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solong [7]
3 years ago
10

Three consecutive integers have a sum of 51 find the integers

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
8 0

the answer is 16 17 18

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The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play
Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

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 = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

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

By the Central Limit Theorem

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

Z = \frac{76 - 75}{0.5}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

6 0
3 years ago
Studies show that a typical giant hummingbird can flap its wings once in 0.08 of a second.
Licemer1 [7]

Answer:

a. 90

b. 360

Step-by-step explanation:

The time taken by humming bird to flap its wings= 0.08 sec

by flying 7.2 seconds a typical giant hummingbird flap its wings \frac{7.2}{0.08} times

= 90 times

Since, A ruby-throated hummingbird can flap its wings 4 times faster than a giant hummingbird, it will flap its wings in every 0.02 sec

so in 7.2 seconds it will flap \frac{7.2}{0.02} times = 360 times

4 0
3 years ago
Does the equation 2x-7=5+x have exactly one solution
Goshia [24]

Answer:

12

Step-by-step explanation:

2x - 7 =5 +x

2x - x =5 +7

x =12 (one solution)

4 0
3 years ago
An amount of 40.000 is borrowed for 6 years at 5% interest, compounded annually If the loan is paid in full at the end of that p
Stella [2.4K]

Answer:

A  =  $56,740

Step-by-step explanation:

Use the Compound Amount formula A = P(1 + r)^t.  Substitute 0.05 for r and $40,000 for P:

A = $40,000(1 + 0.05)^6

A  =  $56,740.26, or, rounded off to the nearest dollar,

A  =  $56,740

4 0
3 years ago
Cole spent a total of 523.46 on holiday gifts for his friends and family. If he bought gifts for eleven people,about how much di
Vlada [557]

Answer:

Cole spend 47.587 on buying gifts for each person.

Step-by-step explanation:

Given:

Total money spend on gifts = 523.46

Number of people gifts were bought for = 11

We need to find how much he spend on each person.

Solution:

To find how much he spend on each person we will divide total money spend on gifts with number of people gifts were bought for.

framing in equation form we get;

Spending on each person = \frac{523.46}{11} = 47.587

Hence Cole spend 47.587 on buying gifts for each person.

6 0
3 years ago
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