Question 1

Determine whether the statement is true or false.
-Some whole numbers are not integers.

Accepted Answer

All whole numbers are integers.

Question 2

Determine whether the statement is true or false.
-All natural numbers are whole numbers.

Accepted Answer

Every natural number is a whole number, as the set of natural numbers includes all positive integers starting from 1, which are also part of the whole numbers.

Question 3

Evaluate the expression for the given values.
-3x + 6, for x = 6
A) 36
B) 12
C) 9
D) 24

Accepted Answer

Substituting x = 6 into the expression 3x + 6 gives 3(6) + 6 = 18 + 6 = 24.

Question 4

Write the English phrase as an algebraic expression. Let x represent the number.
-5 less than 3 times a number
A) 5 - 3x
B) 3x - 5
C) 3 - 5x
D) 5x - 3

Accepted Answer

The phrase "5 less than 3 times a number" translates to subtracting 5 from 3 times the number, which is represented as 3x - 5.

Question 5

Solve.
-Forensic scientists use the lengths of certain bones to calculate the height of a person. When the femur (the bone from the knee to the hip socket) is used, the following formula applies for men: h = 69.09 + 2.24f, where h is the height and f is the length of the femur (both in centimeters). Find the height of a man with a femur measuring 51 centimeters.
A) 3637.83 cm
B) 183.33 cm
C) 120.09 cm
D) 8.08 cm

Accepted Answer

To find the height of a man with a femur measuring 51 centimeters, substitute f = 51 into the formula h = 69.09 + 2.24f. This gives h = 69.09 + 2.24(51) = 69.09 + 114.24 = 183.33 cm.

Question 6

Solve.
-The formula $C = \frac { 5 } { 9 } ( F - 32 )$ converts Fahrenheit to Celsius degrees. The high temperature in a certain city was $59 ^ { \circ } \mathrm { F }$. Find the corresponding Celsius temperature (to the nearest degree).
A) 33°C
B) 15°C
C) 49°C
D) 1°C

Accepted Answer

Substituting $59 ^ { \circ } \mathrm { F }$ into the formula $C = \frac { 5 } { 9 } ( F - 32 )$, we get $C = \frac { 5 } { 9 } ( 59 - 32 ) = \frac { 5 } { 9 } \times 27 = 15$. Therefore, the corresponding Celsius temperature is $15 ^ { \circ } \mathrm { C }$.

Question 7

Solve.
-If a rock falls from a height of 80 meters above the ground, the height H (in meters) after x seconds is approximately H = 80 - 4.9x². What is the height of the rock after 2 seconds? (Round your answer to the nearest tenth.)
A) 70.2 m
B) 300.4 m
C) -16.04 m
D) 60.4 m

Accepted Answer

Substitute x = 2 into the equation: H = 80 - 4.9(2)² = 80 - 19.6 = 60.4 meters.

Question 8

Write the English phrase as an algebraic expression. Let x represent the number.
-A number divided by 50
A) $\frac { 50 } { x }$
B) 50x
C) x 50
D) $\frac { x } { 50 }$
-

Accepted Answer

The phrase "a number divided by 50" translates to $\frac{x}{50}$, where $x$ represents the number.

Question 9

Determine whether the statement is true or false.
-Some whole numbers are not natural numbers.

Accepted Answer

Some whole numbers, such as 0 and -1, are not natural numbers because natural numbers are defined as positive integers greater than 0.

Question 10

Write the English phrase as an algebraic expression. Let x represent the number.
-The sum of a number and 131
A) 131x
B) 131 - x
C) 131 + x
D) 131

Accepted Answer

The phrase "the sum of a number and 131" translates to adding 131 to a variable, represented by x, hence 131 + x.

Question 11

Evaluate the expression for the given values.
-$( x + 3 y ) ^ { 2 } , \text { for } x = 2 , y = 4$
A) 25
B) 14
C) 196
D) 28

Accepted Answer

First, substitute the given values into the expression: $(2 + 3(4))^2 = (2 + 12)^2 = 14^2 = 196.$

Question 12

Write the English phrase as an algebraic expression. Let x represent the number.
-89 less than a number
A) 89
B) x + 89
C) 89x
D) 89 - x

Accepted Answer

The phrase "89 less than a number" translates to subtracting 89 from that number, which is represented by "x". Therefore, the correct expression is "x - 89". However, since the options provided do not include "x - 89", the closest option that represents the concept of "less than" in the context given is "89 - x", assuming a misunderstanding in the formulation of the options.

Question 13

Write the English phrase as an algebraic expression. Let x represent the number.
-8 more than 4 times a number
A) 8x + 4
B) 4(8 + x)
C) 12x
D) 4x + 8

Accepted Answer

The phrase "8 more than 4 times a number" translates to adding 8 to 4 times the number, which is represented as 4x + 8.

Question 14

Determine whether the statement is true or false.
-Every irrational number is a rational number.

Accepted Answer

Irrational numbers cannot be expressed as a fraction of two integers, whereas rational numbers can, making them fundamentally different.

Question 15

Evaluate the expression for the given values.
-$7 x ^ { 2 } + 5 y , \text { for } x = 8 , y = 3$
A) 103
B) 1449
C) 3151
D) 463

Accepted Answer

The answer of Evaluate the expression for the given values.
-\(7...

Question 16

Determine whether the statement is true or false.
-Every rational number is an integer.

Accepted Answer

The statement is false. Rational numbers include both integers and fractions expressed as a ratio of two integers. Therefore, not every rational number is an integer.

Question 17

Write the English phrase as an algebraic expression. Let x represent the number.
-The quotient of 64 and a number
A) 64 - x
B) $\frac { 64 } { x }$
C) x - 64
D) $\frac { x } { 64 }$

Accepted Answer

The phrase "The quotient of 64 and a number" translates to dividing 64 by that number, which is represented as $\frac { 64 } { x }$.

Question 18

Evaluate the expression for the given values.
-3x - y, for x = 9 and y = 5
A) 54
B) 32
C) 22
D) 8

Accepted Answer

Substituting x = 9 and y = 5 into the expression 3x - y gives 3(9) - 5 = 27 - 5 = 22.

Question 19

Determine whether the statement is true or false.
-Some real numbers are integers.

Accepted Answer

This statement is true because integers are a subset of real numbers.

Question 20

Write the English phrase as an algebraic expression. Let x represent the number.
-A number decreased by 78
A) 78x
B) x - 78
C) 78
D) 78 - x

Accepted Answer

The phrase "a number decreased by 78" translates to subtracting 78 from a variable, represented as x - 78.

Quiz 1: Algebra, Mathematical Models, and Problem Solving

Determine whether the statement is true or false. -Some whole numbers are not integers.

Determine whether the statement is true or false. -All natural numbers are whole numbers.

Evaluate the expression for the given values. -3x + 6, for x = 6

Write the English phrase as an algebraic expression. Let x represent the number. -5 less than 3 times a number

Solve. -The formula $C = \frac { 5 } { 9 } ( F - 32 )$ converts Fahrenheit to Celsius degrees. The high temperature in a certain city was $59 ^ { \circ } \mathrm { F }$ . Find the corresponding Celsius temperature (to the nearest degree) .

Solve. -If a rock falls from a height of 80 meters above the ground, the height H (in meters) after x seconds is approximately H = 80 - 4.9x². What is the height of the rock after 2 seconds? (Round your answer to the nearest tenth.)

Write the English phrase as an algebraic expression. Let x represent the number. -A number divided by 50

Determine whether the statement is true or false. -Some whole numbers are not natural numbers.

Write the English phrase as an algebraic expression. Let x represent the number. -The sum of a number and 131

Evaluate the expression for the given values. - $( x + 3 y ) ^ { 2 } , \text { for } x = 2 , y = 4$

Write the English phrase as an algebraic expression. Let x represent the number. -89 less than a number

Write the English phrase as an algebraic expression. Let x represent the number. -8 more than 4 times a number

Determine whether the statement is true or false. -Every irrational number is a rational number.

Evaluate the expression for the given values. - $7 x ^ { 2 } + 5 y , \text { for } x = 8 , y = 3$

Determine whether the statement is true or false. -Every rational number is an integer.

Write the English phrase as an algebraic expression. Let x represent the number. -The quotient of 64 and a number

Evaluate the expression for the given values. -3x - y, for x = 9 and y = 5

Determine whether the statement is true or false. -Some real numbers are integers.

Write the English phrase as an algebraic expression. Let x represent the number. -A number decreased by 78