Question 1

Solve the problem.
-A chemical solution contains  8%8 \%8%  salt. How much salt is in  4ml4 \mathrm{ml}4ml  of solution? Round your answer to three decimal places, if necessary.

Accepted Answer

A)    50ml50 \mathrm{ml}50ml 
B)    5ml5 \mathrm{ml}5ml 
C)    0.32ml0.32 \mathrm{ml}0.32ml 
D)    3.2ml3.2 \mathrm{ml}3.2ml

Question 2

Solve the problem.
-There were 35,000 people at a ball game in Los Angeles. The day's receipts were  $253,000\$ 253,000$253,000 . How many people paid  $11.00\$ 11.00$11.00  for reserved seats and how many paid  $5.00\$ 5.00$5.00  for general admission?

Accepted Answer

A)   13,000 paid  $11\$ 11$11  and 22,000 paid  $5\$ 5$5 
B)   19,500 paid  $11\$ 11$11  and 15,500 paid  $5\$ 5$5 
C)   22,000 paid  $11\$ 11$11  and 13,000 paid  $5\$ 5$5 
D)   15,500 paid  $11\$ 11$11  and 19,500 paid  $5\$ 5$5

Question 3

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
- 12k+186=4(3k+45) 12 \mathrm{k}+186=4(3 \mathrm{k}+45) 12k+186=4(3k+45)

Accepted Answer

A)   Conditional;  {3}\{3\}{3} 
B)   Contradiction;  ∅\varnothing∅ 
C)   Identity; {all real numbers}
D)   Conditional;  {−3}\{-3\}{−3}

Question 4

Express the set in the simplest interval form.
- (−4,6]∩(−2,∞) (-4,6] \cap(-2, \infty) (−4,6]∩(−2,∞)

Accepted Answer

A)    [−2,6][-2,6][−2,6] 
B)    (−4,∞) (-4, \infty) (−4,∞)  
C)    (−2,6](-2,6](−2,6] 
D)    (−4,6](-4,6](−4,6]

Question 5

Solve the inequality and graph the solution set.
- ∣x∣≤7|x| \leq 7∣x∣≤7

Accepted Answer

A)    [−7,7][-7,7][−7,7] 
B)    (−∞,7](-\infty, 7](−∞,7] 
C)    (−∞,−7]∪[7,∞) (-\infty,-7] \cup[7, \infty) (−∞,−7]∪[7,∞)  
D)    (−∞,−7](-\infty,-7](−∞,−7]

Question 6

Provide an appropriate response.
-Determine which of the following is used to solve the inequality  c">∣ax+b∣>c|a x+b|>c∣ax+b∣>c , for  0">c>0c>0c>0 .

Accepted Answer

A) c">ax+b>ca x+b>cax+b>c or ax+b<−ca x+b<-cax+b<−c B) \mathrm{c}">ax+b>c\mathrm{ax}+\mathrm{b}>\mathrm{c}ax+b>c or -\mathrm{c}">ax+b>−c\mathrm{ax}+\mathrm{b}>-\mathrm{c}ax+b>−c C) ax+bax+b>−ca x+b>-cax+b>−c D) c">ax+b>ca x+b>cax+b>c and ax+b<−ca x+b<-cax+b<−c

Question 7

Solve the problem.
-What is the area of a square with side  2.2 cm2.2 \mathrm{~cm}2.2 cm  ?

Accepted Answer

A)    10 cm210 \mathrm{~cm}^{2}10 cm2 
B)    19.36 cm219.36 \mathrm{~cm}^{2}19.36 cm2 
C)    4.84 cm24.84 \mathrm{~cm}^{2}4.84 cm2 
D)    4.4 cm24.4 \mathrm{~cm}^{2}4.4 cm2

Question 8

Which of the following is not a correct answer when the formula  V=13πr2hV=\frac{1}{3} \pi r^{2} hV=31​πr2h  is solved for  hhh  ?

Accepted Answer

A)    3(Vπr2) 3\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl) 3(πr2V​)  
B)    3 Vπr2\frac{3 \mathrm{~V}}{\pi \mathrm{r}^{2}}πr23 V​ 
C)    13(Vπr2) \frac{1}{3}\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl) 31​(πr2V​)  
D)    V13πr2\frac{\mathrm{V}}{\frac{1}{3} \pi \mathrm{r}^{2}}31​πr2V​

Question 9

Each of six decorators has to paint a room (walls only)  and put a wallpaper border around the room at the ceiling. One gallon of paint covers  400sqft400 \mathrm{sq} \mathrm{ft}400sqft , and one roll of border contains five yards. Each decorator has one gallon of paint and three rolls of border.
-The list gives the name of each decorator and the size of the room.

Give the names of the decorators who will not have enough paint, but will have enough border for their rooms. (Assume a ceiling height of 8 ' for each room.)

Accepted Answer

A)    {\{{  Mary, Roger  }\}} 
B)    {\{{  Irina, Sergey }\}} 
C)    {\{{  Juanita, Jose  }\}} 
D)   None

Question 10

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
- 5(2f−31) =10f−1555(2 \mathrm{f}-31) =10 \mathrm{f}-1555(2f−31) =10f−155

Accepted Answer

A)   Conditional;  {0}\{0\}{0} 
B)   Contradiction;  ∅\varnothing∅ 
C)   Identity; {all real numbers}
D)   Identity;  ∅\varnothing∅

Question 11

Solve the equation.
- r+65=r+87\frac{r+6}{5}=\frac{r+8}{7}5r+6​=7r+8​

Accepted Answer

A)    {−1}\{-1\}{−1} 
B)    {1}\{1\}{1} 
C)    {2}\{2\}{2} 
D)    {−2}\{-2\}{−2}

Question 12

For the compound inequality, decide whether intersection or union should be used. Then give the solution set in both interval and graph forms.
- x≥−9x \geq-9x≥−9  and  x<−4x<-4x<−4

Accepted Answer

A)   Intersection;  [−9,−4) [-9,-4) [−9,−4)  
B)   Union;  (−∞,∞) (-\infty, \infty) (−∞,∞)  
C)   Intersection;  (−9,∞) (-9, \infty) (−9,∞)  
D)   Intersection;  ∅\varnothing∅

Question 13

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$. Is this an acceptable solution? Explain.

Accepted Answer

No. The variable r s...

Question 14

Express the set in the simplest interval form.
- (−7,4) ∪[0,9](-7,4)  \cup[0,9](−7,4) ∪[0,9]

Accepted Answer

A)    (−7,9](-7,9](−7,9] 
B)    (−7,4) (-7,4) (−7,4)  
C)    [0,9][0,9][0,9] 
D)    [0,4) [0,4) [0,4)

Question 15

Use the variable  xxx  for the unknown, and write an equation representing the verbal sentence. Then solve the problem.
-When  14\frac{1}{4}41​  of a number is added to 20 , the result is 29 .

Accepted Answer

A)    14x−20=29;196\frac{1}{4} x-20=29 ; 19641​x−20=29;196 
B)    29+14x=20;3629+\frac{1}{4} \mathrm{x}=20 ; 3629+41​x=20;36 
C)    14+x=29;29\frac{1}{4}+x=29 ; 2941​+x=29;29 
D)    20+14x=29;3620+\frac{1}{4} x=29 ; 3620+41​x=29;36

Question 16

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation.
- ∣0.5x−5.3∣+0.2≥0.8|0.5 x-5.3|+0.2 \geq 0.8∣0.5x−5.3∣+0.2≥0.8

Accepted Answer

A)    (−∞,9.4]∪[11.8,∞) (-\infty, 9.4] \cup[11.8, \infty) (−∞,9.4]∪[11.8,∞)  
B)    (−∞,9.4]∩[11.8,∞) (-\infty, 9.4] \cap[11.8, \infty) (−∞,9.4]∩[11.8,∞)  
C)    (9.4,11.8) (9.4,11.8) (9.4,11.8)  
D)    {9.4,11.8}\{9.4,11.8\}{9.4,11.8}

Question 17

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$

Accepted Answer

A) True 
 B)False

Question 18

Solve the problem.
-Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Accepted Answer

A)   3.5 kilometers per hour
B)   2 kilometers per hour
C)   3 kilometers per hour
D)   4 kilometers per hour

Question 19

Solve the inequality. Give the solution set in both interval and graph forms.
- 7x−49<677\frac{7 x-4}{9}<\frac{67}{7}97x−4​<767​

Accepted Answer

A)    (677,∞)  \left(\frac{67}{7}, \infty\right)  (767​,∞)  
B)    (−∞,63149)  \left(-\infty, \frac{631}{49}\right)  (−∞,49631​)  
C)    (63149,∞)  \left(\frac{631}{49}, \infty\right)  (49631​,∞)   
D)    (−∞,677)  \left(-\infty, \frac{67}{7}\right)  (−∞,767​)

Question 20

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
- 2[3−(2−5r) ]−r=−4+3(2+3r) 2[3-(2-5 r) ]-r=-4+3(2+3 r) 2[3−(2−5r) ]−r=−4+3(2+3r)

Accepted Answer

A)   Identity; {all real numbers}
B)   Conditional;  {4}\{4\}{4} 
C)   Contradiction;  ∅\varnothing∅ 
D)   Conditional;  {−2}\{-2\}{−2}

Exam 2: Linear Equations, Inequalities, and Applications

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

Correct Answer
verified

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When $\frac{1}{4}$ of a number is added to 20 , the result is 29 .

Correct Answer
verified

Correct Answer
verified

Express the set in the simplest interval form. - $(-7,4) \cup[0,9]$

Correct Answer
verified

Solve the problem. -A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

Correct Answer
verified

Correct Answer
verified

Which of the following is not a correct answer when the formula $V=\frac{1}{3} \pi r^{2} h$ is solved for $h$ ?

Correct Answer
verified

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$ . Is this an acceptable solution? Explain.

Correct Answer
verified
No. The variable r s...
View Answer

Correct Answer
verified

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - $|0.5 x-5.3|+0.2 \geq 0.8$

Correct Answer
verified

Solve the problem. -Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Correct Answer
verified

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $2[3-(2-5 r) ]-r=-4+3(2+3 r)$

Correct Answer
verified

Solve the inequality and graph the solution set. - $|x| \leq 7$ $Solve the inequality and graph the solution set. - |x| \leq 7 A) [-7,7] B) (-\infty, 7] C) (-\infty,-7] \cup[7, \infty) D) (-\infty,-7]$

Correct Answer
verified

Express the set in the simplest interval form. - $(-4,6] \cap(-2, \infty)$

Correct Answer
verified

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$

Correct Answer
verified

Provide an appropriate response. -Determine which of the following is used to solve the inequality $|a x+b|>c$ , for $c>0$ .

Correct Answer
verified

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$ . How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Correct Answer
verified

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $5(2 \mathrm{f}-31) =10 \mathrm{f}-155$

Correct Answer
verified

Solve the equation. - $\frac{r+6}{5}=\frac{r+8}{7}$

Correct Answer
verified

Solve the problem. -What is the area of a square with side $2.2 \mathrm{~cm}$ ?

Correct Answer
verified

Exam 2: Linear Equations, Inequalities, and Applications

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 12k+186=4(3k+45) 12 \mathrm{k}+186=4(3 \mathrm{k}+45) 12k+186=4(3k+45)

Correct AnswerverifiedShow Answer

Use the variable xxx for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When 14\frac{1}{4}41​ of a number is added to 20 , the result is 29 .

Correct AnswerverifiedShow Answer

Solve the inequality. Give the solution set in both interval and graph forms. - 7x−49<677\frac{7 x-4}{9}<\frac{67}{7}97x−4​<767​

Correct AnswerverifiedShow Answer

Express the set in the simplest interval form. - (−7,4) ∪[0,9](-7,4) \cup[0,9](−7,4) ∪[0,9]

Correct AnswerverifiedShow Answer

Solve the problem. -A chemical solution contains 8%8 \%8% salt. How much salt is in 4ml4 \mathrm{ml}4ml of solution? Round your answer to three decimal places, if necessary.

Correct AnswerverifiedShow Answer

For the compound inequality, decide whether intersection or union should be used. Then give the solution set in both interval and graph forms. - x≥−9x \geq-9x≥−9 and x<−4x<-4x<−4

Correct AnswerverifiedShow Answer

Which of the following is not a correct answer when the formula V=13πr2hV=\frac{1}{3} \pi r^{2} hV=31​πr2h is solved for hhh ?

Correct AnswerverifiedShow Answer

Suppose the formula A=2πrh+2πr2A=2 \pi r h+2 \pi r^{2}A=2πrh+2πr2 is solved for rrr with the following result: r=r=r= A2πh+2πr\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}2πh+2πrA​ . Is this an acceptable solution? Explain.

Correct AnswerverifiedNo. The variable r s...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - ∣0.5x−5.3∣+0.2≥0.8|0.5 x-5.3|+0.2 \geq 0.8∣0.5x−5.3∣+0.2≥0.8

Correct AnswerverifiedShow Answer

Solve the problem. -Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Correct AnswerverifiedShow Answer

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 2[3−(2−5r) ]−r=−4+3(2+3r) 2[3-(2-5 r) ]-r=-4+3(2+3 r) 2[3−(2−5r) ]−r=−4+3(2+3r)

Correct AnswerverifiedShow Answer

Solve the inequality and graph the solution set. - ∣x∣≤7|x| \leq 7∣x∣≤7

Correct AnswerverifiedShow Answer

Express the set in the simplest interval form. - (−4,6]∩(−2,∞) (-4,6] \cap(-2, \infty) (−4,6]∩(−2,∞)

Correct AnswerverifiedShow Answer

The union of the sets (−∞,23](-\infty, 23](−∞,23] and (23,∞)(23, \infty)(23,∞) is (−∞,∞)(-\infty, \infty)(−∞,∞)

Correct AnswerverifiedShow Answer

Provide an appropriate response. -Determine which of the following is used to solve the inequality ∣ax+b∣>c|a x+b|>c∣ax+b∣>c , for c>0c>0c>0 .

Correct AnswerverifiedShow Answer

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $253,000\$ 253,000$253,000 . How many people paid $11.00\$ 11.00$11.00 for reserved seats and how many paid $5.00\$ 5.00$5.00 for general admission?

Correct AnswerverifiedShow Answer

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 5(2f−31) =10f−1555(2 \mathrm{f}-31) =10 \mathrm{f}-1555(2f−31) =10f−155

Correct AnswerverifiedShow Answer

Solve the equation. - r+65=r+87\frac{r+6}{5}=\frac{r+8}{7}5r+6​=7r+8​

Correct AnswerverifiedShow Answer

Solve the problem. -What is the area of a square with side 2.2 cm2.2 \mathrm{~cm}2.2 cm ?

Correct AnswerverifiedShow Answer

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

Correct Answer
verified

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When $\frac{1}{4}$ of a number is added to 20 , the result is 29 .

Correct Answer
verified

Correct Answer
verified

Express the set in the simplest interval form. - $(-7,4) \cup[0,9]$

Correct Answer
verified

Solve the problem. -A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

Correct Answer
verified

Correct Answer
verified

Which of the following is not a correct answer when the formula $V=\frac{1}{3} \pi r^{2} h$ is solved for $h$ ?

Correct Answer
verified

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$ . Is this an acceptable solution? Explain.

Correct Answer
verified
No. The variable r s...
View Answer

Correct Answer
verified

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - $|0.5 x-5.3|+0.2 \geq 0.8$

Correct Answer
verified

Correct Answer
verified

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $2[3-(2-5 r) ]-r=-4+3(2+3 r)$

Correct Answer
verified

Solve the inequality and graph the solution set. - $|x| \leq 7$ $Solve the inequality and graph the solution set. - |x| \leq 7 A) [-7,7] B) (-\infty, 7] C) (-\infty,-7] \cup[7, \infty) D) (-\infty,-7]$

Correct Answer
verified

Express the set in the simplest interval form. - $(-4,6] \cap(-2, \infty)$

Correct Answer
verified

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$

Correct Answer
verified

Provide an appropriate response. -Determine which of the following is used to solve the inequality $|a x+b|>c$ , for $c>0$ .

Correct Answer
verified

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$ . How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Correct Answer
verified

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $5(2 \mathrm{f}-31) =10 \mathrm{f}-155$

Correct Answer
verified

Solve the equation. - $\frac{r+6}{5}=\frac{r+8}{7}$

Correct Answer
verified

Solve the problem. -What is the area of a square with side $2.2 \mathrm{~cm}$ ?

Correct Answer
verified