Question 1

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. w varies directly as q, and  when 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Write the equation that expresses the relationship...

Question 2

Use interval notation to express the solution set of the inequality below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use interval notation to express the solution...

Question 3

A solid silver sphere has a diameter of 14 millimeters, and a second silver sphere has a diameter of 16 millimeters. The spheres are melted down and recast to form a single cube. What is the length of each edge of the cube? Round your answer to the nearest tenth of a millimeter.
A)59.8 millimeters
B)30.6 millimeters
C)169.3 millimeters
D)15.3 millimeters
E)103.7 millimeters

Accepted Answer

The answer of A solid silver sphere has a diameter...

Question 4

Hooke s Law states that the distance a spring stretches varies directly as the weight on the spring. A weight of 70 pounds stretches a spring 9 inches. How far will a weight of 110 pounds stretch the spring? Round to the nearest tenth of an inch. 
A)14.1 inches
B)5.7 inches
C)12.2 inches
D)10.0 inches
E)7.8 inches

Accepted Answer

The answer of Hooke s Law states that the distance...

Question 5

Use interval notation to express the solution set for the inequality below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use interval notation to express the solution...

Question 6

A video store offers two rental plans. The yearly membership fee and the daily charge per video for each plan are shown below. How many one-night rentals can be made per year if the No-fee plan is to be the less expensive of the plans? Rental Plan Yearly Fee Daily Charge per Video Low-Rate $30.00 $2.49 No-Fee None $3.99
A)30 rentals or less
B)25 rentals or less
C)20 rentals or more
D)20 rentals or less
E)25 rentals or more

Accepted Answer

For the No-Fee plan to be less expensive, the total cost of one-night rentals for the year must be less than $30.00 (the yearly fee for the Low-Rate plan).

Let's calculate the total cost of one-night rentals for the year under each plan:

No-Fee Plan: 
Daily charge per video = $3.99
Number of one-night rentals for the year = x

Total cost = 3.99x

Low-Rate Plan:
Yearly fee = $30.00
Daily charge per video = $2.49
Number of one-night rentals for the year = y

Total cost = 30.00 + (2.49y)

We want the total cost under the No-Fee Plan to be less than $30.00.

3.99x < 30.00

x < 7.52

This means that the maximum number of one-night rentals that can be made under the No-Fee Plan for it to be less expensive than the Low-Rate Plan is 7.

Let's check the total cost of one-night rentals for the year under each plan for 7 rentals:

No-Fee Plan:
Total cost = 3.99(7) = $27.93

Low-Rate Plan:
Total cost = 30.00 + (2.49(7)) = $48.43

Since the total cost of one-night rentals for the year under the No-Fee Plan is less than $30.00, and also less than the total cost under the Low-Rate Plan for 7 rentals, the best choice is:

D) 20 rentals or less

Question 7

On a ship, the distance d that you can see to the horizon is given by  , where h is the height of your eye measured in feet above sea level and d is measured in miles. How high is the eye level of a navigator who can see 16 miles to the horizon? Round your answer the nearest foot.
A)114 feet
B)64 feet
C)6 feet
D)5 feet
E)256 feet

Accepted Answer

The answer of On a ship, the distance d that...

Question 8

Find all the real solutions of the following equation by first rewriting the equation as a quadratic equation. 
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of Find all the real solutions of the...

Question 9

Write the equation that expresses the relationship between the variables, and then use the given data to solve for the variation constant. T varies jointly as r and and the cube of s and  when  and  .
A)k = 
B)k = 
C)k = 
D)k = 
E)k =

Accepted Answer

The equation that expresses the relationship between the variables is T = krs³. Using the given values, we can plug in and solve for k: 
11ebfdc1_ec18_b6d8_abe3_1f4af5b3e826_TBX8727_11 = k(11ebfdc1_ec18_b6d9_abe3_b51720305f5b_TBX8727_11)(11ebfdc1_ec18_b6da_abe3_b12a0935eaed_TBX8727_11)³ 
Simplifying this expression and solving for k, we get:
k = 11ebfdc1_ec18_dded_abe3_133be66878a2_TBX8727_11 
Therefore, the best choice is C.

Question 10

The attendance A , in billions of people, at movie theaters has been declining for a few years. A model of the decline is given by  , where  corresponds to the year 2000. According to this model, during what year will movie attendance first be less than 1.25 billion people?
A)2014
B)2012
C)2015
D)2016
E)2013

Accepted Answer

The answer of The attendance A , in billions of...

Question 11

Solve the following compound inequality. Write the solution set using set-builder notation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the following compound inequality. Write the...

Question 12

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the critical value method to solve...

Question 13

Use the critical value method to solve each rational inequality. Write each solution set in interval notation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the critical value method to solve...

Question 14

The pressure a liquid exerts at a given point on a submarine is directly proportional to the depth of the point below the surface of the liquid. If the pressure at a depth of 4 feet is 250 pounds per square foot, find the pressure at a depth of 14 feet.
A)687.5 pounds per square foot
B)1000 pounds per square foot
C)875 pounds per square foot
D)812.5 pounds per square foot
E)1125 pounds per square foot

Accepted Answer

The answer of The pressure a liquid exerts at a...

Question 15

A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?
A)  hours
B)  hours
C)  hour
D)  hour
E)  hours

Accepted Answer

The answer of A worker can build a fence in...

Question 16

Use the critical value method to solve the polynomial inequality below. Use interval notation to write the solution set. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the critical value method to solve...

Question 17

If a researcher wanted to know the mean weight (the mean is the sum of all measurements divided by the number of measurements)of women in the U.S., the weight of every woman would have to be measured, and then the mean weight calculated, an impossible task. Instead, researchers find a representative sample of women and find the mean weight of the sample. Because the entire population of women is not used, there is a possibility that the calculated mean weight is not the true mean weight. For one study, researchers used the formula  where m is the true mean weight, in pounds, of all women, to be 98% sure of the range of values for the true mean weight. Using this inequality, what is the range of mean weights of women in the U.S.? Round to the nearest tenth of a pound.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If a researcher wanted to know the...

Question 18

You can rent a car for the day from Company A for $28 plus $0.11 a mile. Company B charges $22.00 plus $0.22 a mile. Find the number of miles m (to the nearest mile)per day for which it is cheaper to rent from Company A.
A)less than 152 miles
B)less than 55 miles
C)more than 55 miles
D)less than 104 miles
E)more than 152 miles

Accepted Answer

The cost of renting from Company A is 28 + 0.11m, and the cost of renting from Company B is 22 + 0.22m. To find the number of miles for which it is cheaper to rent from Company A, we need to solve the inequality 28 + 0.11m < 22 + 0.22m. Subtracting 0.11m from both sides, we get 28 < 11 + 0.11m. Subtracting 11 from both sides, we get 17 < 0.11m. Dividing both sides by 0.11, we get m > 154.54545454545455. Rounding up to the nearest mile, we get m > 155. Therefore, it is cheaper to rent from Company A for more than 155 miles per day.

Question 19

Solve the compound inequality below. Write the solution set using set-builder notation.  or 
A) 
B) 
C) 
D) 
E)

Accepted Answer

This question is asking us to solve the compound inequality "11ebfdc1_ec16_6caf_abe3_63a21b629e07_TBX8727_11 or 11ebfdc1_ec16_6cb0_abe3_59ae37525349_TBX8727_11". This means we need to find all values that satisfy either one of the inequalities separated by "or".

To solve each inequality, we need to isolate the variable on one side. Let's start with the first one:

11ebfdc1_ec16_6caf_abe3_63a21b629e07_TBX8727_11

x - 3 ≤ -7

We can add 3 to both sides to isolate x:

x ≤ -4

Now let's solve the second inequality:

11ebfdc1_ec16_6cb0_abe3_59ae37525349_TBX8727_11

x + 2 > 6

We can subtract 2 from both sides:

x > 4

Therefore, the compound inequality "x - 3 ≤ -7 or x + 2 > 6" can be written as:

{x | x ≤ -4 or x > 4}

The best answer choice is B, which matches this set-builder notation.

Question 20

Write an equation that represents the relationship between the given variables below. Use k as the variation constant. d varies jointly as r as well as t
A) 
B) 
C) 
D) 
E)

Accepted Answer

The equation that represents the relationship between d, r, and t can be written as d = krt, since d varies jointly as r and t.

Quiz 1: Equations and Inequalities

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. w varies directly as q, and when

Use interval notation to express the solution set of the inequality below.

A solid silver sphere has a diameter of 14 millimeters, and a second silver sphere has a diameter of 16 millimeters. The spheres are melted down and recast to form a single cube. What is the length of each edge of the cube? Round your answer to the nearest tenth of a millimeter.

Hooke s Law states that the distance a spring stretches varies directly as the weight on the spring. A weight of 70 pounds stretches a spring 9 inches. How far will a weight of 110 pounds stretch the spring? Round to the nearest tenth of an inch.

Use interval notation to express the solution set for the inequality below.

On a ship, the distance d that you can see to the horizon is given by , where h is the height of your eye measured in feet above sea level and d is measured in miles. How high is the eye level of a navigator who can see 16 miles to the horizon? Round your answer the nearest foot.

Find all the real solutions of the following equation by first rewriting the equation as a quadratic equation.

Write the equation that expresses the relationship between the variables, and then use the given data to solve for the variation constant. T varies jointly as r and and the cube of s and when and .

The attendance A , in billions of people, at movie theaters has been declining for a few years. A model of the decline is given by , where corresponds to the year 2000. According to this model, during what year will movie attendance first be less than 1.25 billion people?

Solve the following compound inequality. Write the solution set using set-builder notation.

Use the critical value method to solve each rational inequality. Write each solution set in interval notation.

Use the critical value method to solve each rational inequality. Write each solution set in interval notation.

The pressure a liquid exerts at a given point on a submarine is directly proportional to the depth of the point below the surface of the liquid. If the pressure at a depth of 4 feet is 250 pounds per square foot, find the pressure at a depth of 14 feet.

A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?

Use the critical value method to solve the polynomial inequality below. Use interval notation to write the solution set.

You can rent a car for the day from Company A for $28 plus $0.11 a mile. Company B charges $22.00 plus $0.22 a mile. Find the number of miles m (to the nearest mile) per day for which it is cheaper to rent from Company A.

Solve the compound inequality below. Write the solution set using set-builder notation. or

Write an equation that represents the relationship between the given variables below. Use k as the variation constant. d varies jointly as r as well as t