Answer: The required expected value is $3.46.
Step-by-step explanation:
Since we have given that
Number of value of 4 or less are
2,3,4
So, there are 12 in numbers.
So, probability would be
Since Aces are considered as the highest card in the deck.
So, remaining probability would be
Amount paid or value of 4 or less = $165
Amount not paid for other case = $45
So, the expected value would be
Hence, the required expected value is $3.46.
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Disclaimer : The missing figure for the question is attached below.
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Hey!
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x – 3y = 3 is written in standard form. We can write in the slope-intercept form.
x - 3y = 3
x - 3y - x = 3 - x
3y = 3 - x
3y/3 = 3/3 - 3/x
y = 1 - 3/x
y = 1/3x - 1
Now, we know that the y-intercept is -1 and the slope is 1/3
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Hence, the answer is
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Hope This Helped! Good Luck!
