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amm1812
3 years ago
5

The area (A) of a circle with a radius of r is given by the formula A=3.14r^2 and its diameter (d) is given by d=2r. Arrange the

equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.
Mathematics
1 answer:
wariber [46]3 years ago
4 0

Answer:

D=2\sqrt{\frac{A}{3.14}}

Step-by-step explanation:

we know that

The area of a circle is

A=3.14r^{2} ----> equation A

The diameter of a circle is

D=2r ----> equation B

Solve for r in the equation A

That means ---> isolate the variable r

Divide by 3.14 both sides

\frac{A}{3.14}=r^{2}

take the square root both sides

\sqrt{\frac{A}{3.14}}=r

Rewrite

r=\sqrt{\frac{A}{3.14}}

Substitute the value of r in the equation B

D=2\sqrt{\frac{A}{3.14}}

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

Z = \frac{X - \mu}{s}

X = 205

Z = \frac{X - \mu}{s}

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

Z = \frac{X - \mu}{s}

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
Solve the inequality -10w _< 20
Dvinal [7]

Step-by-step explanation:

  • -10w<u><</u><u> </u>20
  • w<u><</u><u> </u>20/-10
  • w<u><</u><u> </u>-2

hope it helps

<h2>stay safe healthy and happy...</h2>
8 0
2 years ago
Express as a trinomial (3x+8) (x+10)
docker41 [41]

Answer:

3x^{2} +38x+80

Step-by-step explanation:

Hello!

A trinomial is a expression consisting of three different terms

To turn this into a trinomial we multiply everything to each other

<u>                     3x                     </u>

3x * x = 3x^{2}

3x * 10 = 30x

<u>                     8                      </u>

8 * x = 8x

8 * 10 = 80

Now we put them all together in an equation

3x^{2} +30x+8x+80

Combine like terms

3x^{2} +38x+80

The answer is 3x^{2} +38x+80

Hope this helps!

7 0
2 years ago
Write the equation of a line that is
il63 [147K]

Answer:

Y= 3x-7

Step-by-step explanation:

Since the line is parallel , the slope is same i.e. 3 .

now the equation should be y= Mx + b where m is the slope and c is the y-intercept

plugging the value of m=3 and ( 3,2) into the equation

2= 3(3) + c

2= 9+ c

c= -7

hence the equation of the line is y=3x-7

8 0
2 years ago
Someone help me with this please, I really need help, and it's due tmrw...PLEASE
levacccp [35]

Answer:

the last one

Step-by-step explanation:

3.5(w) 3.5 per week or 3.5 change per week

hope this was helpful

3 0
2 years ago
Read 2 more answers
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