Q: Which of the following correctly applies the order of operations to evaluate the expression $$3 + 6 \times 2^2$ - (4 + 2)$$?

$$3 + 6 \times 2^2$ - (4 + 2) = 3 + 6 \times 4 - 6 = 3 + 24 - 6 = 21$$

Question 1

Which of the following correctly applies the order of operations to evaluate the expression $$3 + 6 	imes 2^2$ - (4 + 2)$$?

Accepted Answer

$$3 + 6 	imes 2^2$ - (4 + 2) = 3 + 6 	imes 4 - 6 = 3 + 24 - 6 = 21$$

Question 2

A chemist needs to convert $$3.5 	imes 10^3$ milligrams to grams using scientific notation. Which of the following is correct?

Accepted Answer

$$3.5 	imes 10^3$ mg = 3.5$ g

Question 3

Which of the following is the correct simplification of $$\sqrt[3]{x^6$ y^3$}$$, assuming $$x, y \geq 0$$?

Accepted Answer

$$x^2 y$

Question 4

A biologist is studying the growth of a bacteria population modeled by the function $$P(t) = 500 \cdot 2^t$$, where $$t is in $$hours. What is the population after 3 hours?

Accepted Answer

$$P(3) = 500 \cdot 2^3$ = 500 \cdot 8 = 4000$$

Question 5

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

Accepted Answer

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

Question 6

Solve for $$x in $$the equation $$\dfrac{2x}{x-1} = 4.$$

Accepted Answer

$$x = 2$$

Question 7

A solution to the quadratic equation $$x^2 + 6x + 5 = 0$ is:

Accepted Answer

$$x = -1$$ and $$x = -5$$

Question 8

Which of the following is the correct simplification of the complex number $$(3 + 4i) - (1 - 2i)$$?

Accepted Answer

$$2 + 6i$$

Question 9

A line passes through the points $$(2, 3)$$ and $$(6, 11). $$What is the slope of the line?

Accepted Answer

$$2$$

Question 10

Which of the following equations represents a line perpendicular to $$y = -\dfrac{1}{3}x + 2$$?

Accepted Answer

$$y = 3x - 5$$

Question 11

If $$f(x) = 2x + 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$f(g(3)) = 2 \cdot 9 + 5 = 23$$

Question 12

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

Accepted Answer

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

Question 13

Divide $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using polynomial long division. What is the remainder?

Accepted Answer

$$-1$$

Question 14

Solve the inequality $$x^2 - 4x - 5$$ \u003c 0$$.

Accepted Answer

$$-1 \u003c x \u003c 5$$

Question 15

A medical researcher models the decay of a drug in the bloodstream with $$C(t) = 100e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours? (Round to the nearest mg/L.)

Accepted Answer

$$C(5) = 100e$$^{-1}$$ \approx 37 mg/L$$

Question 16

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 17

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

Accepted Answer

$$x = 32$$

Question 18

A company wants to maximize profit $$P = 3x + 2y$$ subject to the constraints $$x + y \leq 10$$, $$x \geq 0$$, $$y \geq 0$$, and $$x \leq 6. $$What is the maximum profit and at which point does it occur?

Accepted Answer

Maximum profit is $$P = 26 at$$ $$(x, y) = (6, 4)$$

Question 19

Which of the following is the correct value of $$\sin(30^\circ)$$?

Accepted Answer

$$\dfrac{1}{2}$$

Topics in Algebra: Course Syllabus and Study Guide

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