Solve for me please thank you
1 answer:
You might be interested in
Answer:
Width = 166.7 ft
Length = 250 ft.
Step-by-step explanation:
From the diagram at the ATTACHMENT
Let us denote the the length of the rectangular area as "x" and
the width of the rectangular area as "y"
Since, cost of the fence on the western side is shared with a neighbor, we can say it is $7 per foot. Otherwise, it is $14 per foot. The northern length is not fenced.
From the question, we know that the cost is not to exceed $7000, therefore we can expressed it as
7y + 14x + 14y = 7000
14x + 21y = 7000
Divide through by 14, we have
(x + 1.5) = 500 ------------- eqn (*)
But the area of the fenced
= A = (x×y) -------------- eqn (**)
Substitute (*) into (**) we have
A = (500 - 1.5y)*y
= 500y - 1.5y²
In other to maximize the Area, we can find the differential of A
A'(y) = 500 - 3y
At A'(y) = 0.
500-3y= 0
3y=500
y= 166.67 ft
From eqn(*)
(x+ 1.5) = 500
x = 500 - 1.5y
500-1.5(166.67)
= 250ft
Therefore, the dimensions for the plot that would enclose the most area are
Width of 166.67 ft and Length = 250 ft.
Answer:
A sample size of at least 228 must be needed.
Step-by-step explanation:
We are given that in the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $61,238. Assume that the standard deviation is $3850.
And we have to find that what sample size do we need to have a margin of error equal to $500 with 95% confidence.
As we know that the Margin of error formula is given by;
<u>Margin of error</u> =
where, = significance level = 1 - 0.95 = 0.05 and
= 0.025.
= standard deviation = $3,850
n = sample size
<em>Also, at 0.025 significance level the z table gives critical value of 1.96.</em>
So, margin of error is ;
= 15.092
Squaring both sides we get,
n = = 227.8 ≈ 228
So, we must need at least a sample size of 228 to have a margin of error equal to $500 with 95% confidence.