20A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 76%. After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 76% of married couples. In a random sample of 205 married couples who completed her program, 172 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor’s claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)(a)State the null hypothesis H0 and the alternative hypothesis H1.H0:H1:(b)Determine the type of test statistic to use. (Choose one ) z Or t OR chi-square Or f(c)Find the value of the test statistic. (Round to three or more decimal places.)(d)Find the p-value. (Round to three or more decimal places.)

Answer:

The probability of one machine breaking down

P(X=1) = 0.13194

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 15

The probability of breaking down of each machine = 0.2

p = 0.2

q = 1-p = 1-0.2 = 0.8

Step(ii)

Let 'X' be the random variable in binomial distribution

\(P(X=r) = n_{C_{r} } p^{r} q^{n-r}\)

The probability of one machine breaking down

\(P(X=1) = 15_{C_{1} } (0.2)^{1} (0.8)^{15-1}\)

On calculation , we get

P(X=1) = 15 ×(0.2)×(0.8)¹⁴

P(X=1) = 0.13194

Final answer:-

The probability of one machine breaking down

P(X=1) = 0.13194

Answer:

a= 18

b=87

​c=75

Step-by-step explanation:

1. We will use Gaussian elimination to solve this problem.

b= 33+3a

c= 57+a

a+b+c= 180

2. Swap Row1 and Row3 to make row reduction easier.

a+b+c=180

-a+c=57

-3a+b=33

3. Apply to Row2 : Row2 + Row1.

a+b+c=180

b+2c=237

-3a+b=33

4. Apply to Row3 : Row3 + 3 Row1.

a+b+c=180

b+2c=237

4b+3c=573

5. Apply to Row3 : Row3 - 4 Row2.

a+b+c=180

b+2c=237

-5c=-375

6.  Simplify rows.

a+b+c=180

b+2c=237

c=75

7. Apply to Row2 : Row2 - 2 2 Row3.

a+b+c=180

b=87

c=75

8.  Apply to Row1 : Row1 - Row3.

a+b=105

b=87

c=75

9. Apply to Row1 : Row1 - Row2.

a=18

b= 87

c= 75

10. Simplify rows.

a=18

b= 87

c=75

​​  

The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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Based on the information given about the combination, the number of different parts of fruits that can be selected from the bowl will be 6.

Since the bowl contains an apple, a plum, a pear, and a banana, the different pairs of fruit that can be selected from the bowl will be 4C2.

We can solve this further which will be:

= 4C2

= 4! /2! (4 - 2)!

= 4! / 2!2!

= (4 × 3 × 2)/ 2 × 2

= 24/4

= 6

Therefore, 6 different pairs of fruit can be selected.

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Answer:

(x-8)(x+8)

Step-by-step explanation:

Answer:

(x + 8)(x − 8)

Step-by-step explanation:

First, let's find the area circular sector:

Where:

r = radius = 7cm

θ = angle (in radians) = 5/6 π

so:

Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:

where:

s = one of the equal sides = 7

θ = angle = 150

so:

Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:

The confidence interval for the slope of the regression line relating performance score is 0.71
                   
sample size (n) = 20

slope (b1) = 3.92 and SE of slope = 0.71

Degrees of freedom = 20 - 2 = 18          

Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,

tα/2=1.734

The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,

B1±Tα/2*SE

3.92±1.734(0.71) (c)

Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.

For example, how commodity prices relate to the shares of companies that trade in those commodities.


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Answer:

B. 1729

I searched it up

Answer:

The range of the data is: 4.5 dollars

Step-by-step explanation:

From the diagram,

The range is given by subtracting the smallest value from the largest value:

\(9.5 - 5 = 4.5\)

Thus, the range of the data is: 4.5 dollars

The values of JL, EF and KM are -19units, 29 units and 22 units respectively.

13. From the diagram shown, we have;

JL = JK + KL

where;

JK = x + 2

KL = 4x - 16

JL = 6x - 13

Substitute the expressions

6x - 13 =  x + 2 + 4x - 16

collect like terms

x = -1

JL = 6x - 13 = 6(-1) - 13 = -6 -13 = -19 units

14.  EG = 2x + 13

EF = x + 14

FG = 14

2x + 13 = x + 14 + 14

collect like terms

x = 15

EF = 15 + 14 = 29 units

15. KL = 6

LM = 2x

KM = 3x - 2

3x - 2 = 6 + 2x

collect like terms

x = 8

KM = 3x - 2 = 22 units

Thus, the values of JL, EF and KM are -19units, 29 units and 22 units respectively.

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Answer:

cant really see it

Step-by-step explanation:

All three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

To calculate the contributions to GDP of the given transactions, we can use the three approaches: the expenditure approach, income approach, and production approach. Let's calculate the GDP using each approach and demonstrate that they give the same answer.

Expenditure Approach:

GDP is calculated as the sum of all final expenditures. In this case, the final expenditures are the sales of the supercomputers.

GDP = Sales of supercomputers

= (3 * AED1,000,000) + (1 * AED800,000)

= AED3,800,000 + AED800,000

= AED4,600,000

Income Approach:

GDP can also be calculated by summing up all the incomes earned during production. In this case, the incomes include wages, interest, and taxes.

GDP = Wages + Interest + Taxes

= (Labour costs for ABC + Labour costs for Jumbo) + (Interest on debt for ABC) + (Taxes for ABC + Taxes for Jumbo)

= (AED1,000,000 + AED200,000) + AED100,000 + (AED200,000 + AED100,000)

= AED1,200,000 + AED100,000 + AED300,000

= AED1,600,000

Production Approach:

GDP can also be calculated by summing the value added at each stage of production. In this case, the value added is the sales price minus the cost of components purchased.

GDP = Sales price of supercomputers - Cost of components

= (3 * AED1,000,000) + (1 * AED800,000) - (4 * AED500,000)

= AED3,000,000 + AED800,000 - AED2,000,000

= AED1,800,000

As we can see, all three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

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Answer:

About 10 i think

Step-by-step explanation:

idk

The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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Answer:

15x - 40 = 8

Step-by-step explanation:

3/4x-2=2/5

Multiply each side by 4*5 or 20

20 (3/4x-2=2/5)

15x - 40 = 8

Answer:

He works until 5:30.

Step-by-step explanation:

ok so first, every day don would take a total of 7 hours and 30 minutes on mon-Thurs. If we subtract his lunch from that total it would be 7 hours so next we do 7 hours times 9.75 which is 68.25$. Now that we know how much he makes per day, we times that by 4 since mon-thurs is 4 days. This would be 273$. Now we need to get to 360.75 so we subtract that. This would be 87.75$. Now if a normal day is 68.25$ and friday is 87.75, we find the diffrence which is 19.50. which is also 9.75(an hour) x 2 resulting in 2 hours extra. Therefore, he works 9 hours and 30 minutes on fridays (until 5:30). Thanks for putting in the work to understand and have a nice day!

Don must work approximately 9 additional hours on Friday to have a total pay of $360.75 for the week.

Don works from 8:00 AM to 3:30 PM Monday through Thursday. Let's calculate his total work hours for these four days:

Total work hours from Monday to Thursday:

(3:30 PM - 8:00 AM) - 0.5 hours (lunch break)

= 7.5 hours - 0.5 hours

= 7 hours (per day)

Total work hours for the week (Monday to Thursday):

4 days x 7 hours/day = 28 hours

Total pay for the week = Hourly rate x Total work hours + Additional hours on Friday

$360.75 = $9.75 x 28 hours + Additional hours on Friday

Additional hours on Friday = ($360.75 - $9.75 x 28) / $9.75

Additional hours on Friday = ($360.75 - $273) / $9.75

Additional hours on Friday = $87.75 / $9.75

Additional hours on Friday ≈ 9 hours (rounded to the nearest hour)

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Answer:

DONT PRESS THAT LINK

Step-by-step explanation:

By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Given: Line segment AC and line segment BD intersect at O.

Prove: ∠AOB ≅ ∠COD

By the supplementary angles property, the equations are given as,

∠AOB + ∠BOC = 180°            .....1

∠BOC + ∠COD = 180°            ....2

By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.

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Answer: By the congruent complements theorem

Step-by-step explanation: I took the test

Answer:

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

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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\(\dfrac{x+4}{3} =7\)

Multiply both sides by 3:

\((\dfrac{x+4}{3} )\times3=(7)\times3\)

\(x+4=21\)

Subtract 4 from both sides:

\(x+4-4=21-4\)

\(\boxed{x=17}\)

The reconciliation for Bane can be summarized as,

Adjusted bank balance = $1380.

A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.

Given that,

Beginning checkbook balance is $1400.

Service charge = $20

Adjusted balance = $1400 - $20 = $1380

Also, given that,

Ending balance on the statement = $1480

Deposit in transit = $200

Checks outstanding = $300

Adjusted balance = $1480 + 200 - 300

                              = $1380

Hence the adjusted balance is $1380.

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Answer:

y = m x + b    standard form of straight line

y = 2 x + 5

The slope is m and = 2

the y intercept is 5  because when x = o y = 5

if y = 0 then x = -2/5 and would be the x intercept

x is the independent variable and y is the dependent variable

I am not familiar with your definitions for domain and range but

both x and y can vary from -∝ to = ∝

Answer:

attached is the answer :)

Step-by-step explanation:

The length of the tangent AB is \(\sqrt{2a^{2}+2b^{2} }\) if the radii of the largest circle is a and the radii of the smallest one is b.

It is a line that touches a single point on the circle.

Firstly we have to draw a perpendicular from O to the radii of the smallest circle. In this way AOLB becomes a rectangle. We let the point where the bisector intersect the radii as L.

OA=a

Lb=a also

O'L=b-a

In triangle OLO' we use pythagoras to calculate the value of OL which wil then equal to AB so,

OL=\(\sqrt{(b-a)^{2}+(a+b)^{2} }\)

=\(\sqrt{2a^{2}+2b^{2} }\)

It will be the length of AB also.

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Answer:

- 7 feet (a)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-14

The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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The incorrect statement is

In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.

A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.

The scale factor used in the dilation is 9/7 instead of 7/3.

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To know if the point(4,2) lies on an equation, we can replace 4 for x and 2 for y and we have to make sure that the result on the left side equals the number on the right side, like this:

1. 5x + 2y=20

5*4+2*2=20

20+4=20

24=20, wrong, 24 is not equal to 20, then the point doesn't lie on this equation.

2. 2x+4y = 16

2*4+4*2 = 16

8 + 8 = 16

16=16, this is correct, then the pint (4,2) lie on the equation 2x+4y = 16

3. x+6y = 16

4+6*2=16

4+12=16

16=16, this is correct, then the pint (4,2) lie on the equation x+6y = 16

4. 3x+3y = 13

3*4+3*2=13

12+6=13

18=13, wrong, 18 is not equal to 13, then the point doesn't lie on this equation.

5. 4x+2y=20

4*4+2*2=20

16+4=20

20=20, this is correct, then the pint (4,2) lie on the equation 4x+2y=20

6. 6x+y=26

6*4+2=26

24+2=26

26=26, this is correct, then the pint (4,2) lie on the equation 6x+y=26