What two numbers multiply -14 and add up to 13
1 answer:
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Answer:
The dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Step-by-step explanation:
Note: Kindly refer to the attached diagram where:
x = Length of the rectangular area
y = Width of the rectangular area.
The fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. This implies that it is $10 per foot. Otherwise, it will be $20 per foot. Since no fencing is needed along the barn, it implies that there is no fence along the northern length.
Since the farmer is not willing to spend more than $7000, we have:
10y + 20x + 20y = 7000
20x + 30y = 7000
Divide through by 20, we have:
x + 1.5y = 350
x = 350 - 1.5y …………………………. (1)
The fenced area is
A = x * y ………………………………….. (2)
Substituting equation (1) into (2), we have:
A = (350 - 1.5y)y
A = 350y - 1.5y^2 ……………. (3)
To maximize A, equation (3) is differentiated with respect to y and equated it to 0 as follows:
That is,
A'(y) = 350 - 3y = 0
Solving for y, we have:
y = 350/3
y = 116.67 ft
Substituting y = 116.67 for y in equation (1), we have:
x = 350 - (1.5 * 116.67)
x = 175ft
Therefore, the dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Answer:
Mean = 339 hours
Standard deviation = 54 hours
Step-by-step explanation:
We are given that approximately 2.5% of the bulbs have lives exceeding 445 hours
So,P(x>445) = 0.025
P(x<445) =1- 0.025 =0.975
z value for 0.975 is 1.96
Formula :
So,
--A
Now we are given that approximately 16% have lives exceeding 393 hours,
So,P(x>393) = 0.16
P(x<393) =1- 0.16 =0.84
z value for 0.84 is 1
Formula :
So,
---B
Solve A and B
Substitute the value of from B in A
Substitute the value in B
So, mean = 339 hours
Standard deviation = 54 hours