Q: A chemist needs to prepare a 250 mL solution of 0.5 M NaCl for an experiment. If the stock solution is 2 M NaCl, how much of the stock solution should be used, and how much water should be added to achieve the desired concentration?

$$62.5\ \text{mL} of $$stock solution, $$187.5\ \text{mL} of $$water

Q: Which of the following is the correct way to convert 5 kilometers to meters using unit conversion?

$$5\ \text{km} \times \dfrac{1000\ \text{m}}{1\ \text{km}} = 5000\ \text{m}$$

Question 1

A chemist needs to prepare a 250 mL solution of 0.5 M NaCl for an experiment. If the stock solution is 2 M NaCl, how much of the stock solution should be used, and how much water should be added to achieve the desired concentration?

Accepted Answer

$$62.5\ 	ext{mL} of $$stock solution, $$187.5\ 	ext{mL} of $$water

Question 2

A car rental company charges a flat fee of $$30 plus 0.20 $$per mile driven. If $$y is $$the total cost and $$x is $$the number of miles driven, which equation models this situation?

Accepted Answer

$$y = 0.20x + 30$$

Question 3

A biologist is studying the growth of a bacterial population. The population doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$4000$$

Question 4

Which of the following is the correct way to convert 5 kilometers to meters using unit conversion?

Accepted Answer

$$5\ 	ext{km} 	imes \dfrac{1000\ 	ext{m}}{1\ 	ext{km}} = 5000\ 	ext{m}$$

Question 5

A patient is prescribed a medication that must be taken every 8 hours. If the first dose is taken at 6:00 AM, at what time will the fourth dose be taken?

Accepted Answer

10:00 PM the same day

Question 6

Which of the following equations represents a line with a slope of $$-3$$ and a $$y-$$intercept of $$5$$?

Accepted Answer

$$y = -3x + 5$$

Question 7

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a batch using 9 cups of sugar, how many cups of flour are needed?

Accepted Answer

$$6$$

Question 8

A company’s profit $$P (in $$dollars) is given by $$P = 50x - 200$$, where $$x is $$the number of units sold. What is the minimum number of units that must be sold for the company to make a profit?

Accepted Answer

$$5$$

Question 9

A student scored 80, 85, and 90 on the first three exams. What score must the student get on the fourth exam to have an average of 88?

Accepted Answer

$$97$$

Question 10

Which of the following is the correct symbolic representation for the statement: 'The sum of twice a number and 7 is equal to 19'?

Accepted Answer

$$2x + 7 = 19$$

Question 11

A hospital needs to dilute a 10% saline solution to make 500 mL of a 2% saline solution. How much of the 10% solution should be used?

Accepted Answer

$$100\ 	ext{mL}$$

Question 12

If the equation $$3x - 2y = 12 is $$solved for $$y$$, what is the resulting equation?

Accepted Answer

$$y = \dfrac{3x}{2} - 6$$

Question 13

A medication is administered at a rate of 15 mg per kg of body weight. If a patient weighs 60 kg, how much medication should be administered?

Accepted Answer

$$900\ 	ext{mg}$$

Question 14

Which of the following best describes the solution to the system of equations: $$\begin{cases} 2x + y = 10 \ x - y = 2 \end{cases}$$?

Accepted Answer

$$(4,2)$$

Question 15

A scientist records the temperature at noon for 5 consecutive days: $$22^\circ C$$, $$24^\circ C$$, $$21^\circ C$$, $$23^\circ C$$, $$20^\circ C. $$What is the mean temperature?

Accepted Answer

$$22^\circ C$$

Question 16

A cell phone plan charges $$25 per month plus 0.10 $$per text message. If a customer sent 150 text messages in a month, what was the total bill?

Accepted Answer

$$40$$

Question 17

Which of the following is the correct way to express 0.00045 in scientific notation?

Accepted Answer

$$4.5 	imes 10$$^{-3}$$

Question 18

A train travels 180 miles in 3 hours. What is its average speed in miles per hour?

Accepted Answer

$$60$$

Question 19

A store is having a 25% off sale. If an item originally costs $80, what is the sale price?

Accepted Answer

$$60$$

MAT 110-4822: Applied Mathematics (College Algebra) – Syllabus and Study Guide

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