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3 years ago

What makes up a trapezoid

Mathematics

1 answer:

Anna007 [38]3 years ago

5 0

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel.

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Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms oc

Anit [1.1K]

Answer:

a) $\hat \sigma^2 =s^2 =30^2 = 900$

b) $567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

c) $23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

Step-by-step explanation:

Data given and notation

s=30 represent the sample standard deviation

$\bar x=290$ represent the sample mean

n=20 the sample size

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Part a

The best point of estimate for the population variance is the sample variance, so on this case:

$\hat \sigma^2 =s^2 =30^2 = 900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,19)" "=CHISQ.INV(0.95,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma \leq \frac{(19)(30)^2}{10.117}$

$567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

Part c

In order to find the confidence interval for the deviation we just need to take the square root for the interval of the variance, and we got:

$23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

7 0

3 years ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand co

Flura [38]

Let f and s denote the amounts of the first and second brands that the chef is going to use.

She wants to end up with 290 mL, so

f + s = 290

Each mL of the first brand contains 0.08 mL of vinegar, and each mL of the second contains 0.13 mL of vinegar. The final mixture should have a concentration of 12% vinegar, so that it contains 0.12 • 290 mL = 34.8 mL of vinegar, and

0.08f + 0.13s = 34.8

Solve for f and s :

f + s = 290 → s = 290 - f

0.08f + 0.13 (290 - f ) = 34.8

0.08f + 37.7 - 0.13f = 34.8

0.05f = 2.9

f = 58

s = 290 - 58

s = 232

8 0

3 years ago

Congruent figures Practice -2 measurement of angle F

ExtremeBDS [4]

Answer:

m∠F = 45°

because

Corresponding

Parts of

Congruent

Triangles are

Congruent

5 0

3 years ago

Which student saved the greatest amount of money each week? Which student saved the least amount of money each week?

zzz [600]

Answer:

htrh trhr thjt h

Step-by-step explanation:

tr h dhfghd t

3 0

3 years ago

How do you solve this problem in the photo?

Klio2033 [76]

Answer: 5^2

Step-by-step explanation:

Since the base are all the same, you will add the exponents and let the exponents stay the same.

5^3 * 5^4= 5^7 * 5^-5= 5^2

6 0

3 years ago

Read 2 more answers