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Using the radius of the circle given, the perimeter of the equilateral triangle is 48 inches

The perimeter of an equilateral triangle is three times the length of one side. Thus, if the length of one side is 'l', the perimeter of the triangle is 3l.

In this problem, the equilateral triangle has 3 circles inside with radius of 6 inches each.

Assuming the circles when combined will cover the entire triangle.

The diameter of the circle = 6 * 2 = 12 in

The length of the equilateral triangle = 2 * 12 = 24in

However, we already know the perimeter of an equilateral triangle is three times the side length of the triangle.

Perimeter of equilateral triangle = 3 * 24

Perimeter = 48 in

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Of the part, the whole, and the percent, a. the exact number of students that are athletes is unknown to Ms. Morgan, which is 36, and b. the total strength of the students is unknown to Mr. Gregory which is 180.

Here we need to know 3 things- the total no. of students each teacher has, the percentage of athletes, and no. of students that are athletes.

a)

As we can see in the case of Ms. Morgan, we know the total strength of the students and the percentage of the students that are Athletes. Hence what we don't know here is the exact number of students that are athletes.

Hence we need to find 30% of 120

= 30/100 X 120

= 36 students.

b)

Here, in Mr. Gregory's case, we know the percentage and the actual number of students that are athletes. Hence, here we don't know the total strength of the students Mr. Gregory has.

Total strength = no. of athletes X 100/percent of athletes

= 27 X 100/15

= 180 students.

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Complete Question

Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his students, are athletes. a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value. b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.

The value of the exponent based on the information is 3. Therefore, 5³ = 35.

It should be noted that the exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Based on the information given, it should be noted that this can be written as:

5^x = 125

5^x = 5³

Since the base is equal

x = 5.

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Answer:

The answer is D) 5, the number of eggs on the charts never exceeds that number.

On solving the provided question, we cans ay that - the value of the each unit in this time will be from unitary method is 85.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

value of the 20 unit is 1700

value of the each unit will be 1700/20 = 85

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The correct option for the given linear equation is option (B).

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is always 1. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

The given equation is y =20x + 35

       y = total amount of money

       x = number of months the customer has been renting the storage unit

A) If x = 355

        y = 20 * 355 + 35 = $7135

    This is not the correct option.

B) If x = 16

      y = 20*16 + 35 = $355

     This is the correct option.

C) if x = 320

      y = 20 * 320 + 35 = $6435

      This is not the correct option.

D) If x = 16

       y = 20*16 + 35 = $355

      This is not the correct option.

Therefore the correct option for the given linear equation is option (B).

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The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),

(- 2, - 2), and (0, 1) with a dilation rule  DO,1/3 (x, y) to [(1/3)x, (1/3)y].

Therefore, The coordinates of the vertex V had a preimage of,

3(V'), which is 3(0, 1) = (0, 3).

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The value of a is  -5. All phrases that involve x become zero when we set their value to zero, leaving only constant terms.

The given equation is 2x^2 + x -a  = 5.

let's try to understand what is an equation.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For example,

The two equations 4x + 56 and 14 are joined by the equal sign to get the equation 4x + 56 = 14. Algebraic equations in mathematics frequently have one or more variables.

There are many different kinds of equations, including cubic, quadratic, and linear equations.

There are many distinct sorts of equations, depending on the degree of the equation.

2x^2 + x -a  = 5. put x = 0.

2*0 + 0 - a  = 5

0 + 0 -a = 5

-a =5

a = -5.

So the value of a is -5.

Given Question is incomplete complete question here:

What should be the value of a if the value of 2x^2+x - a equals to 5

when x = 0?

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Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.

Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.

Here, we have,

Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.

Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.

Therefore, option B is the correct option.

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The area of the shaded regions is 4π + 4, which can be obtained by subtracting 2π - 4 from 3π. This is an exact value, with no further simplification required.

Step 1: Calculate the area of the entire circle.

A = πr^2

A = π(5)^2

A = 25π

Step 2: Calculate the area of the unshaded region.

A = πr^2

A = π(2)^2

A = 4π

Step 3: Subtract the area of the unshaded region from the area of the entire circle.

A = 25π - 4π

A = 21π

Step 4: Calculate the area of the shaded region.

A = 21π - (2π - 4)

A = 21π - 2π + 4

A = 19π + 4

A = 4π + 4

The area of the shaded regions can be found by subtracting the area of the unshaded region from the area of the entire circle. To find the area of the entire circle, we use the formula A = πr^2, where r is the radius of the circle. Plugging in r = 5, we get A = 25π. To find the area of the unshaded region, we use the same formula, but now with r = 2. This gives us A = 4π. Subtracting the area of the unshaded region from the area of the entire circle gives us A = 21π. We then subtract 2π - 4 from 21π to get the area of the shaded region, which is 4π + 4. This is an exact value, with no further simplification required.

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Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

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The common factors and the greatest common integer for each pair of numbers are:

               Common prime factors        Greatest common factor

30, 45        3 and 5                                     5

40, 70         2 and 5                                    5

63, 42         3 and 7                                     7

81, 54          3                                               3

33, 99         3 and 11                                    11

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

30 and 45

3 x  5 x 2 = 30

3 x 3 x 5 = 45

Common prime factors = 3 and 5

Greatest common factor = 5

40 and 70

2 x 5 x 4 = 40

2 x 7 x 5 = 70

Common prime factors = 2 and 5

Greatest common factor = 5

63 and 42

3 x 3 x 7 = 63

2 x 3 x 7 = 42

Common prime factors = 3 and 7

Greatest common factor = 7

81 and 54

3 x 3 x 3 x 3 = 81

2 x 3 x 3 x 3 = 54

Common prime factors = 3

Greatest common factor = 3

33 and 99

3 x 11 = 33

3 x 3 x 11 = 99

Common prime factors = 3 and 11

Greatest common factor = 11

Thus,

Common prime factors are given above.

The greatest common factor is given above.

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Answer: 108000

Step-by-step explanation: Here's how I got my answer:

So, first, we need to know something. Whenever there's a fraction, you need to do this. I'll show you the numbers for this problem:

(60^3) / 2

So, the numerator goes in parentheses, and the denominator is what we are dividing by. So, 60^3 is the same as 60 x 60 x 60. You'd get 216000. Then, divide by 2 to get 108000. I hope this helps!

TIP: do NOT turn 3/2 into an improper fraction; 1 1/2. You would get a completely different answer.

To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

Consider an example where vertex is (2,1) and y-intercept is (0,-3).

The equation of parabola needs to be deduced using these points.

The equation of a parabola in vertex form is -

y=a(x-h)^2+k

Here, a is a constant and (h ,k) are the coordinates of the vertex.

So, (h,k)=(2,1)

⇒y=a(x−2)^2+1

To obtain the value of a, substitute (0,−3) into the equation -

-3=4a+1

4a=-4

a=-1

⇒y=-1(x−2)^2+1

Now, distribute and simplify -

y=-1(x−2)^2+1

y=-(x^2-4x+4)+1

y=-x^2+4x-4+1

y=-x^2+4x-3

On, graphing this equation a parabola is obtained.

Therefore, to write an equation of parabola vertex form is used.

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The measure of angle TQW from the given figure is 25°.

A perpendicular is a straight line that makes an angle of 90° with another line. 90° is also called a right angle and is marked by a little square between two perpendicular lines as shown in the figure. Here, the two lines intersect at a right angle, and hence, are said to be perpendicular to each other.

Given that, QT⊥PQR at Q, QW⊥QS at Q, and m∠SQP=25°.

From the given figure, m∠SQP+m∠SQT=90° -------(I)

m∠TQW+m∠SQT=90° -------(II)

Here, equation (I)=(II), we get

m∠SQP+m∠SQT=m∠TQW+m∠SQT

m∠SQP=m∠TQW

25°=m∠TQW

Therefore, the measure of angle TQW from the given figure is 25°.

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Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

Coefficient definition.

A number or symbol that multiplies another number or symbol is referred to as a "coefficient" (used as a mathematical variable).

Give a co-efficient example in writing.

A coefficient is a result of multiplying an amount by a variable. 6z, for instance, is short for six times z. 6 is a coefficient since z is a variable. The coefficient is one for variables that don't have a value.

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

The expression's coefficient is the term multiplied by x³. Since x³ is not a word, the answer is 1.

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The full question should be:

What is the coefficient form of X³ 2 *?

A value of 20 would fit the best in the table's empty cell to imply that there is no proof of a link between the variable and the outcome.

Option c is accurate.

The pattern between the supplied series must be found in order to determine the missing number. Verify that the series only shows increases, decreases, or both. The difference between two numbers should then be checked; this will help you discover the pattern.

To locate the missing numbers, the candidate must first identify the pattern or relationship between these numbers and then apply it.

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If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.

a. When they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

b. Based on the calculation both of them has the same amount of weight.

a. Weight

Let d represent the number of dieting days for this happen.

Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs

So,

John's weight = Frank's weight

Hence,

208 - 3d = 160 + 2d

Combine like terms

208 - 160 = 2d + 3d

48 = 5d

Divide both side by 5d

d = 48/5

d = 9.6 dieting days

The amount the weigh

Using John equation

Weigh = 208 - 3(9.6)

Weigh = 208 - 28.8

Weigh = 179.2 lbs

b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.

Using Frank's equation

Weigh = 160 + 2(9.6)

Weigh = 160 + 19.2

Weigh = 179.2 lbs

Therefore when they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

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Wilbur drove for 5 hours before Jack caught up with him.

Based on the information, the distance = (Wilbur's speed) x (time) = (Jack's speed) x (time + (time Wilbur drove))

We know that Jack's speed is 75 mph, and that he caught up with Wilbur after 2 hours. We also know that the distance covered by Jack is the same as the distance covered by Wilbur.

So we can write:

distance = (Wilbur's speed) x (time) = (Jack's speed) x (2 hours)

We are given that the Wilbur's speed is 30 mph, so we can substitute that in the above equation:

distance = 30 mph x (time) = 75 mph x 2 hours

Then we can solve for time by dividing both sides of the equation by 30:

time:

= (75 mph x 2 hours) / 30 mph

= 5 hours

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The height of an isosceles triangle can be found by using the Pythagorean Theorem to calculate the length of the hypotenuse, subtracting the lengths of the other two sides, and taking the square root of the difference.

To find the height of an isosceles triangle given three sides, you can use the Pythagorean Theorem. Begin by calculating the length of the hypotenuse (the longest side of the triangle). To do this, square the lengths of the two other sides and add them together. Then, take the square root of that sum. This is the length of the hypotenuse. Next, subtract the lengths of the other two sides from the hypotenuse and take the square root of the difference. The result is the length of the altitude, which is also the height of the triangle.

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Answer: Trapezoid

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trapezoid square and the down right all the way

a) The given relation is function.

b) The function is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he original amount of her loan is 6000.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, no two outputs have same input.

b) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                        = 18.5

So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.

c)  Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+  x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The modeled function. P(m) = 6000 - 300m.

so, the original amount of her loan is 6000.

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Answer: 2 2/3

Step-by-step explanation:

The annual state tax withheld for Kelly Waxman would be 1,662.50 dollars.

Therefore the answer is d) $1,662.50.

Here is the breakdown of the calculation:

Kelly's salary of $30,000 minus the married exemption of $3,000 = $27,000

The first $3,500 are taxed at 3%, which is

= 0.03×3500

= $105

The next $3,500 are taxed at 4.5%, which is

= 0.045×3500

= $157.50

The remaining $27,000 - $3,500 - $3,500 = $20,000 are taxed at 7%, which is

= 0.07×20000

= $1,400

Adding all three amounts together: $105 + $157.50 + $1,400 = $1,662.50. It is the annual state tax withheld.

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The expected mass of the sample in the year of 2021 is given as follows:

9 mg.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial mass was of 130 mg, hence the parameter a is given as follows:

a = 130.

In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:

b² = 80/130

b = square root(80/130)

b = 0.78446454055.

This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:

y = 130(0.78446454055)^x.

2021 is 11 years after 2010, hence the expected mass is obtained as follows:

y = 130(0.78446454055)^11

y = 9 mg.

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the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65

They need at least $1,150

They have already saved $700

They are selling shirts with a profit of $7.00 per shirt

If they sell n number of shirts, they will earn n times $7.00

Since they have already 700, they will earn a total of 700 + 7n

If this quantity has to be equal or greater to 1,150, we can write:

1150 <= 700 + 7n

if we solve this inequality for n:

1150 <= 700 + 7n

1150 - 700 <= 7n

450 <= 7n

450/7 <= n

64.28 <= n

Since the number of shirts has to be an integer (you can not sell "part" of a shirt)

n >= 65

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Answer:

6.2 < x < 26.6

Step-by-step explanation:

The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.

16.4 - 10.2 = 6.2

16.4 + 10.2 = 26.6

Let x = length of third side.

6.2 < x < 26.6

Answer:218

explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218