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3 years ago

Pleas help it is in the screenshot

Mathematics

1 answer:

yuradex [85]3 years ago

3 0

Answer:

10) 8.4

11) 25.6

Step-by-step explanation:

$\cfrac{7}{10}=\cfrac{x}{12}$

$x=12\times \cfrac{7}{10}$

$=8.4$

<h3>11)</h3><h3> $\cfrac{8}{5} =\cfrac{x}{16}$ </h3>

$5\times x=8\times 16$

$\cfrac{5x}{5} =\cfrac{128}{5}$

$x=25.6$

Hope it helps! :)

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1. Find the area of the composite figure to the nearest hundredth.

Leto [7]

Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

<em>12.5 squared is 156.25.</em>

1/2(3.14 * 156.25)

<em>Multiply 3.14 by 156.25 to get 490.625.</em>

1/2(490.625)

<em>Divide 490.625 by 2 to get 245.3125.</em>

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

<em>Multiply 12.5 by 25 to get 312.5.</em>

312.5 + 1/2(31 * 12.5)

<em>Multiply 31 by 12.5 to get 387.5.</em>

312.5 + 1/2(387.5)

<em>Multiply 1/2 by 387.5 to get 193.75</em>

312.5 + 193.75

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

<em>Multiply 40 by 27 to get 1080.</em>

1/2(1080)

<em>Multiply 1/2 by 1080.</em>

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

6 0

3 years ago

Read 2 more answers

-6x+4=8

Bogdan [553]

Answer:

X=2/3

Step-by-step explanation:

-6x+4=8

-6x=8-4

-6x=4

6x=-4

x=4/6

=2/3

HOPE THIS WORKS

5 0

3 years ago

The ages of a random sample of five university professors are 39, 54, 61, 72, and 59. Using this information, find a 99% confide

blsea [12.9K]

Answer:

$38.898 \leq \sigma^2 \leq 2792.356$

Now we just take square root on both sides of the interval and we got:

$6.237 \leq \sigma \leq 52.843$

Step-by-step explanation:

Data given and notation

34,59,61,71,59

We can calculate the sample standard deviation with the following formula:

$s^2= \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$s= \sqrt{s^2}$

s=12.021 represent the sample standard deviation

$\bar x$ represent the sample mean

n=5 the sample size

Confidence=99% or 0.99

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 .

Calculating the confidence interval

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

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

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

$df=n-1=5-1=4$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical values.