Question 1

A car's value depreciates by 15\% each year. If the car is currently worth $20,000, what will its value be after 3 years? (Round to the nearest dollar.)

Accepted Answer

$\$12,337$

Question 2

Given the function $f(x) = 3x^2 - 2x + 5$, what is $f(-2)$?

Accepted Answer

$17$

Question 3

A savings account offers an annual interest rate of 4\% compounded quarterly. If you deposit $\$2,000$, how much will you have after 5 years? (Round to the nearest cent.)

Accepted Answer

$\$2,433.40$

Question 4

Which of the following best describes the domain of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$x \geq 3$

Question 5

A researcher collects the following data set: $\{4, 7, 7, 10, 12\}$. What is the median?

Accepted Answer

$7$

Question 6

If $A = \{1,2,3\}$ and $B = \{a,b\}$, how many elements are in the sample space for the experiment of choosing one element from $A$ and one from $B$?

Accepted Answer

$6$

Question 7

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = 50x - 0.5x^2$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $1,250$ at $x = 50$

Question 8

Which of the following is the equation of the line passing through the points $(2, 5)$ and $(6, 13)$?

Accepted Answer

$y = 2x + 1$

Question 9

Suppose the probability of rain on any given day in April is $0.3$. What is the probability that it does not rain on a randomly chosen day in April?

Accepted Answer

$0.7$

Question 10

A bacteria culture triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$5,400$

Question 11

Given $f(x) = 2x + 3$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$11$

Question 12

A student scores 80, 85, 90, and 95 on four exams. What is the mean score?

Accepted Answer

$87.5$

Question 13

If $P(A) = 0.4$ and $P(B) = 0.5$ and $A$ and $B$ are independent, what is $P(A \cap B)$?

Accepted Answer

$0.2$

Question 14

Which of the following is the correct formula for the future value $A$ of an investment of principal $P$ at an annual interest rate $r$ compounded $n$ times per year for $t$ years?

Accepted Answer

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Question 15

A function $f$ is defined as $f(x) = \frac{1}{x-2}$. What is the domain of $f$?

Accepted Answer

$x 
eq 2$

Question 16

A die is rolled twice. What is the probability that at least one roll shows a 6?

Accepted Answer

$\frac{11}{36}$

Question 17

Which of the following is the correct interpretation of the slope in the linear equation $y = 0.8x + 2$ in the context of a business’s profit (in thousands of dollars) as a function of units sold (in hundreds)?

Accepted Answer

For each additional 100 units sold, profit increases by $800$

Question 18

If $f(x) = 5x - 7$, what is the $x$-intercept of the function?

Accepted Answer

$(1.4, 0)$

Question 19

A population of fish in a lake is modeled by $P(t) = 1200e^{0.05t}$, where $t$ is in years. What is the population after 10 years? (Round to the nearest whole number.)

Accepted Answer

$1,977$

Question 20

Which of the following is NOT a function?

Accepted Answer

A relation where $x = 2$ maps to both $y = 3$ and $y = 5$

Math 119 Final Exam Concept List: College Algebra Study Guide

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