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A train travels 3.5 kilometers on a straight track with grade of 1 degree 10'. What is the vertical rise of the train distance?

denpristay [2]

The answer is
h = AB sin tetha,
tetha is <span>1 degree 10' = 1.1°, and AB = 3.5km

the vertical rise is h = 4.7</span>

3 0

3 years ago

Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor

mel-nik [20]

Answer:

$9$

Step-by-step explanation:

Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.

To find: number that Thea originally entered

Solution:

The final number is $243$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $243$ must be $324$.

As previously the number was squared, so the number before $324$ must be $18$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $18$ must be $81$

As previously the number was squared, so the number before $81$ must be $9$.

6 0

3 years ago

Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if

satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

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 establishes 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.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that $\mu = 64, \sigma = 2$

A) Calculate the standard error for the distribution of means.

Sample of 25 means that $n = 25$ , so $s = \frac{2}{\sqrt{25}} = 0.4$ .

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that $X = 65$ .

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{0.4}$

$Z = \frac{65 - 64}{0.4}$

$Z = 2.5$

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0

2 years ago

If 12x +1 =-7, what’s is the value of x over 8

Sergio [31]

12x+1=-7
-1 -1
12x=-6
/12 /12

x=-1/2 or x=-0.5

8 0

3 years ago

36 is what percent of 90 show work

hodyreva [135]

Answer: 36 is 4% of 90

Step-by-step explanation: create a fraction of 36/90 then divide both numbers by 18.

4 0

2 years ago