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3 years ago

Find the area and perimeter of the given rectangle.

Mathematics

1 answer:

jeka943 years ago

7 0

Answer:

The Area is 99 units², while the perimeter is 40 units

Step-by-step explanation:

Area can be found by multiplying the length of the rectangle by the width of the rectangle. Counting the boxes on the side gives you 11 horizontally and 9 vertically. Multiplying these two gives you an area of 99. The measurement is in units because there is no given unit of measurement such as inches, feet, or meters. Area is always squared which is why there is a ² after units.

Perimeter can be found by adding all 4 sides together. Counting the boxes gives you 11 + 11 + 9 + 9. This gives you a perimeter of 40. The measurement is in units because there is no given unit of measurement such as inches, feet, or meters. Perimeter is not squared like area.

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Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

JulsSmile [24]

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

(38737+50463)/2 = 44600.

The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

$M = \frac{50463-38737}{2} = 5863$

Relating the margin of error with the sample size:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.64.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

For this problem, we have that $\sigma = 14300, M = 5863$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$5863 = 1.645\frac{14300}{\sqrt{n}}$

$5863\sqrt{n} = 1.645*14300$

$\sqrt{n} = \frac{1.645*14300}{5863}$

$(\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2$

$n = 16$

The sample size was of 16.

7 0

3 years ago

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of

Tema [17]

Answer:

Small box weighs 13.75 kg & large box weighs 15.75 kg

Step-by-step explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and 5 small boxes has a total weight of 116 kilograms":

$3l+5s=116$

and

"9 large boxes and 7 small boxes has a total weight of 238 kilograms":

$9l+7s=238$

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

$3l+5s=116\\3l=116-5s\\l=\frac{116-5s}{3}$

now,

$9l+7s=238\\9(\frac{116-5s}{3})+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=\frac{110}{8}=13.75$

now we plug in 13.75 into s into equation of l to find s:

$l=\frac{116-5s}{3}\\l=\frac{116-5(13.75)}{3}\\l=15.75$

5 0

3 years ago

100serihttps://brainly.com/question/23752325#

d1i1m1o1n [39]

Answer:

what?

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Madison has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cup holds 12 o

Troyanec [42]

Answer:

$12x+22(y+10)=1240, y=x$

small cups=30

large cups=40

Step-by-step explanation:

let x be the number of small cups and y the number of large cups.

-Given that 10 more cups than small cups of lemonade were sold:

$12x+22(y+10)=1240$

#Before the 10 more were sold, the number of x and y sold were equal>

$x=y\\\\\therefore 12x+22(x+10)=1240\\\\12x+22x+220=1240\\\\34x=1240-220\\\\34x=1020\\\\x=30$

The number of small cups sold was 30

#Since, the number of large cups was 10 more, y=x+10=30+10=40

7 0

3 years ago

Read 2 more answers

Multiply the following radicals (do NOT simplify) 2/4 x 416

Tpy6a [65]

Answer:

208

Step-by-step explanation:

6 0

3 years ago

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