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Otrada [13]
2 years ago
9

Examine the power 5^4

Mathematics
1 answer:
sveticcg [70]2 years ago
8 0

[ Answer ]

625

[ Explanation ]

5^4 means you are multiplying 5 by itself 4 times.

5 * 5 * 5 * 5

= 625

<> Arsenal <>

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According to the Knot, 22% of couples meet online. Assume the sampling distribution of p follows a normal distribution and answe
Ann [662]

Using the <em>normal distribution and the central limit theorem</em>, we have that:

a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

In this problem:

  • 22% of couples meet online, hence p = 0.22.
  • A sample of 150 couples is taken, hence n = 150.

Item a:

The mean and the standard error are given by:

\mu = p = 0.22

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338

The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 0.25</u>, hence:

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

By the Central Limit Theorem:

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

Z = \frac{0.25 - 0.22}{0.0338}

Z = 0.89

Z = 0.89 has a p-value of 0.8133.

1 - 0.8133 = 0.1867.

There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

Item c:

The probability is the <u>p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15</u>, hence:

X = 0.2:

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

Z = \frac{0.2 - 0.22}{0.0338}

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

X = 0.15:

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

Z = \frac{0.15 - 0.22}{0.0338}

Z = -2.07

Z = -2.07 has a p-value of 0.0192.

0.2776 - 0.0192 = 0.2584.

There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213

4 0
2 years ago
Use the compound interest formula to determine the final value of the given amount.
CaHeK987 [17]

Answer:

342.22$

Step-by-step explanation:

7 0
2 years ago
14 lessons costs $210. What would 72 lessons cost
Oksi-84 [34.3K]

Answer:

$1,080

Step-by-step explanation:

To solve, we can make a proportion

14 lessons are $210 and 72 lessons are $x

14/210=72/x

Cross multiply

14*x=210*72

14x=15120

To solve for x, we need to get x by itself. Since x is being multiplied by 14, divide both sides by 14.

14x/14=15120/14

x=1080

So, 72 lessons will cost $1,080

4 0
2 years ago
Read 2 more answers
Need help filling in the blanks.. also not sure if the answers i filled in are correct or not.
tino4ka555 [31]

Answer:

See below.

Step-by-step explanation:

For item 2:  

The Net Price Rate = 276 / 460 = 0.60 = 60 % (answer).

Item 3: Net Price Rate =  3247 * 100 / 3820 = 85% (answer).

Item 4 Net Price Rate =  675.11 / * 100 / 987 =  68.4%. (answer).

Item 5 Item's Net Price = 987 * 0.675 = $666.23 (answer).

Item 7 Net price Rate =  2945* 100 / 4750 = 62%. (answer).

Item 8: First find the list place $x:

0.90* 0.80 * 0.70x  = 252   ( the 0.90 , 0.80 and 0.70 come from 100 - 10% = 1 - 0.10 = 0.90  and so on)

0.504 x = 252

x = $500

Answer is List Price = $500 and Net Price Rate = 50.4%.

Item 10  List price =  2890.65 / 0.35 = $8259. (answer)

5 0
3 years ago
A. Let a, b, c be positive integers and suppose that
kodGreya [7K]

Answer:

Step-by-step explanation:

a|c means that c=a*k k is some positive integer. We know that b|c so b| ak and (a,b)=1, so it must be b|k, i.e k=b*r, r is some positive integer number. Now we have that c=abr, so ab| c.

B) if x and x’ are both solution then we have that

mi | x-x’ for every i.

By a) we have that m1m2...mk| x-x’, so x and x’ are equal by mod od m1m2...mk.

5 0
3 years ago
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