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

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

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

Absolute value is symmetric about zero

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

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

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: $2(x - 3) < 4$.

Accepted Answer

$x < 5$

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 $a < b$ and $c > 0$, which of the following is true?

Accepted Answer

$ac < bc$

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

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