Answer:
m<AFE = 128°.
Step-by-step explanation:
<u>Step 1: Find the value of x</u>
<em>Angle EFD + Angle DFC = Angle EFC</em>
5x + 6 + 19x - 15 = 17x + 19
24x - 9 = 17x + 19
7x = 28
x = 4
<u>Step 2: Find all angles</u>
<em>Angle AFB=Angle EFD= 5x + 6</em>
5(4) + 6 = 26°
Angle DFC = 19x - 15
19(4) - 15 = 61°
<u>Step 3: Find angle AFE</u>
<em>Line BD is a straight line and all angles on a straight line are equal to 180°.</em>
<em>Angle AFB + Angle AFE + Angle EFD = 180°</em>
26 + BFC + 26 = 180°
BFC = 180 - 52
BFC = 128°
<em>Therefore, m<AFE is equal to 128°.</em>
!!
Answer:
C. Stacy
Step-by-step explanation:
One way to compare is to convert all the fractions into decimals
Rachel works 2/3 of her shift: Approximately= 0.667
Jose works 1/6: approx. = 0.1667
Damon works 4/5= 0.80
Stacy works 6/7: approx. = 0.8571
Now this makes it much easier to compare
And since 0.85714 (Stacy's shift) is the largest number, Stacy has completed the largest portion of her shift
Answer:
3 days is the right answer!!!!! good luck
Step-by-step explanation:
Answer: the length of the extended ladder is 8√3 feet or 13.9 feet
the distance between the wall and the bottom of the ladder is 4√3 feet or 6.9 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine the extended length of the ladder h, we would apply
the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 60 = 12/h
√3/2 = 12/h
h = 12 × 2/√3 = 24√3
h = 24√3 × √3/√3
h = 8√3
To determine the distance between the wall and the bottom of the ladder d, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse.
Therefore,
Cos 60 = d/8√3
0.5 = d/8√3
d = 0.5 × 8√3
d = 4√3
Answer:
1
The probability is 
2
The probability is 
Step-by-step explanation:
From the question we are told that
The population mean is 
The standard deviation is 
The sample size is 
Generally the standard error for the sample mean 
is mathematically evaluated as
substituting values
Apply central limit theorem[CLT] we have that
![P(\= X < 33) = [z < \frac{33 - \mu }{\sigma_{\= x}} ]](https://tex.z-dn.net/?f=P%28%5C%3D%20X%20%3C%2033%29%20%3D%20%20%5Bz%20%3C%20%20%5Cfrac%7B33%20-%20%20%5Cmu%20%7D%7B%5Csigma_%7B%5C%3D%20x%7D%7D%20%5D)
substituting values
![P(\= X < 33) = [z < \frac{33 - 28.29 }{4.48} ]](https://tex.z-dn.net/?f=P%28%5C%3D%20X%20%3C%2033%29%20%3D%20%20%5Bz%20%3C%20%20%5Cfrac%7B33%20-%20%2028.29%20%7D%7B4.48%7D%20%5D)
![P(\= X < 33) = [z < 1.05 ]](https://tex.z-dn.net/?f=P%28%5C%3D%20X%20%3C%2033%29%20%3D%20%20%5Bz%20%3C%20%201.05%20%5D)
From the z-table we have that
For the second question
Apply central limit theorem[CLT] we have that
![P(\= X > 30 ) = [z > \frac{30 - \mu }{\sigma_{\= x}} ]](https://tex.z-dn.net/?f=P%28%5C%3D%20X%20%3E%2030%20%29%20%3D%20%20%5Bz%20%3E%20%20%5Cfrac%7B30%20-%20%20%5Cmu%20%7D%7B%5Csigma_%7B%5C%3D%20x%7D%7D%20%5D)
substituting values
![P(\= X < 33) = [z > \frac{30 - 28.29 }{4.48} ]](https://tex.z-dn.net/?f=P%28%5C%3D%20X%20%3C%2033%29%20%3D%20%20%5Bz%20%3E%20%20%5Cfrac%7B30%20-%20%2028.29%20%7D%7B4.48%7D%20%5D)
From the z-table we have that
Thus
