Question 1

Evaluate the expression. 
A) 4,096
B) -1,024
C) -6,561
D) 6,561
E) -4,096

Accepted Answer

The answer of Evaluate the expression. 
A) 4,096
B) -1,024
C) -6,561
D)...

Question 2

Determine whether the statement below is true for positive real numbers a. |a + 8| = |a| + 8
A) True
B) False

Accepted Answer

|a + 8| = |a| + 8 is not true for all positive real numbers a. For example, if a = 2, then |a + 8| = |2 + 8| = |10| = 10, but |a| + 8 = |2| + 8 = 2 + 8 = 10.

Question 3

Show the interval [6, 8) on a number line.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The interval [6, 8) includes all the numbers starting from 6 and up to, but not including, 8. On a number line, this can be represented by a closed dot at 6 and an open dot at 8, with a line connecting the two dots. The correct option showing these dots and the connecting line is option C.

Question 4

Find the minimum profit P (in dollars) given that  .
A) $ 
B) $ 
C) $ 
D) $ 
E) $

Accepted Answer

The answer of Find the minimum profit P (in dollars)...

Question 5

Simplify the expression. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the expression. 
A) 
B) 
C) 
D)...

Question 6

Simplify the expression. (Assume x and y are positive.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the expression. (Assume x and y...

Question 7

Rewrite the expression using positive exponents only. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rewrite the expression using positive exponents only....

Question 8

Determine whether the statement is true or false. 
A) False
B) True

Accepted Answer

Without any context or information provided, it is impossible to determine whether the statement is true or false. Therefore, the answer is A) False since the statement is being presented as a standalone proposition without any supporting evidence or context.

Question 9

Evaluate the expression. 
A) 1
B) 9
C) 6
D) 8
E) 4

Accepted Answer

The answer of Evaluate the expression. 
A) 1
B) 9
C) 6
D)...

Question 10

Suppose  and  are real numbers other than zero and that  . State whether the inequality is true or false. 
A) False
B) True

Accepted Answer

There is no apparent relation between the three given numbers. Therefore, we cannot determine the truth or falsity of the inequality.

Question 11

Evaluate the expression. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the expression. 
A) 
B) 
C) 
D)...

Question 12

The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality  What is the smallest diameter a ball bearing in the batch can have?
A) 0.4 inches
B) 0.46 inches
C) 0.47 inches
D) 0.43 inches
E) 0.45 inches

Accepted Answer

To find the smallest possible diameter for the ball bearing, we need to find the smallest value of x that satisfies the inequality.

We can start by subtracting 0.4 from both sides of the inequality:

0.04x - 0.23 ≥ 0.17 - 0.4

Simplifying:

0.04x - 0.23 ≥ -0.23

Adding 0.23 to both sides:

0.04x ≥ 0

Dividing both sides by 0.04:

x ≥ 0

Since the diameter of the ball bearing must be positive, the smallest possible diameter is 0.43 inches.

Therefore, the answer is D) 0.43 inches.

Question 13

A salesman's monthly commission is 15% on all sales over $11,000. If his goal is to make a commission of at least $2,400/month, what minimum monthly sales figures must he attain?
A) $ 13,400
B) $ 12,200
C) $ 15,800
D) $ 24,600
E) $ 27,000

Accepted Answer

The answer of A salesman's monthly commission is 15% on...

Question 14

Simplify the expression. (Assume that r, s, and t are positive.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the expression. (Assume that r, s,...

Question 15

Evaluate the expression. 
A) 
B) 1
C) 3
D) 9
E)

Accepted Answer

The answer of Evaluate the expression. 
A) 
B) 1
C) 3
D)...

Question 16

Rationalize the numerator of the expression. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rationalize the numerator of the expression. 
A)...

Question 17

Determine whether the statement is true or false. 
A) True
B) False

Accepted Answer

The answer of Determine whether the statement is true or...

Question 18

Evaluate the expression. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the expression. 
A) 
B) 
C) 
D)...

Question 19

Find the maximum profit P (in dollars) given that  .
A) $ 15,650
B) $ 7,600
C) $ 15,200
D) $ 16,100
E) $ 22,800

Accepted Answer

The answer of Find the maximum profit P (in dollars)...

Question 20

Rationalize the denominator of the expression. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rationalize the denominator of the expression. 
A)...

Quiz 1: Preliminaries

Evaluate the expression.

Determine whether the statement below is true for positive real numbers a. |a + 8| = |a| + 8

Show the interval [6, 8) on a number line.

Find the minimum profit P (in dollars) given that .

Simplify the expression.

Simplify the expression. (Assume x and y are positive.)

Rewrite the expression using positive exponents only.

Determine whether the statement is true or false.

Evaluate the expression.

Suppose and are real numbers other than zero and that . State whether the inequality is true or false.

Evaluate the expression.

The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality What is the smallest diameter a ball bearing in the batch can have?

A salesman's monthly commission is 15% on all sales over $11,000. If his goal is to make a commission of at least $2,400/month, what minimum monthly sales figures must he attain?

Simplify the expression. (Assume that r, s, and t are positive.)

Evaluate the expression.

Rationalize the numerator of the expression.

Determine whether the statement is true or false.

Evaluate the expression.

Find the maximum profit P (in dollars) given that .

Rationalize the denominator of the expression.