Question 1

Heather's first four exam grades are 95, 88, 82, and 85. What is the mean (average) of these grades?

$$	ext{Mean} = \frac{95 + 88 + 82 + 85}{4}$$

Accepted Answer

$$87.5$$

Question 2

Given Heather's first four exam grades: 95, 88, 82, and 85, what is the median of these grades?

Accepted Answer

$$86.5$$

Question 3

Heather needs a mean of $$80 on $$all five exams to earn a B. Her first four grades are $$95, 88, 82, 85. $$What is the minimum grade she must earn on the fifth exam?

$$\frac{95 + 88 + 82 + 85 + x}{5} = 80$$

Accepted Answer

$$50$$

Question 4

Evaluate the following expression:

$$38 \cdot 1011$$

Accepted Answer

$$38418$$

Question 5

Which of the following numbers from the set $$\{-2, -3, -57, 0, 1.63, 7, 3, 614, 77\}$$ are natural numbers?

Accepted Answer

$$3, 7, 77, 614$$

Question 6

Simplify the following expression:

$$a - 2b + 6a - 6b - 3$$

Accepted Answer

$$7a - 8b - 3$$

Question 7

Laura lent her sister $$2000 for 1 year. At the end of the year, her sister repaid the 2000 $$plus $$80 interest. What simple interest rate did her sister pay?

$$	ext{Simple Interest Rate} = \frac{80}{2000} 	imes 100\%$

Accepted Answer

$$4\%$$

Question 8

While traveling, you notice you traveled $$25$$ miles in $$35$$ minutes. If your speed does not change, how long will it take you to travel $$125$$ miles?

Accepted Answer

$$175$$ minutes

Question 9

Solve for $$x in $$the equation:

$$56x - 2 = x - 3$$

Accepted Answer

$$x = -\frac{1}{11}$$

Question 10

Which of the following numbers from the set $$\{-2, -3, -57, 0, 1.63, 7, 3, 614, 77\}$$ are rational numbers?

Accepted Answer

$$-2, -3, -57, 0, 1.63, 7, 3, 614, 77$$

Question 11

Evaluate the following expression:

$$-7 - 56 \div 7 \cdot 22 + 4$$

Accepted Answer

$$-171$$

Question 12

Which of the following is the correct solution for $$2x - 3 - 2x + 4 = -13 + x$$?

Accepted Answer

$$x = 17$$

Question 13

Which of the following is the correct solution for $$9x = 3 - 15$$?

Accepted Answer

$$x = -\frac{4}{3}$$

Question 14

Which of the following numbers from the set $$\{-2, -3, -57, 0, 1.63, 7, 3, 614, 77\}$$ are whole numbers?

Accepted Answer

$$0, 3, 7, 77, 614$$

Question 15

Which of the following numbers from the set $$\{-2, -3, -57, 0, 1.63, 7, 3, 614, 77\}$$ are integers?

Accepted Answer

$$-2, -3, -57, 0, 3, 7, 77, 614$$

Question 16

Which of the following numbers from the set $$\{-2, -3, -57, 0, 1.63, 7, 3, 614, 77\}$$ are irrational numbers?

Accepted Answer

None

Question 17

Evaluate the following expression:

$$-4 + 3 - 1 + 12 \div 22$$

Accepted Answer

$$-1.4545$$

Question 18

Which of the following is the correct solution for $$ax + by + c = 0$$ for $$x$$?

Accepted Answer

$$x = -\frac{by + c}{a}$$

Question 19

A chemist mixes two solutions: one with $$20\%$$ salt and another with $$10\%$$ salt. If she wants $$100$$ liters of a $$15\%$$ salt solution, how many liters of the $$20\%$$ solution should she use?

Let $$x be $$the amount of $$20\%$$ solution.

Accepted Answer

$$50$$ liters

MTH 098 Practice Exam 1: Step-by-Step Algebra Guidance

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