Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
Answer:
3 different choices
Step-by-step explanation:
This problem is a combination problem: She has 3 friends, and we want to know how many groups of 2 friends there are. We can solve this using the combination of 3 choose 2:
C(3,2) = 3!(1! * 2!) = 3*2/2 = 3 possibilities
If we call her three friends A, B and C, the groups that can be formed are:
A and B
A and C
B and C
The function is given by
y=45,200 + 1,900x
and is of the form y = mx+b , where m is the rate of change and b is the fixed value ( or we can say initial value)
Now when we compare we get m = 1,900 for our problem .
So the population increases every year by 1,900.
