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galben [10]
3 years ago
11

1.) 45r^3-15r^2 *Factoring* 2.) 9x^2-3x 3.) X^2+3x

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
4 0

NOTES: Find the common factor of the terms and factor it out:

1. Answer:   15r²(3r - 1)

<u>Step-by-step explanation:</u>

45r³ - 15r²      <em>they both have 15 and r² as factors</em>

15r^2\bigg(\dfrac{45r^3}{15r^2}-\dfrac{15r^2}{15r^2}\bigg)

= 15r²(3r - 1)

************************************************************************************

2. Answer:   3x(3x - 1)

<u>Step-by-step explanation:</u>

9x² - 3x          <em>they both have 13 and x as factors</em>

3x\bigg(\dfrac{9x^2}{3x}-\dfrac{3x}{3x}\bigg)

= 3x (3x - 1)

************************************************************************************

3. Answer:    x(x + 3)

<u>Step-by-step explanation:</u>

x² + 3x         <em>they both have x as a factor</em>

x\bigg(\dfrac{x^2}{x}+\dfrac{3x}{x}\bigg)

= x(x + 3)

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Point A is 3 units to the left from the graph

The graph, if translated 3 units to the left will include the point A.

<u>Horizontal translation is:</u>

  • f(x) ⇒ f(x + 3)

Correct option is 3.

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wlad13 [49]

by multiplication of 15 and 5.81 answer is the

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Order the following decimals from greatest to least (separated by
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According to data released by FiveThirty Eight (data drawn on Monday, August 17th, 2020), Donald Trump wins an Electoral College
sineoko [7]

Answer:

a) P = 0.274925

b) required confidence interval = (0.2705589, 0.2793344)

c) FALSE

d) FALSE

e) TRUE

f) There is still probability that he would win. And it would be highly unusual if he wins assuming that the true population proportion is 0.274925.

Step-by-step explanation:

a)

PROBABILITY

since total number of simulations is 40,000 and and number of times Donald Trump wins an Electoral College majority in the 2020 US Presidential Election is  10,997

so the required Probability will be 10,997 divided by 40,000

P = 10997 / 40000 = 0.274925

b)

To get 95% confidence interval for the parameter in question a

(using R)

>prop.test(10997,40000)

OUTPUT

1 - Sample proportion test with continuity correction

data: 10997 out of 40000, null probability 0.5

x-squared = 8104.5, df = 1, p-value < 2.23-16

alternative hypothesis : true p ≠ 0.5

0.2705589  0.2793344

sample estimate

p

0.274925

∴ required confidence interval = (0.2705589, 0.2793344)

c)

FALSE

This is a wrong interpretation of a confidence interval. It indicates that there is 95% chance that the confidence interval you calculated contains the true proportion. This is because when you perform several times, 95% of those intervals would contain the true proportion but as the confidence intervals will vary so you can't say that the true proportion is in any interval with 95% probability.

d)

FALSE

Once again, this is a wrong interpretation of a confidence interval. The confidence interval tells us about the population parameter and not the sample statistic.

e)

TRUE

This is a correct interpretation of a confidence interval. It indicates that if we perform sampling with same sample size (40000) several times and calculate the 95% confidence interval of population proportion for each of them, then 95% of these confidence interval should contain the population parameter.

f)

The simulation results obtained doesn't always comply with the true population. Also, result of one simulation can't be taken for granted. We need several simulations to come to a conclusion. So, we can never ever guarantee based on a simulation result to say that Donald Trump 'Won't' or 'Shouldn't' win.

There is still probability that he would win. And it would be highly unusual if he wins assuming that the true population proportion is 0.274925.

5 0
3 years ago
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre o
DerKrebs [107]
Given:250 sheep in a 40-acre pasture.Number of sheep grazing in each acre.
250/40 = 6.25 or 6 sheep per acre
n = 6sample proportion: signified by ρSample 1: 4 → 4/6 = 0.67Sample 2: 1 → 1/6 = 0.17Sample 3: 9 → 9/6 = 1.50
multiply the sample proportion by 1-ρSample 1: 0.67(1-0.67) = 0.67(0.33) = 0.2211Sample 2: 0.17(1-0.17) = 0.17(0.83) = 0.1411Sample 3: 1.50(1-1.5) = 1.5(-0.5) = -0.75
divide the result by n. n = 6Sample 1: 0.2211/6 = 0.03685Sample 2: 0.1411/6 = 0.02352Sample 3: -0.75/6 = -0.125
square root of the quotient to get the standard error.Sample 1: √0.03685 = 0.1919Sample 2: √0.02352 = 0.1534Sample 3: √-0.125 = invalid
z value 95% confidence 1.96.
Sample 1: 1.96 * 0.1919 = 0.3761 or 37.61% margin of errorSample 2: 1.96 * 0.1534 = 0.3007 or 30.07% margin of error
3 0
3 years ago
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