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sertanlavr [38]
1 year ago
11

A farmer wants to plant peas and carrots on no more than 200 acres of his farm. If x represents the number of acres of peas and

y represents the number of acres of carrots for solution (x, y), then which is a viable solution?
A.(−50, 160)
B.(80, 160)
C.(75, −200)
D.(60, 135)
Mathematics
2 answers:
n200080 [17]1 year ago
8 0

Answer:

it's D

Step-by-step explanation:

AfilCa [17]1 year ago
5 0

Answer:

Option D.(60, 135)

Step-by-step explanation:

Let

x -----> the number of acres of peas

y ----> the number of acres of carrots

we know that

The inequality that represent the problem is equal to

x+y\leq 200

so

<em>Verify each case</em>

case A) (-50,160)

substitute the value of x and the value of y in the inequality and then compare the result

-50+160\leq 200

110\leq 200 ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case B) (80,160)

substitute the value of x and the value of y in the inequality and then compare the result

80+160\leq 200

240\leq 200 ----> is not true

therefore

The point is not a solution

case C) (75,-200)

substitute the value of x and the value of y in the inequality and then compare the result

75-200\leq 200

-125\leq 200 ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case D) (60,135)

substitute the value of x and the value of y in the inequality and then compare the result

60+135\leq 200

195\leq 200 ----> is true

therefore

The point is a viable solution

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A furniture company is introducing a new line of lounge chairs next quarter. These are the cost and revenue functions, where x r
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No lower than $208, and no higher than $956.8

Step-by-step explanation:

Notice that the revenue (income) function is represented by a quadratic expression (a parabola with branches pointing down), and the cost function is linear with negative slope.

When we plot them, we obtain the graphs shown in the attached image. Notice as well that there are two points of intersection for these two functions. The revenue exceeds (lays above) the cost in between the two points of intersection (marked in red and green).

For the company to make a profit, the revenue has to be larger than the cost, so we study the limiting values for that to happen, which is the points of intersection of these two curves.

The first one (pictured in red) is associated with coordinates (35, 33488) which tells us that is the production of 35 chairs with a revenue of $33,488. That is a cost per chair of $33,488 / 35 = $956.8

The second intersection (pictured in green) is associated with coordinates (125, 26000), which tells us that is the production of 125 chairs with a revenue of $26,000. That is a cost per chair of $26000 / 125 = $ 208

So these values give us the minimum and maximum that the company can charge to make a profit.

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Customers are used to evaluate a preliminary product design. In the past, 95% of highly successful products received good review
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Answer:

a. 61.5%; b. About 61.8%; c. About 36.4%

Step-by-step explanation:

This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.

According to that theorem, the probability of a selected product attains a good review is:

\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P) (1)

In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).

<h3>The probability that a randomly selected product attains a good review</h3>

In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):

P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)

P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)

P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)

P(H) = 40% or 0.40 (probability of  being a highly successful product).

P(M) = 35% or 0.35 (probability of  being a moderately successful product).

P(P) = 25% or 0.25 (probability of  being a poor successful product).

Then,

\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)

\\ P(G) = 0.95*0.40 + 0.60*0.35 + 0.10*0.25

\\ P(G) = 0.615\;or\; 61.5\%

That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.

<h3>The probability that a new product attains a good review is a highly successful product</h3>

We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):

\\ P(H|G) = \frac{P(G|H)*P(H)}{P(G)}

We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,

\\ P(H|G) = \frac{0.95*0.40}{0.615}

\\ P(H|G) =\frac{0.38}{0.615}

\\ P(H|G) =0.618

Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.

<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>

The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:

\\ P(NG) = P(NG|H)*P(H) + P(NG|M)*P(M) + P(NG|P)*P(P)

P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05

P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40

P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90

So

\\ P(NG) = 0.05*0.40 + 0.40*0.35 + 0.90*0.25

\\ P(NG) = 0.385\;or\; 38.5\%

Which is equal to

P(NG) = 1 - P(G) = 1 - 0.615 = 0.385

Well, having all this information at hand:

\\ P(M|NG) = \frac{P(NG|M)*P(M)}{P(NG)}

\\ P(M|NG) = \frac{0.40*0.35}{0.385}

\\ P(M|NG) = \frac{0.14}{0.385}

\\ P(M|NG) = 0.363636... \approx 0.364

Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.

8 0
1 year ago
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