Question 1

Find the indicated intersection or union.
-$\{ q , s , u , v , w , x , y , z \} \cap \{ q , s , y , z \}$

Accepted Answer

The intersection of two sets includes only the elements that are present in both sets. In this case, $\{ q , s , y , z \}$ are the elements common to both sets, making option D correct.

Question 2

Find the indicated intersection or union.
-$\{ 2,9,14,15,22 \} \cap \{ 9,15,22,27 \}$

Accepted Answer

The intersection of two sets includes only the elements that are present in both sets. Here, $\{ 9,15,22 \}$ are the elements common to both sets.

Question 3

Solve.
-In order for a chemical reaction to remain stable, its Celsius temperature $\mathrm { C }$ must be no more than $126.25 ^ { \circ } \mathrm { C }$. At what Fahrenheit temperatures $\mathrm { F }$ will the reaction remain stable. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Accepted Answer

To find the Fahrenheit temperature at which the reaction remains stable, we use the given formula $F = \frac{9}{5}C + 32$ with $C = 126.25$. Plugging in the values, we get $F = \frac{9}{5} \times 126.25 + 32 = 259.25$. Since the Celsius temperature must be no more than $126.25^\circ C$, the Fahrenheit temperature must be less than or equal to $259.25^\circ F$.

Question 4

Solve.
-A salesperson has two job offers. Company A offers a weekly salary of $560 plus commission of 16% of sales. Company B offers a weekly salary of $1120 plus commission of 8% of sales. What is the amount of sales above
Which Company A's offer is the better of the two?

Accepted Answer

For Company A, the total earnings (E_A) can be represented as E_A = 560 + 0.16S, where S is the sales amount. For Company B, the total earnings (E_B) can be represented as E_B = 1120 + 0.08S. To find the point where Company A's offer becomes better, we set E_A > E_B, leading to 560 + 0.16S > 1120 + 0.08S. Simplifying this, we get 0.08S > 560, and solving for S gives S > 7000. Therefore, Company A's offer is better for sales amounts above $7000.

Question 5

Solve.
-$$\frac { 1 } { 4 } ( 12 x + 40 ) - 48 > - \frac { 1 } { 3 } ( 6 x - 21 )$$

Accepted Answer

The answer of Solve.
-\[\frac { 1 } { 4 }...

Question 6

Find the indicated intersection or union.
-$\{ q , s , u , v , w , x , y , z \} \cap \{ s \}$

Accepted Answer

The intersection of two sets includes only the elements that are present in both sets. Since $s$ is the only element present in both given sets, the intersection is $\{ s \}$.

Question 7

Solve.
-In order for a chemical reaction to take place, the Fahrenheit temperature $F$ of the reagents must be at least $151.81 ^ { \circ } \mathrm { F }$. At what Celsius temperatures $\mathrm { C }$ will the reaction occur? $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Accepted Answer

To find the Celsius temperature at which the reaction occurs, we use the given Fahrenheit to Celsius conversion formula $F = \frac{9}{5}C + 32$. Setting $F = 151.81$, we solve for $C$: $151.81 = \frac{9}{5}C + 32$. Rearranging and solving for $C$ gives $C \geq 66.56 ^{\circ}$.

Question 8

Solve.
-$$\frac { 1 } { 2 } ( x - 2 ) > \frac { 1 } { 6 } ( 7 x - 5 )$$

Accepted Answer

The answer of Solve.
-\[\frac { 1 } { 2 }...

Question 9

Find the indicated intersection or union.
-$\{ 3,8,13,18 \} \cup \{ 8,18,20,28 \}$

Accepted Answer

The union of two sets includes all the elements from both sets, without duplicates. Therefore, combining $\{ 3,8,13,18 \}$ and $\{ 8,18,20,28 \}$ gives $\{ 3,8,13,18,20,28 \}$.

Question 10

Solve.
-$$\frac { 5 } { 2 } ( 4 x - 5 ) > 35$$

Accepted Answer

First, distribute the $\frac{5}{2}$ to get $10x - \frac{25}{2} > 35$. Add $\frac{25}{2}$ to both sides to get $10x > \frac{95}{2}$. Divide by 10 to get $x > \frac{19}{4}$.

Question 11

Solve.
-Photography reprints cost $0.52 each at a local photo shop. Through the mail, they cost $0.44 each plus $1.20 postage and handling. How many reprints must a customer purchase to make it less expensive to use mail
Order?

Accepted Answer

For the local photo shop, the cost is $0.52 per reprint. For mail order, the cost is $0.44 per reprint plus $1.20 for postage and handling. To find the break-even point, set the two costs equal: $0.52n = $0.44n + $1.20. Solving for n gives n > 15, meaning after 15 reprints, mail order becomes cheaper.

Question 12

Find the indicated intersection or union.
-$\{ q , s , u , v , w , x , y , z \} \cup \{ q , s , y , z \}$

Accepted Answer

The union of two sets combines all unique elements from both sets, so all elements from both sets are included in the result.

Question 13

Solve.
-The equation y = 0.002x - 0.30 can be used to determine the profit y, in dollars, of producing x items. How many items x must be produced so the profit will be at least $3075?

Accepted Answer

To find the number of items x for a profit of at least $3075, solve the inequality 0.002x - 0.30 ≥ 3075. Solving gives x ≥ 1,537,650.

Question 14

Solve.
-Company A rents copiers for a monthly charge of $120 plus 8 cents per copy. Company B rents copiers for a monthly charge of $240 plus 4 cents per copy. What is the number of copies above which Company A's charges
Are the higher of the two?

Accepted Answer

To find the number of copies above which Company A's charges are higher, we set up an equation to compare the costs of both companies. Let $x$ be the number of copies.For Company A: $120 + 0.08x$For Company B: $240 + 0.04x$We want to find when Company A is more expensive, so we set $120 + 0.08x > 240 + 0.04x$. Solving for $x$, we subtract $0.04x$ from both sides and subtract 120 from both sides to get $0.04x > 120$. Dividing both sides by 0.04, we find $x > 3000$. Therefore, above 3000 copies, Company A's charges are higher.

Question 15

Solve.
-$$0.2 ( 4 x - 3 ) < 1.5 - ( x + 4 )$$

Accepted Answer

The answer of Solve.
-\[0.2 ( 4 x - 3 )...

Question 16

Solve.
-$$\frac { 1 } { 21 } ( 3 x + 2 ) \leq - \frac { 1 } { 3 } + \frac { 1 } { 7 } ( 3 x + 1 )$$

Accepted Answer

The answer of Solve.
-\[\frac { 1 } { 21 }...

Question 17

Solve.
-$$- 3 ( 2 x + 3 ) \geq 2 [ 4 x - 3 ( x - 2 ) ]$$

Accepted Answer

The answer of Solve.
-\[- 3 ( 2 x + 3...

Question 18

Solve.
-$$3 ( 4 x + 1 ) < 7 - 5 ( 4 x - 3 )$$

Accepted Answer

The answer of Solve.
-\[3 ( 4 x + 1 )...

Question 19

Solve.
-Jon has 1101 points in his math class. He must have 84% of the 1500 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the
Term to receive credit for the class?

Accepted Answer

To receive credit, Jon needs 84% of 1500 points, which is 0.84 * 1500 = 1260 points. He already has 1101 points, so he needs 1260 - 1101 = 159 more points.

Question 20

Solve.
-$$22 - ( 3 x + 2 ) \leq 4 ( x - 4 ) + 5 x$$

Accepted Answer

The answer of Solve.
-\[22 - ( 3 x + 2...

Quiz 9: More on Inequalities

Find the indicated intersection or union. - $\{ q , s , u , v , w , x , y , z \} \cap \{ q , s , y , z \}$

Find the indicated intersection or union. - $\{ 2,9,14,15,22 \} \cap \{ 9,15,22,27 \}$

Solve. -A salesperson has two job offers. Company A offers a weekly salary of $560 plus commission of 16% of sales. Company B offers a weekly salary of $1120 plus commission of 8% of sales. What is the amount of sales above Which Company A's offer is the better of the two?

Solve. - $\frac { 1 } { 4 } ( 12 x + 40 ) - 48 > - \frac { 1 } { 3 } ( 6 x - 21 )$

Find the indicated intersection or union. - $\{ q , s , u , v , w , x , y , z \} \cap \{ s \}$

Solve. -In order for a chemical reaction to take place, the Fahrenheit temperature $F$ of the reagents must be at least $151.81 ^ { \circ } \mathrm { F }$ . At what Celsius temperatures $\mathrm { C }$ will the reaction occur? $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Solve. - $\frac { 1 } { 2 } ( x - 2 ) > \frac { 1 } { 6 } ( 7 x - 5 )$

Find the indicated intersection or union. - $\{ 3,8,13,18 \} \cup \{ 8,18,20,28 \}$

Solve. - $\frac { 5 } { 2 } ( 4 x - 5 ) > 35$

Solve. -Photography reprints cost $0.52 each at a local photo shop. Through the mail, they cost $0.44 each plus $1.20 postage and handling. How many reprints must a customer purchase to make it less expensive to use mail Order?

Find the indicated intersection or union. - $\{ q , s , u , v , w , x , y , z \} \cup \{ q , s , y , z \}$

Solve. -The equation y = 0.002x - 0.30 can be used to determine the profit y, in dollars, of producing x items. How many items x must be produced so the profit will be at least $3075?

Solve. -Company A rents copiers for a monthly charge of $120 plus 8 cents per copy. Company B rents copiers for a monthly charge of $240 plus 4 cents per copy. What is the number of copies above which Company A's charges Are the higher of the two?

Solve. - $0.2 ( 4 x - 3 ) < 1.5 - ( x + 4 )$

Solve. - $\frac { 1 } { 21 } ( 3 x + 2 ) \leq - \frac { 1 } { 3 } + \frac { 1 } { 7 } ( 3 x + 1 )$

Solve. - $- 3 ( 2 x + 3 ) \geq 2 [ 4 x - 3 ( x - 2 ) ]$

Solve. - $3 ( 4 x + 1 ) < 7 - 5 ( 4 x - 3 )$

Solve. -Jon has 1101 points in his math class. He must have 84% of the 1500 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the Term to receive credit for the class?

Solve. - $22 - ( 3 x + 2 ) \leq 4 ( x - 4 ) + 5 x$

Quiz 9: More on Inequalities

Find the indicated intersection or union. - {q,s,u,v,w,x,y,z}∩{q,s,y,z}\{ q , s , u , v , w , x , y , z \} \cap \{ q , s , y , z \}{q,s,u,v,w,x,y,z}∩{q,s,y,z}

Find the indicated intersection or union. - {2,9,14,15,22}∩{9,15,22,27}\{ 2,9,14,15,22 \} \cap \{ 9,15,22,27 \}{2,9,14,15,22}∩{9,15,22,27}

Solve. -A salesperson has two job offers. Company A offers a weekly salary of $560 plus commission of 16% of sales. Company B offers a weekly salary of $1120 plus commission of 8% of sales. What is the amount of sales above Which Company A's offer is the better of the two?

Solve. - 14(12x+40) −48>−13(6x−21) \frac { 1 } { 4 } ( 12 x + 40 ) - 48 > - \frac { 1 } { 3 } ( 6 x - 21 ) 41​(12x+40) −48>−31​(6x−21)

Find the indicated intersection or union. - {q,s,u,v,w,x,y,z}∩{s}\{ q , s , u , v , w , x , y , z \} \cap \{ s \}{q,s,u,v,w,x,y,z}∩{s}

Solve. - 12(x−2) >16(7x−5) \frac { 1 } { 2 } ( x - 2 ) > \frac { 1 } { 6 } ( 7 x - 5 ) 21​(x−2) >61​(7x−5)

Find the indicated intersection or union. - {3,8,13,18}∪{8,18,20,28}\{ 3,8,13,18 \} \cup \{ 8,18,20,28 \}{3,8,13,18}∪{8,18,20,28}

Solve. - 52(4x−5) >35\frac { 5 } { 2 } ( 4 x - 5 ) > 3525​(4x−5) >35