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miss Akunina [59]
2 years ago
15

A distributor needs to blend a mix of Gualtemala Antigua coffee that normally sells for $8.50 per pound with a Rift Valley coffe

e that normally sells for $12.50 per pound to create 70 pounds of a coffee that can sell for $10.56 per pound. How many pounds of each kind of coffee should they mix?
A) Write an equation using the information as it is given above that can be solved to answer the question.
Use x as your variable to represent the quantity of Gualtemala Antigua coffee.
Equation: ____________________________________________________

B) (Round your answers to the nearest whole number of pounds.)
Answer: They must mix
___pounds of the Gualtemala Antigua coffee.
___pounds of the Rift Valley coffee.
Mathematics
1 answer:
daser333 [38]2 years ago
4 0

9514 1404 393

Answer:

  • x+y=70; 8.50x+12.50y=10.56(70)
  • 36 pounds Antigua
  • 34 pounds Rift

Step-by-step explanation:

At the insistence of the problem author, we will let x represent pounds of Antigua coffee and y represent pounds of Rift coffee. Then we have ...

  x + y = 70

  8.50x +12.50y = 10.56(70) . . . . . total cost of the mix

__

We like to use the variable to represent the high-cost contributor. Here, that is y, so we'll substitute for x:

  x = 70-y

  8.50(70 -y) +12.50y = 10.56(70)

__

  595 +4y = 739.2 . . . . . . . . . . . . . . simplify

  4y = 144.2 . . . . . . . . . . . subtract 595

  y = 36.05 . . . . . . . divide by 4

  x = 70 -36.05 = 33.95

About 36 pounds of Rift Valley coffee and 34 pounds of Gualtemala Antigua coffee must be mixed.

_____

<em>Additional comment</em>

By letting the variable in our equation 8.50(70 -y) +12.50y = 10.56(70) represent the high-cost coffee, we ensure that the simplified equation will have a positive coefficient for the variable. This means we don't have to mess with negative numbers, so eliminating a common source of math errors.

The problem requirement that we use x for the low-cost contributor meant we introduced an extra equation that would not have been needed.

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Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if
satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that \mu = 64, \sigma = 2

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Sample of 25 means that n = 25, so s = \frac{2}{\sqrt{25}} = 0.4.

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that X = 65.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{0.4}

Z = \frac{65 - 64}{0.4}

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C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

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