Answer:
$68,000
Step-by-step explanation:
we have to determine the total economic costs of going to college = ($40,000 x 2) + ($30,000 x 2) = $140,000
since we want to recover our "college investment" in 5 years or less, then we must earn at least $140,000 / 5 = $28,000 more per year
the minimum salary that we should earn after graduating = $40,000 (our current salary) + $28,000 (to recover college costs) = $68,000
Using the normal distribution, it is found that there are 68 students with scores between 72 and 82.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
The proportion of students with scores between 72 and 82 is the <u>p-value of Z when X = 82 subtracted by the p-value of Z when X = 72</u>.
X = 82:
Z = 1
Z = 1 has a p-value of 0.84.
X = 72:
Z = 0
Z = 0 has a p-value of 0.5.
0.84 - 0.5 = 0.34.
Out of 200 students, the number is given by:
0.34 x 200 = 68 students with scores between 72 and 82.
More can be learned about the normal distribution at brainly.com/question/24663213
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Answer:
.
Step-by-step explanation:
Consider the double angle identity for tangents:
.
Also, for two complementary angles,
.
Subtract from both sides of this equation:
.
Take the tangent of both sides of this equation:
.
Apply the double-angle identity to the left-hand side of this equation:
.
The two angles and are complementary. Therefore, for the right-hand side of this equation,
.
Equate the two sides of this equation:
.