Question 1

A chemist must prepare 350 ml of a chemical solution made up of two parts alcohol and three parts acid. How many milliliters of alcohol should be used?

Accepted Answer

$$140$$

Question 2

The Acme Company produces a product with a variable cost per unit of $$6 and a fixed cost of 80$$,000. Each unit has a selling price of $$10. How many units must be sold to earn a profit of 60$$,000?

Accepted Answer

$$35,000$$

Question 3

A total of $$10,000 was invested in two business ventures, A and B. At the end of the year, A yielded 6% and B yielded 5.75% returns. If the total interest earned was 588.75$$, how much was invested at 6%?

Accepted Answer

$$5,500$$

Question 4

Solve the linear inequality: $$2(x - 3) \u003c 4.$$

Accepted Answer

$$x \u003c 5$$

Question 5

For a company that manufactures aquarium heaters, the combined cost for labor and material is $$21 per heater. Fixed costs are 70$$,000. If the selling price of a heater is $35, how many heaters must be sold to earn a profit?

Accepted Answer

$$5,001$$

Question 6

What is the solution to the absolute value equation $$|x - 3| = 2$$?

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 7

Solve $$|7 - 3x| = 5.$$

Accepted Answer

$$x = \frac{2}{3} or$$ $$x = 4$$

Question 8

Evaluate the sum $$\sum_{j=3}^{7} (5j - 2).$$

Accepted Answer

$$115$$

Question 9

What is the sum $$\sum_{i=1}^{6} (i^2$ + 1)$$?

Accepted Answer

$$97$$

Question 10

List the first four terms of the sequence $$a_k = 2k^2$ + 3k + 1.$$

Accepted Answer

$$6, 15, 28, 45$$

Question 11

Which formula gives the sum of the first $$n$$ positive integers?

Accepted Answer

$$\frac{n(n+1)}{2}$$

Question 12

What is the common difference in the arithmetic sequence $$1.5, 2.2, 2.9, 3.6, 4.3, 5.0$$?

Accepted Answer

$$0.7$$

Question 13

Given a geometric sequence with first term $$a = \sqrt{2}$$ and common ratio $$r = \frac{1}{2}$$, what is the third term?

Accepted Answer

$$\frac{\sqrt{2}}{4}$$

Question 14

What is the sum of the infinite geometric series $$0.151515...$$?

Accepted Answer

$$\frac{5}{33}$$

Question 15

Which of the following is the recursive definition for the Fibonacci sequence?

Accepted Answer

$$F_1 = 1$$, $$F_2 = 1$$, F_{k+2} = F_{k+1} + F_k$$

Question 16

If $$|x + 5| \geq 7$$, what is the solution set for $$x$$?

Accepted Answer

$$x \leq -12 or$$ $$x \geq 2$$

Question 17

Which property of absolute value is illustrated by $$|-a| = |a|$$?

Accepted Answer

Absolute value is symmetric about zero

Question 18

What is the sum of the first $$k$$ terms of an arithmetic sequence with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$S_k = \frac{k}{2}((n-1)d + 2a)$$

Question 19

If $$a  0$$, which of the following is true?

Accepted Answer

$$ac \u003c bc$$

Applications and More Algebra: Fundamental Concepts, Equations, Inequalities, and Sequences

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