Question 1

Solve the formula for the specified variable.
-$\mathrm { d } = \mathrm { rt } ;$ for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { t } { d }$ 
B)  $r = d - t$ 
C)  $r = \frac { d } { t }$ 
D)  $\mathrm { r } = \mathrm { dt }$ 
A)  $r = \frac { t } { d }$ 
B)  $r = d - t$ 
C)  $r = \frac { d } { t }$ 
D)  $\mathrm { r } = \mathrm { dt }$

Question 2

Solve the equation.
-$\frac { 1 } { 2 } = \frac { r } { 3 }$

Accepted Answer

A)  $0.17$ 
B)  $1.5$ 
C)  3 
D)  6 
A)  $0.17$ 
B)  $1.5$ 
C)  3 
D)  6

Question 3

Solve the problem.
-The number of births in County A has been increasing in recent years. Use the information given in the bar graph for the years 1960 and 1990, letting x = 0 represent the year 1960 and letting y represent the number of births. Use the graph to estimate the number of births in 1965.

Accepted Answer

A) 1800 
B) 1750 
C) 1900 
D) 1850 
A) 1800 
B) 1750 
C) 1900 
D) 1850

Question 4

Match the inequality with its correct representation.
-$\{ x \mid - 8 < x \leq 7 \}$

Accepted Answer

A)  $( - 8,7 ]$ 
B)  $( - 8,7 )$ 
C)  $[ - 8,7 ]$ 
D)  $[ - 8,7 )$ 
A)  $( - 8,7 ]$ 
B)  $( - 8,7 )$ 
C)  $[ - 8,7 ]$ 
D)  $[ - 8,7 )$

Question 5

Evaluate.
-$4 ^ { 0 } - 8 ^ { 0 }$

Accepted Answer

A)  0 
B)  1 
C)  $- 4$ 
D)  2 
A)  0 
B)  1 
C)  $- 4$ 
D)  2

Question 6

Find the average rate for an athlete who runs 400 m in 46.91 seconds. Give your answer in meters per second and round to the nearest hundredth.

Accepted Answer

A) 8.53 meters per second 
B) 0.12 meters per second 
C) 18,764 meters per second 
D) 10.66 meters per second 
A) 8.53 meters per second 
B) 0.12 meters per second 
C) 18,764 meters per second 
D) 10.66 meters per second

Question 7

A biologist collected 201 fern and moss samples. There were 85 more moss than fern samples. How many fern samples did the biologist collect?

Accepted Answer

A) 58 fern samples 
B) 116 fern samples 
C) 143 fern samples 
D) 114 fern samples 
A) 58 fern samples 
B) 116 fern samples 
C) 143 fern samples 
D) 114 fern samples

Question 8

In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be at least $139.43 ^ { \circ } \mathrm { F }$. Find the Celsius temperatures at which the reaction may occur. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Accepted Answer

A)  $C \leq 59.68 ^ { \circ }$ 
B)  $\mathrm { C } < 282.97 ^ { \circ }$ 
C)  $\mathrm { C } \geq 282.97 ^ { \circ }$ 
D)  $C \geq 59.68 ^ { \circ }$ 
A)  $C \leq 59.68 ^ { \circ }$ 
B)  $\mathrm { C } < 282.97 ^ { \circ }$ 
C)  $\mathrm { C } \geq 282.97 ^ { \circ }$ 
D)  $C \geq 59.68 ^ { \circ }$

Question 9

Let x represent the unknown, and write an equation for the sentence. Do not solve.
-Four times a number added to 8 times the number equals 36.

Accepted Answer

A) 4x - 8x = 36 
B) 4(x + 8)= 36x 
C) 4x(8 + x)= 36 
D) 4x + 8x = 36 
A) 4x - 8x = 36 
B) 4(x + 8)= 36x 
C) 4x(8 + x)= 36 
D) 4x + 8x = 36

Question 10

Answer the question based on the given graph.
-  The data used to determine the graph were based on the number of tropical storms affecting Country X during the last ten years. A total of 703 tropical storms were reported. In which months
Were more than 84 storms reported?

Accepted Answer

A) February, March, April 
B) March 
C) February, March 
D) January, February, March, April, December 
A) February, March, April 
B) March 
C) February, March 
D) January, February, March, April, December

Question 11

Evaluate the expression.
-$4 ^ { 4 } + 4 ^ { 3 }$

Accepted Answer

A)  80 
B)  28 
C)  5461 
D)  320 
A)  80 
B)  28 
C)  5461 
D)  320

Question 12

Solve the problem.
-If a spring stretches 0.9 m when a 6-kg weight is attached to it, how much will it stretch when a 14-kg weight is attached to it?

Accepted Answer

A) 4.1 m 
B) 1.1 m 
C) 2.1 m 
D) 5.1 m 
A) 4.1 m 
B) 1.1 m 
C) 2.1 m 
D) 5.1 m

Question 13

Answer the question based on the given graph.
-

In which months was the percent of tropical storms at most $5 \%$ ?

Accepted Answer

A)  May 
B)  May, October 
C)  February, March, April 
D)  May, June, July 
A)  May 
B)  May, October 
C)  February, March, April 
D)  May, June, July

Question 14

Decide whether the statement translates into an expression or an equation.
-10% of a number is 5.

Accepted Answer

A) Equation 
B) Expression 
A) Equation 
B) Expression

Question 15

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.
-$2 ( 28 t + 20 ) = 8 ( 2 t + 40 )$

Accepted Answer

A)  Contradiction; $\{ - 9 \}$ 
B)  Conditional; $\{ 7 \}$ 
C)  Conditional; $\{ - 9 \}$ 
D)  Identity; $\{ 7 \}$ 
A)  Contradiction; $\{ - 9 \}$ 
B)  Conditional; $\{ 7 \}$ 
C)  Conditional; $\{ - 9 \}$ 
D)  Identity; $\{ 7 \}$

Question 16

A merchant has coffee worth $5 a pound that she wishes to mix with 70 pounds of coffee worth $8 a pound to get a mixture that can be sold for $7 a pound. How many pounds of the $5 coffee
Should be used?

Accepted Answer

A) 52.5 lb 
B) 17.5 lb 
C) 35 lb 
D) 105 lb 
A) 52.5 lb 
B) 17.5 lb 
C) 35 lb 
D) 105 lb

Question 17

Decide whether the statement translates into an expression or an equation.
-the ratio of a number and 8

Accepted Answer

A) Equation 
B) Expression 
A) Equation 
B) Expression

Question 18

A church steeple casts a shadow 106 ft long, and at the same time a 7.0-ft post casts a shadow 6.0 ft long. How high is the steeple? Round to the nearest unit.

Accepted Answer

A) 124 ft 
B) 7 ft 
C) 91 ft 
D) 107 ft 
A) 124 ft 
B) 7 ft 
C) 91 ft 
D) 107 ft

Question 19

Decide whether the statement translates into an expression or an equation.
-42 divided by a number is 6.

Accepted Answer

A) Equation 
B) Expression 
A) Equation 
B) Expression

Question 20

Tell which brand or which size is the better buy.
-Brand A: 28 oz for $\$ 15.12$
Brand $\mathrm { B } : 24 \mathrm { Oz }$ for $\$ 12.48$

Accepted Answer

A) Brand B 
B) Brand A 
C) Not enough information 
D) Equal value 
A) Brand B 
B) Brand A 
C) Not enough information 
D) Equal value

Solve the formula for the specified variable. - $\mathrm { d } = \mathrm { rt } ;$ for $\mathrm { r }$

Solve the equation. - $\frac { 1 } { 2 } = \frac { r } { 3 }$

Match the inequality with its correct representation. - $\{ x \mid - 8 < x \leq 7 \}$

Evaluate. - $4 ^ { 0 } - 8 ^ { 0 }$

Find the average rate for an athlete who runs 400 m in 46.91 seconds. Give your answer in meters per second and round to the nearest hundredth.

A biologist collected 201 fern and moss samples. There were 85 more moss than fern samples. How many fern samples did the biologist collect?

In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be at least $139.43 ^ { \circ } \mathrm { F }$ . Find the Celsius temperatures at which the reaction may occur. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Let x represent the unknown, and write an equation for the sentence. Do not solve. -Four times a number added to 8 times the number equals 36.

Answer the question based on the given graph. - The data used to determine the graph were based on the number of tropical storms affecting Country X during the last ten years. A total of 703 tropical storms were reported. In which months Were more than 84 storms reported?

Evaluate the expression. - $4 ^ { 4 } + 4 ^ { 3 }$

Solve the problem. -If a spring stretches 0.9 m when a 6-kg weight is attached to it, how much will it stretch when a 14-kg weight is attached to it?

Answer the question based on the given graph. - $Answer the question based on the given graph. - In which months was the percent of tropical storms at most 5 \% ?$ In which months was the percent of tropical storms at most $5 \%$ ?

Decide whether the statement translates into an expression or an equation. -10% of a number is 5.

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $2 ( 28 t + 20 ) = 8 ( 2 t + 40 )$

A merchant has coffee worth $5 a pound that she wishes to mix with 70 pounds of coffee worth $8 a pound to get a mixture that can be sold for $7 a pound. How many pounds of the $5 coffee Should be used?

Decide whether the statement translates into an expression or an equation. -the ratio of a number and 8

A church steeple casts a shadow 106 ft long, and at the same time a 7.0-ft post casts a shadow 6.0 ft long. How high is the steeple? Round to the nearest unit.

Decide whether the statement translates into an expression or an equation. -42 divided by a number is 6.

Tell which brand or which size is the better buy. -Brand A: 28 oz for $\$ 15.12$ Brand $\mathrm { B } : 24 \mathrm { Oz }$ for $\$ 12.48$

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 7: The Basic Concepts of Algebra

Solve the formula for the specified variable. - d=rt;\mathrm { d } = \mathrm { rt } ;d=rt; for r\mathrm { r }r

Solve the equation. - 12=r3\frac { 1 } { 2 } = \frac { r } { 3 }21​=3r​

Match the inequality with its correct representation. - {x∣−8<x≤7}\{ x \mid - 8 < x \leq 7 \}{x∣−8<x≤7}

Evaluate. - 40−804 ^ { 0 } - 8 ^ { 0 }40−80

Find the average rate for an athlete who runs 400 m in 46.91 seconds. Give your answer in meters per second and round to the nearest hundredth.

A biologist collected 201 fern and moss samples. There were 85 more moss than fern samples. How many fern samples did the biologist collect?

Let x represent the unknown, and write an equation for the sentence. Do not solve. -Four times a number added to 8 times the number equals 36.

Answer the question based on the given graph. - The data used to determine the graph were based on the number of tropical storms affecting Country X during the last ten years. A total of 703 tropical storms were reported. In which months Were more than 84 storms reported?

Evaluate the expression. - 44+434 ^ { 4 } + 4 ^ { 3 }44+43

Solve the problem. -If a spring stretches 0.9 m when a 6-kg weight is attached to it, how much will it stretch when a 14-kg weight is attached to it?

Answer the question based on the given graph. - In which months was the percent of tropical storms at most 5%5 \%5% ?

Decide whether the statement translates into an expression or an equation. -10% of a number is 5.

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - 2(28t+20)=8(2t+40)2 ( 28 t + 20 ) = 8 ( 2 t + 40 )2(28t+20)=8(2t+40)

A merchant has coffee worth $5 a pound that she wishes to mix with 70 pounds of coffee worth $8 a pound to get a mixture that can be sold for $7 a pound. How many pounds of the $5 coffee Should be used?

Decide whether the statement translates into an expression or an equation. -the ratio of a number and 8

A church steeple casts a shadow 106 ft long, and at the same time a 7.0-ft post casts a shadow 6.0 ft long. How high is the steeple? Round to the nearest unit.

Decide whether the statement translates into an expression or an equation. -42 divided by a number is 6.

Tell which brand or which size is the better buy. -Brand A: 28 oz for $15.12\$ 15.12$15.12 Brand B:24Oz\mathrm { B } : 24 \mathrm { Oz }B:24Oz for $12.48\$ 12.48$12.48

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Solve the formula for the specified variable. - $\mathrm { d } = \mathrm { rt } ;$ for $\mathrm { r }$

Solve the equation. - $\frac { 1 } { 2 } = \frac { r } { 3 }$

Match the inequality with its correct representation. - $\{ x \mid - 8 < x \leq 7 \}$

Evaluate. - $4 ^ { 0 } - 8 ^ { 0 }$

Evaluate the expression. - $4 ^ { 4 } + 4 ^ { 3 }$

Answer the question based on the given graph. - $Answer the question based on the given graph. - In which months was the percent of tropical storms at most 5 \% ?$ In which months was the percent of tropical storms at most $5 \%$ ?

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $2 ( 28 t + 20 ) = 8 ( 2 t + 40 )$

Tell which brand or which size is the better buy. -Brand A: 28 oz for $\$ 15.12$ Brand $\mathrm { B } : 24 \mathrm { Oz }$ for $\$ 12.48$