S}) ? 6 i-6 j-4 k \cdot(-3 i+12 j+6 k+2 i+2 j+k)$
12. For what value of $\vec{C}$ lying along +y-axis does $\vec{A} \cdot(\vec{Q}-\vec{C})=0$ given that $\vec{A}-3 i-2 j+k$ and $\vec{B}=4 i+5 j+7 k$ ? ） $(-i-10 j+7 k)$
13. Given that $\vec{P}=5 i-6 \mathrm{j}, \vec{Q}=-2 i+3 \mathrm{j}$ and $\vec{R}$ lies in the xy plane perpendicular to $\vec{P}$ 15 If the dot product of $\vec{R}$ and $\vec{Q}$ is 9 . Then get $\vec{R}$ ? $\vec{R} \vec{Q} \overrightarrow{=}=R_{x} Q_{x}+R_{y} Q_{y}$
14. Find $\vec{R}=\mathrm{a} i+\mathrm{bj}+\mathrm{k}$ which is perpendicular to both $\vec{A}=3 i+j-\mathrm{K}$ and $+3 R_{y}$ $\vec{B}=-3 i+2 j+2 k$ . $5 R_{x}-6 R_{y}=0 \quad 4 i-1 / 3 d$
15. Let $\vec{A}=i+j+\hat{K}$ and $\vec{B}=2 i+2 j+2 \mathrm{k}$ what is the angle between $\vec{A}$ and $\vec{B}$ ?
16. Find a such that, the angle between $\vec{A}=i+a j$ and $\vec{B}=i+j$ is $45^{\circ}$ . ( $\sin 45^{\circ}=$ $\left.\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$ it $\sqrt{2}$ $\vec{B}=\stackrel{\alpha}{\alpha i-3 \propto j+5 k}$ orthogonal
17. For what value of $\propto$ are the vectors $\vec{A}=\alpha i-2 j+\hat{k}$ and $\vec{B}=a i-3 \propto j+5$ to each other? $\quad \alpha=-1$ or $\alpha=-5-i-2 j+k \quad-i+3 j+5$
18. Consider a block placed on a horizontal surface and that force $\vec{F}$ is applied on the block to move the block through displacement $\vec{S}$ . If $\vec{F}=(5 i+3 j) N$ and $\vec{s}=(-2 i+4 j) \mathrm{m}$ then calculate the work done? $\quad-5 i-2 j+k \quad 5 i+1 s j+5$ 19.Vector $\vec{A}$ has a magnitude of 6 units along the positve $x-25-30$ , Vector $\vec{B}$ has amagnitude of 4 units and lies on xy-plane making an angle of $60^{\circ}$ with the positive x -axis. What is the scalardot product of $\vec{A}$ and $\vec{B}$ ? 20. i.If $\vec{A} \cdot \vec{B}=|A||B|$ , what can you say about vector $\vec{A}$ and $\vec{B}$ ? ii. if $\vec{P}+\vec{Q}=O$ , then tell about vectors $\vec{P}$ and $\vec{Q}$ ? iii. use the given diagram and express $\vec{N}, \vec{M}$ and $\vec{Z}$ interns of $\vec{Q}$ ? $\begin{array}{c} -36+3 R y=9 \\ R_{y}=15 \\ 18 i+15 y= \\ 18 \\ (\alpha+1)(\alpha+5) \\ \alpha^{2}+6 \alpha+5 \end{array}$

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Problem 8189

27. One quarter of Ciara's money is equal to twice Jenna's money. What fraction of their total money belongs to Jenna?

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Problem 8190

Q.12 A long term investment of $\$ 500,000$ has been made by a small company. If all interest is reinvested at the same rate of interest. Required: a) What will the future value of the investment be after 10 years? The interest rate is $9 \%$ per year compounded quarterly. b) What will the profit value of the investment be after 10 years? The interest rate is $9 \%$ per year compounded quarterly. c) What will future value and net profit of the investment be after $18^{\text {ret }}$ quarters? The interest rate is $12 \%$ per year compounded quarterly. d) What will future value and net profit of the investment be after $7^{\text {th }}$ semi-annual, if the investment rate be $8 \%$ per year compounded semi-annually? e) What will future value and net profit of the investment be after $42^{\text {nd }}$ months, if the investment rate be $9 \%$ per year compounded monthly? Ise single-payment formula to compute desire results.

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Problem 8191

(6.) Für ein Dreeick $A B C$ gilt: $A(3 /-2), A B=(1 / 2), A C=(-1 / 1)$ . Geben Sie die Koordinalen des Schwerpunkts $S$ des Dreiecks an.
9. Geben Sie die in kartesischer Binomialform gegebenen Punkte in Polarform an. $A(-5 /-2), B(0 / 5), C(-6 / 0), D(-6 / 3)$

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Problem 8192

In a randomized controlled trial, insecticide-treated bednets were tested as a way to reduce malaria. Among 322 infants using bednets, 10 developed malaria. Among 252 infants not using bednets, 23 developed malaria. Use a 0.05 significance level to test the claim that the incidence of malaria is lower for infants using bednets. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, do the bednets appear to be effective? a. What are the null and alternative hypotheses?
Let the infants using bednets be sample 1 and let the infants not using bednets be sample 2. Choose the correct hypotheses below. A. $H_{0}: p_{1}=p_{2}$ B. $H_{0}: p_{1} \leq p_{2}$ C. $H_{0}: p_{1} \geq p_{2}$ $H_{1}: p_{1} \neq p_{2}$ $H_{1}: p_{1}>p_{2}$ $H_{1}: p_{1}<p_{2}$ D. $H_{0}: p_{1}=p_{2}$ E. $H_{0}: p_{1}=p_{2}$ $H_{1}: p_{1}>p_{2}$ $H_{1}: p_{1}<p_{2}$ F. $H_{0}: p_{1} \neq p_{2}$ $H_{1}: p_{1}=p_{2}$
Identify the test statistic. -3.07 (Round to two decimal places as needed.) Identify the P -value. .001 (Round to three decimal places as needed.)
What is the conclusion for this test? Since the P -value is $\square$ less than the significance level $\alpha$ , $\square$ reject the null hypothesis. b. Let the infants using bednets be sample 1 and let the infants not using bednets be sample 2 . Use a 0.05 significance level to construct a confidence interval. $\square$ $<\left(p_{1}-p_{2}\right)<$ $\square$ (Round to three decimal places as needed.)

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Problem 8193

11. Geben Sie die in kartesischer Binomialform gegebenen Punkte in Polarform an $A(-6 /-8), B=\left[8 ; 120^{\circ}\right], C(-5 / 3), D(5 / 0), E=\left[\sqrt{ } 12 ; 4,2^{\mathrm{rad}}\right], F=[5 ; \pi / 2]$
12. Skizzieren Sie am Einheitskreis die folgenden Funktionswerte. a. $\sin \left(250^{\circ}\right)$ b. $\cos \left(40^{\circ}\right)$ c. $\sin \left(\pi / 3^{\text {rad }}\right)$ d. $\cos \left(5^{\text {rad }}\right)$ e. $\sin \left(-70^{\circ}\right)$

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Problem 8194

|(^) شبه منحرف مساحة • ^ اسم † وارتفاعهُ . اسم جد طول القاعدتين إذا علمت أن طول أحدهما ضعف الأخرى .

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Problem 8195

ه تريدُ أملُ عَمَلَ شمعةٍ على شكل هرم رباعيّ قائم منتظم، من متوازي مستطيلات من الشمع أبعاده: (١٠سم ، ١٥سم ، ١٠سم). مساحة القواعقة × 20 أحسِبُ أن حسِبُ طول ضلع قاعدة الهرم، علماً بأنّ ارتفاع الهرم المطلوب هو ۲۰سم. ب احسِبُ نسبةً مِساحة قاعدة متوازي المستطيلات إلى مساحة قاعدة الهرم . E

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Problem 8196

6. $x \in R$ olmak üzere, x'in çarpma işlemine göre tersi ile toplamı 6'dır. Buna göre, x'in toplama işlemine göre tersi ile çan işlemine göre tersinin toplamının pozitif değeri kes; A) $3 \sqrt{2}$ B) $4 \sqrt{2}$ C) $5 \sqrt{2}$ D) $6 \sqrt{2}$ E)

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Problem 8197

1. Khorshid factory produces two producers) A B) and the working hours in this factory are equivalent to 8 hours divided into producers and raw materials available 18 tons, if you know that product $A$ needs one hour of working hours and 2 kilos of raw materials while product $B$ needs one hour of work and 3 kilos of raw materials and the profit return from product $A \$ 2$ while the profit return from product $B \$ 3$ .
Required
1. Define the profit function.
2. Define limitations.
3. Draw the solution area.
4. Select Solution points.
5. Find the productive mix that maximizes profits from the two commodities.
6. Determine the type of relationship between the two products.

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Problem 8198

A prism is 46 mm long. Its cross-section is a triangle with a base length of 17 mm and a perpendicular height of 24 mm .
What is the volume of the prism? Give your answer in $\mathrm{mm}^{3}$ .

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Problem 8199

Bookwork code: 3C Calculator not allowed
Over one year, the ratio of footballs to rugby balls produced by a factory was approximately $5: 4$ .
In June, the factory produced 2400 rugby balls. a) Using the information given, how many footballs would you expect the factory to have produced in June? b) Explain why the expected number you calculated may not be the same as the actual number of footballs produced in June. Give at least two reasons.

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Problem 8200

Якщо ранг основної матриці не дорівнює рангу розширеної матриці системи, то система має безліч розв'язків система не має розв'язків система має 2 розв'язки система має єдиний розв'язок

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Word Problem

Problem 8101

Problem 8102

Problem 8103

Problem 8104

Problem 8105

Problem 8106

Problem 8107

18. Two friends can paddle a canoe at a rate of 6 km/h6 \mathrm{~km} / \mathrm{h}6 km/h in still water. It takes them 1 h to paddle 2 km up a river and back again. Find the speed of the current.

Problem 8108

Write down, but do not solve, an equation that correctly states the following relationship. Use xxx to represent the unknown quantity.The sum of the distance driven on Wednesday and 234 is 579. □\square□

Problem 8109

Problem 8110

Problem 8111

Problem 8112

Problem 8113

Problem 8114

Problem 8115

Problem 8116

QQQ is a point on segment PR‾\overline{P R}PR. If PQ=4x+3,QR=3x+8P Q=4 x+3, Q R=3 x+8PQ=4x+3,QR=3x+8, and PR=18P R=18PR=18, what is PQP QPQ ? Simplify your answer and write it as a proper fraction, mixed number, or integer.

Problem 8117

Problem 8118

Problem 8119

Problem 8120

Problem 8121

Problem 8122

Problem 8123

Problem 8124

22. (II) A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75 . What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

Problem 8125

Problem 8126

Problem 8127

Problem 8128

FIGURE 5-38 Problem 26. (II) A child slides down a slide with a 28∘28^{\circ}28∘ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

Problem 8129

Problem 8130

Problem 8131

Problem 8132

Problem 8133

Problem 8134

Problem 8135

Problem 8136

Problem 8137

Problem 8138

5. (I) What is the maximum speed with which a 1200−kg1200-\mathrm{kg}1200−kg car can round a turn of radius 90.0 m on a flat road if the coefficient of static friction between tires and road is 0.65 ? Is this result independent of the mass of the car?

Problem 8139

(I) A child sitting 1.40 m from the center of a merry-go-round moves with a speed of 1.30 m/s1.30 \mathrm{~m} / \mathrm{s}1.30 m/s. Calculate (a)(a)(a) the centripetal acceleration of the child and (b)(b)(b) the net horizontal force exerted on the child (mass =22.5 kg=22.5 \mathrm{~kg}=22.5 kg ).

Problem 8140

(I) A horizontal force of 310 N is exerted on a 2.0−kg2.0-\mathrm{kg}2.0−kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m . Calculate the speed of the ball.

Problem 8141

(I) A jet plane traveling 1890 km/h(525 m/s)1890 \mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})1890 km/h(525 m/s) pulls out of a dive by moving in an arc of radius 4.80 km . What is the plane's acceleration in ggg 's?

Problem 8142

39. (II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/h95 \mathrm{~km} / \mathrm{h}95 km/h ?

Problem 8143

40. (II) A 0.45−kg0.45-\mathrm{kg}0.45−kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?

Problem 8144

41. (II) On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s . If we assume their arms are each 0.80 m long and their individual masses are 55.0 kg , how hard are they pulling on one another?

Problem 8145

42. (II) How fast (in rpm) must a centrifuge rotate if a particle 8.00 cm from the axis of rotation is to experience an acceleration of 125,000 g′s125,000 \mathrm{~g}^{\prime} \mathrm{s}125,000 g′s ?

Problem 8146

Problem 8147

46. (II) Is it possible to whirl a bucket of water fast enough in a vertical circle so that the water won't fall out? If so, what is the minimum speed? Define all quantities needed.

Problem 8148

7. (II) At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5-45) do not fall out? Assume a radius of curvature of 7.6 m .FIGURE 5-45 Problem 47.

Problem 8149

Problem 8150

(II) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 125 m . At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

Problem 8151

Problem 8152

Problem 8153

Problem 8154

Problem 8155

In Butt welding, Chamfer is applied for metal pieces that are less than 3 mm thick.Select one: True False

Problem 8156

Problem 8157

Problem 8158

Problem 8159

A kite is flying 86 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 46∘46^{\circ}46∘. Find the length of the string. Round your answer to the nearest tenth. □\square□ ft

Problem 8160

Problem 8161

18. Two friends can paddle a canoe at a rate of $6 \mathrm{~km} / \mathrm{h}$ in still water. It takes them 1 h to paddle 2 km up a river and back again. Find the speed of the current.

Write down, but do not solve, an equation that correctly states the following relationship. Use $x$ to represent the unknown quantity.
The sum of the distance driven on Wednesday and 234 is 579. $\square$

$Q$ is a point on segment $\overline{P R}$ . If $P Q=4 x+3, Q R=3 x+8$ , and $P R=18$ , what is $P Q$ ? Simplify your answer and write it as a proper fraction, mixed number, or integer.

FIGURE 5-38 Problem 26. (II) A child slides down a slide with a $28^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

5. (I) What is the maximum speed with which a $1200-\mathrm{kg}$ car can round a turn of radius 90.0 m on a flat road if the coefficient of static friction between tires and road is 0.65 ? Is this result independent of the mass of the car?

(I) A child sitting 1.40 m from the center of a merry-go-round moves with a speed of $1.30 \mathrm{~m} / \mathrm{s}$ . Calculate $(a)$ the centripetal acceleration of the child and $(b)$ the net horizontal force exerted on the child (mass $=22.5 \mathrm{~kg}$ ).

(I) A horizontal force of 310 N is exerted on a $2.0-\mathrm{kg}$ ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m . Calculate the speed of the ball.

(I) A jet plane traveling $1890 \mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 4.80 km . What is the plane's acceleration in $g$ 's?

39. (II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of $95 \mathrm{~km} / \mathrm{h}$ ?

40. (II) A $0.45-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?

42. (II) How fast (in rpm) must a centrifuge rotate if a particle 8.00 cm from the axis of rotation is to experience an acceleration of $125,000 \mathrm{~g}^{\prime} \mathrm{s}$ ?

7. (II) At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5-45) do not fall out? Assume a radius of curvature of 7.6 m .
FIGURE 5-45 Problem 47.

In Butt welding, Chamfer is applied for metal pieces that are less than 3 mm thick.
Select one: True False

A kite is flying 86 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is $46^{\circ}$ . Find the length of the string. Round your answer to the nearest tenth. $\square$ ft

Write the standard form of the equation of the circle with the given center and radius. Center $(-5,7), r=8$
Type the standard form of the equation of the circle. (Simplify your answer.)

The equation of an ellipse with center $(2,3)$ that passes through the points $(6,3)$ and $(2,5)$ has the form $f(x, y)=1$ . Find $f(x, 0)$ .

Draw a line that has the indicated slope and $y$ -intercept. slope $=\frac{3}{2}$ and $y$ -intercept $(0,-5)$
Use the graphing tool on the right to draw the line.
Click to enlarge graph

The circumference of a circular field is 200 yards. What is the diameter of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. $\square$ yards

The circumference of a circular lot is 204 yards. What is the diameter of the lot? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. $\square$ yards