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The mathematical way to describe an interaction is: A difference in differences.

In statistics, an interaction may appear when analyzing the relationship between three or more variables, and defines a situation in which the effect of one causal variable on an outcome forms on the state of a second causal variable.

Interactions are often considered in the context of regression analyses or factorial experiments. An interaction happens when an independent variable has a different effect on the outcome depending on the values of another independent variable.

To find an interaction, we need a factorial design, in which the two (or more) independent variables are crossed with one another, so there are reflections at every combination of levels of the two independent variables.

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The probability that exactly 17 households own a DVD player is b) 0.0124

P = probability of own DVD player = 53% = 0.53

n = sample of households = 22

x = number of households own a DVD player = 17

Since it is binomial experiment, we use binomial probability formula to calculate the probability.

P(X) = [tex]^{n}C_{x}\times P^{x}\times (1-P)^{n-x}[/tex]

With combination formula as below,

[tex]^nC_x[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]

P(X) = [tex]^{22}C_{17}\times 0.53^{17}\times (1-0.53)^{22-17}[/tex]

= [tex]\frac{22!}{17!(22-17)!}\times 0.53^{17}\times 0.47^{5}[/tex]

= 26334 × 0.0000205 × 0.0229345

= 0.0123811

= 0.0124

Thus, the probability is 0.0124 for 17 households own DVD player.

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It is concluded that the ratio of female and male viewers who enjoy the game shows the difference.

According to the survey-

360 out of 500 females enjoy the game.

Thus,

Ratio female = number of females who enjoy/ total number of females.

Ratio female = 360/500

Ratio female = 0.72

Now, 600 out of 800 males enjoy a game show.

Ratio male = number of males who enjoy/ total number of males.

Ratio male = 600/800

Ratio male = 0.75

Thus, Ratio female ≠ Ratio male

Therefore, it is concluded that the ratio of female and male viewers who enjoy the game shows the difference.

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If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units

A right triangle's height is 5 times the length of its base

Consider the length of the base as b and the height as h

h = 5b

The area of the triangle = 160 square units

The area of the triangle = 1/2 × b × h

Where b is the base of the triangle

h is the height of the triangle

Substitute the values in the equation

1/2 × b × h = 160

1/2 × b × 5b = 160

1/2 ×5b^2 = 160

5b^2 = 320

b^2 = 320/5

b^2 = 64

b = [tex]\sqrt{64}[/tex]

b = 8 units

Then the height of the triangle h = 5b

= 5 × 8

= 40 units

Therefore, the height of the triangle is 40 units

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The number of ways 3 courses can be selected is 3654.

How to calculate combination?

Total no. of courses available = 29

Courses needed to graduate = 3

No of ways these courses can be selected:

= ²⁹C₃

= 29!/ [(29-3)! - 3!]

= 29! / 26! 3!

= 29 * 28 * 27 * 26!/ 26! 3*2

= 29* 14* 9

=3654

So, the number of ways 3 courses can be selected is 3654.

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The probability that a deck to guarantee that you have 4 of a kind is 40.

Probability:

In math probability refers the possibility of event.

Given,

Here we need to find the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind.

As we know that the total number of cards in the deck is 52.

So, the number of ways of choosing 4 cards from a pack of 52 playing cards is calculated as,

=> ⁵²C₄ = 52!/4!48!

=> ⁵²C₄ = 270725

Similarly, the number of ways of choosing 4 cards of same suit

=> ¹³C₄ = 13!/4!9!

=> ¹³C₄ = 715

So, the number of ways of choosing 4 cards of different suit is calculated as,

=> 715/17 = 40

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The social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                            = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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The final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

For the stated question-

Let initial enrollment = 100.

After one decade, the enrollment added 30% of the initial.

Thus,

= 100 + 30% of 100

= 100 + 130

= 130

Thus, the final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

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Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ \\ \\ \angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

Answer:

C ≈ 241.9 cm

Step-by-step explanation:

the circumference (C) of the circle is calculated as

C = πd ( d is the diameter )

here d = 77 , then

C = π × 77 ≈ 241.9 cm ( to 1 dec. point )

An equation for the nth term of the arithmetic sequence: an =  n - 6.

ad 10th term a10 = 4.

The formula for the nth term of the

an = a + (n -1)d

In which,

The arithmetic sequence is given as-

−5,−4,−3,−2, ...

Then, the equation will be

d = a2 - a1

d = -4 - (-5) = 1

an = a + (n -1)d

an = -5 + n - 1

Put n = 10 in the equation.

a10 = 10 - 6

a10 = 4

Thus, the 10th term of the sequence is 4.

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The correct question is-

Write an equation for the nth term of the arithmetic sequence. Then find a10.

−5,−4,−3,−2, ...

The value of the other leg of the right angled triangle is found as 4√14 cm.

For the given question, the values for the right angled triangle are-

Hypotenuse (H)  - 15 cm

Side (B) = 1 cm

Let the other side be (P).

Then,

H² = P² + B²

P²  = H² - B²

Put the values-

P²  = 15² - 1²

P²  = 225 - 1

P²  = 224

P = 4√14

Thus, the value of the other leg of the right angled triangle is found as 4√14 cm.

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Answer:

[tex]\boxed{\tt 2c-4}[/tex]

Step-by-step explanation:

[tex]\tt 2\left(c-2\right)[/tex]

Apply the distributive property:-

[tex]\tt 2\left(c-2\right)=2c-2\times \:2[/tex]

[tex]\bf 2\times\:2=4[/tex]

[tex]\tt 2c-4[/tex]

___________________

Hope this helps!

Have a great day!

For the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, the equation of the line is

y – 5 = 2(x + 9)

Compare the equation with the standard equation as

y-y₁=m(x-x₁)

y – 5 = 2(x + 9).

y-5=2(x-(-9)

Where x₁ and y₁ are the points on which the line lies.

Thus, for the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

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Answer:

0.8888888..... repeating

Step-by-step explanation:

Answer:

72/1

Step-by-step explanation:

multiply 8 and 9/1

Answer:

Is it 53?

Step-by-step explanation:

3 tens means 30, and adding 23 ones would be 53

Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).

Given that,

One day, a teacher of statistics randomly selected 10 pupils' names from a hat and instructed them to complete as many pushups as they could before class began. The 10 students who were chosen at random performed an average of 15 pushups, with a standard deviation of 9. Assume that the population's distribution of the maximum number of pushups is roughly normal.

We have to find what is the standard error of the mean.

We know that,

For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.

The sample mean is of 15 is x=15 .

The sample standard deviation is of 9 is s=9.

The sample size is of 10 is n=10.

First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.

Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622

The margin of error is of:

M=ts/n

Then:

M=2.2622(9/√10)

M=6

The confidence interval is:

x±M

x-M=15-6=9

x+M=15+6=21

Therefore, Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).

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The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(x + 7)(x² - 8)

Step-by-step explanation:

x³ + 7x² - 8x - 56 =

let's put the total multiplier x² out of brackets

x²(x + 7) - 8x - 56 =

let's put the total multiplier -8 out of brackets

x²(x + 7) - 8(x + 7) =

let's put the total multiplier (x + 7) out of brackets

(x + 7)(x² - 8)

The wage for a worker with 7 years of experience may be calculated using the equation for the line of best fit as follows: D. $55,573.

A trend line, also known as a line of best fit, is a statistical (analytical) technique that is used with a scatter plot to ascertain whether or not there is any link (correlation) between a set of data.

In this case, the pay would be placed on the y-axis of the scatter plot and the employee's years of experience would be put on the x-axis.

A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. To comprehend the idea of how to roughly approximate the equation of a line of best fit and make predictions, we will look at two examples that show a scatter plot with a line of best fit.

We may rationally and logically conclude that the equation for the line of best fit is given by: by carefully examining the scatter plot that models the data in the provided table (see attachment).

y = 2233.3x + 39940

The wage for an employee with seven years of experience would thus be predicted using the equation for the line of best fit as follows:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Answer:

Step-by-step explanation:

for this one you need to solve for x and x=42

Answer:

Step-by-step explanation:

Divide both sides by 2. Divide 24 by 2 to get 12.

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Use the elimination method to get rid of one of the variables.

Find the value of one variable.

Find the value of the remaining variables using substitution.

Clearly state the final answer.

Check your answer by substituting both values into either of the original equations.

Answer:

I think 6.2 years

Step-by-step explanation:

I THINK OK

The true proportion of adults is in the interval 0.4026< P< 0.4594.

Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.

Data provided:

selected (x) = 329

Total(n) = 763

Sample proportion (p') = x/n

                                       = 329/ 763

                                       = 0.431

Critical z-value = 1.59

margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]

                             = 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]

                             = 1.59 × 0.0179

                             = 0.0284

88% confidence interval is:

(p' ± E) = ( 0.431 ± 0.0284)

          = 0.4594 and 0.4026

Therefore the estimate is 0.4026< P< 0.4594.

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The probability of the hand containing 4 queens when picked at random is 0.0026.

We can solve the given question easily using probability,  permutations, and combinations.

 We can pick any card other than the queen in the following number of ways = ⁴⁸C₉  (i)

The queen card can be picked in the following number of ways

= ⁴C₄= 1 (ii)

The total number of ways to choose 13 cards is = ⁵²C₁₃  (iii)

Using the values of (i), (ii), and (iii), we get -

Probability = (⁴⁸C₉ * 1) /  ⁵²C₁₃

= [tex]\frac{48!/9!(48-9)! *1 }{52!/13!(52-13)! }[/tex]

= 1677106640 * 1 / 635013559600

= 0.00264

If this is rounded to four decimal places, we get = 0.0026.

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Answer: $84 i think

Step-by-step explanation:

The correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

What is simplified expression?

Writing a similar expression devoid of similar terms is what is meant by the expression "simplify." In other words, we will rewrite the expression using the fewest number of terms.

Consider, the given expressions

(1)  (6r + 7) + (13 + 7r)

Simplifying this,

6r + 7 + 13 + 7r

13r + 20

(2) (13 - 3/2r) - (1 - r)

Simplifying this,

13 - 3/2r - 1 + r

12 - 1/2r

(3) (-8 - r) + (2r - 4)

Simplifying this,

-8 - r + 2r - 4

-12 + r

(4) (7r - 3/2) - (2/3 + 6r)

Simplifying this,

7r - 3/2 - 2/3 - 6r

r - 13/6

Hence, the correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

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Complete question:

Complete question is attached below,

The required simplified solution of the given expression is -40.

Given that,
To determine the simplified solution of the given expression 10c - cd + d³ at c = -6 and d = 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 10c - cd + d³

Substitute the values,
= -60 + 12 + 8
= -40

Thus, the required simplified solution of the given expression is -40.

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Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.

The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).

We have given that,

A ∆DEF such that m∠d = (2x + 19)°,

m∠e = (3x + 24)°, and m∠f = 87°.

we have to find out the degree measure of the exterior angle to ∠d.

As we know that sum of angles of triangle is equal to 180° .

so, m∠d + m∠e + m∠f = 180°

=> (3x + 24)° + (2x + 19)° + 87° = 180°

=> (5x + 24 + 19 + 87)° = 180°

=> 5x + 130° = 180°

=> 5x = 50°

=> x = 10°

plug this value in angle d , angle e we get ,

m∠d = (3 ×10 + 24 )° = 54°

We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.

measure of Exterior angle of ∠d + measure of ∠d = 180°

Measure of exterior angle of ∠d

= 180° - m∠d

= 180° - 54° = 126°

Hence, the measure of exterior angle of d is 126°.

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