Which event is closest to being fair?
Event C
Event D
Event B
Event A

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The machine is known to have 99 green balls and 78 red balls.

This means that [tex]p = \frac{99}{99+78} = 0.5593[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.5593[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373[/tex]

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.61 - 0.5593}{0.0373}[/tex]

[tex]Z = 1.36[/tex]

[tex]Z = 1.36[/tex] has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

Answer:

133 square centimeters

Step-by-step explanation:

Answer:

Surface A≈146.25 square centimeters

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

and take the natural log of both sides:

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

To solve for x, we now divide both sides by ln(1.035):

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

Answer:Welcome to Brainly

Step-by-step explanation:

Hope this was helpful.

Answer:

1.5 liters × 1000

= 1500 milliliters

Answer:

46/117

Step-by-step explanation:

Answer:

46/117

Step-by-step explanation:

this is a type of fraction which can not be simplified

Answer:

According to the guideline from the Health Department, every over-weight child needs to take a fitness test.

Every ten over-weight children would be randomly grouped together to attend the fitness test. According to

the past experience

Step-by-step explanation:

Answer:

There is only 1 solution

[tex](x,y) = (1,4)[/tex]

Step-by-step explanation:

Given

Lines A and B

Required

The number of solution for a pair of A and B

From the graph, lines A and B have only one point of intersection.

This point of intersection represents the solution

Since, there is only 1 point, there is only one solution.

And the solution is:

[tex](x,y) = (1,4)[/tex]

9514 1404 393

Answer:

  164π cm²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr²

The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...

  1/2A = (1/2)(π)(d/2)² = (π/8)d²

The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.

The total area will be ...

  area of largest + area of middle-size - area of smallest

  = (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²

The area of the shape is 164π cm².

The sum of the angles for a 4 sides figure must add up to 360.

Angle 1 and angle 2 are between similar sides so the 2 angles are identical.

Subtract the known angles from 360:

360 - 72 - 18 = 270

Divide that by 2:

270*2 = 135

Angle 2 = 135 degrees.

Answer: 1/2 cx

Step-by-step explanation: I did the quiz

Answer:

A and B

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

225 ÷ 9 =25

Answer:

X=9

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

The answer to this question is X=3

Step-by-step explanation:

15x3=45

45+1=46

Hope my answer helps you!!!

Answer:

A sample of 2017 people should be taken.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Suppose a 95% confidence level:

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Preliminary estimate of the proportion who smoke of .30.

This means that [tex]\pi = 0.3[/tex]

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)

This is n for which M = 0.02. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.02})^2[/tex]

[tex]n = 2016.84[/tex]

To the nearest whole number, 2017.

A sample of 2017 people should be taken.

Answer: x=-1

Step-by-step explanation:

Answer:1.8

Step-by-step explanation:

Answer:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]

Step-by-step explanation:

Given

[tex]tan\theta = 3[/tex]

Required

Find

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex]

Calculate [tex]tan(\theta + \pi) \ and\ tan(\theta+2\pi)[/tex]

Using tan rule

[tex]tan(\theta + \pi) = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}[/tex]

So:

[tex]tan(\theta + \pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + \pi) = \frac{tan\theta}{1 }[/tex]

[tex]tan(\theta + \pi) = \tan\theta[/tex]

[tex]tan(\theta+2\pi)[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + 2\pi) = \tan\theta[/tex]'

'So:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex] [tex]= tan\theta +tan\theta +tan\theta[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]

Answer:

it's simple just divide

Answer:

21 you is smart 8th

Step-by-step explanation:

smart smart 99

Answer:

180 teenagers were at the game

Answer:

25

Step-by-step explanation:

1/5 x 125 = 25

Answer:

25 :)

Step-by-step explanation:

Answer:

$5740

Step-by-step explanation:

get 2.5% of 5600

5600/x=100/2.5

(5600/x)*x=(100/2.5)*x

5600=40*x

5600/40=x

140=x

x=140 <----- 2.5% of 5600

5600 + 140 = $5740