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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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Answer:

The probability of obtaining exactly 5 correct answers on a ten question examination is 0.1366.

Step-by-step explanation:

Each multiple-choice questions has three options (a), (b) and (c).

The probability of getting a correct answer is, P(Correct)=\frac{1}{3} since one of the three options is correct.

But this students has an unique way of selecting the answers.

He rolls a die and according to the result of the die he marks the answers.

The sample space of rolling a die is: S = {1, 2, 3, 4, 5, 6}

Odds of picking the three options are as follows:

  • To pick (a): If 1 or 2 rolls of the die.

        The probability to pick (a) is,

        P (Selecting\ (a))=\frac{2}{6}=\frac{1}{3}

  • To pick (b): If 3 or 4 rolls of a die.

        The probability to pick (a) is,

         P (Selecting\ (b))=\frac{2}{6}=\frac{1}{3}

  • To pick (c): If 5 or 6 rolls of the die.

        The probability to pick (a) is,

        P (Selecting\ (c))=\frac{2}{6}=\frac{1}{3}

Thus, all the three options have the equal probability of being picked.

Let <em>X</em> = Number of correct answers.

The number of questions is, <em>n</em> = 10 and probability of selecting a correct option is , p = \frac{1}{3}.

The random variable <em>X</em> follows Binomial distribution.

The probability function is:

P(X = x)={n\choose x}p^{x}(1-p)^{n-x}

Compute the probability of obtaining exactly 5 correct answers on a ten question examination as:

P(X = 5)={10\choose 5}(\frac{1}{3} )^{5}(1-\frac{1}{3} )^{10-5}=0.1366

Thus, the probability of obtaining exactly 5 correct answers on a ten question examination is 0.1366.

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Answer:

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Step-by-step explanation:

Assume that they buy x hotdogs and y popcorn

∵ They buy a total of 11 hotdogs and popcorn

∵ The number of hotdogs is x and the number of popcorn is y

∴ x + y = 11 ⇒ (1)

∵ Hot dogs cost $2.50 each

∵ Popcorn costs $1.00 each

∵ They spend $20 on hot dogs and popcorn

→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20

∴ 2.5(x) + 1(y) = 20

∴ 2.5x + y = 20 ⇒ (2)

Now we have a system of equations to solve it

→ Subtract equation (1) from equation (2)

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