Students make a big mess in the cafeteria at lunch. 9 students had 30 minutes to clean up the mess.They got mad and named 3 others that were guilty. The principal added their names to the clean up crew and changed the time limit. How much time should she give them to complete the job?

The equation of circle with center ( -6 , 3 ) is ( x + 6 )² + ( y - 3 )² = 9² , where the radius of circle r = 3 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the first point is A ( -6 , 3 )

Let the second point be B ( -15 , 3 )

Let the third point be C ( 3 , 3 )

And , from the distance formula ,

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

The distance of AB = √ ( -15 + 6 )² + ( 3 - 3 )² = 9 units

The distance of AC = √ ( 3 + 6 )² + ( 3 - 3 )² = 9 units

The distance of BC = √ ( -15 - 3 )² + ( 3 - 3 )² = 18 units

So , the measure of AB = AC and the radius of the circle r = 3 units

Now , the center of the circle is A ( -6 , 3 )

where the standard form of a circle is

( x - h )² + ( y - k )² = r²,

On simplifying , we get

( x + 6 )² + ( y - 3 )² = 9²

Hence , the equation of circle is ( x + 6 )² + ( y - 3 )² = 9²

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380 liters of natural oil is needed

The ratio of natural oil to synthetic oil is 4:5

Total number of petrolyn oil is 855

4x + 5x= 855

9x= 855

x= 855/9

x= 95

The number of natural oil is 4x

= 4(95)
= 380

Hence the number of liters of natural oil that is needed is 380

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Answer:

the answer is D (4,∞)

Step-by-step explanation:

3n-12>4n-16

C.L.T.

3n-4n>-16+12

-n>-4

n>4

Answer: 101.41 lbs.

Step-by-step explanation:

46 kilograms can be converted to pounds by multiplying the number of kilograms by 2.20462.

So, 46 kg = 46 * 2.20462 = 101.41 lbs.

Answer: please look at the image for the answer

Step-by-step explanation:

The solution is: the cost of renting one chair is $2.25

the cost of renting one table is $8.25.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Let x represent the cost of renting one chair.

Let y represent the cost of renting one table.

The total cost to rent 3 chairs and 5 tables is $48. This means that

3x + 5y = 48 - - - - - - - - - -1

The total cost to rent 6 chairs and 2 tables is $30. This means that

6x + 2y = 30 - - - - - - - - - -2

Multiplying equation 1 by 6 and equation equation 2 by 3, it becomes

18x + 30y = 288

18x + 6y = 90

Subtracting, it becomes

24y = 198

y = 198/24 = 8.25

Substituting y = 8.25 into equation 1, it becomes

3x + 5 × 8.25 = 48

3x + 41.25 = 48

3x = 48 - 41.25

= 6.75

x = 6.75/3

= 2.25

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Supplementary angles are important in mathematics because they have a sum of 180 degrees.

This property is used in various geometric constructions and proofs, as well as in solving real-world problems involving angles. For example, in trigonometry, the concept of supplementary angles is used to determine the values of trigonometric functions for angles greater than 90 degrees.

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The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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Measure of angle V is 103°.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

Here is a six sided polygon, which is hexagon.

Sum of interior angles of a polygon = (n - 2) 180, where n is the number of sides of the polygon.

Sum of the interior angles of the given polygon = (6 - 2) 180 = 720

So,

∠S + ∠T + ∠U + ∠V + ∠W + ∠X = 720°

90° + (9x - 19)° + 111° + (5x + 8)° + 128° + (7x + 3)° = 720°

9x + 5x + 7x + 90 - 19 + 111 + 8 + 128 + 3 = 720

21x + 321 = 720

21x = 399

x = 19

∠V = (5 × 19) + 8 = 103°

Hence the angle V is of measure 103°.

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Solving the equations for each given variables, we have:

a. t = 15

b. a = 12.5

c. p = 5/2

d.

y = 4

Finding the value of a variable in an equation involves solving the equation for that variable. This process typically involves several steps, including isolating the variable on one side of the equation, using inverse operations to simplify the expression, and substituting known values into the equation to find the value of the variable.

Therefore:

a. 2/5t = 6

Multiply both sides by 5/2:

t = 6 * 5/2

t = 15

b. -4.5 = a - 8

Add 8 to both sides:

-4.5 + 8 = a

12.5 = a

a =12.5

c. 1/2 + p = 3

p = 3 - 1/2

p = 5/2

d. -12 = -3y

-12/-3 = y

4 = y

y = 4

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19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.

A multiple of number is product of that number and  other integer.

To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:

19 × 1 = 19

19 × 2 = 38

19 × 3 = 57

19 × 4 = 76

19 × 5 = 95

19 × 6 = 114

19 × 7 = 133

19 × 8 = 152

19 × 9 = 171

19 × 10 = 190

and so on.

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(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Two or more expressions with an Equal sign is called as Equation.

For the first 8 hours: The flat rate is $9.50 per hour, so 15% of that rate is 0.15 x 9.50 = $1.43.

The cost for the first 8 hours is (9.50 + 1.43) x 8 = $96.64.

For the next 8 hours: The flat rate is still $9.50 per hour, so 10% of that rate is 0.10 x 9.50 = $0.95.

The cost for the next 8 hours is (9.50 + 0.95) x 8 = $76.40.

Total cost estimate = $96.64 + $76.40 = $173.04

We can also write the equations for the costs as follows:

For the first 8 hours: Cost = (9.50 + 0.15 x 9.50) x Hours = 1.15 x 9.50 x Hours

For the next 8 hours: Cost = (9.50 + 0.10 x 9.50) x Hours = 1.10 x 9.50 x Hours

Using these equations, we can calculate the cost for any number of hours up to 16.

Hence, (9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

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Answer:

(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Step-by-step explanation:

The solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -1/2(8x-32)< -4

Multiply by -2 on both the sides of an inequality, we get

(8x-32)>8

Add 32 on both the sides of an inequality, we get

8x>40

Divide 8 on both the sides of an inequality, we get

x>5

So, solution set is {6, 7, 8, 9, 10,.....}

Therefore, the solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

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The inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

What is meant by the inverse of a function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."

Given a function m = 35g

 where m = distance in miles travelled by the truck

            g = gallons of gas used to travel m distance

If the function is m = 35g

Then the inverse function is g = m/35.

The inverse of the given function tells us how many gallons of gas are needed for a given number of miles.

Therefore the inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

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The ratio of the height of the triangle to the side of the square is 6.

A triangle is a three-sided polygon with three vertices and three angles. Triangles can have different shapes and sizes, including equilateral, isosceles, and scalene triangles.

Let's call the side of the square x. Since the base of the triangle is equal to the side of the square, we can use x for both. The area of the square can then be found by x² and the area of the triangle can be found by (x)(h)/2, where h is the height of the triangle.

We know that the area of the square is one-third the area of the triangle, so we can set up an equation:

x² = (1/3)(x)(h)/2

Expanding the right side of the equation:

x² = (1/3)(xh)/2

Now we can isolate the height of the triangle by multiplying both sides by 6 and dividing by x:

6x² = (xh)

Finally, we can divide both sides by x to find the ratio of the height of the triangle to the side of the square:

6x = h

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Answer: x = 11

Step-by-step explanation:

divide both sides by 12

12x/12 = 132/12

simplify it and you get your answer :)

x = 11

In 3 years, Aubrey will be able to spend $106.08 on a new bicycle.

First we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (balance)

P = principal (starting amount) = $100.00

r = interest rate as a decimal = 2% = 0.02

n = number of times per year that the interest is compounded = 1 (annually)

t = time in years = 3

Plugging in these values, we get:

A = $100.00 * (1 + 0.02/1)^(1 * 3)

A = $100.00 * (1.02)^3

A = $100.00 * 1.0608

A = $106.08

Therefore, in 3 years, Aubrey will be able to spend $106.08 on a new bicycle.

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Step-by-step explanation:

Let n= The first number

Let x= The second number

(5n-7)+9x

This is if the number are different numbers.

If they are the same:

Let n= a number

(5n-7)+9n=

7n-7

The distance of P to Q is given as follows:

89.6 feet.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

The parameters for this problem are given as follows:

a = 120, b = 100, C = 47º.

Hence the distance is obtained as follows:

c² = 120² + 100² - 2 x 120 x 100 x cosine of 47 degrees

c² = 8032

c = sqrt(8032)

c = 89.6 feet.

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Answer:

6x - 5 = 6x - 5

Step-by-step explanation:

If we have the same quantity on both sides of the equation, then the equation becomes an identity — an equation that is true for any value of the present variables.

If we set 6x - 5 equal to 6x - 5, then there are infinite solutions.

For example,

when x is 3:

6(3) - 5 = 6(3) - 5

18 - 5 = 18 - 5

13 = 13 ✔

when x is 5:

6(5) - 5 = 6(5) - 5

30 - 5 = 30 - 5

25 = 25 ✔

68.4 is approximately 95% of 72.

Here, we have,

To find out what percent of 72 is 68.4, we can follow these steps:

Step 1: Divide 68.4 by 72.

68.4 / 72 = 0.95

Step 2: Convert the decimal to a percentage by multiplying by 100.

0.95 * 100 = 95

Therefore, 68.4 is approximately 95% of 72.

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Answer:

the probability of event B is approximately 0.48.

Step-by-step explanation:

P(A) = P(B) (given)

P(A∪B) = P(A) + P(B) - P(A∩B) (probability rule for the union of two events)

Since events A and B are independent, we know that P(A∩B) = P(A) × P(B).

Substituting the given values, we get:

0.63 = P(A) + P(B) - P(A) × P(B)

Since P(A) = P(B), we can substitute P(B) for P(A):

0.63 = 2P(B) - P(B)^2

Rearranging this equation, we get:

P(B)^2 - 2P(B) + 0.63 = 0

This is a quadratic equation that we can solve using the quadratic formula:

P(B) = [2 ± sqrt(4 - 4×0.63)] / 2

P(B) = [2 ± sqrt(1.48)] / 2

P(B) ≈ 1 or P(B) ≈ 0.48

Since probabilities must be between 0 and 1, we can discard the solution P(B) = 1, and the only possible solution is:

P(B) ≈ 0.48

Therefore, the probability of event B is approximately 0.48.

59 is a prime number.

This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.

To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.

If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.

For example, with the number 59:

59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)

Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.

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Note that the area of the smaller square will be depicted by: 20inches.

Area of the larger square  - Area of the 4 Right Angled Triangles

Since the Area of the larger square  = is 36inches; and

Area of the one of the  Right Angled Triangles = 4inches

Thus, the Boxes will be completed as follows;


[36in] - (4) [4] or [20in]

Since

36 - 16 = 20 inches.

Note that a square is a closed two-dimensional form having four equal sides and four vertices. Its opposing sides are perpendicular to one other. A square can alternatively be thought of as a rectangle with equal length and width.

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Answer:

6

Step-by-step explanation:

7 1/3 ÷ 1 2/9

7 1/3 = 22/3

1 2/9 = 11/9

22/3 ÷ 11/9

= 22/3 x 9/11

= 198/33

= 66/11

= 6

The length of JM is given as follows:

JM = 16.875.

Similar polygons are polygons that share these two features presented as follows:

The polygons for this problem are similar, hence the proportional relationship for the segment lengths is given as follows:

16/15 = JM/18

Then the length of JM is obtained applying cross multiplication as follows:

16JM = 15 x 18

JM = 15 x 18/16

JM = 16.875.

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No, Mandisa's interpretation is incorrect because range does not describes the weight of the cats.

The range of a data set is the difference between the largest and smallest values in the set. In this case, the range of the data set is 5, which means the difference between the highest value and the lowest value is 5. This does not necessarily mean that half the cats at the shelter weigh no more than 5 pounds.

For example, if the smallest value is 2 and the largest value is 7, the range would be 7 - 2 = 5. This means that the range of the data set is 5, and yet the weight of a cat can be 7 pounds (more than 5 pounds). It does not mean that half the cats weigh no more than 5 pounds.

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Answer:

Step-by-step explanation:

Let us consider the Ginger to be x years old.

Therefore, her grandmother will be 10x years old(10 times Ginger's age)

So,

10x+x=66

(adding both Ginger and her grandmother's age)

11x=66

(adding x and 10x)

x=66/11

x=6

Ginger's age is 6.

Her grandmother is 10 times her age.

Therefore she is 60 years old.

The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)

The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).

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Answer:

9(4+5)-16=

Explanation:

P (parenthesis) E (exponents) M (multiply) D (divide) A (add) S (subtract)

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