if the circumference of a circle is 12 and the angle measure of an arc is 60 which is the length of the arc

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

when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four s

Eva8 [605]

Answer:

The stone would take approximately 10.107 seconds to fall 500 meters.

Step-by-step explanation:

According to the statement of the problem, the following relationship of direct proportionality is built:

$t \propto y^{1/2}$

$t = k\cdot t^{1/2}$

Where:

$t$ - Time spent by the stone, measured in seconds.

$y$ - Height change experimented by the stone, measured in meters.

$k$ - Proportionality constant, measured in $\frac{s}{m^{1/2}}$ .

First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

$k = \frac{t}{y^{1/2}}$

If $t = 4\,s$ and $y=78.4\,m$ , then:

$k = \frac{4\,s}{(78.4\,m)^{1/2}}$

$k \approx 0.452\,\frac{s}{m^{1/2}}$

Then, the expression is $t = 0.452\cdot y^{1/2}$ . Finally, if $y = 500\,m$ , then the time is:

$t = 0.452\cdot (500\,m)^{1/2}$

$t \approx 10.107\,s$

The stone would take approximately 10.107 seconds to fall 500 meters.

4 0

3 years ago

What is the rule input numbers are 17 18 _ 28_40

Lelu [443]

19 27 28 29 30 315 64 29 46 is the
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4 0

3 years ago

The Board of Directors of a small company consists of five people. Two of those directors are considered "strong leaders". If th

Pavel [41]

1: 40%
2: 30%
3: 20%

If we know one of the succeeded, then
1: 44.44%
2: 33.33%
3: 22.22%

If under the circumstance that they all fail to meet a strong leader, the board picks one of them at random,
1: 43.33%
2: 33.33%
3: 23.33%

The first person has a 2 in 5 chance of randomly getting a strong leader. If the first person doesn't find a strong leader, the second person has a 2/4 chance of getting a strong leader. If neither the first nor second person gets a strong leader, the third sales person has a 2/3 chance of getting a strong leader.

1: 2/5=40% Chance
2: (3/5)*(2/4)=30% Chance You have to take the probability the first rep failed to get a strong leader, then multiply by the probability the second rep gets a strong leader.
3: (3/5)*(2/4)*(2/3)=20% You have to take the probability both the other people failed, then multiply by the probability they succeeded.

7 0

3 years ago

3. Mrs Green bakes muffins.

Sphinxa [80]

Answer:

85%

Step-by-step explanation:

Monday:

200 x 0.70 = 140

200 - 140 = 60

Tuesday:

400 x ? = 60

400 x 0.85 = 340

400 - 340 = 60

8 0

3 years ago