How many ways can 3 boys and 2 girls stand in a row so that the two girls are not next to each other?

Answer:

62

Step-by-step explanation:

Sn=1/2(3n^2+7n)

S1=1/2(3+7)=5

S2=1/2(3*4+7*2)=26/2=13

We know

S1=a1=5

S2=a1+a2=13

S2-s1=a1+a2-a1

13-5=a2

a2=8

We know d=a2-a1

d=8-5=3

nth term of AP =an=5+(n-1)3

an= 2+3n

Therefore 20th term =

a20= 2+3(20)=62

Hence 20th term of AP is 62

I hope this helps

Answer:

16 Years

Step-by-step explanation:

Answer:

The sampling is dependent because an individual selected for one sample does dictate about which individual to be selected in the second sample.

The variable is qualitative because it classifies the individual.

Step-by-step explanation:

The sample is dependent as the second individual selected in the sample is dependent on the first individual selection. The sample selection is not random and is dictated. The variables selected are qualitative in nature because they identify the quality of response variable which is non numerical in nature.

Step-by-step explanation:

a) The Roughly shape of the probability model is bell shaped or symmetric

( normal )

(b) Roughly, guess the center (mean) of the probability model

The mean is 5/10 =0.5

Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .

(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.

Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .

Answer:

B

Step-by-step explanation:

Answer:

The answer for this Question is Elementary

It is B.

Answer:  8x³ + 12x² - 16x - 16

Step-by-step explanation:

  (4x² - 2x - 4)(2x + 4)

= (2x + 4)(4x² - 2x - 4)

= 2x(4x² - 2x - 4)  +  4(4x² - 2x - 4)

=   8x³ - 4x² - 8x   +  16x² - 8x - 16

=   8x³ + (-4x² + 16x²) + (-8x - 8x) - 16

=   8x³ + 12x² - 16x - 16

Answer:

[tex]\huge\boxed{x=\pm4.5}[/tex]

Step-by-step explanation:

The quadratic formula of

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]

substitute

[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]

Answer:

1/2

Step-by-step explanation:

i think sin 5 pi/6

[tex]sin \frac{5 \pi}{6} =sin (\frac{\pi}{2} +\frac{\pi}{3} )=cos \frac{\pi}{3} =\frac{1}{2} \\or\\sin\frac{5 \pi}{6} =sin (\pi-\frac{\pi}{6} )=sin \frac{\pi}{6} =\frac{1}{2}[/tex]

The exact Value of sin 5x/6 is 1/2.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin 5x/6

We can Split it as

sin (5π / 6) = sin (π/2 + π/3)

                  = cos π/3

                  = 1/2

Also, sin (5π / 6) = sin (π - π/6)

                  = sin π/6

                  = 1/2

Hence, the exact value is 1/2.

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Answer:

We conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.

Step-by-step explanation:

We are given that based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25.

A random sample of 52 claims showed that 43 were made by single people under the age of 25.

Let p = population proportion of claims made by single people

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 67%     {means that the insurance claims of single people under the age of 25 is smaller than or equal to the national percent reported by the large insurance company}

Alternate Hypothesis, [tex]H_A[/tex] : p > 67%      {means that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company}

The test statistics that will be used here is One-sample z-test for proportions;

                          T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of claims made by single people under the age of 25 = [tex]\frac{43}{52}[/tex] = 0.83

           n = sample of claims = 52

So, the test statistics =  [tex]\frac{0.83-0.67}{\sqrt{\frac{0.67(1-0.67)}{52} } }[/tex]  

                                    =  2.454

The value of z-test statistics is 2.454.

Since in the question, we are not given the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 2.454 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.

Answer:

  1

Step-by-step explanation:

David Joyner might be the first name, so you may only have to check 1 name.

Answer:

It is not normally distributed as it has it main concentration in only one side.

Step-by-step explanation:

So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).

So, let us begin the groupings into their different classes, shall we?

Data given:

0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.

(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.

(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31

(3). 0.4 - 0.6 : there are 2 values that falls into this category.

(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.

Class interval            frequency.

0.00 - 0.20.                   15.

0.20 - 0.40.                    2.

0.4 - 0.6.                        2.

Answer:

Length of Shortest Side = 12 inches

Step-by-step explanation:

Length of Shortest Side = L = 3x

Length of Longest Side = W = 5x-4

Condition:

2L+2W = Perimeter

2(3x)+2(5x-4) = 56

6x+10x-8 = 56

16x-8 = 56

Adding 8 to both sides

16x = 56+8

16x = 64

Dividing both sides by 14

=> x = 4

Now,

Length of the Shortest Side = L = 3(4) = 12 inches

Length of the Longest Side = W = 5(4)-4 = 16 inches

Answer:

12 inches

Step-by-step explanation:

The length is the longest side.

The width is the shortest side.

Length : [tex]l=5x-4[/tex]

Width : [tex]w=3x[/tex]

Apply formula for the perimeter of a rectangle.

[tex]P=2l+2w[/tex]

[tex]P=perimeter\\l=length\\w=width[/tex]

Plug in the values.

[tex]56=2(5x-4)+2(3x)[/tex]

[tex]56=10x-8+6x[/tex]

[tex]56=16x-8[/tex]

[tex]64=16x[/tex]

[tex]4=x[/tex]

The shortest side is the width.

[tex]w=3x[/tex]

Plug in the value for x.

[tex]w=3(4)[/tex]

[tex]w=12[/tex]

Answer:

Step-by-step explanation:

The vertices of the already rotated triangle are:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Answer:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Step-by-step explanation:

Answer:

Option b = 90 degrees of freedom.

Step-by-step explanation:

So, in this particular Question we are given the following parameters or data or information which is going allow us to be able to solve this particular problem or Question;

=> "A regression analysis involved 8 independent variables"

=> "99 observations. "

Requirement : to determine the critical value of t for testing the significance of each of the independent variable's coefficient.

Hence, the formula below will used in Calculating or in the determination of the degree of freedom;

Degree of freedom= total number of observations - number of independent variables- 1.

Thus, slotting bin the values into the formula above, we have;

The degree of freedom = 99 - 8 - 1 = 90.

3*5 ≡ 15 ≡ 3 (mod 12)

3*7 ≡ 21 ≡ 9 (mod 12)

3*9 ≡ 27 ≡ 3 (mod 12)

5*7 ≡ 35 ≡ 11 (mod 12)

5*9 ≡ 45 ≡ 9 (mod 12)

7*9 ≡ 63 ≡ 3 (mod 12)

Your table should look like the attached.

It's unclear what you're supposed to evaluate for part (b)...

Answer:

1.

A. H0 :  μ1 = μ2 = μ3

Ha : μ1 ≠ 2μ ≠ μ3

2. Test Statistics = 95%

3. Critical F-Value = 3.76

4. P-Value = 2.32

5. Conclusion : Reject the null hypothesis

6. Type of vehicle does effect the amount of green house gas emissions.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

A. H 0  μ1 = μ2 = μ3

Ha  μ1 ≠ 2μ ≠ μ3

2. Test Statistics is 95%

3. Critical F-Value is 3.76.

4. P-Value is 2.32.

5. Conclusion  Reject the null hypothesis.

6. Type of vehicle does effect the amount of green house gas emissions.

The correct order of the steps of a hypothesis test is given below.

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

All steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

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Answer:

Angle 2= 45

Angle 3= 45

Angle 4= 135

Angle 5= 135

Angle 6= 45

Angle 7= 45

Angle 8= 135

Step-by-step explanation:

D.

chord

hope you like this

stay at home stay safe

Answer: d

Step-by-step explanation:

Answer:

y > -x/6 + 1

Step-by-step explanation:

Hope this can help

The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]  

now first we take out points to plot graph for that we will assume inequality to equation

i.e  

[tex]y = -(\frac{1}{6} )x+1[/tex]

x          y  

0          1

6          0

Now , as inequality have > sign

i.e according to the graph of inequality rules:

The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.

Therefore,

Graph will be option "A" only .

Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

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Answer: [tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Step-by-step explanation:

A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.

Let p be the population proportion of workers got their job through networking.

Given: 29% of workers got their job through networking.

i.e. [tex]H_0:p=0.29[/tex]

A researcher feels this percentage has changed.

i.e. [tex]H_a: p \neq0.29[/tex]

Hence, the required null and alternative hypotheses in symbolic form for this claim:

[tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Answer:

The answer is

Step-by-step explanation:

(4k – 4) + ( –9k – 5)

Remove the bracket and simplify

That's

4k - 4 + - 9k - 5

4k - 4 - 9k - 5

Group like terms

4k - 9k - 4 - 5

We have the final answer as

- 5k - 9

Hope this helps you

We can use FOIL to solve:

(4k - 4) + (-9k - 5)

(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)

-36k - 20k + 36k + 20

-20k + 20

Best of Luck!

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.

Answer:

false

Step-by-step explanation:

When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter

Answer:

C. 0.0009

Step-by-step explanation:

0.09/100

= 0.0009

Answer:A

Step-by-step explanation:0.09=0.9

Answer:

90°

Step-by-step explanation:

Theres a right angke beside x

And Angles on a straight line = 180 so 180-90°= 90°

Answer:

90

Step-by-step explanation:

I looked it up on the internet

Answer:

Your correct answer is 3.75

Step-by-step explanation:

0.25 x 15 = 3.75

Answer:

3.75

Step-by-step explanation:

You can do this many ways. Write a table that looks like this:

0.25

   15

--------

Ignore all decimal points. Multiply the 5's together and carry the 2 to the next column. Multiply 2 x 5 + 2, write the second digit (which is 2) and carry the 1. Multiply 0 by 5 + 1 = 1, so your top number should be 125. Then, multiply all the numbers by the 1. 5 x 1 = 5; 2 x 1 = 2; 0 x 1 = 0. We now have something that looks like:

   0.25

       15

   --------

    1  2  5

0  2  5

Add these numbers together and add the decimal point 2 numbers from the right, since that's what was in the original decimal.

    1  2  5

0  2  5

---------------

    3.75

Answer:

The slope of line is -1.

Step-by-step explanation:

This equation is in the form Y=mx+b form, where m is the slope of the line. in this equation, -1 is m.

Answer:

Option (3)

Step-by-step explanation:

Standard deviation for the binomial distribution is given by,

σ = [tex]\sqrt{n\times P(1-P)}[/tex]

where n = Number of trials

P = probability of success of an individual trail

If n = 47 and P = 0.4

σ = [tex]\sqrt{47\times 0.4(1-0.4)}[/tex]

  = [tex]\sqrt{47\times 0.24}[/tex]

  = [tex]\sqrt{11.28}[/tex]

  = 3.3586

  ≈ 3.36

Therefore, standard deviation for the binomial distribution will be 3.36.

Option (3) will be the answer.

Answer:

21 wins, table is attached.

Step-by-step explanation:

The ratio of 7 wins to 2 losses is 7:2. A ratio is just saying that every time one value is increased by 7, the other is increased by 2.

So we can fill out the table, in every iteration wins increases by 7 and losses increases by 2.

When we fill this out, we find that when losses is 6, wins is 21, so when you have 2 losses you have 21 wins.

Hope this helped!