Equation

Problem 2101

Test the claim that the mean body temperature of normal and healthy adults is equal to $37^{\circ} \mathrm{C}$ . Sample data consist of 20 randomly selected healthy adults who have body temperatures with a mean of $36.78^{\circ}$ and a standard deviation of $0.35^{\circ}$ . Use a 0.05 level of significance,, $\cup=37$ $\begin{array}{ll} \text { ificance } J=37 & t=36.78-37 \\ H_{0}: J \neq 37 & 0.351 \sqrt{20} \\ H_{a}: 0.81 & t=-\frac{0.22}{0.0783} \end{array}$
Jsing the same sample data given in problem 1, test the claim that the standard leviation of body temperatures for normal healthy adults is less than $1.00^{\circ} \mathrm{C}$ . Use 05 level of significance.

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Problem 2102

The line $k$ has a slope of -2 . The line $j$ makes an angle of $30^{\circ}$ with $k$ . Find one possible value of the slope of the line $j$ . Give your answer in the form $d+e \sqrt{f}$ , where $d, e, f \in \mathbb{Z}$ .

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Problem 2103

The volume of a rectangular prism is 4,860 cubic centimeters. Its length is 20 centimeters, and its height is 3 times its width.
Which equation can you use to find the width of the rectangular prism, w? $\begin{array}{c} 4,860 \cdot 20= \\ w \cdot 3 w \end{array}$ $\begin{array}{c} 4,860=20 \\ w \cdot 3 w \end{array}$
How wide and tall is the prism? centimeters wide and centimeters tall

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Problem 2104

3. [0/1 Points] DETAILS MYNOTES
A plane flying horizontally at an altitude of 3 miles and a speed of $440 \mathrm{mi} / \mathrm{h}$ passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 4 miles away from the station. (Round your answer to the nearest whole number.)
292 $x$ mi/h
Enhanced Feedback Please try again. Keep in mind that distance $=\sqrt{(\text { altitude })^{2}+(\text { horizontal distance })^{2}}$ (or $y^{2}=x^{2}+h^{2}$ .) Differentiate with respect to $t$ on both sides of the equation, using the Chain Rule, to solve for $\frac{d y}{d t}$ . The given speed of the plane is $\frac{d x}{d t}$ . Need Help? Read It

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Problem 2105

12. Extend Your Thinking How can you find $316 \div 4$ two different ways by using different partial quotients in each solution?

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Problem 2106

1) A $10.31-\mathrm{kg}$ box is at rest when Joseph begins pushing it with a force of +18.66 N , causing it to move 3.64 m . Neglect friction. a) How much work did Joseph do on the box? \begin{tabular}{|l|l|} \hline & J \\ \hline \end{tabular} b) How fast is the box moving after 3.64 m ? \begin{tabular}{|ll|} \hline $3.63 \mathrm{~m} / \mathrm{s}$ \\ \hline \end{tabular}

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Problem 2107

Solve for all possible values of x . $\sqrt{14-2 x}=x-7$

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Problem 2108

If an object travels upward at a velocity of $v$ feet per second from $s$ feet above the ground, the object's height in feet, $h$ , after $t$ seconds can be modeled by the formula $h=-16 t^{2}+v t+s$ . $\begin{array}{c} 10=-16 t^{2}+ \\ 22 t+5 \end{array}$ $\begin{array}{c} 10=-16 t^{2}+ \\ 5 t+22 \end{array}$
To the nearest tenth of a second, how long is the ball in the air before going through the hoop? $\square$ seconds

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Problem 2109

Return Next
1 Fill in the Blank 1 point Question 10 Consider the equation $x^{2}-39=0$ . a. Does the quadratic formula work to solve this equation? Explain or show how you know. choose your answer... $a=$ type your answer... $1 \quad, \mathrm{~b}=$ type your answer... $\square$ , and $c=$ $\square$ type your answer.. $\square$ , $\qquad$ b. Can you solve this equation using square roots? Explain or show how you know. choose your answer... $\square$ you would choose your answer... Next

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Problem 2110

$y=\frac{4}{5} x+3$ $y=3 x+\frac{4}{5}$ $y=\frac{1}{5} x+\frac{4}{5}$ $y=-\frac{4}{5} x+3$

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Problem 2111

Practice Quiz: Perimeter and Circumference 0:07:42 elapsed
Question 9 (5 points) Listen Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi. 6 15.7 9.42 3

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Problem 2112

Return
Question 7 Next
Choose the method you would recommend (the one that would be easiest) for each student to solve their quadratic efficiently. Explain why you recommend that method.
Kiran: $x^{2}-6 x+5=0$ Diego: $2 x^{2}+7 x-4=0$ Lin: $x^{2}-4=18$ Noah: $25 x^{2}+40 x+16=8$ Claire: $17 x^{2}-2 x-1=0$

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Problem 2113

Return 5.5 Practice Problem
Mai and Jada are solving the equation $2 x^{2}-7 x=15$ 9 using the quadratic formula but found different solutions.
Mai wrote: $\begin{array}{l} x=\frac{-7 \pm \sqrt{7^{2}-4(2)(-15)}}{2(2)} \\ x=\frac{-7 \pm \sqrt{49-(-120)}}{4} \\ x=\frac{-7 \pm \sqrt{169}}{4} \\ x=\frac{-7+13}{4} \\ x=-5 \text { or } x=\frac{3}{2} \end{array}$
Jada wrote: $x=\frac{-(-7) \pm \sqrt{-7^{2}-4(2)(-15)}}{2(2)}$ $x=\frac{7 \pm \sqrt{-49-(-120)}}{4}$ $x=\frac{7 \pm \sqrt{71}}{4}$
Fill in the Blank 1 point Question 1a If this equation is written in standard form, $a x^{2}+b x+c$ , what are the values of $a, b$ and $c$ ? $a=$ type your answer... $b=$ type your answer... and $c=$ type your answer... Next

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Problem 2114

Assigment
Practice with proportions.
A company sold 3,000 computers in one month, but 12 were returned. If 3,500 were sold the next month, the company would expect 14 to be returned.
What is a valid proportion to represent the problem? $\frac{3,000}{12}=\frac{14}{3,500}$ $\frac{12}{3,000}=\frac{3,500}{14}$ $\frac{3,500}{3,000}=\frac{12}{14}$ $\frac{3,000}{12}=\frac{3,500}{14}$

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Problem 2115

Explaining a Solution
Solve the proportion using equivalent ratios. Explain the steps you used to solve the proportion, and include the answer in your response. $\frac{10}{3}=\frac{20}{x}$

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Problem 2116

The figure below contains two right triangles with one common side. The length of the segment $B C$ is $|B C|=2 \mathrm{~cm}$ , the length of the segment $A D$ is $|A D|=8 \mathrm{~cm}$ , and the angle $\angle D A B$ is $\angle D A B=53^{\circ}$ .
Find each of the following (note that the angles you plug into trigonometric functions must be in radians): The length of the line segment $B D:|B D|=6.389$ $\square$ cm . The tangent of angle $\theta=\angle B D C: \tan (\theta)=0.313$ The length of the line segement $C D:|C D|=1$ (1) cm .

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Problem 2117

The hypotenuse of a right triangle is 3 times as long as its shorter leg. The longer leg is 12 centimeters long
To the nearest tenth of a cenfimeter, what is the length of the triangle's shorter leg? ) $\square$ Gentimeters

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Problem 2118

Return Next Matching 5 points
Question 7 Choose the method you would recommend (the one that would be easiest) for each student to solve their quadratic efficiently. Explain why you recommend that method.
Kiran: $x^{2}-6 x+5=0$ Diego: $2 x^{2}+7 x-4=0$ Lin: $x^{2}-4=18$ Noah: $25 x^{2}+40 x+16=8$ Claire: $17 x^{2}-2 x-1=0$

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Problem 2119

Sample response: To solve using equivalent ratios you would consider the values in both numberators. The second numerators. The second numerator is 2 times the value of the first, so the second denominator should be 2 times the value of the first. Thus, $x$ should equal 6 because 2 times 3 is 6 .
Which facts did you include in your response? Check all that apply. The numerator of the second ratio is 2 times the numerator of the first. For the ratios to be equivalent, the denominator of the second ratio must be 2 times the denominator of the first. 2 times 3 tequals 6. $x=6$

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Problem 2120

onvert 8.8 C to Fahrenheit. Round to the nearest tenth when necessary. 88.4 F 47.8 F 87.4 F 48.9 F

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Problem 2121

Solve $\frac{1 / 3}{5}=\frac{a}{20}$ $a=3 / 5$ $a=3 / 4$ $a=4 / 3$ $a=5 / 3$

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Problem 2122

Martin can run 1 mile in 7 minutes. What valid proportions can be written from this information? Check all that apply. $\frac{1}{7}=\frac{3}{21}$ $\frac{1}{21}=\frac{3}{7}$ $\frac{7}{1}=\frac{3}{21}$ $\frac{7}{1}=\frac{21}{3}$ $\frac{1}{7}=\frac{21}{3}$

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Problem 2123

What is the interest earned after 1 year in a savings account with an initial investment of $\$ 826$ and a 3.5\% simple interest rate?
Interest = \\square$ ?

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Problem 2124

Assume an employee of Rocco Rock Company earns $\$ 1,900$ of gross wages during the current pay period and is required to remit to the government $\$ 190$ for income tax and $\$ 95$ for FICA. Consider the following two procedures for paying the employee: \begin{tabular}{ll} \multicolumn{1}{c}{ Procedure 1 (Withholdings) } & \multicolumn{1}{c}{ Procedure 2 (No Withholdings) } \\ Rocco Rock Company pays the employee net & Rocco Rock Company pays the employee gross \\ wages of $\$ 1,615$ and will remit income taxes & wages of $\$ 1,900$ and the employee is \\ and FICA on behalf of the employee. & responsible for remitting income taxes and \\ & FICA. \end{tabular}
Required:
1. Ignoring employer payroll taxes, under each procedure calculate: a. the total amount to be paid by the company and b. the amount of cash the employee will have after satisfying all responsibilities to the government. Do your answers for procedures 1 and 2 differ for (a)? For (b)?
2. Which approach does the government require?
3. Considering that employers are responsible for matching employees' FICA contributions, which procedure will employers prefer?
4. Prepare the journal entries required by the employer under procedure 1, assuming the employee is paid in cash, but the withholdings and matching employer FICA contribution have not yet been paid. (Do not ignore employer payroll taxes, but assume no unemployment taxes.)

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Problem 2125

On February 1, the home mortgage balance was $\$ 129,000$ for the home owned by Tom Bryant. The interest rate for the loan is 7 percent. Assuming that Tom makes the February monthly mortgage payment of $\$ 1032$ , calculate the following: (a) The amount of interest included in the February payment (round your answer to the nearest cent). (b) The amount of the monthly mortgage payment that will be used to reduce the principal balance. (c) The new balance after Tom makes this monthly mortgage payment.

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Problem 2126

7. A tower that is 65 m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59 m . What obtuse angle does the tower make with the ground, to the nearest hundredth of a radian?

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Problem 2127

When creating vases for the craft fair, Thomas used the proportion 3 pounds of clay is to 8 vases as 9 pounds of clay is to 24 vases. Which proportion can be used to represent the situation? $\frac{3}{8}=\frac{24}{9}$ $\frac{3}{8}=\frac{9}{24}$ $\frac{3}{9}=\frac{24}{8}$ $\frac{9}{3}=\frac{8}{24}$

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Problem 2128

Question 18 of 30 The price of a company's share dropped by $3.50 \%$ by the end of the first year, down to $\$ 46.25$ . During the second year the price of the share dropped by $\$ 2.08$ . a. What was the price of the share at the beginning of the first year? $\square$ Round to the nearest cent b. What was the price of the share at the end of the second year? $\square$ Round to the nearest cent c. What was the percent change in the price of the share over the two years?

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Problem 2129

What is the value of $x$ in the proportion below? $\frac{1 / 2}{4}=\frac{x}{28}$ $3 \frac{1}{2}$ $7 \frac{1}{2}$ 14 56

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Problem 2130

2.) Which equation has no real solution(s)? Select all that apply. A. $2(x-3)^{2}=0$ $\begin{array}{c} 2+x+x-3-3 \\ 2+2 x-6 \end{array}$ B. $(x+3)^{2}+4=1$ C. $(x-1)^{2}+4=8$ D. $(x+1)^{2}+4=2$

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Problem 2131

1 2 3 4 5 E (2) 6 A 10
To make 12 ounces of hot chocolate, 3 tablespoons of cocoa are needed. How many tablespoons of cocoa are needed to make 72 ounces of hot chocolate? 4 tablespoons 10 tablespoons 12 tablespoons 18 tablespoons

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Problem 2132

Megan bought 3 tickets to the ballet for $\$ 57.50$ . How much would it cost for her to buy 15 tickets? \$172.50 \$230.00 \$287.50 \$862.50

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Problem 2133

Conndence interval tor the popilation standard deviation
The standard deviation of the daily demand for a product is an important factor for inventory control for the product. Suppose that a pharmacy wants to estimate the standard deviation of the daily demand for a certain antibiotic. It is known that the daily demand for this antibiotic follows an approximately normal distribution. A random sample of 30 days has a sample mean of 124 orders for this antibiotic with a standard deviation of 10.1 orders. Find a $99 \%$ confidence interval for the population standard deviation of the daily demand for this antibiotic. Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places, Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)
Lower limit: $\square$ Upper limits $\square$

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Problem 2134

bra Essentials A CR-Imag SSOLogout Inagine Eagenuly ror n/player/
Proportions Quiz Active
1 2 3 4 5 6 7 8 9 10 TIME RE 51
To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should to a patient who weighs 138 pounds? 400 milligrams 480 milligrams 550 milligrams 600 milligrams

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Problem 2135

If there are 90 calories in $\frac{3}{4}$ cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270 calories 360 calories

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Problem 2136

(1 point)
Consider the points $(-3,3)$ and $(5,6)$ . a) Find the equation for the line passing through these two points and write the equation in the form $y=m x+b$ . $y=\square$ b) Find parametric equations for the line through these two points. $\begin{array}{l} x(t)= \\ y(t)=\square \end{array}$ c) Calculate the derivative $\frac{d y}{d x}$ of each of the equations in parts $(a)$ and $(b)$ .
From part (a): $\frac{d y}{d x}=$ $\square$ From part (b): $\frac{d y}{d x}=$ $\square$

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Problem 2137

Consider the integral $\int \frac{e^{y}}{e^{y}+4} d y$ : This can be transformed into a basic integral by letting $\begin{array}{l} u=e^{y}+4 \checkmark 0^{b} \text { and } \\ d u=e^{y} \quad \checkmark \sigma^{b} d y \end{array}$
After perfroming the substitution, you obtain the integral $\int \square d u$

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Problem 2138

Contidance interval tor the population standard deviation 25
Suppose that the lifetimes of the AAA batteries of a certain manufacturer are approximately normally distributed. The manufacturer wants to estimate the standard deviation of the lifetime of these batteries. A random sample of 15 AAA batteries produced by this manufacturer lasted a mean of 9.9 hours with a standard deviation of 2.1 hours. Find a $95 \%$ confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer. Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places, (If necessary, consult a list of formulas.)
Lower limit: $\square$ Upper limit: $\square$

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Problem 2139

Fiona enlarges a parallelogram that has a perimeter of 17 meters.
Not drawn to scale What is the perimeter of the enlarged parallelogram? 30 meters 73.5 meters 102 meters 105 meters

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Problem 2140

1. Gregory earned $\$ 84$ lawns. If he charg dollars mowing how many bwns ges $\$ 7$ per bawn, how many lawns did he mow?

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Problem 2141

Consider the indefinite integral $\int \frac{x^{6}}{\left(x^{7}-2\right)^{7}} d x$ : This can be transformed into a basic integral by letting $u=\left(x^{7}-2\right) \vee 0^{\infty}$ and $d u=7 x^{6} \quad \vee 0^{\infty} d x$
Performing the substitution yields the integral $\int \square d u$
Performing the integration yields the final answer (in terms of $x$ , not $u$ ). $\int \frac{x^{6}}{\left(x^{7}-2\right)^{7}} d x=$

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Problem 2142

(6) The mass of a cake is 1.216 kilograms.
Gabrielle gives 456 grams of cake to her neighbour and divides the rest of the cake into five equal pieces. What is the mass of each piece of cake? ? 9

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Problem 2143

Malik considers the enlargement of the trapezoid.
Not drawn to scale
What is the correct cross product that he should use to solve for the missing dimension? $(10)(25)=18 x$ $(10)(18)=25 x$ $(18)(25)=10 x$ $(18)(10)=18 x$

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Problem 2144

2. Sophia tests 25 pens. Five of the pens do not write the first time. Sophia says the experimental probability that a pen will not write the first time is 0.2 . Is Sophia correct? Why? a. No, because you cannot predict whether the next pen will write or not b. No, because $\frac{20}{25}$ is 0.8 c. Yes, because $\frac{20}{25}$ is 0.2 d.) Yes, because $\frac{5}{25}$ is 0.2

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Problem 2145

Give a parametric equation representation for each curve. $\begin{array}{l} a) y=x^{5}-x \\ x(t)=\square \\ y(t)=\square \end{array}$ b) $9 x^{2}+y^{2}=1$ $x(t)=$ $\square$ $y(t)=$ $\square$

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Problem 2146

Pre-Test Active 1 2 3 4 5 6 7 a 9 10
Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be? 460 pixels 945 pixels 1,680 pixels 1,860 pixels

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Problem 2147

5. The odds against a new car needing major repairs in the next few years are 24 to 1. What is the probability that the car will need major repairs in the next few years?

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Problem 2148

1. $2 \pi$ For each of the following word problems, write and explain multiplication and division equations that model the problem, using a question mark for the unknown amount. Determine which interpretation of division is involved (the how-many-groups or the now-many-units-in-1-group) and solve the problem.
If 252 dinner rolls are to be put in packages of 12, how many packages of dinner rolls can be made? If you have 506 stickers to give out equally to 23 children, how many stickers will each child get? Given that 1 gallon is 8 pints, how many gallons of water are 48 pints of water? If your car used 12 gallons of gasoline to drive 360 247 miles, then how many miles per gallon did your car get?

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Problem 2149

Iving Scale Problems Using Proportions -Test Active 2 3 4 5 6 7 8 9 10
Paolo was asked to find the original dimension of an enlarged pentagon. His solution is shown next to the pentagons.
Not draum to scale
Write a proportion. $\frac{3}{12}=\frac{x}{8}$ Cross multiply. $8 x=3 ६$ Solve for $x . x=4.5$
What error did Paolo make in his solution? Paolo set up an incorrect proportion. Paolo made an error when he cross multiplied the proportion. Paolo divided incorrectly when he solved for $x$ . Save and Exit Submit Mank this end reeum

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Problem 2150

Module Knowledge Cheals Question 9
Pilots who cannot maintain regular sleep hours due to their work schedule often suffer from insomnia. A random sample of 26 commercial airline pilots was taken, and the pilots in the sample reported the time at which they went to sleep on their most recent working day. These times measured in hours after midnight. (Thus, if the pilot reported going to sleep at $11 \mathrm{p} . \mathrm{m}$ ., the measurement was -1 .) The sample mean was 0.5 hours, and the standard deviation was 1.9 hours. Assume that the sample is drawn from a normally distributed population. Find a $90 \%$ confidence interval for the population standard deviation, that is, the standard deviation of the time (hours after midnight) at which pilots go to sleep on their work days. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list. of formulas.)
Lower limit: $\square$ Upper limit: $\square$

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Problem 2151

Module Knowlsdge Chsck Question 9 Sophi
Pilots who cannot maintain regular sleep hours due to their work schedule often suffer from insominia. A random sample of 26 commercial airline pilots was taken, and the pilots in the sample reported the time at which they went to sleep on their most recent working day. These times measured in hours after midnight. (Thus, if the pilot reported going to sleep at 11 p.m., the measurement was -1 .) The sample mean was 0.5 hours, and the standard deviation was 19 hours. Assume that the sample is drawn from a normally distributed population. Find a $90 \%$ confidence interval for the population standard deviation, that is, the standard deviation of the time (hours after midnight) at which pilots go to sleep on their work days. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.) $\square$

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Problem 2152

Find the value or values of $c$ that satisfy the equation $\frac{f(b)-f(a)}{b-a}=f^{\prime}(c)$ in the conclus of the Mean Value Theorem for the function and interval. $f(x)=x+\frac{12}{x},[3,4]$ A) $-2 \sqrt{3}, 2 \sqrt{3}$ B) 3,4 C) $2 \sqrt{3}$ D) $0,2 \sqrt{3}$

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Problem 2153

$\begin{array}{l} 4.74-30 c=-43-82 c-4.26 \\ c= \end{array}$
Submit

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Problem 2154

Import favorites Google Clever | Portal ALEKS - Magdalena Frelek - Learn https://www-awy.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkr7j8P3jH-IQsB5p57mqwiHv-fgOzocXR7H3Quபsrn-hHq0... Percents Finding the sale price without a calculator given the original price and... $0 / 5$ Magdalena Español
An item is regularly priced at $\$ 40$ . Hong bought it at a discount of $20 \%$ off the regular price. How much did Hong pay? \\square$

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Problem 2155

In 1 and 2, answer to solve a two-step problem.
Fourteen friends went to the county fair. All except 6 of them bought a hot dog. Each hot dog costs $\$ 3$ . How much did the friends spend on hot dogs?
1. Tell what you know. Then explain what you need to find first to solve the problem.
2. Tell which operations you will use. Then solve the problem.

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Problem 2156

This question is typical on some driver's license exams: A car moving at $42 \mathrm{~km} / \mathrm{h}$ skids 12 m with locked brakes.
How far will the car skid with locked brakes at $126 \mathrm{~km} / \mathrm{h}$ ? Assume that energy loss is due only to sliding friction.
Answer in units of $m$ .

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Problem 2157

Confidence in banks: A poll conducted in 2012 asked a random sample of 1259 adults in the United States how much confidence they had in banks and other financial institutions. A total of 154 adults said that they had a great deal of confidence. An economist claims that greater 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 $\alpha=0.01$ and $\alpha=0.05$ levels of significance and the $P$ -value method with the TI-84 Plus calculator.
Part: $0 / 4$
Part 1 of 4 (a) State the appropriate null and alternate hypotheses. $H_{0}$ : $\square$ $H_{1}$ : $\square$
This hypothesis test is a (Choose one) $\nabla$ test. $\square$ - $\square$ $\square$ $\square$ $\square$ $\square$ $1 \neq$ $\square$ $p$
3

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Problem 2158

Given: $\overline{A B} \cong \overline{B C}$ and $\overline{B C}$ bisects $\angle A C D$ . Prove: $\angle A \cong \angle B C D$ .
Note: quadrilateral properties are not permitted in this proof.
Step
1 try Type of Statement

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Problem 2159

2 A recipe for making incense sticks calls for 6 tablespoons of joss powder, $1 \frac{1}{2}$ teaspoons of frankincense, and $\frac{3}{4}$ teaspoon of myrrh. To make incense sticks that would smell the same, how much of the other two ingredients would you need to mix with: a. 4 tablespoons of joss powder? b. 9 tablespoons of joss powder? c. 1 teaspoon of myrrh?

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Problem 2160

(3) A 25-foot ladder is leaned against a wall. If the base of the ladder is 7 ft from the wall, how high up the wall will the ladder reach?
The mast of a sailing ship is 20 ft tall. A rope is stretched 26 ft from the top of the mast to a cleat on the deck of the ship. How far is the cleat from the base of the mast?
Each side of an equilateral triangle measures 12 cm . Find the height, $\boldsymbol{h}$ , of the triangle. $\square$ $\square$ $\square$ $\square$ - $\square$ $\square$ Two jets left an airport at the same time. One traveled east at 300 miles per hour. The other traveled south at 400 miles per hour. How far apart were the jets at the end of an hour? $\square$ 85.4
12 9.8
24 500 26 10.4
520 25.5 9.4 17.8 16.6 87.1 9.7 18.5 : 8.3

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Problem 2161

The circle graph shows how the annual budget for a company is divided by department. If the total annual budget is $\$ 5,000,000$ , what amount is budgeted for Sales? Español $\square$ 6 Malwarebytes Improve your protection! Trusted Advisor has a recommendation or two that can boost your protection. Manage settings Check Trusted Advisor Explelanation Check - 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use। Privacy Center I Accessiblity

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Problem 2162

Finding simple interest winout a calcuiatul Español
Lucy deposits $\$ 800$ into an account that pays simple interest at a rate of $5 \%$ per year. How much interest will she be paid in the first 2 years? s! $\square$ Explanation Check O 2024 McGraw Hill LLC. All Rights Resenved. Terms of Use | Privacy Center｜Accessibility

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Problem 2163

Use algebra steps to find the fraction exactly equal to the infinitely repeating decimal 7.4878787 .... Write your answer as a fraction of whole numbers $a$ and $b$ in the form $a / b$ . Type the product of $a$ and $b$ . (You do NOT need to divide $a$ and $b$ by a common factor to simplify the fraction prior to finding the product of a and b.)

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Problem 2164

Find the axis of symmetry of the parabola defined by the equation $(y+6)^{2}=40(x+6)$ .

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Problem 2165

Find an equation of the line with a $y$ -intercept at $(0,-5)$ and slope of 10. $y=$ $\square$ Write your answer in the slope-intercept form $y=m x+b$ . Question Help: $\square$ Video Submit Question

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Problem 2166

What is the approximate volume of the cylinder? Use 3.14 for $\pi$ . $904.32^{2} \mathrm{~cm}^{3}$ $226.08 \mathrm{~cm}^{3}$ $150.72 \mathrm{~cm}^{3}$ $301.44 \mathrm{~cm}^{3}$

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Problem 2167

c. 1 teaspoon of myrrh?
3 At a deli counter, - Someone bought $1 \frac{3}{4}$ pounds of ham for $\$ 14.50$ . - Someone bought $2 \frac{1}{2}$ pounds of turkey for $\$ 26.25$ . $\qquad$ - Someone bought $\frac{3}{8}$ pound of roast beef for $\$ 5.50$ . $26.93 \times \frac{2}{5}=1 . \frac{82.54}{5}$ 5:50 $\times \frac{8}{3}=\frac{44}{3}=14.6$
Which meat is the least expensive per pound? Which meat is the most expensive per pound? Explain how you know. 48.29 $\square$ st expenste $\qquad$ racest pen pound. The Practice Problems

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Problem 2168

Which is an equation of the line through $(-1,-4)$ and parallel to the line $3 x+y=5$ ? $y=-3 x+7$ $y=3 x+1$ $y=3 x-1$ $y=-3 x-7$

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Problem 2169

010 (part 1 of 2 ) 10.0 points A crate is lifted vertically 1.5 m and then held at rest. The crate has weight 100 N (i.e., it is supported by an upward force of 100 N ).
How much work was done in lifting the crate from the ground to its final position?
1. 150 J
2. None of these
3. A bit less than 150 J
4. No work was done.
5. More than 150 J

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Problem 2170

012 (part 1 of 2) $\mathbf{1 0 . 0}$ points A 17.2 kg block is dragged over a rough, horizontal surface by a constant force of 89.6 N acting at an angle of $27.8^{\circ}$ above the horizontal. The block is displaced 33.7 m , and the coefficient of kinetic friction is 0.234 . $\mu=0.234$
Find the work done by the 89.6 N force. The acceleration of gravity is $9.8 \mathrm{~m} / \mathrm{s}^{2}$ .
Answer in units of J. 013 (part 2 of 2) 10.0 points Find the magnitude of the work done by the force of friction.
Answer in units of J.

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Problem 2171

4. Determine the equation of the graphed function given that it is of the form $y=a \sin b x$ or $y=a \cos b x$ , where $b$ is positive.
Fnter your next step here $\square$

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Problem 2172

$11 / 14$
Figure the total amount based on the information given, using the simple interest formula and the compound interest formula. Then show the difference (amount) from simple to compound.:
1. $\$ 1,000.00$
2\% 5 Years
2. $\$ 5,000.00$
5\% 10 Years
3. $\$ 10,000.00$ $7 \%$ 5 Years
4. $\$ 15,000.00$
3\% 5 Years
5. $\$ 20.000 .00$ 1.5\%
5 Years

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Problem 2173

Find all solutions of the equation in the interval $[0,2 \pi)$ . $\sin ^{2} x-2 \sin x-3=0$
Write your answer in radians in terms of $\pi$ . If there is mort than one solution, separate them with commas.

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Problem 2174

Write an equation for the line that has a slope of $\frac{1}{2}$ and passes through $(6,-3)$ $y=$ Question Help: Video Submit Question

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Problem 2175

Determine the equation of the line below using the given point and slope. Point: $(2,-5)$ , Slope: 4
Write your answer as an equation using variables x and y : $\square$ Question Help: Video 1 Video 2 Written Example 1 Submit Question

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Problem 2176

$\times 15=315$

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Problem 2177

$4 \sin \theta+3 \sqrt{3}=\sqrt{3}$

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Problem 2178

Question Watch Video Show Examples
The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{2}-2 x-5 \sin (2 x-2)$ for $-2<x<4$ . Find all intervals in the given domain where the function $f$ is increasing. You may use a calculator and round all values to 3 decimal places. Answer Attempt 2 out of 3

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Problem 2179

Write the equation of the line below in slope-intercept form State the slope as an integer or reduced fraction. State the $-37 x-14 y=-21$
Equation in slope-intercept form: $\square$ Slope: $\square$ y-intercept: $\square$ Question Help: Video 1 Video 2 Submit Question

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Problem 2180

Establish the identity. $(\csc \theta+1)(\csc \theta-1)=\cot ^{2} \theta$
Multiply and write the left side expression as the difference of two squar $\square$

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Problem 2181

Find all solutions of the equation in the interval $[0,2 \pi)$ . $\sin 2 x+\cos x=0$
Write your answer in radians in terms of $\pi$ . If there is more than one solution, separate them with com $x=$ $\square$
$\pi$

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Problem 2182

$a, b$ , and $c$ are all nonzero real numbers.
1. $a x+b y=c$

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Problem 2183

Find all the roots of the polynomial: $y=-x^{5}+11 x^{3}-6 x^{2}-28 x+24$

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Problem 2184

Attempt 1: 10 attempts remaining.
You have $\$ 5000$ . The best interest rate you can find is $1.5 \%$ compounded quarterly. For how long should you deposit the money in order to have $\$ 9400$ ? $\square$ years
Submit answer Next item

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Problem 2185

- Jenny has a problem. She knows that the roots of a quadratic function are $x=$ $3+4 i$ and $x=3-4 i$ , but in order to get credit for the problem she needs to know the equation of the function. She is having a hard time with the complex roots, but luckily, her friends are full of advice. a. Mercedes says, "Just remember when we made factors from the roots. If the - roots are 7 and 4 the equation is $y=(x-7)(x-4)$ ." Use Mercedes's idea to help Jenny write the equation of a quadratic function. b. Darin says, "No, no, no. You can do it that way, but that's too complicated. If think you just start with $x=3+4 i$ and work bachwards. So $x-3=4 i$ , then, square both sides... Yeah, that lll work " Try Darin's method. c. Whose method do you think Jenny should use? Explain your choice.

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Problem 2186

2. It takes Juwan exactly 35 minutes by car to get to his grandmother's. The nearest parking area is a 4-minute walk from her apartment. One week, he realized that he spent 5 hours and 12 minutes traveling to her apartment and then back home. How many round trips did he make to visit his grandmother?

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Problem 2187

11) An 800 kg truck is driving down the road. The truck now goes up a 7.5 -meter hill and is still going 8.0 $\mathrm{m} / \mathrm{s}$ on top of the hill. a) Calculate the total Energy the truck has on top of the hill. b) Calculate how fast the Truck was going at the bottom of the hill.

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Problem 2188

Find the root of each equation. (hessan $3=2$
9. $x+8=0$
10. $4 x-24=0$
11. $18+8 x=0$
12. $\frac{3}{5} x-\frac{1}{2}=0$

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Problem 2189

Find all solutions of the equation in the interval $[0,2 \pi)$ . $4 \sin ^{2} x=5+4 \cos x$
Write your answer in radians in terms of $\pi$ . If there is more than one solution, separate them with co

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Problem 2190

Question Watch Video Show Examples
Evaluate the left hand side to find the value of $a$ in the equation in simplest form. $x^{\frac{6}{5}} x=x^{a}$
Answer Attempt 2 out of 4 $\square$ Submit Answer

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Problem 2191

Evaluate the left hand side to find the value of $a$ in the equation in $x^{\frac{4}{5}} x^{\frac{5}{4}}=x^{a}$
Answer Attempt 1 out of 4

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Problem 2192

b) Suppose a financial institution has assets with market value of GH\&105 million liabilities with market value of $\mathrm{GH} \phi 98$ million. Suppose also that the institution has contingent assets of GH\& 20 million and contingent liabilities of GH\& 17 million. What is the financial institution's true networth position?

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Problem 2193

024 (part 1 of 3 ) 10.0 points A 4.0 kg block is pushed 2.0 m at a constant velocity up a vertical wall by a constant force applied at an angle of $26.0^{\circ}$ with the horizontal, as shown in the figure.
The acceleration of gravity is $9.81 \mathrm{~m} / \mathrm{s}^{2}$ .
Drawing not to scale. If the coefficient of kinetic friction between the block and the wall is 0.20 , find a) the work done by the force on the block. Answer in units of J.
025 (part 2 of 3 ) 10.0 points b) the work done by gravity on the block. Answer in units of J .
026 (part 3 of 3 ) 10.0 points c) the magnitude of the normal force between the block and the wall.
Answer in units of N .

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Problem 2194

024 (part 1 of 3 ) 10.0 polnts A 4.0 kg block is pushed 2.0 m at a constant velocity up a vertical wall by a constant force applied at an angle of $26.0^{\circ}$ with the horizontal, as shown in the figure.
The acceleration of gravity is $9.81 \mathrm{~m} / \mathrm{s}^{2}$ .
Drawing not to scale. If the coefficient of kinetic friction between the block and the wall is 0.20 , find a) the work done by the force on the block. Answer in units of J.
025 (part 2 of 3 ) 10.0 points b) the work done by gravity on the block. Answer in units of J.
026 (part 3 of 3 ) 10.0 points c) the magnitude of the normal force between the block and the wall.
Answer in units of N .

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Problem 2195

Add parentheses to make true. $36 \div 9-3=6$

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Problem 2196

15. $4 i-3 i^{2}+2 i^{3}-i^{4}=$ A. $-2+2 i$ B. $-2-2 i$ . C. $2+2 i$ . D. $2-2 i$ .
16. The figure shows the graph of $y=a x^{2}-6 x+c$ , where $a$ and $c$ are constants. The graph cuts the $x$ -axis and the $y$ -axis at -1 and -9 respectively. The equation of the axis of symmetry of the graph is A. $x=-1$ . B. $x=\frac{1}{2}$ . C. $x=1$ . D. $x=2$ .
17. For $0^{\circ} \leq \theta \leq 360^{\circ}$ , how many roots does the equation $2 \sin ^{2} \theta-3 \sin \theta+1=0$ have? A. 2 B. 3 C. 4 D. 5

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Problem 2197

Given a = 4 m, and Mo = 40 Nm, A Mo E Mo C G F TT B - a - — a - — a - Plot out the shear and moment diagrams for the beam.

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Problem 2198

Find all solutions to the equation. $2 \sin \left(\frac{1}{2} x\right)-\sqrt{3}=0$
Write your answer in radians in terms of $\pi$ , and use the "or" button as necessary. Example: $x=\frac{\pi}{5}+2 k \pi, k \in \mathbb{Z}$ or $x=\frac{\pi}{7}+k \pi, k \in \mathbb{Z}$ Help with this notation

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Problem 2199

41. a. $e^{-x}=8$ b. $10^{-x}=125$

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Problem 2200

43. a. $10^{5-3 x}=0.041$ b. $10^{2 x-1}=515$

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1 ...19 20 21 22 23 24 25 ...188

Equation

Problem 2101

Problem 2102

The line kkk has a slope of -2 . The line jjj makes an angle of 30∘30^{\circ}30∘ with kkk. Find one possible value of the slope of the line jjj. Give your answer in the form d+efd+e \sqrt{f}d+ef​, where d,e,f∈Zd, e, f \in \mathbb{Z}d,e,f∈Z.

Problem 2103

Problem 2104

Problem 2105

12. Extend Your Thinking How can you find 316÷4316 \div 4316÷4 two different ways by using different partial quotients in each solution?

Problem 2106

Problem 2107

Solve for all possible values of x . 14−2x=x−7\sqrt{14-2 x}=x-714−2x​=x−7

Problem 2108

Problem 2109

Problem 2110

y=45x+3y=\frac{4}{5} x+3y=54​x+3 y=3x+45y=3 x+\frac{4}{5}y=3x+54​ y=15x+45y=\frac{1}{5} x+\frac{4}{5}y=51​x+54​ y=−45x+3y=-\frac{4}{5} x+3y=−54​x+3

Problem 2111

Practice Quiz: Perimeter and Circumference 0:07:42 elapsedQuestion 9 (5 points) Listen Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi. 6 15.7 9.42 3

Problem 2112

Problem 2113

Problem 2114

Problem 2115

Explaining a SolutionSolve the proportion using equivalent ratios. Explain the steps you used to solve the proportion, and include the answer in your response. 103=20x\frac{10}{3}=\frac{20}{x}310​=x20​

Problem 2116

Problem 2117

The hypotenuse of a right triangle is 3 times as long as its shorter leg. The longer leg is 12 centimeters longTo the nearest tenth of a cenfimeter, what is the length of the triangle's shorter leg? ) □\square□ Gentimeters

Problem 2118

Problem 2119

Problem 2120

onvert 8.8 C to Fahrenheit. Round to the nearest tenth when necessary. 88.4 F 47.8 F 87.4 F 48.9 F

Problem 2121

Solve 1/35=a20\frac{1 / 3}{5}=\frac{a}{20}51/3​=20a​ a=3/5a=3 / 5a=3/5 a=3/4a=3 / 4a=3/4 a=4/3a=4 / 3a=4/3 a=5/3a=5 / 3a=5/3

Problem 2122

Problem 2123

What is the interest earned after 1 year in a savings account with an initial investment of $826\$ 826$826 and a 3.5\% simple interest rate?Interest = \ \square$ ?

Problem 2124

Problem 2125

Problem 2126

7. A tower that is 65 m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59 m . What obtuse angle does the tower make with the ground, to the nearest hundredth of a radian?

Problem 2127

Problem 2128

Problem 2129

What is the value of xxx in the proportion below? 1/24=x28\frac{1 / 2}{4}=\frac{x}{28}41/2​=28x​ 3123 \frac{1}{2}321​ 7127 \frac{1}{2}721​ 14 56

Problem 2130

Problem 2131

1 2 3 4 5 E (2) 6 A 10To make 12 ounces of hot chocolate, 3 tablespoons of cocoa are needed. How many tablespoons of cocoa are needed to make 72 ounces of hot chocolate? 4 tablespoons 10 tablespoons 12 tablespoons 18 tablespoons

Problem 2132

Megan bought 3 tickets to the ballet for $57.50\$ 57.50$57.50. How much would it cost for her to buy 15 tickets? \$172.50 \$230.00 \$287.50 \$862.50

Problem 2133

Problem 2134

Problem 2135

If there are 90 calories in 34\frac{3}{4}43​ cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270 calories 360 calories

Problem 2136

Problem 2137

Problem 2138

Problem 2139

Fiona enlarges a parallelogram that has a perimeter of 17 meters.Not drawn to scale What is the perimeter of the enlarged parallelogram? 30 meters 73.5 meters 102 meters 105 meters

Problem 2140

1. Gregory earned $84\$ 84$84 lawns. If he charg dollars mowing how many bwns ges $7\$ 7$7 per bawn, how many lawns did he mow?

Problem 2141

Problem 2142

(6) The mass of a cake is 1.216 kilograms.Gabrielle gives 456 grams of cake to her neighbour and divides the rest of the cake into five equal pieces. What is the mass of each piece of cake? ? 9

Problem 2143

Problem 2144

Problem 2145

Give a parametric equation representation for each curve. a)y=x5−xx(t)=□y(t)=□\begin{array}{l} a) y=x^{5}-x \\ x(t)=\square \\ y(t)=\square \end{array}a)y=x5−xx(t)=□y(t)=□​ b) 9x2+y2=19 x^{2}+y^{2}=19x2+y2=1 x(t)=x(t)=x(t)= □\square□ y(t)=y(t)=y(t)= □\square□

Problem 2146

Problem 2147

5. The odds against a new car needing major repairs in the next few years are 24 to 1. What is the probability that the car will need major repairs in the next few years?

Problem 2148

Problem 2149

Problem 2150

Problem 2151

Problem 2152

Problem 2153

4.74−30c=−43−82c−4.26c=\begin{array}{l} 4.74-30 c=-43-82 c-4.26 \\ c= \end{array}4.74−30c=−43−82c−4.26c=​Submit

Problem 2154

Problem 2155

Problem 2156

Problem 2157

Problem 2158

The line $k$ has a slope of -2 . The line $j$ makes an angle of $30^{\circ}$ with $k$ . Find one possible value of the slope of the line $j$ . Give your answer in the form $d+e \sqrt{f}$ , where $d, e, f \in \mathbb{Z}$ .

12. Extend Your Thinking How can you find $316 \div 4$ two different ways by using different partial quotients in each solution?

Solve for all possible values of x . $\sqrt{14-2 x}=x-7$

$y=\frac{4}{5} x+3$ $y=3 x+\frac{4}{5}$ $y=\frac{1}{5} x+\frac{4}{5}$ $y=-\frac{4}{5} x+3$

Practice Quiz: Perimeter and Circumference 0:07:42 elapsed
Question 9 (5 points) Listen Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi. 6 15.7 9.42 3

Explaining a Solution
Solve the proportion using equivalent ratios. Explain the steps you used to solve the proportion, and include the answer in your response. $\frac{10}{3}=\frac{20}{x}$

The hypotenuse of a right triangle is 3 times as long as its shorter leg. The longer leg is 12 centimeters long
To the nearest tenth of a cenfimeter, what is the length of the triangle's shorter leg? ) $\square$ Gentimeters

Solve $\frac{1 / 3}{5}=\frac{a}{20}$ $a=3 / 5$ $a=3 / 4$ $a=4 / 3$ $a=5 / 3$

What is the interest earned after 1 year in a savings account with an initial investment of $\$ 826$ and a 3.5\% simple interest rate?
Interest = \\square$ ?

What is the value of $x$ in the proportion below? $\frac{1 / 2}{4}=\frac{x}{28}$ $3 \frac{1}{2}$ $7 \frac{1}{2}$ 14 56

1 2 3 4 5 E (2) 6 A 10
To make 12 ounces of hot chocolate, 3 tablespoons of cocoa are needed. How many tablespoons of cocoa are needed to make 72 ounces of hot chocolate? 4 tablespoons 10 tablespoons 12 tablespoons 18 tablespoons

Megan bought 3 tickets to the ballet for $\$ 57.50$ . How much would it cost for her to buy 15 tickets? \$172.50 \$230.00 \$287.50 \$862.50

If there are 90 calories in $\frac{3}{4}$ cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270 calories 360 calories

Fiona enlarges a parallelogram that has a perimeter of 17 meters.
Not drawn to scale What is the perimeter of the enlarged parallelogram? 30 meters 73.5 meters 102 meters 105 meters

1. Gregory earned $\$ 84$ lawns. If he charg dollars mowing how many bwns ges $\$ 7$ per bawn, how many lawns did he mow?

(6) The mass of a cake is 1.216 kilograms.
Gabrielle gives 456 grams of cake to her neighbour and divides the rest of the cake into five equal pieces. What is the mass of each piece of cake? ? 9

Give a parametric equation representation for each curve. $\begin{array}{l} a) y=x^{5}-x \\ x(t)=\square \\ y(t)=\square \end{array}$ b) $9 x^{2}+y^{2}=1$ $x(t)=$ $\square$ $y(t)=$ $\square$

$\begin{array}{l} 4.74-30 c=-43-82 c-4.26 \\ c= \end{array}$
Submit

Given: $\overline{A B} \cong \overline{B C}$ and $\overline{B C}$ bisects $\angle A C D$ . Prove: $\angle A \cong \angle B C D$ .
Note: quadrilateral properties are not permitted in this proof.
Step
1 try Type of Statement

Find the axis of symmetry of the parabola defined by the equation $(y+6)^{2}=40(x+6)$ .

Find an equation of the line with a $y$ -intercept at $(0,-5)$ and slope of 10. $y=$ $\square$ Write your answer in the slope-intercept form $y=m x+b$ . Question Help: $\square$ Video Submit Question

What is the approximate volume of the cylinder? Use 3.14 for $\pi$ . $904.32^{2} \mathrm{~cm}^{3}$ $226.08 \mathrm{~cm}^{3}$ $150.72 \mathrm{~cm}^{3}$ $301.44 \mathrm{~cm}^{3}$

Which is an equation of the line through $(-1,-4)$ and parallel to the line $3 x+y=5$ ? $y=-3 x+7$ $y=3 x+1$ $y=3 x-1$ $y=-3 x-7$

4. Determine the equation of the graphed function given that it is of the form $y=a \sin b x$ or $y=a \cos b x$ , where $b$ is positive.
Fnter your next step here $\square$

Find all solutions of the equation in the interval $[0,2 \pi)$ . $\sin ^{2} x-2 \sin x-3=0$
Write your answer in radians in terms of $\pi$ . If there is mort than one solution, separate them with commas.

Write an equation for the line that has a slope of $\frac{1}{2}$ and passes through $(6,-3)$ $y=$ Question Help: Video Submit Question