Hi there hopefully this helps!
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Answer: C.
Explanation:
A New Leash On Life's Graph has: 3, 11, 21, 13, and 4.
The mean: 10.4
No Ruff Stuff's graph has: 1, 9, 16, 16, 8, 1, and 1.
The mean: 7.43.
Answer:
The answer to the given problem is given below.
Step-by-step explanation:
What values do p, q,n,E and p represents?
The value of p is the sample proportion.
The value of q is found from evaluating 1− p.
The value of n is the sample size.
The value of E is the margin of error.
The value of p is the population proportion.
If the confidence level is 90%, what is the value of α?
α = 1- 0.90
α = 0.10
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:
The reference angle is 
Step-by-step explanation:
The given angle is
The reference angle is the acute angle, that a given angle makes with the x-axis.
First let us make a sketch of the given angle. <em>See diagram in attachment.</em>
Let
be the reference angle of 
Then, from the diagram, we need to subtract
from
to get to
.
We can therefore write the following equation and solve for
.

We group like terms to get,

We collect LCM to get,

We simplify to get,

We divide through by 
to get,
The correct answer is D.