write equations to solve problems 13 and 14. 13. the store owner makes a profit of 40% of the selling price…

write equations to solve problems 13 and 14. 13. the store owner makes a profit of 40% of the selling price of an item. if an item sells for $12, how much profit does the store owner make? 14. analyze fifty percent of what number is 0.4? 15. simplify: 16 2/3 / 100 use ratio boxes to solve problems 16 and 17. 16. justify in a restaurant, 21 of the 25 tables are round. what percent of the tables are round? tell what you did to find out. 17. twenty percent of the 4000 acres were plowed. how many acres were not plowed? 18. if the measure of ∠abc is 140°, then a. what is the measure of ∠cbd? how do you know? b. what is the measure of ∠dbe? how do you know? c. what is the measure of ∠eba? how do you know? d. what is the sum of the measures of ∠abc, ∠cbd, ∠dbe, and ∠eba? 19. write the prime factorization of the two terms of this fraction. then reduce the fraction. 3000/6300 20. a. find the area of this isosceles trapezoid. dimensions are in inches. b. trace the trapezoid on your paper. then draw its line of symmetry. 21. write the rule of this function with words and as an equation. then find the missing number. x y -1 -3 3 5 4 7 6 11 0

write equations to solve problems 13 and 14. 13. the store owner makes a profit of 40% of the selling price of an item. if an item sells for $12, how much profit does the store owner make? 14. analyze fifty percent of what number is 0.4? 15. simplify: 16 2/3 / 100 use ratio boxes to solve problems 16 and 17. 16. justify in a restaurant, 21 of the 25 tables are round. what percent of the tables are round? tell what you did to find out. 17. twenty percent of the 4000 acres were plowed. how many acres were not plowed? 18. if the measure of ∠abc is 140°, then a. what is the measure of ∠cbd? how do you know? b. what is the measure of ∠dbe? how do you know? c. what is the measure of ∠eba? how do you know? d. what is the sum of the measures of ∠abc, ∠cbd, ∠dbe, and ∠eba? 19. write the prime factorization of the two terms of this fraction. then reduce the fraction. 3000/6300 20. a. find the area of this isosceles trapezoid. dimensions are in inches. b. trace the trapezoid on your paper. then draw its line of symmetry. 21. write the rule of this function with words and as an equation. then find the missing number. x y -1 -3 3 5 4 7 6 11 0

Answer

Explanation:

Step1: Solve problem 13

The profit is 40% of the selling - price. The selling price is $12. So the profit $P = 0.4\times12$. $P=0.4\times12 = 4.8$

Step2: Solve problem 14

Let the number be $x$. We know that $50%$ (or 0.5) of $x$ is 0.4. So the equation is $0.5x = 0.4$. Solving for $x$, we get $x=\frac{0.4}{0.5}=0.8$.

Step3: Solve problem 15

$16\frac{2}{3}=\frac{16\times3 + 2}{3}=\frac{50}{3}$. Then $\frac{16\frac{2}{3}}{100}=\frac{\frac{50}{3}}{100}=\frac{50}{3}\times\frac{1}{100}=\frac{1}{6}$.

Step4: Solve problem 16

To find the percentage of round tables, we use the formula $\text{Percentage}=\frac{\text{Number of round tables}}{\text{Total number of tables}}\times100%$. Here, the number of round tables is 21 and the total number of tables is 25. So $\text{Percentage}=\frac{21}{25}\times100% = 84%$.

Step5: Solve problem 17

If 20% of 4000 acres were plowed, then the number of plowed acres is $0.2\times4000 = 800$ acres. The number of un - plowed acres is $4000-800=3200$ acres.

Step6: Solve problem 18

a. If $\angle ABC = 140^{\circ}$ and $\angle ABC+\angle CBD = 180^{\circ}$ (linear pair), then $\angle CBD=180 - 140=40^{\circ}$. b. As above, $\angle CBD = 40^{\circ}$ because it forms a linear pair with $\angle ABC$. c. If we assume $\angle DBE = 90^{\circ}$ (since no other information is given and it looks like a right - angle from the diagram), then $\angle DBE = 90^{\circ}$. d. $\angle EBA+\angle ABC+\angle CBD+\angle DBE=360^{\circ}$ because they are angles around a point.

Step7: Solve problem 19

Prime - factorize 3000: $3000 = 2^{3}\times3\times5^{3}$. Prime - factorize 6300: $6300=2^{2}\times3^{2}\times5^{2}\times7$. Then $\frac{3000}{6300}=\frac{2^{3}\times3\times5^{3}}{2^{2}\times3^{2}\times5^{2}\times7}=\frac{2\times5}{3\times7}=\frac{10}{21}$.

Step8: Solve problem 20

a. The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 10$, $b = 20$, and $h = 12$. So $A=\frac{(10 + 20)\times12}{2}=180$ square inches. b. The line of symmetry of an isosceles trapezoid is the vertical line that passes through the mid - points of the non - parallel sides.

Step9: Solve problem 21

The rule in words: "Multiply the input $x$ by 2 and then subtract 1 to get the output $y$". The equation is $y = 2x-1$. When $x = 0$, $y=2\times0 - 1=-1$.

Answer:

  1. $4.8$
  2. $0.8$
  3. $\frac{1}{6}$
  4. $84%$
  5. 3200 acres
  6. a. $40^{\circ}$; linear pair with $\angle ABC$. b. $40^{\circ}$; linear pair with $\angle ABC$. c. $90^{\circ}$ (assumed from diagram). d. $360^{\circ}$; angles around a point.
  7. $\frac{10}{21}$
  8. a. 180 square inches. b. Vertical line through mid - points of non - parallel sides.
  9. Rule in words: Multiply the input $x$ by 2 and then subtract 1 to get the output $y$. Equation: $y = 2x-1$. Missing number: $-1$