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ladessa [460]
3 years ago
10

Rico has $87 in his checking account and Darius asked to borrow $34 to buy a shirt. Rico wants to give him the money and buy a s

hirt of his own that cost $33. Would he have enough money to do so?
Mathematics
1 answer:
Volgvan3 years ago
6 0

Answer:

Yes!

Step-by-step explanation:

87 - 34 = 53

he would have $53 left

53-33 = 20

he would have $20 after buying both shirts

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Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame
lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

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 normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, 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.

In this problem, we have that:

\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

Z = \frac{207.9 - 208}{0.1678}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0
3 years ago
Shane went bowling with his friends. The bowling alley charges $20 for an hour of group bowling plus a fee to rent each pair of
ValentinkaMS [17]

Answer:

4x+20=31

Step-by-step explanation:

So one hour of bowling is 20 dollars and they bowled for one hour hence the 1x20 which is equal to 20. That is the base coast we add to the variable of x that is the cost of renting one pair of shoes. And since they rented 4 pairs of shoes you multiply x by 4 to get 4x. Add the 20 dollars they paid to bowl and it is 4x+20. They paid 31 dollars in total so equal the equation to 31. 4x+20=31. Solution is $2.75 per pair of shoes. (If you want an explanation as to how to get the answer, just ask

4 0
2 years ago
The sum of two numbers is 50
salantis [7]

Answer:

2X=50

Step-by-step explanation:

X+X=50 I hope that help

7 0
3 years ago
Read 2 more answers
Suppose you are explaining to a friend who missed class how to solve equations. Explain, in complete sentences, the steps necess
pashok25 [27]

Answer:

First, take x off of both sides making it: “5 -4 = 3 + 10”

Then subtract 3, making it “3(-7) = 10”

Then do 3 multiply 3 by -7, getting -21 = 10

that is how you would find out the equation is false

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2 years ago
Help plz!! 3/4=1/8+v
sasho [114]

V is going to equal 5/8

8 0
3 years ago
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