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nirvana33 [79]
3 years ago
5

Are two equilateral triangles always similar

Mathematics
1 answer:
sukhopar [10]3 years ago
4 0
Yes because all equilateral triangles have equal angles and side lengths so they are all similar. hope i helped -J

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The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili
Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

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

By the Central Limit Theorem

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

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

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

Z = \frac{77 - 74}{1.2274}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 71

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

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

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

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0
3 years ago
50 points!! Help needed
babunello [35]

Answer:

1) Enlargement

2) Reduction

Step-by-step explanation:

Question 1

200% means double, a factor 2

a) 2(2.5) = 5 inches

it's an enlargement

b) 2(original) = new/on the page

Question 2

a) 0.6(24) = 14.4 inches

Reduction

b) 0.6(original) = new/sketch

4 0
3 years ago
Read 2 more answers
For four weeks in June Cameron baked 3 1/4 miles each week and swim 2 1/2 miles each week for three weeks in July he baked 4 3/4
Tems11 [23]
For June:
 Bike:
 (4) * (3 1/4) = 13 miles
 Swim:
 (4) * (2 1/2) = 10 miles
 Total:
 13 + 10 = 23 miles
 For July:
 Bike:
 (3) * (4 3/4) = 14.25 miles
 Swim:
 (3) * (3 1/2) = 10.5 miles
 Total:
 14.25 + 10.5 = 24.75 miles
 The difference between both months is:
 24.75 - 23 = 1.75 miles
 Answer:
 
the total distance Cameron bike and swim in July compared to the total distance he bike in swim in June was 1.75 miles greater
6 0
3 years ago
Yoshiko is a real estate agent. This
Serhud [2]

Answer:

5,750-2,480=3270

Step-by-step explanation:

5,750-2,480=3270

5 0
2 years ago
Can u answer this for me please step by step I'm desperate<br> -| -40 |
kicyunya [14]

Answer:

- 40

Step-by-step explanation:

The absolute value always returns a positive value , that is

- | - 40 | = - | 40 | = - 40

3 0
2 years ago
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