Q: A company’s profit $$P is $$given by $$P = 3x - 2y$$, where $$x is $$the number of products sold and $$y is $$the number of defective products. If $$x = 100$$ and $$y = 10$$, what is the profit?

$$3 \times 100 - 2 \times 10 = 300 - 20 = 280$$

Q: A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Write an algebraic expression for the total cost $$C if$$ $$m$$ miles are driven, and find the cost for $$m = 150.$$

$$C = 25 + 0.2m$$, so $$C = 25 + 0.2 \times 150 = 25 + 30 = 55$$

Question 1

A biologist is studying the population of bacteria in a petri dish. The population doubles every hour. If the initial population is 500 bacteria, what will the population be after 5 hours?

Accepted Answer

$$500 	imes 2^5$ = 16,000$$

Question 2

Simplify the expression: $$\dfrac{3x^2$y}{6xy^2$}$$

Accepted Answer

$$\dfrac{x}{2y}$$

Question 3

A chemical solution contains $$\dfrac{2}{5}$$ liters of acid and $$\dfrac{3}{10}$$ liters of base. What is the total volume of the solution?

Accepted Answer

$$\dfrac{7}{10}$$ liters

Question 4

Which of the following is the degree of the polynomial $$4x^3y^2$ - 7x^2$y + 5$?

Accepted Answer

$$5$$

Question 5

A patient’s medication dosage is calculated by the formula $$D = \dfrac{mg}{kg} 	imes W$$, where $$W is $$the patient’s weight in kilograms. If the recommended dosage is $$2 \ mg/kg$$ and the patient weighs $$70 kg$$, what is the total dosage?

Accepted Answer

$$140 \ mg$$

Question 6

Simplify the expression: $$(-2)^3 + 4$$ 	imes (-2)$$

Accepted Answer

$$-8 + (-8) = -16$$

Question 7

Which of the following sets does the number $$-\dfrac{7}{2}$$ belong to?

Accepted Answer

Rational numbers, Real numbers

Question 8

A company’s profit $$P is $$given by $$P = 3x - 2y$$, where $$x is $$the number of products sold and $$y is $$the number of defective products. If $$x = 100$$ and $$y = 10$$, what is the profit?

Accepted Answer

$$3 	imes 100 - 2 	imes 10 = 300 - 20 = 280$$

Question 9

Which of the following is the additive inverse of $$-15$$?

Accepted Answer

$$15$$

Question 10

Simplify the expression: $$\dfrac{5}{8} - \dfrac{1}{4}$$

Accepted Answer

$$\dfrac{3}{8}$$

Question 11

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Write an algebraic expression for the total cost $$C if$$ $$m$$ miles are driven, and find the cost for $$m = 150.$$

Accepted Answer

$$C = 25 + 0.2m$$, so $$C = 25 + 0.2 	imes 150 = 25 + 30 = 55$$

Question 12

Which of the following is the simplified form of $$\dfrac{2x^2$y}{4xy^2$}$$?

Accepted Answer

$$\dfrac{x}{2y}$$

Question 13

A student scored $$85$$, $$90$$, and $$95 on $$three exams. What is the average score?

Accepted Answer

$$\dfrac{85 + 90 + 95}{3} = 90$$

Question 14

Which of the following is the product of $$(-3x^2y)(4xy^3$)$?

Accepted Answer

$$-12x^3y^4$

Question 15

A rectangular garden has a length of $$2x + 3$$ meters and a width of $$x - 1$$ meters. Write an expression for the area and simplify.

Accepted Answer

$$(2x + 3)(x - 1) = 2x^2$ + 3x - 2x - 3 = 2x^2$ + x - 3$$

Question 16

Which of the following is the value of $$\left(\dfrac{1}{2}\$$right)^{-3}$$?

Accepted Answer

$$8$$

Question 17

A train travels at a constant speed of $$60$$ miles per hour. How far will it travel in $$2.5$$ hours?

Accepted Answer

$$60 	imes 2.5 = 150$$ miles

Question 18

Simplify the expression: $$3(x - 2) + 4(x + 5)$$

Accepted Answer

$$7x + 14$$

Question 19

Which of the following is the solution to the equation $$2x - 5 = 11$$?

Accepted Answer

$$x = 8$$

Foundations and Problem Solving in College Algebra: Key Concepts and Practice

Guida di studio - Domande di pratica

Study guide - Flashcard