If pentagon opqrs is dilated by a scale factor of seven over four from the origin to create o′p′q′r′s′, what is the ordered pair of point p′? (−8.75, 5.25) (−1.25, 0.75) (−3.5, 8.75) (−1.75, 3.5)

Answer:

m = - 3 , c = 26

Step-by-step explanation:

the diagonals of a rhombus are perpendicular bisectors of each other.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{3}\) x + 5 ← equation of DB is in slope- intercept form

with slope m = \(\frac{1}{3}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{1}{3} }\) = - 3 , then

y = - 3x + c ← is the partial equation of diagonal AC

to find c substitute A (5, 11 ) into the partial equation

11 = - 15 + c ⇒ c = 11 + 15 = 26

y = - 3x + 26 ← equation of diagonal AC

with m = - 3 and c = 26

Expectation = ($1 + $0.50 + $0.40) x $4.00 = $7.40

The expectation of winning amount if a person buys one ticket is $7.40. This can be calculated using the probability distribution below.

Lottery Prize:  | Probability: | Win Amount: | Probability x Win Amount:

$1000  |  1/1000  |  $1000  |  1/1000 x $1000 = $1

$500  |  1/1000  |  $500  |  1/1000 x $500 = $0.50

$50   |  2/1000  |  $50   |  2/1000 x $50 = $0.40

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Answer:

6kilometers ,8 kilometers,10kilometers

The value today of a money machine is $4,712.25. The value of the investment is $31,323.15.

Question 9:

To calculate the present value of the money machine, we can use the formula for the present value of an ordinary annuity:

PV = P * [(1 - (1 + r)^(-n)) / r],

where PV is the present value, P is the annual payment, r is the interest rate per period, and n is the number of periods.

Given:

Annual payment (P) = $1000,

Interest rate per period (r) = 4% = 0.04,

Number of periods (n) = 6 - 2 = 4.

Plugging in the values, we get:

PV = $1000 * [(1 - (1 + 0.04)^(-4)) / 0.04] = $4712.25.

Therefore, the value today of the money machine is $4712.25.

Question 10:

To calculate the present value of the investment, we can use the formula for the present value of a perpetuity:

PV = P / r,

where PV is the present value, P is the periodic payment, and r is the interest rate per period.

Given:

Periodic payment (P) = $500,

Interest rate per period (r) = 12% / 12 = 0.12 / 12 = 0.01.

Plugging in the values, we get:

PV = $500 / 0.01 = $31,500.

Therefore, the value of the investment today is $31,323.15.

In summary, the value today of the money machine that will pay $1000 per year for 6 years is $4712.25, and the value of the investment that will pay $500 per month starting four years from today and continue indefinitely is $31,323.15.

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Answer:

easy just divide it

98.40 / 8 = 12.3

12.3

breainest please

Answer:

x=66

Step-by-step explanation:

180-114=66

Interior angles on the same side of transversal are supplementary (180°).

So,

x + 114° = 180°

=> x = 180° - 114°

=> x = 66°

Answer:

It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.

Step-by-step explanation:

The equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

To find an equation equivalent to the given equation, we can start by simplifying both sides and rearranging the terms. Let's go step by step:

Given equation: (2/3)x - 5/6 = (-5/12)x + 1/4

First, let's eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 12.

12 * [(2/3)x - 5/6] = 12 * [(-5/12)x + 1/4]

Simplifying:

4x - 10 = -5x + 3

Now, let's gather like terms on each side of the equation:

4x + 5x = 3 + 10

Combining like terms:

9x = 13

Finally, to isolate x, divide both sides of the equation by 9:

(9x)/9 = 13/9

x = 13/9

So, the equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

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Answer:

145°

Step-by-step explanation:

180 - 35 = 145

145°

Answer:

Cerian is 28 years old

Step-by-step explanation:

The given parameters are;

The average age of the staffs in the mathematics department = 40

The number of staffs in the department = 7

The average age of Jill, Nicky and Wendy = 41

The average age of Andy, Alan and Cathy = 43

From the given parameters, we have;

The average age of the staffs in the mathematics department = (The sum total of the ages of the members of the math department)/(The number of staffs in the department)

Therefore;

40 = (The sum total of the ages of the members of the math department)/ (7)

From which we have;

The sum total of the ages of the members of the math department = 40 × 7 = 280

Which gives;

Jill's age + Nicky's age + Wendy's age + Cathy's age + Cerian's age + Alan's age + Andy's age = 280 years

The average age of Jill, Nicky and Wendy = 41

Given that Jill, Nicky, and Wendy make up 3 of the 7 members of staffs, we have;

The average age of Jill, Nicky and Wendy = (The sum total of the ages of Jill, Nicky, and Wendy)/(The number of staff Jill, Nicky, and Wendt make)

Therefore;

The sum total of the ages of Jill, Nicky, and Wendy = 41 × 3 = 123

Which gives;

Jill's age + Nicky's age + Wendy's age = 123 years

Similarly, the sum total of the ages of Andy, Alan, and Cathy = 43 × 3 = 129

Which gives;

Andy's age + Alan's age + Cathy's age = 129 years

Therefore;

Cerian's age = (Jill's age + Nicky's age + Wendy's age + Cathy's age + Cerian's age + Alan's age + Andy's age) - (Jill's age + Nicky's age + Wendy's age) + (Andy's age + Alan's age + Cathy's age)

∴ Cerian's age = 280 years - 123 years - 129 years = 28 years

Answer:

He needs to read 14 pages on Thursday to finish the book

The reported sky cover is one continuous overcast layer, its thickness is 5,780 feet.

To calculate the thickness of a cloud layer, you need to subtract the cloud base height from the cloud top height. In this case, the sky cover is reported as one continuous layer, and the cloud top is reported at 6,500 feet.

Aviation Routine Weather Reports (METARs) typically include cloud height information in increments of 100 feet above ground level (AGL). If the sky cover is reported as overcast (OVC) with no height information, it is assumed to be at or below 6,000 feet AGL.

Therefore, the thickness of the cloud layer in this scenario can be calculated as follows:

Cloud base height = 620 feet (field elevation) + 100 feet = 720 feet AGL

Cloud thickness = Cloud top height - Cloud base height

= 6,500 feet - 720 feet

= 5,780 feet

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Answer: She should have multiply each of the sides the scale value before multiplying to find the area.

Step-by-step explanation:

They are two sides to the triangle which is the base and the height  and each side have a different length so you will have to first multiply each side length by the scale value to find the new length of the enlarged triangle.

base:  4 *5 = 20

height :  3.5 * 5 = 17.5

Now since the base is 20 cm and the height is 17.5 cm you will use the area of a triangle formula to solve for the area.

A = 1/2* b * h

A = 1/2 * 20 * 17.5

A =  10* 17.5

A = 175  

or she could have multiply 35 which is the number he obtained by another 5 to find the area.

Answer:

c i think not sure sorry

Step-by-step explanation:

The expressions are:
- Francisco's distance: x
- Meredith's distance: x
- Total distance: 2x
- Distance between Francisco and Meredith: 230 - 2x.

To answer your question, let's break it down into the different expressions:

1. The expression that represents the number of feet Francisco has walked toward Meredith since they started walking can be written as x.

2. The expression that represents the number of feet Meredith has walked toward Francisco since they started walking can also be written as x.

3. The expression that represents the total number of feet Francisco and Meredith have walked toward one another since they started walking can be written as x + x, which simplifies to 2x.

4. The expression that represents the distance between Francisco and Meredith can be written as 230 - (x + x), which simplifies to 230 - 2x.

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The statistics are as follows:

- Test Statistic: The calculated test statistic is approximately 1.02.

- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.

- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.

To solve the problem completely, let's go through each step in detail:

1. Test Statistic:

The test statistic can be calculated using the formula:

z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

Substituting these values into the formula, we get:

z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

z ≈ 0.02 / √(0.0001386 + 0.0002493)

z ≈ 0.02 / √0.0003879

z ≈ 0.02 / 0.0197

z ≈ 1.02 (rounded to two decimal places)

Therefore, the test statistic is approximately 1.02.

2. P-value:

To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.

The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.

3. Confidence Interval:

To estimate the difference in proportions with a 95% confidence interval, we can use the formula:

(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

z = 1.96 (for a 95% confidence interval)

Substituting these values into the formula, we get:

(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

0.02 ± 1.96 * √(0.0001386 + 0.0002493)

0.02 ± 1.96 * √0.0003879

0.02 ± 1.96 * 0.0197

0.02 ± 0.0386

The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).

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No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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The employee's total earnings on $81,500 in Sales is $3,797.50.

The employee's total earnings on $81,500 in sales, we need to consider the graduated commission rates for the different portions of the sales.

For the first $50,000 in sales, the employee earns a 3.5% interest. So the earnings on the first $50,000 would be:

(0.035)(50,000) = $1,750

For the remaining sales over $50,000, the employee earns a 6.5% interest. So the earnings on the sales over $50,000 would be:

(0.065)(81,500 - 50,000) = (0.065)(31,500) = $2,047.50

The total earnings, we add the earnings from the first $50,000 to the earnings on the sales over $50,000:

$1,750 + $2,047.50 = $3,797.50

Therefore, the correct expression that represents the employee's total earnings on $81,500 in sales is option b:

(0.035)(50,000) + (0.065)(31,500)

Calculating this expression, we get:

$1,750 + $2,047.50 = $3,797.50

Hence, the employee's total earnings on $81,500 in sales is $3,797.50.

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Answer:

y = 7, when x = 21

Step-by-step explanation:

Since 6 is 1/3 of 18 we could use that to find y

1/3 x 21 = 7

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.

The solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the Intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3

Given that the number graph ranges from negative eight to eight on the x-axis and negative eight to eight on the y-axis.

Two lines that are perpendicular to each other intersect at (three, zero). The line with a positive slope is labeled a, and the line with a negative slope is labeled b.

The system is given byx – y = 3 (line a)x + y = 3 (line b)We know that both the lines a and b pass through (3,0).

Let's first find the points of intersection of the line a with the x-axis and the y-axis.

To find the point of intersection of the line a with the x-axis, put y = 0 in the equation x - y = 3x - 0 = 3x = 3So, the point of intersection of line a with the x-axis is (3,0).

To find the point of intersection of the line a with the y-axis, put x = 0 in the equation x - y = 3 0 - y = 3y = -3So, the point of intersection of line a with the y-axis is (0,-3).

Similarly, let's find the points of intersection of the line b with the x-axis and the y-axis.

To find the point of intersection of the line b with the x-axis, put y = 0 in the equation x + y = 3x + 0 = 3x = -3So, the point of intersection of line b with the x-axis is (-3,0).

To find the point of intersection of the line b with the y-axis, put x = 0 in the equation x + y = 3 0 + y = 3y = 3So, the point of intersection of line b with the y-axis is (0,3).

Now, we can plot the graph of the two lines a and b and then find the points of intersection as follows:

Therefore, the solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3.

Hence, the answer is (0, 3).Option B. (0, 3)

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The allowance for sampling risk is included in the computed upper deviation rate of 7.8 is 3.8%.

The substantial percentage variation identified in the audit samples that the auditing expert would approve by adhering to the particular internal controls is known as the tolerable deviation rate. The auditor won't rely on those internal controls if the deviation rate is higher than the predetermined limit.

a) Tolerable = Allowance for sampling risk + Expected Deviation

Upper Deviation = Allowance for sampling risk + Actual Deviation

Sample deviation rate = No. of deviation/Sample size

= 6/150

= 4%

Allowance for sampling rate = Upper deviation rate - sample deviation

= 7.8% - 4%

= 3.8%

allowance for sampling risk is 3.8%.

b) 1.) In order to assure effective controls, Mr. M may increase the sample size because the tolerated deviation level is lower than the estimated deviation level.

2.) Because the computed maximum deviation is more than the anticipated and acceptable deviation rates, Mr. M may raise the initial control risk assessment.

3.) As the sample deviation rate is lower than the allowable deviation rate, Mr. M may continue his consideration in addition to creating the first risk assessment. The tolerance rate, nevertheless, is less than the estimated deviation rate. The auditor must, however, use professional discretion.

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Complete question;

Nathan Matthews conducted a test of controls where the tolerable deviation rate was set at 6 percent and the expected population deviation rate was 3 percent. Using a sample size of 150, Matthews performed the planned test of controls. He found six deviations in the sample, and he calculated the computed upper deviation rate to be 7.8 percent.

Required:

a. Based on the sample results, what allowance for sampling risk is included in the computed upper deviation rate of 7.8?

b. Assume that Matthews preliminarily assessed control risk as “low.” Given the results above, the auditor could decide to do one of three things: (1) increase the sample size, (2) increase the preliminary assessment of control risk, or (3) not adjust the preliminary assessment of control risk. Describe how Matthews could justify each of those three actions

To use Lagrange multipliers to find the shortest distance from the point (7, 0, −8) to the plane x y z = 1, we need to set up the following optimization problem:

Minimize the distance function D(x, y, z) = √((x-7)^2 + y^2 + (z+8)^2) subject to the constraint f(x, y, z) = x y z - 1 = 0.

Using Lagrange multipliers, we set up the following system of equations:

∇D(x, y, z) = λ∇f(x, y, z)
f(x, y, z) = 0

Taking the partial derivatives, we have:

∇D(x, y, z) = (x-7, y, z+8)
∇f(x, y, z) = (y z, x z, x y)

Setting these equal to each other and solving for x, y, z, and λ, we get:

x-7 = λ y z
y = λ x z
z+8 = λ x y
x y z = 1

Multiplying the first three equations together and using the fourth equation, we get:

(x-7)yz = λxzy = (z+8)xy
(x-7)yz = (z+8)xy
xz - 7z = yz + 8xy
xz - yz = 8xy + 7z
z(x-y) = 8xy + 7z
z = (8xy)/(y-x)

Substituting this into the equation x y z = 1, we get:

x y (8xy)/(y-x) = 1
8x^2 y - xy^2 = x^2 y - xy^2
7x^2 y = 0
x = 0 or y = 0

If x = 0, then we have yz = 1, and substituting into the equation z = (8xy)/(y-x), we get z = -8, which is not on the plane x y z = 1.

If y = 0, then we have xz = 1, and substituting into the equation z = (8xy)/(y-x), we get z = -1/8.

Therefore, the point on the plane x y z = 1 closest to the point (7, 0, −8) is (0, 0, -1/8), and the shortest distance is:

D(0, 0, -1/8) = √((0-7)^2 + 0^2 + (-1/8+8)^2) = √(49 + 63/64) ≈ 7.98.

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Answer:

119,940 books are not about math.

What I did:

60x2000=120,000

120,000-60=119,940

Answer:

119940

Step-by-step explanation:

.05 % are about math

b= books

b * .05% = 60

Change to decimal form

b * .0005 = 60

Divide each side by .0005

b = 60/.0005

b =120000 books in the store

we want the ones not about math

120000-60

119940

Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

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Answer:

No because the first one will get an answer of -2 while the second one will get an answer of 14

Step-by-step explanation:

Hope This Helped

Answer:

no

Step-by-step explanation:

To solve this we can plug in 2 for x and 2 for y and see if the equations are true

we have

2= -4(2)+6

2= -8+6

2= -2

this is false, the answer is no

Answer:

500=D 100=M

Step-by-step explanation:

I hope that helps :D

Tim drove at a distance of 511 km in 7 h. His average driving speed in km/h is 73.

By computing Tim's average driving speed, we have to divide the total distance that he traveled by the time it takes him to complete the whole journey. In this respect, Tim drove a total distance of 511 km in 7 hours.

Average driving speed = Total distance/Total time taken

By putting the values in the equation we get :

Average driving speed =\(\frac{ 511 km}{7 h}\)

Now by computing  the average driving speed:

Average driving speed = 73 km

So, Tim's average driving speed was 73 km/h.

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Answer:

C=r-p

Step-by-step explanation:

r-c=p

We need to solve the equation for Variable C

To get c alone we need to remove r from the left hand side

Subtract R from both sides

r-c=p

r-r-c=-r+P

-c=-r+P

Now divide both sides by -1 to get c alone

c=r-p

C is alone, it is solved for C

Answer:

2^3

Step-by-step explanation:

Same bases(2) means it becomes 2^-3+5/2^-1

Then it becomes 2^2/2^-1

After this, the power with the denominator comes up to the numerator, hence, it further becomes 2^2+1

=2^3