Answer:
Step-by-step explanation:
Considering the complete question attached in figure.
Consider
Hadley = x
Parker = y
Greenville = z
Distance between Greenville and Parker = yz = 29
Given that distance between Hadley and Greenville is 13 miles less than the distance between Parker and Greenville.
xz = yz -13 --- (1)
Distance between hardley and greenville = xz = ?
From (1)
xz = 29 -13
xz = 16 miles
So Alan is right that distance between Hadley and Greenville is 16 miles
Answer:
-3/2
Step-by-step explanation:
Using the slope formula, we can find the slope of the line shown
m = ( y2-y1)/(x2-x1)
= ( -1-3)/(-3-3)
= -4/-6
= 2/3
A line that is perpendicular is the negative reciprocal
-1/ (2/3) = -3/2
Answer:
b) 95%
Step-by-step explanation:
We have been given that scores on an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. We are asked to find the percentage of the data that is between 64.2 points and 88.6 points.
First of all, we will find z-scores of each data point as:




Let us find z-score corresponding to normal score 88.6.



To find the percentage of the data is between 64.2 points and 88.6 points, we need to find area under a normal distribution curve that lie within two standard deviation of mean.
The empirical rule of normal distribution states that approximately 95% of data points fall within two standard deviation of mean, therefore, option 'b' is the correct choice.
Y = height
x = distance from tower
tan(19.9) = y/x
tan(21.8) = y/(x-50) ( x is 50 feet closer so subtract 50 from x)
find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400
replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)
rewrite to solve for height:
0.362x = y
0.400(x-50) = y distribute the 0.400 and rewrite as 0.400x-20 =y
now solve:
0.362x = 0.400x-20
add 20 to each side:
0.362x +20 = 0.400x
subtract 0.362x from each side:
20 = 0.038x
divide both sides by 0.038
x = 20 / 0.038 = 526.3 feet
now that x is known replace x in the original equation and solve for y:
tan19.9 = y /x
0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5
the height of the tower is 190.5 feet