11. volume of a cylinder: ( r = 3 mathrm{cm}, h = 8 mathrm{cm} ) (use ( pi = 3.14 ))\n12. surface area of a…

11. volume of a cylinder: ( r = 3 mathrm{cm}, h = 8 mathrm{cm} ) (use ( pi = 3.14 ))\n12. surface area of a rectangular prism: ( 3 \times 4 \times 2 )\n13. write an expression for: \ten more than triple a number\\n14. what is ( 40% ) of ( 90? )\n15. a ( $ 120 ) jacket is marked down ( 20% ). what is the sale price?\n16. find the slope of the line through ( (2,1) ) and ( (4,5) )\n17. graph the inequality: ( x>-2 )\n18. what is the probability of flipping a head on a coin?\n19. convert ( 0.6 ) to a fraction in simplest form.\n20. a jar has 2 blue, 3 green, 5 red marbles. what is the probability of pulling a green marble?

11. volume of a cylinder: ( r = 3 mathrm{cm}, h = 8 mathrm{cm} ) (use ( pi = 3.14 ))\n12. surface area of a rectangular prism: ( 3 \times 4 \times 2 )\n13. write an expression for: \ten more than triple a number\\n14. what is ( 40% ) of ( 90? )\n15. a ( $ 120 ) jacket is marked down ( 20% ). what is the sale price?\n16. find the slope of the line through ( (2,1) ) and ( (4,5) )\n17. graph the inequality: ( x>-2 )\n18. what is the probability of flipping a head on a coin?\n19. convert ( 0.6 ) to a fraction in simplest form.\n20. a jar has 2 blue, 3 green, 5 red marbles. what is the probability of pulling a green marble?

Answer

Explanation:

Step1: Volume of a cylinder

The formula for the volume of a cylinder is (V=\pi r^{2}h). Given (r = 3) cm, (h=8) cm and (\pi = 3.14). [ \begin{align*} V&=3.14\times3^{2}\times8\ &=3.14\times9\times8\ &=3.14\times72\ & = 226.08\text{ cm}^3 \end{align*} ]

Step2: Surface area of a rectangular prism

The formula for the surface area of a rectangular prism (S = 2(lw+lh + wh)). Given (l = 3), (w = 4), (h=2) [ \begin{align*} S&=2(3\times4+3\times2+4\times2)\ &=2(12 + 6+8)\ &=2\times26\ &=52 \end{align*} ]

Step3: Expression for "Ten more than triple a number"

Let the number be (x). Triple the number is (3x). Ten more than that is (3x + 10)

Step4: 40% of 90

To find a percentage (p%) of a number (n), use the formula (\frac{p}{100}\times n). Here (p = 40), (n=90) [ \frac{40}{100}\times90=0.4\times90 = 36 ]

Step5: Sale price of the jacket

The markdown is (20%) of (120). The amount of markdown is (\frac{20}{100}\times120=24). The sale price (=120-24 = 96)

Step6: Slope of the line

The slope formula (m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}). Given ((x_{1},y_{1})=(2,1)) and ((x_{2},y_{2})=(4,5)) [ m=\frac{5 - 1}{4-2}=\frac{4}{2}=2 ]

Step7: Graph of (x>-2)

On a number line, draw an open circle at (-2) and shade to the right.

Step8: Probability of flipping a head

A coin has 2 outcomes ((n = 2): head or tail). Flipping a head ((m = 1)). Probability (P=\frac{m}{n}=\frac{1}{2})

Step9: Convert (0.6) to a fraction

(0.6=\frac{6}{10}=\frac{3}{5})

Step10: Probability of pulling a green marble

Total number of marbles (n=2 + 3+5=10). Number of green marbles (m = 3). Probability (P=\frac{m}{n}=\frac{3}{10})

Answer:

  1. (226.08\text{ cm}^3)
  2. (52)
  3. (3x + 10)
  4. (36)
  5. ($96)
  6. (2)
  7. Open circle at (-2), shade right on number - line
  8. (\frac{1}{2})
  9. (\frac{3}{5})
  10. (\frac{3}{10})