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gogolik [260]
2 years ago
7

Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 5 more than 3 times the number o

f marbles Mark has, how many does each boy have to sell if the total number of marbles is 97? Mark has Number marbles to sell. Don has Number marbles to sell.
Mathematics
1 answer:
trasher [3.6K]2 years ago
3 0

Answer:

Mark has 23 marbles, Don has 74 marbles

Step-by-step explanation:

Mark has x marbles, Don has y marbles

y = 5 + 3x

x + y = 97

so

x + (5 + 3x) = 97

4x = 97 - 5 = 92

x = 92/4 = 23

y = 97 - 23 = 74

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Suppose the expected returns on equity of two firms, Macrosoft and Microsoft, that operate in the same business are 10.50% and 1
Komok [63]

Answer:

The return on assets in this business for Macrosoft is

ROA = 10.50%

Step-by-step explanation:

Return on Equity:

ROE represents how much a firm is generating profits by using the shareholder's money.

ROE is calculated as

$ {ROE = \frac{Annual \:\: net\: \: income}{Average \:\: shareholder's \:\: equity} $​  ​

Return on Assets:

ROA represents how much a firm is generating profits for every dollar of its assets.

ROA is calculated as

$ {ROA = \frac{Annual \:\: net\: \: income}{Total \:\: assests} $​  ​ ​

What is the return on assets in this business if Macrosoft has no debt?

Debt plays an important role in the calculations of return on assets.

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3 years ago
Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distributio
andrew-mc [135]

Answer:

0.64%.

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:

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

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 estabilishes 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.

Mean of 75 grams and a standard deviation of 22 grams.

This means that \mu = 75, \sigma = 22

Sample of 144:

This means that n = 144, s = \frac{22}{\sqrt{144}} = 1.8333

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

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

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Z = -2.73

Z = -2.73 has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.

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