From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.

The little lines theu each section are telling you all those sections are identical, which mean they are the same length.

You are told one section is 10, which means x is also 10

X = 10

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

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.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that [tex]\mu = 85, \sigma = 8[/tex]

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

[tex]Z = \frac{100 - 85}{8}[/tex]

[tex]Z = 1.875[/tex]

[tex]Z = 1.875[/tex] has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

[tex]-0.84 = \frac{X- 85}{8}[/tex]

[tex]X - 85 = -0.84*8[/tex]

[tex]X = 78.28[/tex]

The weight that 80% of the apples exceed is of 78.28g.

Both figures r similar (given )

[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]

The solution of the inequality will be;

⇒ x ≤ 9

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 15 + x ≤ 24

Now,

Since, The inequality is,

⇒ 15 + x ≤ 24

Solve the inequality as;

⇒ 15 + x ≤ 24

Subtract 15, we get;

⇒ 15 + x - 15 ≤ 24 - 15

⇒ x ≤ 9

Thus, The solution of the inequality will be;

⇒ x ≤ 9

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Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Interest amount paid on loan = $90

Principal value, amount borrowed = $500

Period, t = 16 days

The equivalent annual interest :

Using the simple interest formula :

simple interest = principal * rate * time

Using, days of year = 365

Plugging in the values into the formula :

90 = 500 * rate * (16/365)

90 = 500 * rate * 0.0438356

90 = 21.917808 * rate

Rate = 90 / 21.917808

Rate = 4.10 = 4.10 * 100% = 410%

If days of year = 360 is used :

90 = 500 * rate * (16/360)

Rate = 90 / 22.222

Rate = 4.05 = 4.105 * 100% = 405%:

Answer:

381 cm³

Step-by-step explanation:

Volume of the pot = volume of a cylinder

Volume of the pot = πr²h

Where,

π = 3.14

radius (r) = 4.5 cm

h = 6 cm

Substitute

Volume of the pot = 3.14*4.5²*6

Volume of the pot = 381.51 ≈ 381 cm³ (nearest whole number)

-10369

too lazy but that's the exact value

Answer:

Step-by-step explanation:

(-2)³ *(-4)² * 3⁴ = (-8) * 16 * 81

                      = -10368

Answer:

25/30

5/8

Step-by-step explanation:

Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?

to determine which fractions are greater than 1/2, convert the fractions to decimals

to convert to decimals, divide the numerator by the denominator

1/2 = 0.5  less than half

6/14 = 0.43 less than half

5/8 = 0.625 greater than half

25 / 30 = 0.83 greater than half

3 / 6 = 0.5 equal to half

Answer:

The answer is below

Step-by-step explanation:

The empirical rule states for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviations and 99.7% falls within three standard deviations.

z score is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given that mean (μ) = 42 ounces, standard deviation (σ) = 10 ounces.

a) 99.7% falls within three standard deviations. Therefore:

99.7% falls within μ ± 3σ = 42 ± 3(10) = 42 ± 30 = (12, 72)

Therefore 99.7% falls within 12 ounce and 72 ounce.

b) For x > 26

[tex]z=\frac{26-42}{10}=-1.6\\[/tex]

For x < 66

[tex]z=\frac{66-42}{10}=2.4\\[/tex]

From the normal distribution table, P(26 < x < 66) = P(-1.6 < z < 2.4) = P(z < 2.4) - P(z < -1.6) = 0.9918 - 0.0548 = 0.937 = 93.7%

c) For x > 34

[tex]z=\frac{34-42}{10}=-0.8\\[/tex]

From the normal distribution table, P(x > 34) = P(z > -0.8) = 1 - P(z < -0.8) = 1 - 0.2119 = 0.7881 = 78.81%

Answer:

Step-by-step explanation:

Given that:

Mean [tex]\mu[/tex] = 42

standard deviation [tex]\sigma[/tex] = 10

Using Empirical Rule:

[tex]\mu[/tex]  - [tex]\sigma[/tex] = 42 - 10 = 32                   [tex]\mu[/tex]  + [tex]\sigma[/tex] = 42 + 10 = 52                  

[tex]\mu[/tex]  - 2[tex]\sigma[/tex] = 42 - 2(10) = 22            [tex]\mu[/tex]  + 2[tex]\sigma[/tex] = 42 + 2(10) = 62         

[tex]\mu[/tex]  - 3[tex]\sigma[/tex] = 42 - 3(10) = 12             [tex]\mu[/tex]  + 3[tex]\sigma[/tex] = 42 + 3(10) = 72      

The curve is attached in the image below.

a). the widget of 99.7% lies between 12 and 72

b) 68 + 13.5 = 81.5%

c) 50 + 34 = 84%

Step-by-step

I hope it helps you

Answer:

B. y + z = x

Step-by-step explanation:

x is an exterior angle of the triangle.

y and z are the opposite angles opposite the exterior angle.

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.

Thus:

y + z = x

Ans : the measure of WX = 8

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the attached file.

For question 1:

Forecast for December:

[tex]\to \frac{(77+75+83)}{3} \\\\ \to 78.33[/tex]

For question 2:

Forecast for December:

[tex]\to (77 \times .5+75 \times 3+83 \times .2) \\\\\to 79.40[/tex]

For question 3:

Forecast for December:

[tex]\to 72.22+(83-72.22)\times 0.2 \\\\\to 74.37[/tex]

For question 4:

So, the 3-month weighted moving average (3.58)

Answer:

ans: 4

Step-by-step explanation:

corresponding sides are proportional since given triangle are similar triangle, I.e

(4/5.5) = { (2x+8)/(6x-2)}

8/11 = ( x+ 4 ) / ( 3x - 1 )

8( 3x - 1 )= 11( x + 4 )

24x - 8 = 11x + 44

13x = 52

x = 4

Answer:

yes...

Step-by-step explanation:

its a congrate triangle

9514 1404 393

Answer:

  $400

Step-by-step explanation:

The word "per" in math often means "divided by". To find price per square foot, find price divided by square feet.

  $700,000/(1750 ft²) = $400 /ft²

The price per square foot of House 4 was $400.

Answer:

The total number of ways to give the answer of the question is 16777216.

Step-by-step explanation:

Total number of questions = 24

The number of possibilities so that the answer is given is only 2. It is either true or false.

So, the total number of ways to complete the test is

[tex]2^{24} = 16777216[/tex]

Answer:

(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]

(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant

Step-by-step explanation:

Given

[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation

[tex]n = 30[/tex]

[tex]p = 4[/tex] --- independent variables i.e. x1 to x4

[tex]SSR = 1760[/tex]

[tex]SST = 1805[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test of significance

We have:

[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

First, we calculate the t-score using:

[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]

[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]

[tex]t = 440 \div \frac{45}{25}[/tex]

[tex]t = 440 \div 1.8[/tex]

[tex]t = 244.44[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

Solving (c): [tex]SSE(x_2 ,x_3)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

Solving (d): F test of significance

The null and alternate hypothesis are:

We have:

[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant

[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant

For this model:

[tex]y =11.1 -3.6x_2+8.1x_3[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

[tex]SST = 1805[/tex]

[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

[tex]p_{(x_2,x_3)} = 2[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the t-score

[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]

[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]

[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]

[tex]t = 27.5 \div 1.8[/tex]

[tex]t = 15.28[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Hence, we reject the null hypothesis

Step-by-step explanation:

a=16

r=3

48/16=3

144/16=3

6th term

=ar^(n-1)

= 16(3)^(6-1)

=3888

Answer:

The answer is C

Step-by-step explanation:

You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.

Answer:

Follows are the response to the given question:

Step-by-step explanation:

The volume of the box:

[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]  

The surface area of the open box is:

[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]

Use above formula

[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]

[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]

Now

[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]

therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.

[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]

Answer:

What’s the numbers? Or the question?

Step-by-step explanation:

Answer:

7.56

Step-by-step explanation:

Kevin should expect to pay approximately $7.56 for 18 juice boxes based on the given information.

To find out how much Kevin should expect to pay for 18 juice boxes based on the given information, we can set up a proportion using the number of juice boxes and the cost:

In general, an expression refers to a combination of symbols, numbers, variables, and operators that represent a specific computation or value. Expressions are a fundamental concept in mathematics, programming, and logic.

Let "x" be the cost of 18 juice boxes.

We have the proportion:

6 juice boxes / $2.52 = 18 juice boxes / x

To solve for "x," we can cross-multiply:

6x = 18 x $2.52

6x = $45.36

Now, divide both sides by 6 to isolate "x":

x = $45.36 / 6

x ≈ $7.56

Therefore, According to the data provided, Kevin should budget about $7.56 for 18 juice cartons.

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Answer:

x=-16

Step-by-step explanation:

x/4-3=-7

x/4=-4

x=-16

Answer:

Reason 5

Step-by-step explanation:

Reason 1 and 2 are Given

Reason 3 is Reflexive

Reason 4 is Side-Side-Side congruency

Answer:

Reason 5

Step-by-step explanation:

It helps to know what CPCTC means and how it's used.

CPCTC means "corresponding parts of congruent triangles are congruent."

To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.

Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.

In step 4, the triangles are proven congruent by SSS.

Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.

Answer:

a13 square root

..cv

..

..

Step-by-step explanation:

[tex]f(x) = g(x)h(x)[/tex]

Taking the derivative of f(x), we get

[tex]f'(x) = g'(x)h(x) + g(x)h'(x)[/tex]

Then [tex]f'(1)[/tex] becomes

[tex]f'(1) = (-1)(-2) + (1)(3) = 5[/tex]