Word Problem

Problem 6901

2. ( 6 points) Fill in the blank with simplified answers. If the expression is undefined, writ Assume all variables are positive real numbers, not equal to 1. (a) $\log _{8}(64)=$ $\qquad$ (b) $\log _{9}(27)=$ 1.5 $\qquad$ (c) $6^{\log _{6}(14)}=$ $\qquad$ 14 (d) $\ln \sqrt[7]{e}=$ $\qquad$ (e) $\log _{a}(1)=$ $\qquad$ (f) $\log _{c} \frac{1}{c^{3}}=$ $\qquad$
3. (12 points) Fill in the blanks. (a) If you reflect the graph of $y=5^{x}$ across the $y$ -axis, you get the graph of $\qquad$ (b) If you reflect the graph of $y=5^{x}$ across the line $y=x$ , you get the graph of (c) The domain of $y=5^{x}$ is $\qquad$ (d) The range of $y=5^{x}$ is $\qquad$ (e) The domain of $y=\log _{5}(x)$ is $\qquad$ (f) The range of $y=\log _{5}(x)$ is $\qquad$ (g) As $x \rightarrow-\infty, y=5^{x} \rightarrow$ $\qquad$ (h) As $x \rightarrow \infty, \quad y=5^{x} \rightarrow$ $\qquad$ (i) As $x \rightarrow 0^{+}, y=\log _{5}(x) \rightarrow$ $\qquad$ (j) As $x \rightarrow \infty, y=\log _{5}(x) \rightarrow$ $\qquad$ (k) As $x \rightarrow-\infty, \quad y=\left(\frac{1}{5}\right)^{x} \rightarrow$ $\qquad$ (l) As $x \rightarrow \infty, y=\left(\frac{1}{5}\right)^{x} \rightarrow$ $\qquad$

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Problem 6902

11 Ein Erdwall hat im Querschnitt näherungsweise die Form einer Parabel (Fig. 1). Er ist 2 m hoch und auf 1 m Höhe 10 m breit. Wie breit ist er am Boden?

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Problem 6903

16. Use the compound interest formulas to solve the following. Round answers to the nearest cent. a. Find the accumulated value of an investment of $\$ 25,000$ for 4 years at an interest rate of $7 \%$ if the money is compounded monthly. b. Find the accumulated value of an investment of $\$ 25,000$ for 4 years at an interest rate of $7 \%$ if the money is compounded countinuously.

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Problem 6904

Write an exponential function for the yearly interest rate then rewrite the function to find the equivalent monthly interest rate.
APR stands for annual (yearly) interest rate.
12\% APR
Use the variable $t$ for time.
Equation for yearly interest rate: $A(t)=P(\square)$
Equation for monthly interest rate: $A(t)=P(\square)=$
Monthly interest rate: $\square$

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Problem 6905

Dwayne will spend $\$ 80$ on video games. Used video games cost $\$ 10$ each, and new video games cost $\$ 20$ each. Let $x$ represent the number of used video games and let $y$ represent he number of new video games he can buy. Which ordered pairs represent possible combinations of video games that Dwayne can buy? A. $(0,4)$ B. $(2,3)$ C. $(1,6)$ D. $(7,2)$ E. $(8,0)$

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Problem 6906

$(n+n)(n-1)(n+1)$ Find the LCD of each group of fractions.
21. $\frac{1}{4}, \frac{5}{6}$
22. $\frac{1}{2}, \frac{3}{8}$
23. $\frac{3}{2}, \frac{2}{5}, \frac{1}{4}$
24. $\frac{2}{3}, \frac{5}{9}, \frac{1}{15}$
25. $\frac{5}{8}, \frac{2}{5}, \frac{4}{3}$
26. $\frac{2}{3}, \frac{3}{4}, \frac{5}{9}$ $\frac{6}{241}$
Find the LCD of each group of fractions.
27. $\frac{a+2 b}{4}, \frac{2 b-a}{6}$
28. $\frac{n-2}{12}, \frac{n+3}{15}$
29. $\frac{n-1}{15}, \frac{n+3}{20}$
36. $\frac{3}{2 x+10}, \frac{x}{5 x+25}$
37. $\frac{3 a}{a+1}, \frac{2}{a-1}$
38. $\frac{3}{a^{2}-4}, \frac{5}{a+2}$ implify.
7. $\frac{3}{n^{2}}+\frac{2}{n}$
18. $\frac{6}{x^{2} y}-\frac{4}{x y}$
19. $\frac{5}{2 x}-\frac{1}{4 x^{2}}$
20. $\frac{1}{3 x^{2}}+\frac{5}{6 x}$

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Problem 6907

5-2 Mathematical Literacy and Vocabulary Bisectors in Triangles For Exercises 1-6, match the term in Column A with its description in Column B. The first one is done for you.
Column A
1. concurrent
2. point of concurrency
3. circumcenter of a triangle
4. circumscribed
5. incenter of a triangle
6. inscribed
Column B the point of intersection of three or more lines the intersection point of the three angle bisectors of a triangle when a circle touches the three sides of a triangle term that describes three or more lines that intersect at a single point when a circle passes through the three vertices of a triangle the intersection point of the three perpendicular bisectors of a triangle

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Problem 6908

of games in a community center. They charge $\$ 8$ per person for entry into the event. The group wol to earn at least $\$ 600$ , after paying for the cost of renting the space, which is $\$ 40$ an hour.
1. If $x$ represents the number of entry tickets sold and $y$ the hours of space rental, which inequal represents the constraints in the situation? a. $8 x-40 y<600$ b. $8 x-40 y \leq 600$ c. $8 x-40 y>600$ d. $8 x-40 y \geq 600$

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Problem 6909

Practice--Space Calculations.
1. Convert the following into km. a. 52.1 AU

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Problem 6910

The line $y-14=6(x-2.5)$ represents Barry's profit, $y$ , from selling $x$ paintings, after buying some canvas. What was the cost of the canvas? \$

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Problem 6911

Using the Law of Sines to solve the all possible triangles if $\angle B=50^{\circ}, a=107, b=43$ . Round to 3 decimal places. If no answer exists, enter DNE for all answers. $\angle A=$ $\square$ degrees $\angle C=$ $\square$ degrees $c=$ $\square$ Assume $\angle A$ is opposite side $a, \angle B$ is opposite side $b$ , and $\angle C$ is opposite side $c$ .

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Problem 6912

1. List five rational numbers between: (i) -1 and 0 (ii) -2 and -1 (iii) $\frac{-4}{5}$ and $\frac{-2}{3}$ (iv) $-\frac{1}{2}$ and $\frac{2}{3}$
2. Write four more rational numbers in cach of the folloming pattems: (i) $\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}, \ldots .$ . (ii) $\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}, \ldots$ .

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Problem 6913

It costs $\$ 10$ to play a dice game. For this game, two dice are rolled. If a sum greater than 10 is rolled, the player receives $\$ 45$ . If a sum less than six is rolled, the player receives $\$ 30$ . If a player rolls two odd numbers, then they receive $\$ 7$ . A player can only receive one prize. Therefore, if a roll meets the description of more than one prize, the player only receives the higher prize value (not both). The expected value (to the nearest cent) of the game is $\$$ $\square$ In the long run, does the game favor the player? $\square$

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Problem 6914

1. In the diagram below, a force, $F$ , is applied to the handle of a lawnmower inclined at angle $\theta$ to the ground.
The magnitude of the horizontal component of force $F$ depends on A) the magnitude of force $F$ , only B) the measure of angle $\theta$ , only C) both the magnitude of force $F$ and the measure of angle 0 D) neither the magnitude of force $F$ nor the measure of angle $\theta$ $\therefore$ Base your answer to the following question on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of $35^{\circ}$ with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.]
The horizontal component of the ball's initial velocity is approximately A) $3.6 \mathrm{~m} / \mathrm{s}$ B) $7.0 \mathrm{~m} / \mathrm{s}$ C) $4.9 \mathrm{~m} / \mathrm{s}$ D) $13 \mathrm{~m} / \mathrm{s}$ i. Base your answer to the following question on the diagram below which represents a ball being kicked by a foot and rising at an angle of $30 .^{\circ}$ from the horizontal. The ball has an initial velocity of 5.0 meters per second. [Neglect friction.]
As the ball rises, the vertical component of its velocity A) decreases B) increases C) remains the same
4. As the angle between a force and level ground decreases from $6^{1}$ to $30^{\circ}$ , the vertical component of the force A) decreases B) increases C) remains the same
5. A force of 100 . Newtons is applied to an object at an angle of $3 C$ from the horizontal as shown in the diagram below. What is the magnitude of the vertical component of this force? A) 0 N B) 50.0 N C) 86.7 N D) $100 . \mathrm{N}$
6. The diagram below shows a child pulling a 50 .-kilogram friend on a sled by applying a 300 --newton force on the sled rope at an angle of $40^{\circ}$ with the horizontal.
The vertical component of the 300 .-newton force is approximately A) 510 N B) 230 N C) 190 N D) 32 N
7. The vector diagram below represents the horizontal component, H , and the vertical component, $F$ , of a 24 -newton force acting at $35^{\circ}$ above the horizontal.
What are the magnitudes of the horizontal and vertical components? A) $F_{H}=3.5 \mathrm{~N}$ and $F_{V}=4.9 \mathrm{~N}$ B) $F_{H}=4.9 \mathrm{~N}$ and $F_{V}=3.5 \mathrm{~N}$ C) $F_{H}=14 \mathrm{~N}$ and $F_{V}=20 . \mathrm{N}$ D) $F_{H}=20 . \mathrm{N}$ and $F_{V}=14 \mathrm{~N}$ Page I

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Problem 6915

It costs $\$ 10$ to play a dice game. For this game, two dice are rolled. If a sum greater than 10 is rolled, the player receives $\$ 50$ . If a sum less than six is rolled, the player receives $\$ 20$ . If a player rolls two odd numbers, then they receive $\$ 8$ . A player can only receive one prize. Therefore, if a roll meets the description of fnore than one prize, the player only receives the higher prize value (not both). The expected value (to the nearest cent) of the game is $\$$ $\square$ In the long run, does the game favor the player? yes $\checkmark \checkmark ~ ০^{\infty}$

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Problem 6916

In order to accumulate enough money for a down payment on a house, a couple deposits $\$ 641$ per month into an account paying 6\% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years?
Type the amount in the account: \\square$ (Round to the nearest dollar.)

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Problem 6917

In order to accumulate enough money for a down payment on a house, a couple deposits $\$ 641$ per month into an account paying 6\% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years?
Type the amount in the account: \\square$ (Round to the nearest dollar.)

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Problem 6918

A multiple-choice exam contains questions that each have 4 answer choices. One point is awarded for each correct answer, and 0.25 points are deducted for each incorrect answer. If an answer is left blank, then points are not awarded or deducted. Round the expected value to the nearest hundreth. a. What is the expected value if a student guesses on a question? $\square$ b. Is it advantageous to guess if an answer is unknown? ? V c. What is the expected value if 0.5 points are deducted for each incorrect answer? $\square$

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Problem 6919

Complete the following acid-base reaction with balanced molecular, total ionic, and net ionic equations. Be sure to include states of matter in your answer. calcium hydroxide $(a q)+\operatorname{acetic} \operatorname{acid}(a q) \rightarrow$

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Problem 6920

Exercice $\mathrm{n}^{\circ} 5$ ( 5 pts ). (Relations binaires). Les questions suivantes sont indépendantes 1) On définit sur $\mathbb{R}^{2}$ la relation $\ll$ par: $(x, y) \ll\left(x^{\prime}, y^{\prime}\right) \Leftrightarrow\left|x^{\prime}-x\right| \leq y^{\prime}-y$ . Vérifier qu'il s'agit d'ume relation d'ordre. Cet ordre est-il total ? 2) On définit sur $\mathbb{R}^{2}$ la relation $\mathcal{S}$ par: $(x, y) \mathcal{S}\left(x^{\prime}, y\right) \Leftrightarrow x-5 y^{\prime}=x^{\prime}-5 y$ a) Montrer que $\mathcal{S}$ est une relation d'équivalence. b) Vérifier que la classe d'équivalence du couple $(0,0)$ est une droite $\mathcal{D}$ à préciser.

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Problem 6921

It costs $\$ 10$ to play a dice game. For this game, two dice are rolled. If a sum greater than 10 is rolled, the player receives $\$ 30$ . If a sum less than six is rolled, the player receives $\$ 25$ . If a player rolls two odd numbers, then they receive $\$ 5$ . A player can only receive one prize. Therefore, if a roll meets the description of more than one prize, the player only receives the higher prize value (not both). The expected value (to the nearest cent) of the game is $\$$ $\square$
In the long run, does the game favor the player? $\square$ yes $\square$ $\checkmark$ ) Submit Question

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Problem 6922

You decide to work part-time at a local supermarket. The job pays $\$ 14.00$ per hour and you work 23 hours per week. Your employer withholds $10 \%$ of your gross pay for federal taxes, $7.65 \%$ for FICA taxes, and $3 \%$ for state taxes. Complete parts (a) through (f) below. a. What is your weekly gross pay?
The weekly gross pay is $\$$ $\square$ (Round to the nearest cent as needed.)

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Problem 6923

\begin{enumerate} \item $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}$ . Hexaamminecobalt (III) chloride \item $\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}$ Pentaamminechlorocobalt (III) ion \item $\left[\mathrm{CoSO}_{4}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{NO}_{3}$ . Tetraamminesulphatocobalt (III) nitrate \item $\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]$ Triamminetrinitrocobalt (III) \item $\mathrm{Na}_{2}\left[\mathrm{ZnCl}_{4}\right]$ Sodium tetrachlorozincate \item $\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{5}(\mathrm{NO})\right]$ Potassium pentacyanonitrosylferrate \item $\mathrm{Fe}\left(\mathrm{C}_{5} \mathrm{H}_{5}\right)_{2}$ . Bis(cyclopentadienyl) iron (II) \end{enumerate} Discuss the crystal field splitting of a square planar complex.

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Problem 6924

For a class assignment, Tyler wanted to study whether or not the color of a person's car correlates with the color of his or her hair. He spent an hour at a stoplight recording the color of each car that passed and the hair color of its driver. The probability that a driver has a purple car is 0.02 , the probability that a driver has black hair is 0.57 , and the probability that a driver has a purple car and has black hair is 0.01 . What is the probability that a randomly chosen driver has a purple car or has black hair? Write your answer as a whole number, decimal, or simplified fraction. $\square$

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Problem 6925

5. Schreibe als Bruch. Kürze so weit wie möglich. a) $6 \%$ b) $25 \%$ c) $30 \%$ d) $75 \%$ e) $24 \%$ f) $70 \%$ g) $15 \%$ ${ }^{+}$ h) $36 \%$ +i) $18 \%$ +j) $44 \%$ ${ }^{+} \mathbf{k )} 45 \%$

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Problem 6926

+6. Notiere in der Prozentschreibweise: a) 0,47 b) 0,68 c) 0,03 d) 0,07 e) 0,6 f) 0,40 g) 0,8

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Problem 6927

\begin{tabular}{|c|c|} \hline \multicolumn{2}{|r|}{Paper (2)} \\ \hline 1 & \begin{tabular}{l} The diagram shows a force being applied to a lever to lift a heavy weight. \\ Which change would enable the heavy weight to be lifted with a smaller force? \\ A Move the force to the right. \\ B Move the heavy weight to the right. \\ C Move the force to the left. \\ D Move the pivot to the left. \end{tabular} \\ \hline 2 & \begin{tabular}{l} A plane lamina with centre of mass $X$ touches the ground at point $P$ . \\ Which diagram shows the lamina in equilibrium? \\ A \\ C \\ B \\ D \end{tabular} \\ \hline 3 & \begin{tabular}{l} A girl of mass 50 kg runs at $6.0 \mathrm{~m} / \mathrm{s}$ . \\ What is her momentum? \\ A 300J \\ B $\quad 300 \mathrm{kgm} / \mathrm{s}$ \\ C 900 J \\ D $900 \mathrm{kgm} / \mathrm{s}$ \end{tabular} \\ \hline \end{tabular} 2
Eng. Hussein Khaled

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Problem 6928

\begin{tabular}{|c|c|} \hline 4 & \begin{tabular}{l} A vehicle of mass 900 kg is travelling with a velocity of $20 \mathrm{~m} / \mathrm{s}$ . \\ What is the momentum of the vehicle? \\ A $45 \mathrm{kgm} / \mathrm{s}$ \\ B $450 \mathrm{kgm} / \mathrm{s}$ \\ C $18000 \mathrm{kgm} / \mathrm{s}$ \\ D $180000 \mathrm{kgm} / \mathrm{s}$ \end{tabular} \\ \hline 5 & \begin{tabular}{l} A bullet of mass 0.10 kg travels horizontally at a speed of $600 \mathrm{~m} / \mathrm{s}$ . It strikes a stationary wooden block of mass 1.90 kg resting on a frictionless, horizontal surface. \\ The bullet stays in the block. \\ What is the speed of the bullet and the block immediately after the impact? \\ A $30 \mathrm{~m} / \mathrm{s}$ \\ B $32 \mathrm{~m} / \mathrm{s}$ \\ C $60 \mathrm{~m} / \mathrm{s}$ \\ D $134 \mathrm{~m} / \mathrm{s}$ \end{tabular} \\ \hline 6 & \begin{tabular}{l} A moving body undergoes a change of momentum. \\ What is a unit for change of momentum? \\ A Nm \\ B $\mathrm{N} / \mathrm{m}$ \\ C Ns \\ D $\mathrm{N} / \mathrm{s}$ \end{tabular} \\ \hline 7 & \begin{tabular}{l} The diagram shows a uniform bridge, 4.0 m long and weighing 10000 N . \\ The bridge is pivoted at one end. A force at the other end gradually increases until the bridge begins to lift. \\ What is the lifting force as the bridge starts to move upwards? \\ A 2500 N \\ B 5000 N \\ C $\quad 10000 \mathrm{~N}$ \\ D 20000 N \end{tabular} \\ \hline 8 & \begin{tabular}{l} The diagram shows a wooden beam of weight 20 N . The centre of mass of the beam is labelled $M$ . \\ There is a pivot at one end of the beam. The beam is kept horizontal by an upward force, F. \\ What is the magnitude of $F$ ? \\ A $\quad 12 \mathrm{~N}$ \\ B 20 N \\ C 30 N \\ D 33 N \end{tabular} \\ \hline \end{tabular}

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Problem 6929

\begin{tabular}{|c|c|} \hline 5 & \begin{tabular}{l} A bullet of mass 0.10 kg travels horizontally at a speed of $600 \mathrm{~m} / \mathrm{s}$ . It strikes a stationary wooden block of mass 1.90 kg resting on a frictionless, horizontal surface. \\ The bullet stays in the block. \\ What is the speed of the bullet and the block immediately after the impact? \\ A $30 \mathrm{~m} / \mathrm{s}$ \\ B $32 \mathrm{~m} / \mathrm{s}$ \\ C $60 \mathrm{~m} / \mathrm{s}$ \\ D $134 \mathrm{~m} / \mathrm{s}$ \end{tabular} \\ \hline 6 & \begin{tabular}{l} A moving body undergoes a change of momentum. \\ What is a unit for change of momentum? \\ A Nm \\ B $\mathrm{N} / \mathrm{m}$ \\ C Ns \\ D N/s \end{tabular} \\ \hline 7 & \begin{tabular}{l} The diagram shows a uniform bridge, 4.0 m long and weighing 10000 N . \\ The bridge is pivoted at one end. A force at the other end gradually increases until the bridge begins to lift. \\ What is the lifting force as the bridge starts to move upwards? \\ A 2500 N \\ B 5000 N \\ C 10000 N \\ D 20000 N \end{tabular} \\ \hline 8 & \begin{tabular}{l} The diagram shows a wooden beam of weight 20 N . The centre of mass of the beam is labelled $M$ . \\ There is a pivot at one end of the beam. The beam is kept horizontal by an upward force, $F$ . \\ What is the magnitude of $F$ ? \\ A $\quad 12 \mathrm{~N}$ \\ B 20 N \\ C 30 N \\ D 33 N \end{tabular} \\ \hline \end{tabular}

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Problem 6930

Bob makes his first $\$ 900$ deposit into an IRA earning $7.3 \%$ compounded annually on his 24 th birthday and his last $\$ 900$ deposit on his 38th birthday ( 15 equal deposits in all). With no additional deposits, the money in the IRA continues to earn $7.3 \%$ interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob retires?
The amount in the IRA when Bob retires is $\$$ $\square$ (Round to the nearest cent as needed.)

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Problem 6931

4. Juan solves a multiplication problem vy muviry ure decimal point in 0.02 five places to the right. What is the second factor in Juan's multiplication problem? Explain how you know. $\square$ $\qquad$ $\qquad$
Fill in the blank to complete the statement.
5. The distance around the earth's equator can be written as $24.9 \times 1,000$ miles. To multiply 24.9 by 1,000 , move the decimal point $\qquad$ places to the right.
6. The earth's volume is about $2.6 \times 10^{11}$ cubic miles. To multiply 2.6 by $10^{11}$ , move the decimal point $\qquad$ places to the right.
7. Weather satellites are in an orbit about $0.36 \times 100,000$ kilometers above the earth's surface. To multiply 0.36 by 100,000 , move the decimal point $\qquad$ places to the right.

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Problem 6932

Let $k$ be a constant. Compute $\frac{d}{d x}[\ln (k x)]$ in two ways. a) Using the Chain Rule, first decompose $y=\ln (k x)$ into an outside and inside function Outside function (in terms of $u$ ): $y=$ $\square$ Inside function (in terms of $x$ ): $u=$ $\square$ .
Then find the derivative, $\frac{d}{d x}[\ln (k x)]=$ $\square$ (simplify your answer). b) Using a law of logarithms to simplify first: $\ln (k x)=$ $\square$ $+\widehat{v}$ $\ln x$ . (Fill in the blanks to make this a true statement.) Now take the derivative of the simplified function: $\frac{d y}{d x}=$ $\square$ Note: You can earn partial credit on this problem.

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Problem 6933

Find the simple interest on the loan of $\$ 2500$ for 2 years at $5 \%$ . \\square$ (Simplify your answer. Round to the nearest cent as needed.)

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Problem 6934

Gegeben ist die lineare Funktion f mit der Gleichung $\mathrm{y}=0,5 \mathrm{x}-2$ a) Übernehmen Sie die folgende Wertetabelle und vervollständigen Sie diese für die Funktion f. \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -3 & 0 & 1 & 6 \\ \hline $y$ & & & & \\ \hline \end{tabular}
Zeichnen Sie den Graphen der Funktion $f$ in ein Koordinatensystem. b) Geben Sie für $y=-1$ den zugehörigen Wert für $x$ an. c) Der Graph der Funktion $f$ schneidet die $x$ -Achse im Punkt $S$ .
Geben Sie die Koordinaten des Punktes $S$ an. d) Durch den Punkt $P(1 ; 1)$ verläuft der Graph der Funktion g parallel zum Graphen der Funktion f. Zeichnen Sie den Graphen der Funktion g in dasselbe Koordinatensystem. Für Aứgabe 2 erreichbare BE: 6

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Problem 6935

14 Gwen saves $15 \%$ of her income. This month her income is $\$ 500$ more than last month. The expression $0.15(x+500)$ represents the amount of money she saves this month, where $x$ is last month's income. Gwen saves $\$ 210$ this month. What was Gwen's income last month?

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Problem 6936

Save
The principal $P$ is borrowed at simple interest rate $r$ for a period of time $t$ . Find the loan's future value, $A$ , or the total amount due at time t. $P=\$ 9000, r=6.5 \%, t=8 \text { months }$
The future value is $\$$ $\square$ (Simplify your answer. Type an integer or a decimal.)

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Problem 6937

BUSINESS A Mason jar company wants to increase the volume of its cylindrical jars by 6 cubic inches. The company's designer wants a formula that states the height $h$ of a jar given its volume $V$ and radius $r$ . The volume of a cylindrical jar is modeled by the equation $V=\pi r^{2} h$ . Part A What formula should be used to find the height $h$ ? A. $h=\pi \cdot r^{2}$ B. $h=\sqrt{\frac{V}{\pi r}}$ C. $h=\frac{V}{\pi r^{2}}$ D. $h=\frac{V}{r^{2}}$
Part B If the radius of the jar is 1.5 inches and the original volume is 30 cubic inches, then what height should the company make its new jar to increase the volume by 6 cubic inches?

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Problem 6938

Find the value of $r+3$ , when $\frac{r}{2}=5$ . $r+3=\ldots$

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Problem 6939

Exercice 29 (1 point) $D$ Au moment des soldes un affiches.
ATTENTION : Détaillez tous vos calculs
QUESTION N ${ }^{\circ} 1$ (4 points) A. La commune de Waterville possède une piscine municipale avec un bassin sportif de 25 m de longueur sur 12,5 m de largeur, et d'une profondeur de 2,4 m (uniforme dans tout le bassin), plan en annexe 1. Déterminez le volưne d'eau en litres nécessaire pour son remplissage. B. Le débit de la vanne d'arrivée d'eau est de $8,5 \mathrm{~m}^{3} /$ heure. Calculez le nombre d'heures nécessaires

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Problem 6940

Suppose that $\$ 14.225$ is invested at an interest rate of $5.8 \%$ per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time $t$ , in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is $\mathrm{P}(\mathrm{t})=14225 e^{0.058 t}$ (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) b) The balance after 1 year is $\$$ $\square$ (Simplify your answers. Round to two decimal places as needed.)

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Problem 6941

Find an equation for the perpendicular bisector of the line segment whose endpoints are $(1,-6)$ and $(-7,6)$ .

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Problem 6942

$\checkmark 1$ 2 3 4 5 6 7 8 9 10 11 12
A pollster is going to sample a number of voters in a large city and construct a $90 \%$ confidence interval for the proportion who support the incumbent candidate for mayor. Find a sample size so that the margin of error will be no larger than 0.05 . Be sure to round up to the next whole number.
The required sample size is $\square$ .

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Problem 6943

10.
If $f(x)=-6-12 x$ and $f(x)=18$ what is the value of $x$ ? A -222 B -2 C 2 D 222

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Problem 6944

Mila's psychology test contains 10 true/false questions and 8 multiple choice questions. If Mila guesses on each question, find the probability that she will answer 5 true/false and 1 multiple-choice questions correctly. Each multiple-choice question has 5 answer choices.
State answer as a decimal rounded to six decimal places.

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Problem 6945

Put the numbers in each category to which they belong. clear CHECK $\frac{15}{3}$ $-\frac{1}{5}$ 3,458 $\frac{2}{9}$
Rational Numbers Integers Whole Numbers
DRAG AND DRAG AND DRAG AND DROP ITEMS DROP ITEMS DROP ITEMS HERE HERE HERE

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Problem 6946

Cans of soda vary slightly in weight. Given below are the measured weights of seven cans, in pounds. Find the mean and median of these weights. Which, if any, of these weights would be considered an outlier? What are the mean and median weights if the outlier is excluded? $\begin{array}{lllllll} 0.8159 & 0.8192 & 0.8163 & 0.8176 & 0.7907 & 0.8144 & 0.8125 \end{array}$
Find the mean and median of the weights The mean is $\square$ (Round to five decimal places as needed.)

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Problem 6947

JR makes $88 \%$ of all three-point shots and $85 \%$ of all free-throw shots while playing basketball. Suppose she shoots 8 three-point shots and 5 free-throw shows. What is the probability that she makes 5 three-point shots and 3 free-throw shots?

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Problem 6948

7 Multiple Choice 1 point Suppose a company finds that its revenue can be modeled by $R(q)=600 q$ and that its cost is modeled by $C(q)=5 q^{2}+500 q$ . Given these functions what quantity will maximize this company's profit? 25 5 10 15 20 Clear my selection

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Problem 6949

Jaymes is taking a 19-question science test. a. If Jaymes guesses on each question, and the test contains 19 true-false questions, find the probability that he answers 9 questions correctly. $\square$ State answer as a decimal rounded to six decimal places. b. If Jaymes guesses on each question, and the test contains 19 multiple-choice questions, find the probability that he answers 9 questions correctly when each question has 4 answer options. $\square$ State answer as a decimal rounded to six decimal places.

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Problem 6950

1. Apply Math Models In Jacksonville Beach, Florida, the ocean temperature decreased by an average of $5^{\circ} \mathrm{F}$ each month for 5 months and then increased by an average of $3^{\circ} \mathrm{F}$ for 7 months. In St. Petersburg, Florida, the ocean temperature decreased by $4^{\circ} \mathrm{F}$ for 5 months and then increased by $4^{\circ} \mathrm{F}$ for 7 months. In which location did the ocean have a greater change in temperature? Explain.

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Problem 6951

3. A graph of the parabola $y=x^{2}+$ this function in the order shown: a. A vertical translation 4 units down b. A horizontal translation 2 units left c. A vertical stretch about the $x$ -axis by a factor of 0.5 d. Reflection in the $x$ -axis
For each transformation, a. Graph the image on the grid b. Write the newest equation in the table below

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Problem 6952

3. A graph of the parabola $y=x^{2}+1$ this function in the order shown: a. A vertical translation 4 units down b. A horizontal translation 2 units left c. A vertical stretch about the $x$ -axis by a factor of 0.5 d. Reflection in the $x$ -axis
For each transformation, a. Graph the image on the grid b. Write the newest equation in the table below

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Problem 6953

Using the MACRS rates from the following table, what is the book value of a $\$ 4,000$ computer after 2 years? \begin{tabular}{|c|r|} \hline Year & MACRS Rate \\ \hline 1 & $20.0 \%$ \\ \hline 2 & $32.0 \%$ \\ \hline 3 & $19.2 \%$ \\ \hline 4 & $11.52 \%$ \\ \hline 5 & $11.52 \%$ \\ \hline 6 & $5.76 \%$ \\ \hline \end{tabular}
Book Value = \ $[?] Round to the nearest cent.$ \square$ Enter

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Problem 6954

Eurrent Attempt in Progress
A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about $140 \mathrm{~m}^{3} / \mathrm{hr}$ at 6 am and increases steadily to about 280 $\mathrm{m}^{3} / \mathrm{hr}$ at 9 am . Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.
Best estimate = i $\square$ $\mathrm{m}^{3}$

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Problem 6955

A new drug has shown to be effective in $68 \%$ of participants during the trials. In a group of 50 patients; what is the probability that the drug is not effective for at most 5 patients?
State answer as a decimal rounded to six decimal places. $\square$

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Problem 6956

Save \& Exit Certify Lesson: 7.4 11.1b Systems of Equations Ap... WILLIAM BURRIS
Question 2 of 10, Step 1 of 1 0/10 Correct 1
Two angles are complementary if the sum of their measures is $90^{\circ}$ . Find two complementary angles such that the smaller angle is $57^{\circ}$ less than 2 times the larger angle. (Round to two decimal places if necessary.)
Answer Keypad
How to enter your answer (opens in new window) Keyboard Shortcuts $\qquad$ ${ }^{\circ}$ the smaller complementary angle $\square$ - the larger complementary angle Submit Answer

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Problem 6957

Question 3 of 10, Step 1 of 1 WILLIAM BURRIS $1 / 10$ Correct
Use a system of equations to solve the following problem.
An investor decides to invest some cash in an account paying $6 \%$ annual interest, and to put the rest in a stock fund that ends up earning $9 \%$ over the course of a year. The investor puts $\$ 800$ more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $\$ 1950$ . How much money was invested at each of the two rates? Round to the nearest integer.
Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts \\square $at$ 6 \% $\$$ \square $at$ 9 \%$ Submit Answer

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Problem 6958

\begin{enumerate} \item A shallow trench for a 1,000-foot waterline installation will take ten days. It will take four days to install the first 400 feet of pipe. A water meter will then be installed during the following two days at the end of the pipe. After the meter is installed, the remaining 600 feet of pipe will be installed in six days. Develop a linear schedule for this project. \item In the context of scheduling, what do we mean by resources? What is resource allocation and leveling? Why level resources in construction projects? \item You are a southern California contractor. You have been awarded two projects: one in downtown Los Angeles and one near the Mojave reservation. \begin{enumerate} \item Each project needs a bulldozer, a tower crane, and a safety manager. Do you share these resources between the two projects? Justify your answer. \item Which materials management theory would you lean toward in each project? \end{enumerate} \item What type of projects is best for LSM application? What are the steps for preparing an LSM schedule? \item Define Time Buffer and Distance Buffer. Use words and graphs to explain your answer. \end{enumerate}

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Problem 6959

Given the building layout for Store A, Store B, Store C, and Store D, what portion of the shared \7500 maintenance costs should be apportioned to Store D? \begin{tabular}{|l|l|c|c|} \hline \multirow{4}{*}{$2500 \mathrm{ft}^{2}$} & B 1250 \mathrm{ft}^{2}$ & C & D \\ & & & \\ & & & \\ & & & \end{tabular}
Apportioned Cost = \$ [?] Round to the nearest cent.

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Problem 6960

Higher Order Thinking Explain how to use absolute value to find the distance on the number line between any positive number and any negative number. Give an example.

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Problem 6961

A fair die is rolled four times. What is the probability that it comes up 3 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.
The probability that it comes up 3 at least once is $\square$ . $\square$

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Problem 6962

7. The ion-electron equations below represent the reduction and oxidation reactions which take place when an acidified solution of dichromate ions react with sulfite ions. $\begin{array}{l} \text { ctron equations below represent the reduction with sulfite } \\ \text { an acidified solution of dichromate ions react with } \\ \left.\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq})+6 \mathrm{H}_{2}^{-} \mathrm{l}\right) \\ \qquad \mathrm{SO}_{3}^{2-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{SO}_{4}^{2-}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq})+2 e^{-} \end{array}$
Write the REDOX equation for this reaction.
8. Sulfur dioxide is added to wine as a preservative. A mass of 20 to 40 mg of sulfur dioxide per litre of wine will safeguard the wine without affecting its taste. a. Describe clearly, with full experimental detail, how $0.05 \mathrm{~mol} \mathrm{l}^{-1}$ iodine solution would be diluted to give $250 \mathrm{~cm}^{3}$ of $0.005 \mathrm{~mol} \mathrm{l}^{-1}$ solution. b. The equation for the reaction which takes place is: $\begin{array}{l} \text { for the reaction which takes place is: } \\ \mathrm{SO}_{2}(\mathrm{aq})+\mathrm{I}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 4 \mathrm{H}^{+}(\mathrm{aq})+\mathrm{SO}_{4}{ }^{2-}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq}) \end{array}$ (i) The indicator used in this reaction causes a change from blue to colourless at the end point. Name a substance which could be used as this indicator. (ii) Write the ion-electron equation for the reduction reaction taking place.
9. In acid solution, iodate ions, $\mathrm{IO}_{3}^{-}(\mathrm{aq})$ , are readily converted into iodine $\mathrm{I}_{2}(\mathrm{aq})$ . a. Write an ion-electron equation for this half-reaction. b. Use the equation to explain whether the iodate ion is an oxidising or a reducing agent.
10. Before 1980, the concentration of alcohol in drinks was measured in terms of degrees proof. The concentration of alcohol in two drinks is shown in the table below, both as \% abv and degrees proof. \begin{tabular}{|c|c|c|} \hline Sample & \begin{tabular}{c} Alcohol \\ concentration \\ $/ \%$ abv \end{tabular} & \begin{tabular}{c} Alcohol \\ concentration \\ /degrees proof \end{tabular} \\ \hline Wine & $14 \cdot 0$ & $24 \cdot 5$ \\ \hline Sherry & $20 \cdot 0$ & $35 \cdot 0$ \\ \hline \end{tabular} a. A cask strength whisky has an alcohol concentration of $65 \%$ abv.
Calculate the alcohol concentration of this whisky in degrees proof. b. A barrel containing 195 litres of cask strength whisky costs $£ 1300$ .
The cask strength whisky is diluted with water to reduce the concentration of alcohol from $65 \%$ abv to $46 \%$ abv before it is bottled. Calculate the cost of the cask strength whisky needed to produce a 0.70 litre bottle. Show your working clearly.

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Problem 6963

A scooter is purchased for $\$ 4,000$ and has a resale value of $\$ 200$ after a useful life of 5 years. Using a book value depreciation chart, calculate the number of years until the book value of the scooter is $\$ 2,480$ . [?] years Enter

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Problem 6964

Finding a Job Math Quiz p.m. Yas pel a 30 minute unpaid lunch bresk every warkidy. How many hours will you be prid for mis week?
0 4) 17.5 t) 1185 8) 10.35 d) 25 Submit Cxest keymange Mither, leve.

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Problem 6965

Application: 5 Marks
7. A catering company charges $\$ 590$ for 20 guests and $\$ 740$ for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

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Problem 6966

Determine whether Rolle's theorem can be applied to $f$ on the closed interval $[a, b]$ . (Select all that apply.) $f(x)=\frac{x^{2}}{9-x^{2}}, \quad[-10,10]$
Yes, Rolle's theorem can be applied. No, because $f$ is not continuous on the closed interval $[a, b]$ . No, because $f$ is not differentiable in the open interval $(a, b)$ . No, because $f(a) \neq f(b)$ . If Rolle's theorem can be applied, find all values of $c$ in the open interval $(a, b)$ such that $f^{\prime}(c)=0$ . (Enter your answers as a comma-separated list. If Rolle's theorem cannot be applied, enter NA.) $c=$

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Problem 6967

Indicate the total number of $4 d$ electrons in $\mathrm{Ba}(\mathrm{Z}=56)$ .

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Problem 6968

A ferris wheel is 32 meters in diameter and makes one revolution every 7 minutes. For how many minutes of any revolution will your seat be above 24 meters?
For $\square$ minutes of any one revolution you will be above 24 meters. Preview My Answers Submit Answers

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Problem 6969

The cost of 2 rackets and 3 squash balls is $£ 21.63$ . The cost of 5 rackets and 7 squash balls is $£ 52.90$ .
Work out the cost of a) a racket. b) a squash ball.

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Problem 6970

Fill in each blank with the appropriate word or phrase.
Part 1 of 2
An outcome or collection of outcomes from a sample space is called (Choose one) .
Part 2 of 2
The collection of all possible outcomes of a probability experiment is called (Choose one)

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Problem 6971

368. Mootorpaat sõitis jõel vastuvoolu 16 km ja pöördus siis tagasi, kulutades tagasiteel 40 minutit vähem aega kui liikumisel vastuvoolu. Leidke paadi kiirus seisvas vees, kui jõe voolu kiirus on $2 \mathrm{~km} / \mathrm{h}$ .

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Problem 6972

For the given confidence level and values of $x$ and $n$ , find the following. $x=44, n=96, \text { confidence level } 98 \%$
Part 1 of 3 (a) Find the point estimate. Round the answers to at least four decimal places, if necessary.
The point estimate for the given data is 0.4583 .
Part: $1 / 3$
Part 2 of 3 (b) Find the standard error. Round the answers to at least four decimal places, if necessary.
The standard error for the given data is $\square$

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Problem 6973

Übung 6 Untersuchen Sie die Funktion f auf Wendepunkte. Skizzieren Sie den Graphen oder stellen Sie ihn mit dem TR/Computer dar. a) $f(x)=2 \cdot e^{x}-e^{-x}$ b) $f(x)=\left(x^{2}-1\right) \cdot e^{-0,5 x}$

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Problem 6974

22) Which of the following is equivalent to $i^{3}$ ? A. $i$ B. $-i$ C. 1 D. -1

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Problem 6975

A. It has a double root B. Two distinct, real roots C. Two imaginary roots

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Problem 6976

Word Problems (3 points each) 17) Abigail tosses a coin off a bridge into the stream below. The height, in feet, the coin is above the water is modeled by the equation $y=-16 x^{2}+96 x+112$ . $X$ represents the time in seconds. What is the greatest height of the coin? 18) American astronauts working on a space station on the moon toss a ball into the air. The height of the ball is represented by the equation $y=-2.7 t^{2}+13.5 t+14$ where $t$ represents time in seconds since the ball was thrown and $y$ represents the height of the ball in feet. At what time will the ball hit the ground?

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Problem 6977

17. Apply Wath Models The temperature at noon in Miami Beach was $90^{\circ} \mathrm{F}$ . The semperature then changed $Z^{\circ}$ Fer hour for the next 7 hours. The expression $90-|-2 \cdot 7|$ represents the current temperature. a. Is the current temperature higher or lower than $90^{\circ} \mathrm{F}$ ? b. What is the current temperature?

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Problem 6978

18) American astronauts working on a space station on the moon toss a ball into the air. The height of is represented by the equation $y=-2.7 t^{2}+13.5 t+14$ where $t$ represents time in seconds since the thrown and $y$ represents the height of the ball in feet. At what time will the ball hit the ground?

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Problem 6979

Which of the two annual interest rates would yield the larger amount in 1 year? $12 \%$ compounded monthly or $12 \frac{1}{2} \%$ compounded annually
Select the correct choice and fill in the answer box to complete your choice. (Do not round until the final answer. Then round to three decimal places as needed.) A. The effective interest rate for $12 \%$ compounded monthly is $\square$ $\%$ which would yield the larger amount in 1 year. B. The effective interest rate for $12 \frac{1}{2} \%$ compounded annually is $\square$ \% which would yield the larger amount in 1 year.

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Problem 6980

Situation: Un fermier voudrait lancer un élevage estimé à 3000000FCFA. Dans la recherche des financements, un ami lui propose de placer les 1000000FCFA représentant la totalité de ses économies dans une banque a pour commencer son projet, la banque $\beta$ lui reverse alors après un an, la somme de 1123500 FCFA. Ne disposant pas de bêtes au départ, un partenaire lui donne à crédit, trois fois de suite et aux mêmes prix des bêtes dont 60 poussins, 25 moutons et 10 chevreaux à 195000FCFA au premier tour, 50 poussins, 20 moutons et 30 chevreaux à 245000 FCFA au deuxième tour et enfin 60 poussins, 20 moutons et 20 chevreaux à 210000 FCFA au troisième tour. Au moment de vérifier ses comptes, il ne retrouve pas tous ses documents financiers. Tâches:
1. A quel taux le fermier a-t-il placé ses économies dans ląoanque $\alpha$ ?
2. Déterminer le taux unitaire de chaque espèce de bêtes que lui a donnée le partenaire. $1,5 \mathrm{pt}$
3. La proposition de son ami pourra - - - elle permettry au fermier de financer entièrement son projet au bout de 8 ans ?

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Problem 6981

Q4 (10 marks) PH10 $10^{\circ}$ (a) A $5.00-\mathrm{g}$ bullet moving with an initial speed of $400 \mathrm{~m} / \mathrm{s}$ is fired into and passes through a $1.00-\mathrm{kg}$ block as shown in Figure 4(a). The block, initially at rest on a frictionless, horizontal surface, is connected to a spring with force constant $900 \mathrm{~N} / \mathrm{m}$ . The block moves a maximum distance of 5.00 cm to the right after the bullet exits the block.
Figure 4(a) (i) Find the speed at which the bullet emerges from the block.
ANS: (ii) Find the mechanical energy converted into internal energy in the collision.
ANS: Note: Question 4 continues on page 9

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Problem 6982

How long does it take for an investment to double in value if it is invested at $7 \%$ compounded monthly? Compounded continuously?
At 7\% compounded monthly, the investment doubles in about (Round to two decimal places as needed.) $\square$ years.

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Problem 6983

The Nicols are buying a house selling for $\$ 355,000$ . They pay a down payment of $\$ 55,000$ from the sale of their current house. To obtain a 15 -year mortgage at a $6 \%$ interest rate, the Nicols must pay 2.5 points at the time of closing. a) What is the amount of the mortgage? b) What is the cost of the 2.5 points?

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Problem 6984

How many roots, real or complex, does the polynomial $7+5 x^{4}-3 x^{2}$ have in all?
7 3 4 5

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Problem 6985

A caravan was bought for $£ 20,000$ . It depreciated by $11 \%$ in the first year. It then depreciated by a further 6\% each year over the next two years. Calculate the value of the caravan three years after it was bought.

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Problem 6986

weight is attached to a spring suspended from a beam. At time $t=0$ , it is pulled down to a point 7 cm above the ground and leased. After that, it bounces up and down between its minimum height of 7 cm and a maximum height of 25 cm , and its height $(t)$ is a sinusoidal function of time $t$ . It first reaches a maximum height 0.8 seconds after starting. (a) Follow the procedure outlined in this section to sketch a rough graph of $h(t)$ . Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur. (b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean $\square$ amplitude $\square$ phase shift $\square$ period $\square$ (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) $\square$ (d) Write down a formula for the function $h(t)$ in standard sinusoidal form; i.e. as in the equation shown below. $\begin{array}{l} h(t)=A \sin \left(\frac{2 \pi}{B}(t-C)\right)+D \\ h(t)=\square \end{array}$ (e) What is the height of the weight after 2.4 seconds? $\square$ cm (f) During the first 10 seconds, how many times will the weight be exactly 19 cm above the floor? (Note: This problem does not require inverse trigonometry.) $\square$

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Problem 6987

408 Сравните значения выражений: а) $3 \sqrt{3}$ и $\sqrt{12}$ ; в) $5 \sqrt{4}$ и $4 \sqrt{5}$ ; б) $\sqrt{20}$ и $3 \sqrt{5}$ ; г) $2 \sqrt{5}$ и $3 \sqrt{2}$ .

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Problem 6988

Write a quadratic function with zeros 0 and 9. )）㸚 Write your answer using the variable x and in standard form with a leading coefficient of 1 .

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Problem 6989

HReady Numerical Expressions with Exponents-Instruction-Level F A scientist keeps track of bacteria cells. She starts with 1 cell. After one hour, there are 2 cells. The number of cells continues to double in each of the following hours. Hour Expression Number of Cells 1 2 Hour 1 2 2.2 Hour 2 3 2.2.2 8 Hour 3 4 2.2.2.2 16 4) Complete the statements. The number of cells increases by a factor DELL PA 1 Hour 4 L ΛΛΛΛ ЛЛЛЛЛЛЛЛ 7 8 4 5 1 2 0 " X 6 9 3 (-) -

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Problem 6990

[i]. Write a quadratic function with zeros 8 and -3 . [啹, Write your answer using the variable x and in standard form with a leading coefficient of 1 . $g(x)=$

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Problem 6991

23. Question from 1.12: Modeling Variation
The cost $C$ of printing a magazine is jointly proportional to the number of pages $p$ in the magazine and the number of magazines printed $m$ . (a) Write an equation that expresses this joint variation. (Use $k$ for the constant of proportionality.) $\square$ (b) Find the constant of proportionality if the printing cost is $\$ 55,037.5$ for 3700 copies of a 119 -page magazine. $k=$ $\square$ (c) How much would the printing cost be for 5500 copies of a 52 -page magazine? \\square$

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Problem 6992

24. Question from 1.12: Modeling Variation
The power $P$ that can be obtained from a windmill is directly proportional to the cube of the wind speed $s$ . (a) Write an equation that expresses this variation. (Use $k$ for the constant of proportionality.) $\square$ (b) Find the constant of proportionality for a windmill that produces 128 watts of power when the wind is blowing at $20 \mathrm{mi} / \mathrm{h}$ . $k=$ $\square$ (c) Hoyv much power will this windmill produce if the wind speed increases to $30 \mathrm{mi} / \mathrm{h}$ ? $\square$ watts

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Problem 6993

Home | iCampus ALEKS A ALEKS - Matilda Brown - Learn www-awu.aleks.com/alekscgi/x/lsl.exe/1o_u-IgNslkr7j8P3jH-lv-6txjbonmDn7WsVrRAXK6XnHkiRvH2t18oGG26_9bCYMDyJvgKuz_5ynmc6T1g7PIGWwLDsQ0Uzof_Zd57eqEibJxKJnQh?1oB... Consumer Mathematics Mean of a data set 0/5 Matilda Español
On a survey, 7 students reported how many minutes it takes them to travel to school. Here are their responses. $13,6,15,16,13,6,10$ Send data to calculator
Find the mean travel time for these students. If necessary, round your answer to the nearest tenth. $\square$ minutes Elomplanation Check @ 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center I Accessibility 2:57 PM 11/25/2024

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Problem 6994

PROBLEM \#2. Sickle-cell anemia is an interesting genetic disease. Normal homozygous individials (SS) have normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals become very ill from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, but generally not enough to cause mortality. In addition, malaria cannot survive well within these "partially defective" red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If $9 \%$ of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

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Problem 6995

Mean, median, and mode: Computations Matilda QUESTION Español
Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for 8 customers at the bank. Here are the 8 waiting times (in minutes). $24,6,14,10,14,20,25,21$ Send data to calculator \begin{tabular}{|l|l|} \hline (a) What is the median of this data set? If your answer is not \\ an integer, round your answer to one decimal place. \end{tabular}
OO EXPLANATION

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Problem 6996

iClicker Question Systolic blood pressures of healthy adults follow a normal distribution. We would like to conduct a hypothesis test at the $5 \%$ level of significance to determine if the true mean systolic blood pressure of healthy adults is greater than 120 . We take a random sample of 25 healthy adults. The sample mean systolic blood pressure is calculated to be 122 and the sample standard deviation is calculated to be 7.8. The P -value and conclusion of the appropriate test of significance are, respectively: (A) between 0.05 and 0.10 , fail to reject $\mathrm{H}_{0}$ . (B) between 0.10 and 0.15 , reject $\mathrm{H}_{0}$ . (C) between 0.10 and 0.15 , fail to reject $\mathrm{H}_{0}$ . (D) between 0.15 and 0.20 , reject $\mathrm{H}_{0}$ . (E) between 0.15 and 0.20 , fail to $\mathrm{H}_{0}$ .

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Problem 6997

PROBLEM \#2. Sickle-cell anemia is an interesting genetic disease. Normal homozygous individials (SS) have normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals become very ill from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, but generally not enough to cause mortality. In addition, malaria cannot survive well within these "partially defective" red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If $9 \%$ of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

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Problem 6998

iClicker Question A scientist is concerned about radiation levels in her laboratory. A room is only considered safe if the mean radiation level is 425 or less. A random sample of 16 radiation measurements is taken at different locations within the laboratory. These 16 measurements have a mean of 437 and a standard deviation of 20. Radiation levels in the laboratory are known to follow a normal distribution. We conduct a hypothesis test at the $5 \%$ level of significance to determine whether there is evidence that the laboratory is unsafe.

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Problem 6999

id Doris paid 5.28 for 4.4 pounds of Swiss cheese, what was the price of 1 pound of Swiss cheese?

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Problem 7000

20. How many different representations of -3 can be made with 20 or fewer counters?

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1 ...67 68 69 70 71 72 73 ...122

Word Problem

Problem 6901

Problem 6902

11 Ein Erdwall hat im Querschnitt näherungsweise die Form einer Parabel (Fig. 1). Er ist 2 m hoch und auf 1 m Höhe 10 m breit. Wie breit ist er am Boden?

Problem 6903

Problem 6904

Problem 6905

Problem 6906

Problem 6907

Problem 6908

Problem 6909

Practice--Space Calculations.1. Convert the following into km. a. 52.1 AU

Problem 6910

The line y−14=6(x−2.5)y-14=6(x-2.5)y−14=6(x−2.5) represents Barry's profit, yyy, from selling xxx paintings, after buying some canvas. What was the cost of the canvas? \$

Problem 6911

Problem 6912

Problem 6913

Problem 6914

Problem 6915

Problem 6916

Problem 6917

Problem 6918

Problem 6919

Complete the following acid-base reaction with balanced molecular, total ionic, and net ionic equations. Be sure to include states of matter in your answer. calcium hydroxide (aq)+acetic⁡acid⁡(aq)→(a q)+\operatorname{acetic} \operatorname{acid}(a q) \rightarrow(aq)+aceticacid(aq)→

Problem 6920

Problem 6921

Problem 6922

Problem 6923

Problem 6924

Problem 6925

5. Schreibe als Bruch. Kürze so weit wie möglich. a) 6%6 \%6% b) 25%25 \%25% c) 30%30 \%30% d) 75%75 \%75% e) 24%24 \%24% f) 70%70 \%70% g) 15%15 \%15% +{ }^{+}+h) 36%36 \%36% +i) 18%18 \%18% +j) 44%44 \%44% +k)45%{ }^{+} \mathbf{k )} 45 \%+k)45%

Problem 6926

+6. Notiere in der Prozentschreibweise: a) 0,47 b) 0,68 c) 0,03 d) 0,07 e) 0,6 f) 0,40 g) 0,8

Problem 6927

Problem 6928

Problem 6929

Problem 6930

Problem 6931

Problem 6932

Problem 6933

Find the simple interest on the loan of $2500\$ 2500$2500 for 2 years at 5%5 \%5%. \ \square$ (Simplify your answer. Round to the nearest cent as needed.)

Problem 6934

Problem 6935

Problem 6936

Problem 6937

Problem 6938

Find the value of r+3r+3r+3, when r2=5\frac{r}{2}=52r​=5. r+3=…r+3=\ldotsr+3=…

Problem 6939

Problem 6940

Problem 6941

Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,−6)(1,-6)(1,−6) and (−7,6)(-7,6)(−7,6).

Problem 6942

Problem 6943

10.If f(x)=−6−12xf(x)=-6-12 xf(x)=−6−12x and f(x)=18f(x)=18f(x)=18 what is the value of xxx ? A -222 B -2 C 2 D 222

Problem 6944

Problem 6945

Put the numbers in each category to which they belong. clear CHECK 153\frac{15}{3}315​ −15-\frac{1}{5}−51​ 3,458 29\frac{2}{9}92​Rational Numbers Integers Whole NumbersDRAG AND DRAG AND DRAG AND DROP ITEMS DROP ITEMS DROP ITEMS HERE HERE HERE

Problem 6946

Problem 6947

JR makes 88%88 \%88% of all three-point shots and 85%85 \%85% of all free-throw shots while playing basketball. Suppose she shoots 8 three-point shots and 5 free-throw shows. What is the probability that she makes 5 three-point shots and 3 free-throw shots?

Problem 6948

7 Multiple Choice 1 point Suppose a company finds that its revenue can be modeled by R(q)=600qR(q)=600 qR(q)=600q and that its cost is modeled by C(q)=5q2+500qC(q)=5 q^{2}+500 qC(q)=5q2+500q. Given these functions what quantity will maximize this company's profit? 25 5 10 15 20 Clear my selection

Problem 6949

Problem 6950

Problem 6951

Problem 6952

Problem 6953

Problem 6954

Problem 6955

A new drug has shown to be effective in 68%68 \%68% of participants during the trials. In a group of 50 patients; what is the probability that the drug is not effective for at most 5 patients?State answer as a decimal rounded to six decimal places. □\square□

Problem 6956

Problem 6957

Problem 6958

Problem 6959

Problem 6960

Higher Order Thinking Explain how to use absolute value to find the distance on the number line between any positive number and any negative number. Give an example.

Problem 6961

A fair die is rolled four times. What is the probability that it comes up 3 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.The probability that it comes up 3 at least once is □\square□ . □\square□

Problem 6962

Problem 6963

Practice--Space Calculations.
1. Convert the following into km. a. 52.1 AU

The line $y-14=6(x-2.5)$ represents Barry's profit, $y$ , from selling $x$ paintings, after buying some canvas. What was the cost of the canvas? \$

Complete the following acid-base reaction with balanced molecular, total ionic, and net ionic equations. Be sure to include states of matter in your answer. calcium hydroxide $(a q)+\operatorname{acetic} \operatorname{acid}(a q) \rightarrow$

5. Schreibe als Bruch. Kürze so weit wie möglich. a) $6 \%$ b) $25 \%$ c) $30 \%$ d) $75 \%$ e) $24 \%$ f) $70 \%$ g) $15 \%$ ${ }^{+}$ h) $36 \%$ +i) $18 \%$ +j) $44 \%$ ${ }^{+} \mathbf{k )} 45 \%$

Find the simple interest on the loan of $\$ 2500$ for 2 years at $5 \%$ . \\square$ (Simplify your answer. Round to the nearest cent as needed.)

Find the value of $r+3$ , when $\frac{r}{2}=5$ . $r+3=\ldots$

Find an equation for the perpendicular bisector of the line segment whose endpoints are $(1,-6)$ and $(-7,6)$ .

10.
If $f(x)=-6-12 x$ and $f(x)=18$ what is the value of $x$ ? A -222 B -2 C 2 D 222

Put the numbers in each category to which they belong. clear CHECK $\frac{15}{3}$ $-\frac{1}{5}$ 3,458 $\frac{2}{9}$
Rational Numbers Integers Whole Numbers
DRAG AND DRAG AND DRAG AND DROP ITEMS DROP ITEMS DROP ITEMS HERE HERE HERE

JR makes $88 \%$ of all three-point shots and $85 \%$ of all free-throw shots while playing basketball. Suppose she shoots 8 three-point shots and 5 free-throw shows. What is the probability that she makes 5 three-point shots and 3 free-throw shots?

7 Multiple Choice 1 point Suppose a company finds that its revenue can be modeled by $R(q)=600 q$ and that its cost is modeled by $C(q)=5 q^{2}+500 q$ . Given these functions what quantity will maximize this company's profit? 25 5 10 15 20 Clear my selection

A new drug has shown to be effective in $68 \%$ of participants during the trials. In a group of 50 patients; what is the probability that the drug is not effective for at most 5 patients?
State answer as a decimal rounded to six decimal places. $\square$

A fair die is rolled four times. What is the probability that it comes up 3 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.
The probability that it comes up 3 at least once is $\square$ . $\square$

A scooter is purchased for $\$ 4,000$ and has a resale value of $\$ 200$ after a useful life of 5 years. Using a book value depreciation chart, calculate the number of years until the book value of the scooter is $\$ 2,480$ . [?] years Enter

Finding a Job Math Quiz p.m. Yas pel a 30 minute unpaid lunch bresk every warkidy. How many hours will you be prid for mis week?
0 4) 17.5 t) 1185 8) 10.35 d) 25 Submit Cxest keymange Mither, leve.

Application: 5 Marks
7. A catering company charges $\$ 590$ for 20 guests and $\$ 740$ for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

Indicate the total number of $4 d$ electrons in $\mathrm{Ba}(\mathrm{Z}=56)$ .

A ferris wheel is 32 meters in diameter and makes one revolution every 7 minutes. For how many minutes of any revolution will your seat be above 24 meters?
For $\square$ minutes of any one revolution you will be above 24 meters. Preview My Answers Submit Answers

The cost of 2 rackets and 3 squash balls is $£ 21.63$ . The cost of 5 rackets and 7 squash balls is $£ 52.90$ .
Work out the cost of a) a racket. b) a squash ball.

Fill in each blank with the appropriate word or phrase.
Part 1 of 2
An outcome or collection of outcomes from a sample space is called (Choose one) .
Part 2 of 2
The collection of all possible outcomes of a probability experiment is called (Choose one)

368. Mootorpaat sõitis jõel vastuvoolu 16 km ja pöördus siis tagasi, kulutades tagasiteel 40 minutit vähem aega kui liikumisel vastuvoolu. Leidke paadi kiirus seisvas vees, kui jõe voolu kiirus on $2 \mathrm{~km} / \mathrm{h}$ .

Übung 6 Untersuchen Sie die Funktion f auf Wendepunkte. Skizzieren Sie den Graphen oder stellen Sie ihn mit dem TR/Computer dar. a) $f(x)=2 \cdot e^{x}-e^{-x}$ b) $f(x)=\left(x^{2}-1\right) \cdot e^{-0,5 x}$

22) Which of the following is equivalent to $i^{3}$ ? A. $i$ B. $-i$ C. 1 D. -1