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sukhopar [10]
3 years ago
11

The Pythagorean Theorem and Irrational numbers

Mathematics
1 answer:
Natalka [10]3 years ago
3 0
49=16+x^2
x^2= 33
x= square root of 33
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A distribution of values is normal with a mean of 220 and a standard deviation of 13. From this distribution, you are drawing sa
Paraphin [41]

Answer:

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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 distributied random variable X, with mean \mu and standard deviation \sigma, the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 220, \sigma = 13, n = 35, s = \frac{13}{\sqrt{35}} = 2.1974

Find the interval containing the middle-most 48% of sample means:

50 - 48/2 = 26th percentile to 50 + 48/2 = 74th percentile. So

74th percentile

value of X when Z has a pvalue of 0.74. So X when Z = 0.643.

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

By the Central Limit Theorem

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

0.643 = \frac{X - 220}{2.1974}

X - 220 = 0.643*2.1974

X = 221.41

26th percentile

Value of X when Z has a pvalue of 0.26. So X when Z = -0.643

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

-0.643 = \frac{X - 220}{2.1974}

X - 220 = -0.643*2.1974

X = 218.59

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

5 0
3 years ago
A lawn sprinkler sprays water 5 ft in every direction as it rotates. What is the area of the sprinkled lawn?
Karolina [17]

Answer:

78.57

Step-by-step explanation:

Radius is 5 feet

Area of circle is pi*r  Squared

22/7*5*5

78.57 square feet

6 0
2 years ago
Read 2 more answers
HELPPP
Rudiy27

Formula: A = 2wl + 2lh + 2hw

So... : A = 2(4x8) + 2(8x3) + 2(3x4)

         A = 2(32)   + 2(24)   + 2(12)

         A = 64 + 48 + 24

<u>Answer: A = 136</u> (add them all up)

Hope this helps!!!

:)

8 0
3 years ago
At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equa
MrRa [10]

Answer:

13 seashells

Step-by-step explanation:

p=number of seashells pierre collected

p+3p=52

4p=52

p=13

13 seashells

7 0
3 years ago
Read 2 more answers
Devon invests in an account for 10 years that pays 2.15% compound interest annually. He uses the expression P(1+r)t to find the
zheka24 [161]

Answer:

FV= $4,948.16

Step-by-step explanation:

Giving the following information:

Number of periods (n)= 10

Interest rate (i)= 2.15% compound interest annually

Present value (PV)= 4,000

<u>To calculate the future value, we need to use the following formula:</u>

FV= PV*(1+i)^n

FV= 4,000*(1.0215^10)

FV= $4,948.16

7 0
2 years ago
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