Question 1

Which of the following best describes the solution set of the system of equations below?

$$
\begin{cases}
2x + 3y = 7 \
4x + 6y = 14
\end{cases}
$$

Accepted Answer

The system has infinitely many solutions.

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units produced (in thousands). What is the maximum profit, and for how many units produced does it occur?

Accepted Answer

Maximum profit is $$20 at$$ $$x = 3$$ units.

Question 3

Which of the following is the correct solution to the inequality $$3x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 4$$

Question 4

Given the function $$f(x) = \frac{1}{x-2}$$, which of the following statements is true about its domain?

Accepted Answer

The domain is all real numbers except $$x = 2.$$

Question 5

A biologist models the population of a bacteria culture by $$P(t) = 500e$$^{0.3t}$$, where t$ is time in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1.5}$$ \approx 2240$$

Question 6

Which of the following is the correct graph for the equation $$y = -2x + 3$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$3.$$

Question 7

A loan of $$\10$$,000$$ is taken out at an annual interest rate of 6$$\%$$, compounded monthly. What is the balance after 2 years? Use the formula A = P$$\left(1 + \frac{r}{n}\$$right)^{nt}$.

Accepted Answer

$$A \approx \11$$,270$

Question 8

Which of the following is the solution to the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 9

A student is analyzing the function $$f(x) = x^2$ - 4x + 3. $$What are the coordinates of the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 10

Which of the following is the correct solution to the system of equations below?

$$
\begin{cases}
x + y = 5 \
2x - y = 1
\end{cases}
$$

Accepted Answer

$$x = 2$$, $$y = 3$$

Question 11

A medical researcher uses the formula $$C = 2e$$^{-0.5t}$$ to model the concentration of a drug in the bloodstream, where t$ is time in hours. What is the concentration after 4 hours?

Accepted Answer

$$C = 2e$$^{-2}$$ \approx 0.27$$

Question 12

Which of the following is the correct solution to $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 13

A chemical reaction is modeled by $$C(t) = 100 - 20\ln(t+1)$$, where $$C is $$the concentration after $$t$$ minutes. What is the concentration after 4 minutes?

Accepted Answer

$$C(4) = 100 - 20\ln(5) \approx 67.89$$

Question 14

Which of the following is the correct solution to the equation $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 15

A student invests $$\2$$,000$$ in an account that earns 4$$\%$$ annual interest, compounded quarterly. What is the value of the investment after 3 years? Use A = P$$\left(1 + \frac{r}{n}\$$right)^{nt}$.

Accepted Answer

$$A \approx \2$$,255$

Question 16

Which of the following is the correct solution to the equation $$2^{x} = 20$?

Accepted Answer

$$x = \log_{2}(20) \approx 4.32$$

Question 17

A survey found that 60 students take mathematics, 40 take chemistry, and 20 take both. How many students take at least one of the two subjects?

Accepted Answer

80

Question 18

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 4$$?

Accepted Answer

$$x = 11$$

Question 19

A die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

College Algebra Syllabus and Study Guide: Course Structure, Policies, and Key Topics

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