Q: A car depreciates in value according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years?

$$20000 \times 0.85^3$ = 12262.5$$

Q: If $$A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$, what is $$A + B$$?

$$\begin{pmatrix} 3 & 1 \\ 3 & 5 \end{pmatrix}$$

Q: A box contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both are red?

$$\frac{5}{12} \times \frac{4}{11} = \frac{20}{132} = \frac{5}{33}$$

Question 1

A pharmaceutical company is testing a new drug. Out of 200 patients, 120 showed improvement, 50 showed no change, and 30 experienced side effects. What is the probability that a randomly selected patient either showed improvement or experienced side effects?

Accepted Answer

$$\frac{150}{200}$$

Question 2

Which of the following is the correct equation for the line passing through the points $$(2, 5)$$ and $$(4, 9)$$?

Accepted Answer

$$y = 2x + 1$$

Question 3

A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 36 meters, what is the width of the garden?

Accepted Answer

$$5$$ meters

Question 4

Which of the following expressions is equivalent to $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2}$$

Question 5

A car depreciates in value according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years?

Accepted Answer

$$20000 	imes 0.85^3$ = 12262.5$$

Question 6

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 7

A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?

Accepted Answer

$$10 cm$$

Question 8

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 9

A chemist needs to mix a $$30\%$$ saline solution with a $$10\%$$ saline solution to obtain $$20$$ liters of a $$25\%$$ solution. How many liters of the $$30\%$$ solution should be used?

Accepted Answer

$$15$$ liters

Question 10

Which of the following is the inverse function of $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{3}$$

Question 11

If $$A = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{pmatrix} 3 & 1 \ 3 & 5 \end{pmatrix}$$

Question 12

A circle has the equation $$(x - 2)^2$ + (y + 3)^2$ = 25. $$What are the center and radius of the circle?

Accepted Answer

Center: $$(2, -3)$$, Radius: $$5$$

Question 13

Which of the following is the solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 14

A box contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both are red?

Accepted Answer

$$\frac{5}{12} 	imes \frac{4}{11} = \frac{20}{132} = \frac{5}{33}$$

Question 15

Which of the following is the correct simplification of $$\frac{2x^2$ - 8}{4x}$$?

Accepted Answer

$$\frac{x - 2}{2}$$

Question 16

A student scored 80, 85, 90, and 95 on four tests. What is the standard deviation of the scores?

Accepted Answer

$$5.59$$

Question 17

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 13 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 4, y = 3$$

Question 18

Which of the following is the correct solution to $$\log_{2}(x) = 3$$?

Accepted Answer

$$x = 8$$

Question 19

A triangle has sides of length 7, 24, and 25. Is this triangle a right triangle?

Accepted Answer

Yes, because $$7^2$$ + $$24^2$$ = $$25^2$$

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