The length of a rectangle is 15 ft greater than its width. If each dimension is decreased by 2 ft, the area will be decreased by
1 answer:
Answer:
length = 35ft, width = 20ft
Step-by-step explanation:
We are working with length (L), width (W), and area (A). We are asked to find the 2 dimensions. The question tells us that L = W + 15, so we can express L in terms of W. However, we still don't know what A is. Since we have 2 unknowns, we somehow need to develop 2 equations to get a solvable system.
We can set up the first equation using the relationship between L and W:
We can set up the second equation using the information in the second sentence:
Now we can plug the first equation, already isolated for A, into the second equation and solve for W:
A pretty nasty-looking equation actually becomes pretty easy to solve. We know the length is 15ft greater than the width, so if W=20, L=35.
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This question is incomplete, the complete question;
The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.
The 95% Confidence Interval is ($, $ )
Answer:
at 95%, confidence interval is ( $43312, $54288 )
Step-by-step explanation:
Given the data in the question;
sample size n = 36
mean x' = 48,800
standard deviation σ = 16,800
at 95% confidence level;
∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
z critical value, = 1.96
now, confidence interval for population mean is given by the formula
x' ± ( σ/√n )
so we substitute
⇒ 48800 ± 1.96( 16800/√36 )
⇒ 48800 ± 1.96( 2800 )
⇒ 48800 ± 5488
⇒ 48800 - 5488, 48800 + 5488
⇒ ( 43312, 54288 )
Therefore, at 95%, confidence interval is ( $43312, $54288 )