Question 1

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Accepted Answer

To find the amount of 30% solution needed, set up the equation: 0.3x + 0.8(90) = 0.6(x + 90). Solving for x gives x = 60 liters.

Question 2

Write the word or phrase that best completes each statement or answers the question.
-Graph the function $y = \frac { 1 } { x - 2 }$ in connected mode in the standard viewing window of your calculator. Does your calculator draw a nearly vertical line in the neighborhood of $x = 2$ ? Should this line be present? Why or why not?

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Solve the problem.
-On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Accepted Answer

Let the speed on the first part be x mph. Then, the speed on the second part is (x - 20) mph. The time for the first part is 200/x hours, and for the second part is 80/(x - 20) hours. The total time is 4 hours: 200/x + 80/(x - 20) = 4. Solving this equation gives x = 77 mph.

Question 4

Choose the one alternative that best completes the statement or answers the question.
-For the graph shown, at which point does the function change from increasing to decreasing?

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 5

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 6

Solve the problem.
-Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments
Amounts to 11%?

Accepted Answer

The answer of Solve the problem.
-Helen Weller invested $14,000 in...

Question 7

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 400 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they
Meet, how far are they from Denver?

Accepted Answer

The first plane travels for 0.5 hours before the second plane starts, covering 200 miles. The remaining distance between the planes is 650 miles. The planes approach each other at a combined speed of 870 mph (400 mph + 470 mph). They meet after 650/870 hours, which is approximately 0.747 hours. The second plane travels 0.747 * 470 = 351 miles from Denver.

Question 8

Choose the one alternative that best completes the statement or answers the question.
-What are the $x$-intercepts of $f ( x + 2 ) ?$

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 9

True or False. The function $y = \frac { x ^ { 2 } - 1 ^ { 2 } } { x - 1 }$ is not continuous at $x = 1$.

Accepted Answer

The function simplifies to $y = x + 1$ for $x \neq 1$, but at $x = 1$, the original expression is undefined, causing a discontinuity.

Question 10

Solve the problem.
-In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

To solve this problem, we use the equation for mixture problems: (amount of solute in the first solution + amount of solute in the second solution) / (total volume of solution) = desired concentration. Let x be the liters of the 10% solution needed. The amount of silver iodide in the 7 liters of 4% solution is 0.04 * 7. The amount in the x liters of 10% solution is 0.10 * x. The total volume of the solution is 7 + x liters, and we want a 6% solution, so the equation is: (0.04*7 + 0.10*x) / (7 + x) = 0.06. Solving for x gives x = 3.5 liters.

Question 11

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 12

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 13

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 14

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 15

Solve the problem.
-The speed of a freight train is 23 mph slower than that of a passenger train. The freight train travels 350 mi in the same time it takes the passenger train to travel 440 mi. Find the speed of the passenger train.

Accepted Answer

The time it takes for both trains to complete their respective distances is the same. Let the speed of the passenger train be $x$ mph. Then, the speed of the freight train is $x - 23$ mph. Using the formula $time = \frac{distance}{speed}$, we set up the equation $\frac{350}{x - 23} = \frac{440}{x}$. Solving for $x$, we find the speed of the passenger train to be 112 mph.

Question 16

Solve the problem.
-A traveling salesperson averaged 48 miles per hour on a 246 mile trip. How many hours were spent on the trip?

Accepted Answer

To find the time spent on the trip, divide the total distance by the average speed: 246 miles / 48 miles per hour = 5.125 hours, which rounds to 5.13 hours.

Question 17

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

The answer of Tell which of the following types of...

Question 18

Choose the one alternative that best completes the statement or answers the question.
-Sketch the graph of $y = - x ^ { 2 }$. At which of these points is the function decreasing?

Accepted Answer

The function is decreasing for all x < 0.

Question 19

Solve the problem.
-Mardi received an inheritance of $60,000. She invested part at 11% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6800. Find the amount invested at 11%.

Accepted Answer

Let the amount invested at 11% be x dollars. Therefore, the amount invested at 12% is $60,000 - x. The total annual income from these investments is given by 0.11x + 0.12($60,000 - x) = $6,800. Solving this equation for x gives x = $40,000, which is the amount invested at 11%.

Question 20

Solve the problem.
-Anne and Nancy use a metal alloy that is 18.6% copper to make jewelry. How many ounces of a 12% alloy must be mixed with a 23% alloy to form 75 ounces of the desired alloy?

Accepted Answer

To solve this problem, we can use the concept of weighted averages or the method of alligation. Let $x$ be the amount of 12% alloy and $75 - x$ be the amount of 23% alloy. The equation to represent the mixture is: $0.12x + 0.23(75 - x) = 0.186 \times 75$. Solving for $x$ gives us 30 ounces.

Quiz 1: Functions and Graphs

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Choose the one alternative that best completes the statement or answers the question. -For the graph shown, at which point does the function change from increasing to decreasing?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Solve the problem. -Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments Amounts to 11%?

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 400 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they Meet, how far are they from Denver?

Choose the one alternative that best completes the statement or answers the question. -What are the $x$ -intercepts of $f ( x + 2 ) ?$

True or False. The function $y = \frac { x ^ { 2 } - 1 ^ { 2 } } { x - 1 }$ is not continuous at $x = 1$ .

Solve the problem. -In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Solve the problem. -The speed of a freight train is 23 mph slower than that of a passenger train. The freight train travels 350 mi in the same time it takes the passenger train to travel 440 mi. Find the speed of the passenger train.

Solve the problem. -A traveling salesperson averaged 48 miles per hour on a 246 mile trip. How many hours were spent on the trip?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Choose the one alternative that best completes the statement or answers the question. -Sketch the graph of $y = - x ^ { 2 }$ . At which of these points is the function decreasing?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 11% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6800. Find the amount invested at 11%.

Solve the problem. -Anne and Nancy use a metal alloy that is 18.6% copper to make jewelry. How many ounces of a 12% alloy must be mixed with a 23% alloy to form 75 ounces of the desired alloy?

Quiz 1: Functions and Graphs

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Choose the one alternative that best completes the statement or answers the question. -For the graph shown, at which point does the function change from increasing to decreasing?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Solve the problem. -Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments Amounts to 11%?

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 400 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they Meet, how far are they from Denver?

Choose the one alternative that best completes the statement or answers the question. -What are the xxx -intercepts of f(x+2) ?f ( x + 2 ) ?f(x+2) ?

True or False. The function y=x2−12x−1y = \frac { x ^ { 2 } - 1 ^ { 2 } } { x - 1 }y=x−1x2−12​ is not continuous at x=1x = 1x=1 .

Solve the problem. -In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Solve the problem. -The speed of a freight train is 23 mph slower than that of a passenger train. The freight train travels 350 mi in the same time it takes the passenger train to travel 440 mi. Find the speed of the passenger train.

Solve the problem. -A traveling salesperson averaged 48 miles per hour on a 246 mile trip. How many hours were spent on the trip?

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Choose the one alternative that best completes the statement or answers the question. -Sketch the graph of y=−x2y = - x ^ { 2 }y=−x2 . At which of these points is the function decreasing?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 11% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was $6800. Find the amount invested at 11%.

Solve the problem. -Anne and Nancy use a metal alloy that is 18.6% copper to make jewelry. How many ounces of a 12% alloy must be mixed with a 23% alloy to form 75 ounces of the desired alloy?

Choose the one alternative that best completes the statement or answers the question. -What are the $x$ -intercepts of $f ( x + 2 ) ?$

True or False. The function $y = \frac { x ^ { 2 } - 1 ^ { 2 } } { x - 1 }$ is not continuous at $x = 1$ .

Choose the one alternative that best completes the statement or answers the question. -Sketch the graph of $y = - x ^ { 2 }$ . At which of these points is the function decreasing?