The confidence interval would be (10.44, 12.16). This means that if we take repeated samples, the true mean lies in 90% of these intervals.
To find the confidence interval, we use:
We first find the z-value associated with this. To do this:
Convert 90% to a decimal: 90% = 90/100 = 0.9
Subtract from 1: 1-0.9 = 0.1
Divide by 2: 0.1/2 = 0.05
Subtract from 1: 1-0.05 = 0.95
Using a z-table (http://www.z-table.com) we see that this is directly between two z-scores, 1.64 and 1.65; we will use 1.645:
MOE = +\- 1.27
The 99% confidence interval ranges from 53.73 to 56.27 hours.
Answer:
p = 4
Step-by-step explanation:
The usually recommended procedure for solving a proportion is to "cross multiply", then divide by the coefficient of the variable. (Solve the remaining one-step equation.)
<h3>Cross multiply</h3>
This means multiply both sides of the equation by the product of the denominators:
(15/6)(6p) = (10/p)(6p) . . . . "cross multiply"
15p = 60 . . . . . . simplify
<h3>Second step</h3>
Now, divide by the coefficient of the variable.
15p/15 = 60/15
p = 4
The solution is p = 4.
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<em>Additional comment</em>
If the variable is in the <em>numerator</em> of the proportion, using cross multiplication, you will find that you end up multiplying and dividing by the other denominator. To solve it in that case, you only need to multiply by the denominator under the variable.
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For example, to solve ...
2/5 = p/10
you only need to multiply by 10. You don't need to multiply by 50, then divide by 5.
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Any proportion can be written 4 ways:
This suggests another strategy: invert the whole proportion, then solve it as one with p in the numerator:
6/15 = p/10 ⇒ p = 10(6/15) = 4
Answer:
The distance of the foot of the ladder to the building is 14 ft.
Step-by-step explanation:
The length of ladder = 20 ft
Angle formed by ladder with level ground, θ = 46
We are required to find out the distance of the foot of the ladder from the building
The above question can be found out by using trigonometric relations as follows;
The adjacent side of the right triangle formed by the ladder the building and the ground is the distance of the foot of the ladder from the building
The hypotenuse side is the length of the ladder = 20 ft
Therefore;
Adjacent side of triangle = Hypotenuse × cosθ
∴ Distance of the foot of the ladder from the building = Hypotenuse × cosθ
Distance of the foot of the ladder from the building = 20 ft × cos(56)
Distance of the foot of the ladder from the building = 13.893 ft
To the nearest foot, the distance of the foot of the ladder to the building = 14 ft.
Answer:
16m
8m
50.24m
200.96m^2
Step-by-step explanation:
13. 8*2=16
14. 8m
15. 2pi r = 2* pi* 8= 50.24
16. pi r^2 = pi * 8^2= 200.96m^2
