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vovangra [49]
2 years ago
11

A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The enclosed area is 1500 square fee

t. Fencing for the side parallel to the river is $ 10 per​ foot, and fencing for the other two sides is $ 3 per foot. The four corner posts are $ 20 each. Let x be the length of one of the sides perpendicular to the river.
a) Write a function C(x) that describes the cost of the project.
b) What is the domain of C?
Mathematics
1 answer:
ZanzabumX [31]2 years ago
5 0

Answer:

a) C(x) = 15000/x + 6x +80

b) Domain of C(x)  { R x>0 }

Step-by-step explanation:

We have:  

Enclosed area = 1500 ft²   = x*y      from which     y  =  1500 / x    (a) where x is perpendicular to the river

Cost = cost of sides of fenced area perpendicular to the river  + cost of side parallel to river + cost of 4 post then

Cost = 10*y + 2*3*x + 4*20 and accoding to (a)  y = 1500/x

Then

C(x)  = 10* ( 1500/x ) + 6*x + 80

C(x) = 15000/x + 6x +80

Domain of C(x)  { R x>0 }

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-4 + x ≤ 9

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Step-by-step explanation:

Locate the designated space on the diagram and list all the numbers in it.

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Katarina [22]

Answer:

a)Smoke but doesn't drink alcoholic beverages

P=0.176  or 17.6%

b)eats between meals and drinks alcoholic beverages but doesn't smoke

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c.) neither smokes nor eats between meals

P=0.342  or 34.2%

Step-by-step explanation:

Using a Venn diagram with three circles, one for each bad health habit. Let us a for the students that only smoke, b for only drink alcoholic beverages, and c for only eat between meals. Following this logic, d represents smoke and drink alcoholic beverages but not eat between meals,  e drink alcoholic beverages and eat between meals but not smoke,f eat between meals and smoke but not drink alcoholic beverages. Finally g for having all the three, this means g=52.

To find f, subtract 52 (the three problems) from 97 because this last number represents all the students that smoke and eat between meals, including the students that have the three bad habits. The same goes for 'd' and 'e'.

f=97-52=45

e=83-52=31

d=122-52=70

To find a, subtract e, f, and g from the total of smokers. This is because e, f, and g represent smoke and at least another bad habit and a represents only smoking.

a=210-d-f-g=210-70-45-52=43

The same goes for b and c.

b=258-d-e-g=258-70-31-52=105

c=216-e-f.-g=216-31-45-52=88

Adding all letters and subtract from the total to see if there is any healthy student:

500-a+b+c+d+e+f+g =500-43+105+88+70+31+45+52=500- 434=66

a)Smoke but doesn't drink alcoholic beverages

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b)eats between meals and drinks alcoholic beverages but doesn't smoke

This probability is 'e' divided by the total of students.

P=31/500=0.062

c.) neither smokes nor eats between meals

This will be 'b' (only drinks) plus the healthy students (66) divided by the total of students.

P=(105+66)/500=0.342

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