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2 years ago

F (10) = 10/2 = 5 . how to solve this problem

Mathematics

2 answers:

qwelly [4]2 years ago

5 0

For a function

f(x)=y

x is the input or domain

y is the output or range

Here

f(10)=10/2

x=10

y=10/2

Hence the function is

f(x)=x/2

Sonja [21]2 years ago

3 0

Answer:

f(10) means to input x = 10 into the function.

From inspection of the given function:

$\sf f(10)=\dfrac{10}{2}=5$

the "10" is the numerator of the fraction.

Therefore, swap the "10" for "x" to give the function in terms of x:

$\sf f(x)=\dfrac{x}{2}$

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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.

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3 years ago

0.5 grams of salt is equal to how many milligrams show you work

elena55 [62]

Answer:

500 milligrams (mg)

Step-by-step explanation:

1 Gram (g) is equal to 1000 milligrams (mg). To convert grams to milligrams, multiply the gram value by 1000. For example, to convert 2 grams to mg, multiply 2 by 1000, that makes 2000 mg is 2 grams.

6 0

3 years ago

Read 2 more answers

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly samp

aleksklad [387]

Answer:

95.44% probability the resulting sample proportion is within .04 of the true proportion.

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 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.

For the sampling distribution of the sample proportion in sample of size n, the mean is $\mu = p$ and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = 0.2, n = 400$

$\mu = 0.2, s = \sqrt{\frac{0.2*0.8}{400}} = 0.02$

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.

X = 0.24

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

By the Central Limit Theorem

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

$Z = \frac{0.24 - 0.2}{0.02}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 0.16

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

$Z = \frac{0.16 - 0.2}{0.02}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

95.44% probability the resulting sample proportion is within .04 of the true proportion.

6 0

3 years ago

Read 2 more answers

When BA=10 ft, find the area of the region that is NOT shaded. Round to the nearest whole number. (reply so i can draw it out, p

nexus9112 [7]

The area of the region that is not shaded in the diagram is determined through the following solution:

A = (1 − (60°/360°)*π) * (10 ft ) ^2 A = 56*π*100 [ft2] A = 250/3 π [ft2]
A = 262 [ft2]

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3 years ago

For the following exercises, find a formula for an exponential function that passes through the two points given. (0,6) and (3,7

kirill [66]

$\boxed{\boxed{f(x)=6(5)^x}}$

<h2>Explanation:</h2>

An exponential function is given by the following form:

$y=ab^x \\ \\ Where: \\ \\ a \ is \ a \ constant \ and \ b \ is \ the \ base$

Here we know two points:

$(0,6) \ and \ (3,750)$

$\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}$

Finally, our exponential function is:

$\boxed{\boxed{f(x)=6(5)^x}}$

<h2>Learn more:</h2>

Behavior of functions: brainly.com/question/12891789

#LearnWithBrainly

5 0

3 years ago

F (10) = 10/2 = 5 . how to solve this problem​

F (10) = 10/2 = 5 . how to solve this problem