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2 years ago

6

Joshua teaches an SAT preparation class where each student takes a pre-test on the first day of class and a post-test on the las

t day of class. Here are summary statistics for the scores of a recent group of students

Advanced Placement (AP)

1 answer:

Andreas93 [3]2 years ago

5 0

Answer:

Standard Deviation of D: It cannot be determined from the information given because the scores are not independent.

Explanation:

Khan academy

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1. The rate at which people enter a movie theater on a given day is modeled by the function S defined by S(t) = 80 -12 cos 6 The

Arlecino [84]

Hi there!

a.

To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

$\text{Amount that entered} = \int\limits^{20}_{10} {S(t)} \, dt \\\\ = \int\limits^{20}_{10} {80 - 12cos(\frac{t}{5})} \, dt$

Evaluate using a calculator:

$= 899.97 \approx \boxed{900\text{ people}}$

b.

To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.

In other terms:
$\text{Amount of people} = \int\limits^{20}_{10} {S(t)} \, dt - \int\limits^{20}_{10} {R(t)} \, dt$

We can evaluate using a calculator (math-9 on T1-84):

$\text{\# of people} = \int\limits^{20}_{10} {80-12cos(\frac{t}{5})} \, dt - \int\limits^{20}_{10} {12e^{\frac{t}{10}}+20} \, dt$

$= 899.97 - 760.49 = 139.47 \approx \boxed{139 \text{ people}}$

c.

If:
$P(t) = \int\limits^t_{10} {S(t) - R(t)} \, dt$

Then:

$\frac{dP}{dt} = P'(t)= \frac{d}{dt}\int\limits^t_{10} {S(t) - R(t)} \, dt = S(t) - R(t)$

Evaluate at t = 20:

$S(20) = 80 - 12cos(\frac{20}{5}) = 87.844\\\\R(20) = 12e^{\frac{20}{10}} + 20 = 108.669$

$S(20) - R(20) = 87.844 - 108.669 = -20.823$

This means that at t = 20, there is a <u>NET DECREASE</u> of people at the movie theater of around 20.823 (21) people per hour.

d.

To find the maximum, we must use the first-derivative test.

Set S(t) - R(t) equal to 0:

$80 - 12cos(\frac{t}{5}) - 12e^{\frac{t}{10}} - 20 = 0\\\\60 - 12(cos(\frac{t}{5}) + e^{\frac{t}{10}})= 0$

Graph the function with a graphing calculator and set the function equal to y = 0:

According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.

<u>Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.</u>

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2 years ago

Which statement describes a weather condition?

atroni [7]

Answer:

I think its the first one

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2 years ago

Tulong kailangan tama

vivado [14]

Answer:

1.D

2.P

3.E

4D

5.P

Explanation:

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3 years ago

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What strategies and techniques were used in the mongol conquests of northern China and Persia?

Bess [88]

Answer:

Mongols were given masterful training for every type of possibility so that they could react accordingly whenever it occurred.

Explanation:

The Mongols conquered Iran, Iraq, the Caucasus, and parts of Syria and Turkey, Palestine as far as Gaza in 1260 and 1300. Various strategies and techniques were used in the Mongol conquests of northern China and Persia. Mongols were given masterful training for every type of possibility so that they could react accordingly whenever it occurred. The Mongols also tried to protect their ranking officers.

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2 years ago

If all chlorine and bromine from human sources were eliminated from the stratosphere, which statement would be correct?

Naily [24]

The statement that would be correct is that Current total chlorine would decrease by half.

<h3>What is the presence of chlorine and bromine in the stratosphere?</h3>

The both in the stratosphere leads to Ozone Depletion this is because if chlorine and bromine atoms unit with ozone in the stratosphere, they tend to destroy ozone molecules.

Hence, The statement that would be correct is that Current total chlorine would decrease by half as it is the most valuable options among them.

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2 years ago

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