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4 years ago

How do you do this question?

Mathematics

1 answer:

LiRa [457]4 years ago

3 0

Step-by-step explanation:

arctan(x) is less than π/2 for x > 0. Therefore, if we say g(x) = 13 (π/2) / eˣ, then f(x) < g(x) for all values of x > 0.

g(x) = 13 (π/2) / eˣ

g(x) = 13π/2 · (1/e)ˣ

So g(x) is a geometric series where r = 1/e. Since |r| < 1, the series converges.

Since g(x) converges, the smaller f(x) also converges.

You might be interested in

Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college. You survey 10

neonofarm [45]

Answer: 1.460

Step-by-step explanation:

Given : Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college.

Let $\mu$ represents the population mean .

Then, the set of hypothesis will be:-

$H_0: \mu=15$

$H_a:\mu\neq15$

We assume that this is normal distribution.

Sample size : n = 10, which is a small sample (n<30) ,s o we use t-test.

Sample mean : $\overliene{x}=16.2\ lbs$

Standard deviation : $\sigma=2.6$

The test statistic for population mean for small sample is given by :-

$t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t=\dfrac{16.2-15}{\dfrac{2.6}{\sqrt{10}}}=1.45951276623\approx1.460$

Hence , the value of test statistic = 1.460

4 0

3 years ago

How are integers and their opposites related? give an example with numbers.

alukav5142 [94]

Answer:

Integers are the set of whole numbers and their opposites. Whole numbers greater than zero are called positive integers. Whole numbers less than zero are called negative integers. The integer zero is neither positive nor negative, and has no sign. Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. Positive integers can be written with or without a sign. an example with numbers is 17positive and 17 negative both are 17 (clicks/jumps/etcetera) away from 0. There is no 0 positive or negative.

7 0

3 years ago

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be 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

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

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$