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3 years ago

Find the circumference of a circle if the diameter is 24 feet.

Mathematics

2 answers:

Vikentia [17]3 years ago

8 0

Answer: 24π ft

Step-by-step explanation: To find the circumference of a circle with a diameter of 24 feet, start with the formula c = πd.

Now we can plug the diameter into our formula.

So we have (π)(24 ft) which is equal to 24π ft.

So the area of the circle is 24π ft.

Eddi Din [679]3 years ago

4 0

Answer:

~75.4 ft

Step-by-step explanation:

C = 2*pi*r = pi*d = pi*24 = ~75.4 ft

C: circumference

r: radius

d: diameter

pi = ~3.14

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The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal proba

Sphinxa [80]

Answer:

Step-by-step explanation:

n = 12

Mean = (4.58 + 5.72 + 4.77 + 4.76 + 5.19 + 5.05 + 4.80 + 4.77 + 4.75 + 5.02 + 4.74 + 4.56)/12 = 4.8925

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (4.58 - 4.8925)^2 + (5.72 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.76 - 4.8925)^2 + (5.19 - 4.8925)^2 + (5.05 - 4.8925)^2 + (4.80 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.75 - 4.8925)^2 + (5.02 - 4.8925)^2 + (4.74 - 4.8925)^2 + (4.56 - 4.8925)^2 = 1.122225

Standard deviation = √(1.122225/12

s = 0.31

a) Point estimate = sample mean = 4.8925

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

Margin of error = z × s/√n

Where

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 12 - 1 = 11

b) Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.201

Margin of error = 2.201 × 0.31/√12

= 0.197

95% confidence interval = 4.8925 ± 0.197

Upper limit = 4.8925 + 0.197 = 5.0895

Lower limit = 4.8925 - 0.197 = 4.6955

We are 95% confident that the population mean of the rain water ph lies between 4.6955 and 5.0895

c) For 99% confidence level, z = 3.106

Margin of error = 3.106 × 0.31/√12

= 0.278

99% confidence interval = 4.8925 ± 0.278

Upper limit = 4.8925 + 0.278 = 5.1705

Lower limit = 4.8925 - 0.278 = 4.6145

We are 99% confident that the population mean of the rain water ph lies between 4.6145 and 5.1705

d) The interval gets wider as the confidence level is increased. This is logical since the test score is higher for 99% and therefore, increases the range of values. Since we want to be more confident, the range of values must be extended.

3 0

3 years ago

A vendor pays a rock band 1/3 of the total profit from T-shirts and sweatshirts sold at every concert. The vendor paid the rock

Damm [24]

Answer:

$546

Step-by-step explanation:

726 is 1/3. 3/3 is 2178. - 1632= 546.

5 0

3 years ago

Which measure of center will provide the most accurate estimation of the deposits for the savings account? Why?

faust18 [17]

Hello,

First you have order all the number least to the greater. That gives 30, 75, 80, 85, 85, 95, 95, 100, 100, 110.

Afterwards you have to find the median. Why ?

I will explain you. It's because the median is robust. In fact, it can't be influenced by extreme values (example : 110) but the mean yes. So the mean won't be accurate.

"Then why don't you choose the mode ? " you will ask me. That's because the mode takes the number which appears most often in a set of numbers. It couldn't be accurate at all. It will be useless for this set of numbers.
Furthermore, here there are 3 numbers which appears the most ( 2 times for each) : $85, $95 and $100. Which one will you take ?

Therefore the median is the most suitable and the most accurate to know the center because it is robust.

Now, let's find the median :

There are 10 values, so the median will be the average of the 5th and 6th values.

5th value = 85
6th value = 95

$\frac{(85+95)}{2}$
$= 90$

Therefore the median is 90.

Hope this helps !

Photon

4 0

3 years ago

Write the numbers 57,000,000,000 and 19,000 in scientific notation. Then show how to divide 57,000,000,000 by 19,000 using prope

LenaWriter [7]

Answer:

the first number is 57 to the ninth power and the second is 19 to the third power, not to sure about the dividing but a quick google search should do the trick

Step-by-step explanation:

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3 years ago

Find the lateral surface area of this

Allushta [10]

Answer:226.2

Step-by-step explanation

Lateral= 2πrh

H=12

R=3

2*π*3*12=226.19

Round to nearest 10th is 226.2

6 0

3 years ago