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guapka [62]
3 years ago
10

At noodles & company restaurant, the probability that a customer will order a nonalcoholic beverage is .48. Find the probabi

lity that in a sample of 12 customers, none of the 12 will order a nonalcoholic beverage.
Mathematics
1 answer:
dlinn [17]3 years ago
8 0

Answer:

           \large\boxed{\large\boxed{0.00039}}

Explanation:

Notice that there are only two possibilities: <em>ordering a nonalcoholic beverage</em> or not ordering a nonalcoholic beverage; hence, <em>the probability that in a sample of 12 customers, none of the 12 will order a nonalcholic beverage</em> is a binomial experiment.

Now, you know that he probability that a customer will order a nonalcoholic beverage is 0.48.

Hence, the probability that a customer does not order a nonalcholic beverage is 1 - 0.48 = 0.52.

The probability that none of the 12 customers order a nonalcoholic beverage is determined by the product of 0.52 twelve times. Naming P(X=12) such probability it is:

           P(X=12)=(0.52)^{12}\approx 0.00039

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In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees
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Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling:  when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

Ay(x)=150\ ,\ x\leqslant 100

When x is more than 100:

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The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

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If we doubled x to 120, we would have to use the second function

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If we started with x=30, then  

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We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

Y(x)=150x\ ,\ x\leqslant 100

Y(x)=150x-x^2\ ,\ 100< x\leqslant 150

To find the maximum total yield we take the first derivative

Y'(x)=150\ ,\ x\leqslant 100

Y'(x)=150-2x\ ,\ 100< x\leqslant 150

The first expression has no variable, so the total yield must be evaluated in the endpoints

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Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

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