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3 years ago

Find four consecutive integers whose sum is 114.

Mathematics

1 answer:

ziro4ka [17]3 years ago

6 0

27, 28, 29 and 30

consecutive integers have a difference of 1 between each one

let n be the first integer then the next three are

n + 1, n + 2 and n + 3

hence n + n + 1 + n + 2 + n + 3 = 114

4n + 6 = 114

subtract 6 from both sides of the equation

4n = 114 - 6 = 108

divide both sides by 4

n = $\frac{108}{4}$ = 27

n = 27, n+ 1 = 28, n + 2 = 29, n + 3 = 30

the consecutive integers are 27, 28, 29 and 30

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The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums fo

Harrizon [31]

Using confidence interval concepts, it is found that:

a) The point estimate is the sample mean.

b) The confidence interval is: $\overline{x} \pm T\frac{s}{n}$

c) If $1411 is between the bounds of the interval yes, otherwise no.

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At item a, it asks to provide a point estimate for the population mean, which is the sample mean $\overline{x}$

--------------

Item b:

In the spreadsheet, it is possible to find the <em>standard deviation for the sample</em>, thus, the t-distribution is used.
The confidence interval will be given by:

$\overline{x} \pm T\frac{s}{n}$

In which:

$\overline{x}$ is the sample mean.
T is the critical value, from the t-distribution, with a two-tailed area of $\frac{1 - 0.95}{2} = 0.025$ and n-1 degrees of freedom.
s is the standard deviation for the sample.
n is the sample size.

--------------

Item c:

We have to check if 1411 is between $\overline{x} - T\frac{s}{n}$ and $\overline{x} +T\frac{s}{n}$ .

If it is, the interval includes the National Average, otherwise, it does not.

A similar problem is given at brainly.com/question/24232455

7 0

2 years ago

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play.

bearhunter [10]

Answer:

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7.</h3>

Step-by-step explanation:

Given that there are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
Let x be the number of ushers ( or helpers ).
Therefore x=7 helpers.
Let y be the number of technicians.
Therefore y=11 technicians.

<h3>To find the ratio of technicians to all helpers :</h3>

That is to find the ratio of y to x.

We can write the ratio of technicians to all ushers(helpers) as y : x

Which implies that 11 : 7, (since y=11 and x=7)

Or $\frac{11}{7}$ or 11 to 7

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7</h3>

4 0

3 years ago

74386 divided by 874

Mice21 [21]

Answer:

85.11