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11 days ago

Please consider the following data set. The initial row provides labels for two variables (i.e., X1 and X2). Each subsequent row

represents a pair of related scores from the same person at two different points in time.
X1 X2
2 4
6 7
7 6
3 5
8 9
Compute the appropriate t statistic to test the null hypothesis that there is no difference between means. When computing the t statistic, please retain a minimum of four decimal places for all intermediate steps (when relevant). For your final answer, please report the absolute magnitude of the t statistic with a minimum of three decimal places.

Mathematics

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While in college, why did Euler work through advanced math books on his own? His father required it. The quality of education of

Inessa [12570]

The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I completed the assignment and got it correct.

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2 months ago

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According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

tester [12383]

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

d) $P(r = 15) = 3.2768 *10^{-11}$

Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

$P(r = n) = ^nC_r * p^r * q^{n-r}$

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=> $q = 1 - p$

Thus

$P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}$

$P(r = 15) = 3.2768 *10^{-11}$ Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

$P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}$

$P(r = 5) = 0.1032$

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

$P(r \ge 1 ) = 1 - P (r = 0 )$

$P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]$

$P(r \ge 1 ) = 1 - 0.0352$

$P(r \ge 1 ) = 0.9648$

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2 months ago

A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as i

tester [12383]

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.

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3 months ago

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give me 3 pictures showing the application of the sum and the product of the roots of quadratic equations in real life . describ

babunello [11817]

Quadratic equations find their application in various real-world scenarios such as: sports, bridges, projectile motion, the curvature of bananas, and so on.

Here are three images representing real-world instances of quadratics:

Example 1: A cyclist travels along a parabolic trajectory to leap over obstacles.

Example 2: A person throws a basketball towards the hoop, moving in a gently upward path described by a quadratic curve.

Example 3: A football player kicks the ball upward, which follows a quadratic path as it travels a distance.

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2 months ago

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Which expression is equivalent to StartFraction 3 x Superscript negative 6 Baseline y Superscript negative 3 Baseline Over 15 x

zzz [12365]

Answer:

The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

Step-by-step explanation:

In order to simplify the expression $\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }$ where x ≠ 0, y ≠ 0, we must work through the given expression.

$\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }\\= \frac{3}{15} x^{-6-2}y^{-3-10}\\ = \frac{3}{15}x^{-8}y^{-13} \\ =\frac{1}{5}x^{-8}y^{-13} \\$

The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

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2 months ago