291 divided by 30 standard algorithm​

Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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Answer:

1,596cm ^3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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Considering it's concept and the tree diagram, the probability of an incorrect test result is of 0.08.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

An incorrect result is a negative with pet allergy, or a positive without allergy, hence the probabilities at the tree diagram are:

Hence the probability is given by:

p = 0.19 x 0.18 + 0.06 x 0.82 = 0.0834.

To two decimal places, 0.08 probability, as 34 < 50.

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A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Given

The objective is to solve for y, that is, isolate the y-term in one side of the expression.

The first step is to pass "-1/5y" to the left side of the expression by applying the inverse operation

Next pass "+2" to the right side of the expression

Finally multiply both sides by -5

Answer:

Step-by-step explanation:

Midpoints of two coordinates is expressed using the formula;

M(X, Y) = (x2+x1/2, y2+y1/2)

Given the coordinates  c(5,3) and d(-3,-6)

x1 = 5, y1 = 3, x2 = -3 and y2 = -6

X = x1+x2/2

X = 5+(-3)/3

X = 5-3/2

X = 2/2

X = 1

Also;

Y = y1+y2/2

Y = 3+(-6)/2

Y = 3-6/2

Y = -3/2

Y = -1.5

Hence the coordinates of the midpoint M is (1, -1.5)

Answer:

Step-by-step explanation:

Hence the coordinates of the midpoint M is (1, -1.5)

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

To determine the width of the statue:

A local park has a length (L), width (W), and height (H) (all in feet)

Solve equation 1 and 2 simultaneously,

Solve equation 3 & 4 simultaneously, make W the subject of formular

Therefore the value of width of the statue = 12 feet

Answer:

m∠R= 87°

Step-by-step explanation:

The angles in a polygon add up to (n-2)180

(5-2)180= 540°

You can set up an equation to add all the angles together equaling 540°.

Once you solve for x, plug that back into the formula for the angle of R(7x-11)

The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.

It follows from the task content that the equation which correctly represents the Given situation is to be determined.

Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;

Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.

Consequently, answer choice C; w = 5 × 15 is correct.

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Answer:

-log_4

Step-by-step explanation:

The value of log1/4 rounded to the nearest hundredth is -0.60

Given the parameter which is needed for our Calculation:

Using a calculator, the value of log1/4 is -0.602059

Rounding to the nearest hundredth, is two digits after the decimal point.

Hence, we have ;

Therefore, log1/4 is -0.60

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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The simplified form of the fraction is A = -1 / (x - 2)

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = (6 - x) / (x² - 8x + 12)

On factorizing the denominator , we get

(x² - 8x + 12) = ( x - 6 ) ( x - 2 )

So , the new fraction is

A = ( 6 - x ) / ( x - 6 ) ( x - 2 )

A = - ( x - 6 ) / ( x - 6 ) ( x - 2 )

Taking the common factor out , we get

A = -1/ ( x - 2 )

Hence , the fraction is A = -1/ ( x - 2 )

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Answer:

b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day.

Step-by-step explanation:

The confidence interval calculated from the sample at a particular confidence level, gives a certain percentage of confidence based on the confidence level that the true mean of the population exists within the confidence interval Calculated.

For the scenario above, we can say that there is a 90% chance that the population mean number of annual pass holders in the park on a given day is within the interval (35, 51)

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

Below in bold.

Step-by-step explanation:

f(x)=2x^3-3x^2

Finding the derivative and equating to zero:

f'(x) = 6x^2 - 6x = 0

6x(x - 1) = 0

So there are turning point at x = 0 and 2 = 1.

Finding the relative maximum:

Second derivative is negative when we have a maximum value:

f"(x) = 12x - 5

- which is negative when  x = 0.

So the relative maximum is at x = 0 where f(x) = 2(0)^3 - 3(0)^2 = 0.

At x = 1, second derivative  = 12(1) - 5 = +7 so this is a relative  minimum.

The function is increasing  in interval -∝ < x < 0

decreasing in interval 0 < x < 1

then increasing in interval   1 < x < ∝

The circumference of a circle = pi x diameter

Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)

The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.

Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:

Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08

Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.

Answer:

$1603.47

Step-by-step explanation:

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

The complete order of the inverse function of the function f(x) = x + 5 is:

1. y = x + 5

2. x = y + 5

3. x - 5 = y

4. y = x - 5

The function is given as:

f(x) = x + 5

The opposite of the function f(x) = x + 5 is the inverse of the function.

So, we have:

f(x) = x + 5

Express f(x) as y

y = x + 5

Swap the positions of x and y

x = y + 5

Make x the subject of the formula

x - 5 = y

Rewrite as:

y = x - 5

Hence, the inverse function of the function f(x) = x + 5 is y = x - 5

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There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer: 5 calories

Step-by-step explanation:

Given the data:

Minute ____calorie burned

40__________200

80__________400

120_________ 600

160_________ 800

We need to find the rate at which calorie is burned :

Rate of burn = (Number of calorie burned/ time taken)

Take any of the points :

Time = 80 ; calorie burned = 400

Rate of burn = (400 calorie / 80 minute )

Rate of burn = 5calorie/minute

If time = 1 minute ; rate = 5

Calorie burned in 1 minute :

Amount of calorie = rate of burn × time taken

Amount burned in 1 minute = 5 × 1 = 5 calories

Hence, amount of calorie burned in one minute is 5 calories.

Answer:

5

Step-by-step explanation:

Maps Testing I have done it.

Answer:

The number of ways = 151200

Step-by-step explanation:

Below is the calculation of the number of ways:

Total number of people = 10

Total number of posts = 6

The number of ways = 10P6

The number of ways = \(\frac{10!}{10! - 6!}\)

The number of ways = 10 x 9 x 8 x 7 x 6 x 5

The number of ways = 151200