two years ago, paul was 7 times as old as matt was. two year from now, paul will be five times as old as matt will be. find the present age of each

The difference between the area of the square and the area of the circle is C. 9x²(4 - π).

The area of the square will be:

= Side ×Side

= 6x × 6x

= 36x²

The area of the circle will be:

= πr²

= 3.14 × (3x)²

= π × 9x²

= 9πx²

The difference will be:

= 36x² - 9πx²

= 9x²(4 - π)

Therefore, the correct option is C.

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The difference between the area of the square and the area of the circle is 9x²(4 - π)

area of circle = πr²

where

Therefore,

area of a square = l²

where

The circle is inscribed in the square.

Therefore, the difference in area of the square and circle is as follows:

area of circle = π × (3x)² = 9x²π

area of the square = (6x)² = 36x²

Hence,

difference in area = 36x² - 9x²π

difference in area = 9x²(4 - π)

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Answer: 6 hours

Step-by-step explanation: The distance is 294 miles. The speed is 49 miles per hour. In that case, we divide 294 by 49, which gives us 6.

The number of people working on that day are 107 people in the staff.

According to the statement

We have to find that the number of people were working that day.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

a hospital day staff consists of 25 registered nurses, 75 unlicensed assistants, five phlebologists, six receptionists and office staff, and 45 physicians. one summer day the staff was at only 68% strength.

Then

Total number of staff = 25+75+5+6+45

Total number of staff = 156

Then

the staff was at strength = 68%

And then

Number of people working on that day = 68% of 156

And

Number of people working on that day = 68/100 *156

Number of people working on that day = 0.68*156

Number of people working on that day = 106.08

Approximate 107 people.

So, The number of people working on that day are 107 people in the staff.

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The solution to the give inequality is x < d-a/c

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given the inequality expression

d - cx < a

Make x the subject of formula to have:

-cx < a - d

Divide both sides by -c

-cx <(a-d)/-c
x < -(a-d)/c

x < d-a/c

Hence the solution to the give inequality is x < d-a/c

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The corrected mean and median, respectively, are 557.3 and 557.

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The length of hypotenuse is 4.5 meters.

The length of hypotenuse can be calculated using Pythagoras theorem. Writing the Pythagoras theorem below -

Hypotenuse² = Base² + Perpendicular²

The given other two sides will be base and perpendicular. So, keeping the values in mentioned equation of Pythagoras theorem to find the value of Hypotenuse.

Hypotenuse² = 2² + 4²

Taking square of the numbers to find the value of Hypotenuse

Hypotenuse² = 4 + 16

Performing addition to find the value of Hypotenuse

Hypotenuse² = 20

Hypotenuse = [tex]\sqrt{20}[/tex]

Taking square root to find the value of Hypotenuse

Hypotenuse = 4.5 meters

Hence,  the length in meters of a right triangle's hypotenuse is 4.5 meters

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There are 11 questions worth 5 points and 3 questions worth 15 points.

To find the correct number of questions:

Let, 5-point questions are x and 15 marks questions are y.

The total points are 100 so the other equation will be:

Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

Now,

So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

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Answer:

7GB, $12

Step-by-step explanation:

I used subtraction to find the difference.

The equation used to represent the context is 1041.50 + 62.75p = 2045.50.

From the information, they rented a bus for $1041.50 and budgeted $62.75 per player for meals.

Therefore, the equation will be:

1041.50 + (62.75 × p) = 2045.50

1041.50 + 62.75p = 2045.50

Therefore, the equation will be 1041.50 + 62.75p = 2045.50.

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Jack has left with the 19/8 yards fraction part of material.

In mathematics, yard is the unit of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:

        1 yard = 36 inches

        1 yard = 3 feets

        1 yard = 0.914 meters

For the question given,

If we have to find the remaining material that has been left we must find the difference between the two i.e. used and purchased material by simply subtracting them.

So, Material purchased = 3 yards

      Material used = 5/8 yards

now, material left = Material purchased - material used

                             =  3 - 5/8

                             = 19/8 yards

Thus, Jack has left with the 19/8 yards material.

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The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.

Expression

An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.

Given that:-

Expression : 5x -2y + 3z

x = 7, y = 11 , z = -1

We have to find the value of 5x - 2y + 3z

According to the data given in the question, we can write,

The value of the expression 5x - 2y + 3z is:-

5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.

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The least amount of money you can spend to buy the same number of candles and mints is $125.

The prime factorization of 12 and 15 is:

12= 2*2*3

15= 2*5*5

Now the factor of both appears in both number's factorization so least common multiple is:

LCM of 12 and 15 = 2*2*3*5*5=300

It is given that candies come in packs of 12 and mints in packs of 50.

Hence, the total quantity of packs of each thing is:

Candles: 300÷12=25

Mints: 300÷50=6

The least amount of money to be spent is:

25×$3.50 + 6×$6.25= $87.5 + $37.5= $125

Thus, the least amount of money you can spend to buy the same number of candles and mints is $125.

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Answer:125

Step-by-step explanation: no explanations sorry but it is right thank me later

Answer:

90 m

Step-by-step explanation:

a. Perimeter = 2( length + breadth) 2(x + y)

Answer: Perimeter:  2(x + y) = 420
or 2x + 2y = 420

Using the values given

b.

2x + 2y = 420 (perimeter p= 420)
2(120) + 2y = 420   (length x = 120)
240 + 2y = 420
2y =  420 - 240 = 180 (subtract 240 on both sides)

y = 190/2 = 90 m

Answer: 8 tacos

Step-by-step explanation: To turn 15 into 3 students you would divide 15 by 5. You would also have to divide 40 by 5 too so that would be 8 tacos.

Answer:

3.435973837*10^10

Step-by-step explanation:

4 to the 7th power is 16384

and 8 to the 7th power is 2097152

multiplied by each other is 3.435973837*10 to the 10th power

if you have to round to the nearest 10th the answer is 3.44

The number of times that blue will be expected will be 100 times.

It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.

It simply means that each color has a 1/4 chance for each scenario.

Therefore, the number of times that blue will be expected will be:

= 1/4 × 400

= 100 times

Therefore, the number of times that blue will be expected will be 100 times.

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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?

Answer:

96

Step-by-step explanation:

It is a straight linek so it adds up to 189.

53+31 = 84

180-84=96

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The length of the pen in the drawing will be 2 millimeters.

As we can't create a real-life dimension in a  small sheet of paper,  we opted for a small scale that covers up the large length.As we are given, the scale of the drawing is 1 millimeter: 10 meters, which is 1 millimeter for every 10 meters

As we have been given that the  actual  size of the goat pen  is 20 meters, so the length of the pen in the drawing is =  20*(1/10)

                                                                                  =   2 millimeters

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'

3/13              least

1/7

1/4               greatest

Answer:

Step-by-step explanation:

Givens

Let the Length = L

Let the width = w

w = 2*L - 3

Area = L * w

Area = 193

Solution

Area = 193

193 = L*(2L - 3)

193 = 2L^2 - 3L       Subtract 193 from both sides.

2L^2 - 3L - 193 = 0

You have to use the quadratic formula get the answer. Without going through all all that, I will tell you that the only value you can use for L is 10.6

L = 10.6

w = 2* 10.6 - 3 = 18.4

But you want the diagonal. Use the Pythagorean Theorem to get it.

Diagonal^2 = L^2 + w^2

Diangonal^2 = 10.6^2 + 18.4^2

Diagonal^2 = 450.92                   Take the square root of both sides

√diagonal^2 = √450.92

Answer

The diagonal is 21,23

Answer:

1st Question 24 ÷ (-6) = -4

2nd Question -15 ÷ 0.3 = -50

3rd Question -4 ÷ (-20) = 0.2

This should be correct. I used a calculator Lol. :3.

Using translation concepts, the y-coordinate of R' will be of -10.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the rule is given by:

(x,y) -> (x + 4, y - 7)

y -> y - 7 means that for the image, the 7 is subtracted from the y-coordinate of the pre-image. The y-coordinate of R is of -3, -3 -7 = -10, hence the y-coordinate of R' will be of -10.

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Answer:

6 x 10^7

Step-by-step explanation:

(2x3)(10^4 x 10^3)

6 x 10^4+3

6 x 10^7

The perimeter of a square is proportional to the sides of its length

The statement is given as

The perimeter of a square is four times as great as the length of any of the sides

The above statement can be represented as

P = 4L

Where P represents the perimeter and L represents the side length

A proportional equation is represented as

y = kx

Where k a constant

By comparing y = kx and P = 4L, we have

y = P, k = 4 and x = L

Hence, the perimeter of a square is proportional to the sides of its length

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We need to know about logic statements to solve this problem. The solution of the logic statements are 0 and 1 respectively.

Logical operators are used to form logical statements, logical operators compute result based on boolean values true and false or binary 1 and 0. The common logical operators are AND and OR. AND is represented by ^ symbol and OR is represented by v symbol, ' means negation of the value, which means that true becomes false and vice versa. For AND operator, it works like multiplication, 0 and 1 yield 0, 1 and 1 yields 1 and 0 and 0 yields 0. For OR operator it works like addition, 0 and 1 yields 1, 1 and 1 yields 1 and 0 and 0 yields 0. For the logical statements given in the question we need to first compute the logical statement inside the bracket and then compare the inner result with the outer value.

(1'^0)^1 =(0^0)^1=0^1=0

(1v0')^(0v1)=(1v1)^(0v1)=1^1=1

Therefore we found the values of the logical statements to be 0 and 1 respectively.

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The percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

The normal distribution, also recognized as that of the Gaussian distribution, would be a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far away from the mean. The normal distribution is represented graphically as a "bell curve."

Now, according to the question;

The formula for finding the z-score is;

z = (x - μ)/σ

where,

x is the score

μ is the mean

σ is the standard deviation.

Summer vacation costs $1,755 for the average local family.

The distribution is normal, with a standard deviation of $390.

We need to figure out what percentage of families took vacations less than $1200.

The mean is $1,755

∴ μ = $1,755

∵ The standard deviation is $390

∴ σ = 390

∵ The vacation cost is under $1200

∴ x = $1200

Substitute the values in the formula of z score.

z-score = (1200 - 1,755)/390 = -1.42

Use the negative normal distribution table of z

P(z < 1,200) = 0.07782

P(x < 1,200) = P(z < 1,200)

P(x < 1,200) = 0.07782

P(x < 1,200) = 7.78%

Therefore, the percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.

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The complete question is -

International travel is usually more expensive than domestic travel. A recent survey found that the average per-person cost of a 12-day international vacation is  $1,755. This includes transportation, food, lodging, and entertainment.

a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.

Answer:

-3.4 or -17/5

Step-by-step explanation:

3 and 2/5= 17/5 or 3.4

-7 and 1/5 = -34/5 or -6.8