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3 years ago

Hint # 2 - First, rewrite the mixed numbers as fractions greater than one, then multiply.

Mathematics

2 answers:

Stolb23 [73]3 years ago

7 0

Answer:

Here is what you need to do.

Step-by-step explanation:

Volume = Length * Width * Height

Multiply 89 1/10 with 20 1/4, after you get that multiply with 72 and you will have your answer.

Greeley [361]3 years ago

3 0

Answer:

129907 4/5 in^3

...........

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Answer:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

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3 years ago

Find the value of x and y

Natalija [7]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

value of x
value of y

Let's gather some information:

ΔA'BC' and ΔABC are similar triangles

⇒ Angle B is shared by both triangles

⇒ Angle A' and A are the same, as they are both on parallel

lines, A'C' and AC, and both angles are formed with the

same line AB

⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

⇒ their side lengths are proportional to each other

let's find x's value

⇒ let's set up a proportion

$\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143$

let's find y's value

⇒ let's set up a proportion

$\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25$

Answer:

x= 17.143
y = 26.25

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