4.) What is the area of this shape?​

Answer:

(1) 0.058

(2) 601

Step-by-step explanation:

(1)

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

[tex]\mu_{\hat p}=p\\[/tex]

The standard deviation of this sampling distribution of sample proportion is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 350 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of adults in a certain country work from home.

Compute the probability that fewer than 42 out of a random sample of 350 adults will work from home:

Sample proportion: [tex]\hat p=\frac{42}{350}=0.12[/tex]

[tex]P(\hat p < 0.12)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.12-0.15}{\sqrt{\frac{0.15(1-0.15)}{350}}})\\\\=P(Z<-1.57)\\\\=0.05821\\\\\approx 0.058[/tex]

Thus, the probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.058.

(2)

The (1 - α)% confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The margin of error for this interval is:

[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Given:

MOE = 0.04

Confidence level = 95%

Assume that the sample proportion is 50%.

The critical z-value for 95% confidence level is 1.96.

Compute the required sample size as follows:

[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.50(1-0.50)}}{0.04}]^{2}\\\\=600.25\\\\\approx 601[/tex]

Thus, the required sample size is 601.

1. Using the normal approximation to the binomial, it is found that there is a 0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.

2. Solving the equation for the margin of error of a confidence interval of proportions, it is found that we must survey 601 randomly selected teenagers.

Question 1:

Normal Probability Distribution

In a normal distribution 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]

In this problem:

Then, for the approximation:

[tex]\mu = np = 350(0.15) = 52.5[/tex]

[tex]\sigma = \sqrt{np(1-p)} = \sqrt{350(0.15)(0.85)} = 6.68[/tex]

Using continuity correction, the probability is [tex]P(X < 42 - 0.5) = P(X < 41.5)[/tex], which is the p-value of Z when X = 41.5. So:

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

[tex]Z = \frac{41.5 - 52.5}{6.68}[/tex]

[tex]Z = -1.65[/tex]

[tex]Z = -1.65[/tex] has a p-value of 0.05.

0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.

Question 2:

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]\alpha[/tex], we have the following confidence interval of proportions.

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

The margin of error is:

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

In this problem:

We have to solve for n, then:

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

[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]

[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96(0.5)}{0.04})^2[/tex]

[tex]n = 600.25[/tex]

Rounding up:

We must survey 601 randomly selected teenagers.

A similar problem is given at https://brainly.com/question/24261244

D: She needs to keep going to find more digits.

Answer:

n will be -32

............... ....

Answer:

Q1

|a-b| = b-a when a<b

Q2

104159/33000

Step-by-step explanation:

Q1

If a<b then a-b will always be negative.  To get the absolute value, we can take -(a-b) = -a+b = b-a.

Q2

Let x = 3.12789789789...

We isolate the repeating decimal to start after the decimal, so we multiply by 100.

100x = 312.789789789...

We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.

100000x = 312789.789789

Subtracting the two...

x(100000-100) = 312789.789789 - 312.789789

99900x = 312477

x = 312477/99000 = 104159/33000

Answer:

2 is the constant of proportionality in the equation y = 2x .

Step-by-step explanation:

Definition of constant of proportionality

When two variables are directly proportional to each others .

Let us assume that u and v .

u \propto vu∝v

Than the equation becomes u= kv

Where k is called the constant of proportionality .

Thus in the question x and y are proportional variables .

i.e

y \propto xy∝x

y = kx

Where k is called the constant of proportionality .

Compare the equation y = kx with y=2x .

Thus

k = 2

Therefore 2 is the constant of proportionality in the equation y = 2x

the explanation is not mine only the answer

Answer:

0.0006

Step-by-step explanation:

Answer:

I don't understand your question

Answer:

140°

Step-by-step explanation:

Since we know that a circle is 360 degrees, and we are given three angles, we can subtract what we know from 360 to get ∠PTQ:

360 = 120 + 60 + 40 + ∠PTQ

360 = 220 + ∠PTQ

-220   -220

140 = ∠PTQ

∠PTQ = 140°

Join my math help server in discord to get more help in mathematics:

Friend me at: GeoGuy#0187

Answer:

7.6 repeating or if you want the whole answer its 7.66666666667

Step-by-step explanation:

remember its always best to plug in your equation in the calculator after you answered the equation just to see if your answer is correct.

hope this helps :D

Answer:

its still 69 HA im joking its 7.66666666666

Answer:

102.4?

Step-by-step explanation:

Answer:

h=2A/b

2 (64dm)/1.6m

128dm/1.6m

=80d

Answer:

The answer should be A. $125.00

Step-by-step explanation:

I rounded and added them jajaja.

Answer:

0.95% decrease

Step-by-step explanation:

247/260 to get your answer

Answer:

∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)

Step-by-step explanation:

Start with the Maclaurin series for cos x.

cos x = ∑ₙ₌₀°° (-1)ⁿ x²ⁿ / (2n)!

Substitute ⅓ x².

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓ x²)²ⁿ / (2n)!

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓)²ⁿ x⁴ⁿ / (2n)!

cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)

Multiply by 8x.

8x cos (⅓ x²) = ∑ₙ₌₀°° 8x (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)

8x cos (⅓ x²) = ∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)

Answer:

(B).

Step-by-step explanation:

Statement B is not correct. PR and ST are not corresponding segments.

Whoops! It looks like your question was not part of an academic assignment. Since Brainly is only intended for homework questions, we had to remove it. Please keep the question feed clear of personal questions so other users can get the help they need. Thanks! ߷

Answer:

θ = 36.9°, 90°, 216.9°, or 270°

Step-by-step explanation:

4 sin 2θ − 3 cos 2θ = 3

Use double angle formulas:

4 (2 sin θ cos θ) − 3 (cos²θ − sin²θ) = 3

8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3

Use Pythagorean identity:

8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 (sin²θ + cos²θ)

8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 sin²θ + 3 cos²θ

8 sin θ cos θ − 6 cos²θ = 0

2 cos θ (4 sin θ − 3 cos θ) = 0

2 cos θ = 0

θ = 90° or 270°

4 sin θ − 3 cos θ = 0

4 sin θ = 3 cos θ

tan θ = 3/4

θ = 36.9° or 216.9°

Answer:

the axis of symmerty is 4 and vertex is (4,3) correct me if i am wrong and you can use desmos to help you it is a graphing calculator

Step-by-step explanation:

Answer:

3 1/3 feet

Step-by-step explanation:

100 feet : 15 inches

3 1/3 feet : 1/2 inch

Answer:

[tex]3\frac{1}{3}[/tex] feet

Step-by-step explanation:

Inches : Feet = 15 : 100

Let 'x' be the feet required to find

15 : 100 :: 1/2 : x

Product of extremes  = product of means

          15 * x = 100 * (1/2)

          15 * x = 50

                  x = 50/15

                 x  =  10/3

                 x = [tex]3\frac{1}{3}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

welp you asked me to answer but I don't do this stuff anymore. sorry I hlp you.

Random fact? If you cut off all your skin you could last up to 7 more hours?

I think

Answer:

D

Step-by-step explanation:

21,871 x 0.96 = 20,996

Answer:

1.11

Step-by-step explanation:

Answer:

Original number is 86

Step-by-step explanation:

              Original:   10x + y

Double reversed:   2(10y + x)

Constraints:

  x + y = 14                                     ===>            x = 14 - y

  2(10y + x) + 10x + y = 222          ===>           21y + 12x = 222

Substitution to find y:

  21y + 12x = 222

  21y + 12(14 - y) = 222

  21y + 168 - 12y = 222

            9y + 168 = 222

                      9y = 54

                        y = 6

Substitution to find x:

  x = 14 - y

  x = 14 - 6

  x = 8

Original:   10x + y

                 10(8) + (6)

                 80 + 6

                 86