Q) Help With Math Homework!!?

Question

5.The sales tax in a state is 8%. Write an equation for the amount of tax t on an item that costs p dollars.
6.An airplane is traveling at 550 miles per hour. Write an equation for the distance d the lane travels in h hours.
7.Potatoes sell for $0.25 at the produce market. Write an equation for the cost of c of p pounds of potatoes.
8.A cellular family phone plan costs $49 per month plus $0.05 per minute of long-distance service. Write an equation for the monthly bill when m minutes of long-distance service are used
9.The wheels on Kai's bike are 27 inches in diameter. His little sister, Masako, has a bike with wheels that are 20 inches in diameter. Kai and Masako are on a bike ride
A.How far does Kai go in one complete turn of her wheels
B.How far does Masako go in one complete turn of her wheels?

C.How far does Kai go in 500 turns of his wheels?
d.How far does Masako go in 500 turns of her wheel?
e.How many times do Kai's wheels have to turn to cover 100 feet?
f.How many times do Masako's wheels have to turn to cover 1000 feet? To cover 1 mile?
Thanks!!!

Answer 1

5.     t = p × 8 /100

        t = p  × 0.08

6.    d = velocity × time

      d = 550 × h

7.    c = p × $0.25

8.   A cellular family phone plan costs per month  is $49

      Long distance service per one month per m minutes is  m × $0.05

      Let B is the monthly bill when m minutes of long-distance service are used

      So, the monthly bill is   B = $49 + m × $0.05

    

Answer 2

9) Let the diameter of Kali's bike wheel be d₁ = 27 inches.

Let the diameter of Masako's bike wheel be d₂ = 20 inches.

A) One complete turn means, one rotation i.e., circumference of the wheel.

The circumference is the distance around the outside of the circle. It is also called the perimeter of the circle.

It can be found by multiplying π (3.14) by the diameter of the circle.

Therefore circumference of the circle is πd.

Therefore one complete turn of Kali's wheels can move a distance of 3.14 * 27 = 84.78 inches.

B) One complete turn of Masako's wheels can move a distance of 3.14 * 20 = 62.8 inches.

C) In 500 turns Kali's wheels can move a distance of 500 * 84.78  = 42390 inches.

D) In 500 turns Masako's wheels can move a distance of 500 * 62.8 = 31400 inches.

E) For 1 turn, distance covered = 84.78 inches.

1 inch = 1 / 84.78 turns.

1 feet = 12 inches = 12*(1/84.78) turns = 0.14 turns.

100 feet = 100 * (0.14) = 14 turns.

Therefore, the Kali's wheels had turned 14 times to cover 100 inches.

F) For 1 turn, distance covered = 62.8 inches.

1 inch = 1 / 62.8 turns.

1 feet = 12 inches = 12*(1/62.8) turns = 0.19 turns.

1000 feet = 1000 * (0.19) = 190 turns.

Therefore, the Masako's wheels had turned 190 times to cover 1000 inches.

1 mile = 5280 feet.

= 5280 * (0.19) turns

= 1003.2 turns

Therefore, the Masako's wheels had turned 1003 times to cover 1 mile.