(2r^2t ^3)^2
4t^2
explain what you would do first to simplify the expression below.

Answer:

The length of arc PRQ is 16.7 in.

Step-by-step explanation:

So,

arc length = 2πr × (θ/360)

arc length = 2(3.14)(8) × (120/360)

arc length = 2(3.14)(8) × (120/360)

arc length = 50.24 × (1/3)

arc length = 16.7 inches

Thus, The length of arc PRQ is 16.7 in.

The variance of 2, 4, 6, 8, 10 is 8.

To calculate the variance of a set of numbers, you first need to calculate the mean of the set. The mean of 2, 4, 6, 8, 10 is 6. Then, for each number in the set, you need to calculate the difference between that number and the mean, and square the result. Finally, you need to sum those squared differences and divide by the number of items in the set.

Here's the calculation:

(2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2 = (-4)^2 + (-2)^2 + 0^2 + (2)^2 + (4)^2 = 16 + 4 + 0 + 4 + 16 = 40

40 / 5 = 8

So, the variance of 2, 4, 6, 8, 10 is 8.

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

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The value of a,b,c,d, and e is 45, 60, 58, 77, and 135 respectively, required to complete the two-way table.

A two-way table shows the connections between two sets of category data visually. Labels are positioned at the top and left sides of the table, which has rows and columns.

The sums for each row are displayed to the right, while the sums for each column are displayed at the bottom. 

We must create a two-way table based on the issue to ascertain the worth of each letter.

| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

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| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

The number of real solutions of the system are 2 if y=x²-3, y = -2x +4

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4). There is often only one solution to a system of linear equations, however it is possible for there to be infinite or no solutions (parallel lines) on occasion (same line).

Given,

y=x²-3 -----(1)

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

Solving equations 1 and 2, we get

x²-3=-2x +4

x²+2x-3-4=0

x²+2x-7=0

We have to solve by using quadratic formula,

x= (-b±√b²-4ac)/2a

x= (-2±√2²-4(1)(-7))/2(1)

x= (-2±√4+28)/2

x= (-2±√32)/2

x= (-2±4√2)/2

x= -1±2√2

x= -1-2√2, -1+2√2

Thus, the system has two solutions.

Therefore, the number of real solutions of the system are 2.

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Answer:

Brand A Forks $0.08, Brand B Forks $0.06, Better Buy is Brand B

Step-by-step explanation:

Unit price is price per unit (in this case, forks)

You need to find the $ for 1 fork for Brand A and B, since they have different unit prices.

total price/units = price/unit

Brand A: $1.97/25 forks = $0.0788 (rounded up is $0.08)

Brand B: $2.98/48 forks = $0.06208 (rounded up is $0.06)

Better brand is Brand B because it is cheaper.

Divide the base for that period by the appropriate commission rate to determine your commission for that period. Mark earns more money.Since $1680 > $1080, Mark earns more.

This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.

Mark: $24/h; 150% OT

Calculate Mark's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.5

Mark's OT wage is 1.5*$24 = $36

Mark worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Joe: 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Mark earns more.

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Answer:

approximately 1.732

Step-by-step explanation:

To solve this expression, we need to start by performing the operations inside the parentheses first. The square root of 8 is equal to 2, so 3 minus 2 is equal to 1. Then, we can divide 1 by the square root of 3, which is equal to approximately 1.732. Therefore, the expression 3 minus square root of eight divided by square root of 3 is equal to approximately 1.732.

Yes,  All equilateral triangles are similar to each other.

No,  All equilateral triangles are not congruent to each other.

The fact that every angle in an equilateral triangle is equal to 60 degrees is one of its characteristics.

According to the AAA Triangle Similarity Postulate, two triangles are similar  if all of their angles are identical to their corresponding angles in another triangle.

According to the AAA Postulate, all equilateral triangles are similar because their angles are all 60 degrees.

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

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The asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at

x = -3 and x = 8.

The asymptotes of a function are the lines that the graph approaches, but never touches as it continues to infinity. In the given function, f(x) = 7/(x^2-2x-24), the asymptotes are located at x = -3 and x = 8.

To find the asymptotes of a function, you first need to factor the denominator of the function. In this case, the denominator is[tex]x^2-2x-24,[/tex]which can be factored into (x+3)(x-8). This means that there are two potential zeroes in the denominator, x=-3 and x=8. These two points are the two asymptotes of the graph of the given function.

To explain further, the two asymptotes divide the x-axis into three intervals. On the interval (-infinity, -3), the graph of the function will approach negative infinity as x approaches -3 from the left. On the interval (-3, 8), the graph of the function will approach positive infinity as x approaches 8 from the right. On the interval (8, infinity), the graph of the function will approach negative infinity as x approaches 8 from the right.

In summary, the asymptotes for the given function f(x) = 7/(x^2-2x-24) are located at x = -3 and x = 8.

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The given equation A) 5x -2 + x = x - 4 and B) 5x + x = x - 4 are not equivalent.

The term equation in math refers the mathematical statement that is made up of two expressions connected by an equal sign.

Here we have given that the tow equations are

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

And we need to find if they are equivalent or not.

While we looking into the given question, we have given the following equations,

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

In order to find if they are equivalent or not, we have to simplify each of then then we get,

=> A) 6x - 2 = x - 4

=> A) 6x - 2 - x + 4

=> A = 5x + 2

Now, we have to do the same to simplify the equation (B), then we get

=> B) 6x = x - 4

=>  B = 6x - x + 4

=> B = 5x + 4

Now, we compare the two solved equation,

=> A = B

=> 5x + 2 = 5x + 4

Here the variable part is equal but the constant value is not same.

Therefore, we have identified the the two equation are not equivalent.

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62,800,000 is the product of (6.28 x 10^3) x 10,000.

It refers to the result of one or more multiplications.

Given number is (6.28 x 10^3) x 10,000.

6.28 x 10^3 =  6280

Therefore, 6280 x 10,000 = 628,000,00

Hence, the product of (6.28 x 10^3) x 10,000 is  628,000,00.

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The  equation is 3x² - 4x + 15 is polynomial in one variable.

An algebraic expression with one or more terms and a non-zero coefficient is called a polynomial. A polynomial is an expression composed of variables, coefficients, and constants connected by a mathematical operator. A polynomial is an expression connected by mathematical operations like addition, subtraction, multiplication, and division. An algebraic expression with only one variable is called a polynomial in one variable.

Given equation 3x² - 4x + 15

An algebraic expression with only one variable is a polynomial in one variable.

some examples of one variable polynomial

x + 2

y+ 5

x² + ax + b

ax³ + bx + c

all the equations that contain only 1 variables are  polynomial in one variable.

Hence the expression is polynomial in one variable.

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Radical Equations

Step 1

To demonstrate how to solve a radical equation, let's use the following equation as an example:

We calculated standard deviation 4 for the given set of numbers.

In the statistics, standard deviation is an estimation that implies how far each data value apart from the mean value. A high standard deviation indicates that all data are dispersed around the mean. And a low score of standard deviation implies data values are close enough in relation to the mean.

Let, X be the list of data value, X² be the square of the data value.

    X          X²

   2           4

   4           16

  6            36

  8            64

  10         100

  12         144

  14        196

we add all the data value and get ∑X = 56

We add all the squared value and get ∑X² = 560

Standard deviation is calculated by using the formula

SD =

√ [∑X²/N - (∑X/N) ²]

where N is the number of data present N= 7

SD = √[560/7 - (56/7)²]

     = 4

Hence, calculated standard deviation is 4

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Given that:  

Angle CBD=6x-40

Angle BFH=4x

From the given diagram, angle CBD=angle BFH ("corresponding angles")

Therefore 6x-40=4x,

                  6x-4x=40,

                   2x=40,

                    x=20

now Angle CBD= 6(20)-40

                          = 80

The formula of commutative property of addition is a + b = b + a and the formula of commutative property of multiplication is a × b = b ×  a.

The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The commutative property of addition states that a + b = b + a

The commutative property of multiplication states that a × b = b ×  a.

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There are 9 values in the sample: 2, 4, 6, 7, 8, 9, 10, 12, and 13. Since there are an odd number of values, the median is the middle value. In this case, the median is the 5th value, which is 8.

The median is a measure of central tendency, which means it is used to describe the "typical" or "average" value in a sample of data. To find the median, we first need to arrange the data in numerical order. In this case, the data is already in numerical order, so we can proceed directly to finding the median.

There are 9 values in the sample: 2, 4, 6, 7, 8, 9, 10, 12, 13. Since there are an odd number of values, the median is the middle value. In this case, the median is the 5th value, which is 8. This means that 8 is the middle value, with 4 values smaller than it and 4 values larger than it.

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The measure of the angle ∠GKJ, m∠GKJ, at the circumference of the circle H, which is subtends the same arc GJ as the angle ∠GHJ at the center of the circle is 27°

An arc of a circle is a part of the circle's circumference.

The measure of angle ∠GHJ, m∠GHJ = 54°

The measure of angle ∠GKJ, m∠GKJ = Required

Please find attached a possible drawing of the circle H created with MS Word and based on a similar question posted online

The circle, Angle at the Center Theorem states that the angle subtended at the center by arc is twice the angle subtended by the arc at the circumference of the circle.

The question indicates that the angle subtended by the arc GJ at the center of the circle, ∠GHJ = 2 × The angle subtended by the arc GJ at the circumference, ∠GJK

Therefore;

m∠GHJ = 2 × m∠GKJ

54° = 2 × m∠GKJ

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Risk is used to say the probability of an adverse outcome.

Option (a) (Risk) is the correct choice.

Through risk assessment, businesses, governments, projects, and investors may determine the likelihood that a bad occurrence will have a detrimental effect on their operations.

Risk assessment is crucial for figuring out the value of a particular project or investment and the appropriate process(es) to manage such risks.

Different methods may be used to evaluate the risk and reward tradeoff of a possible investment opportunity using the information provided by risk analysis.

A risk analyst begins by determining what may go wrong.

These drawbacks must be compared to a probability meter that assesses the chance that the event will occur.

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The correct question may be:

What word is used to say the probability of an adverse outcome?

(a) risk

(b) variance

(c) random statistics

(d) None of the above

Always begin by separating the variable y from the inequality's left side is the first step to graph an inequality.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

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The relationship between the volume of a rectangular prism and pyramid is defined as that the pyramid takes up 1/3 of the volume of a prism.

Here we need to identify  the relationship between the volume of a rectangular prism and pyramid.

As we all know that the volume of rectangle prism is written as,

=> Volume of a prism = (area of base) * height

Now, let us consider the volume of a pyramid that the pyramid takes up 1/3 of the volume of a prism when their bases and height are equal.

So, here the volume of a pyramid is 1/3 multiplied by the volume of a prism.

Then we get the volume of pyramid is written as,

Volume of a pyramid = 1/3 (area of the base) * height

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The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.

Answer:

Step-by-step explanation:

[tex]x^{2} -6x[/tex]

Therefore, the Z set represents the all integers numbers .

Describe integer.

An integer is a whole number, not a fraction, that can be negative, positive, or zero. The numerals  set of 5, 1, 5, 8, 97, and 3, 043 are a few examples. Non-integer numbers include 1.43, 1 3/4, 3.14, and other numbers.

According to the given question:

The set of integers represented here by Z is..., 2,..., 1, 0, 1, 2,... Q stands for the collection of rational numbers (the set of all possible fractions, including the integers).

The set of real numbers is designated as R. The group of complex numbers is designated as C.

Therefore, the Z set represents the all integers numbers .

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500 ≤x≤ 600  is the recommended range of doses. Typically, a phase I or early phase II clinical trial involves dose range.

To solve this problem using Clark's rule, we need to determine the range of pediatric doses for a child who weighs less than 90 pounds and for whom the adult dose is 1,000 mg.

A mathematical formula known as Clark's rule is used in medicine to determine the right dosage of medication for patients aged 2 to 17 depending on their weight and the recommended adult dose.

First, we can use the formula provided to calculate the child dose:

Child dose = (Weight of child / 150) * Adult dose

Since the weight of the child is less than 90 pounds, we can set the weight of the child to the minimum value in the range, which is 50 pounds. This gives us:

Child dose = (50 / 150) * 1000 mg

= 333.33 mg

Next, we can set the weight of the child to the maximum value in the range, which is 89 pounds. This gives us:

Child dose = (89 / 150) * 1000 mg

= 593.33 mg

Therefore, the recommended range of doses for a child who weighs less than 90 pounds and for whom the adult dose is 1,000 mg is 500 mg ≤ x ≤ 600 mg.

So, the correct answer is D. 500 ≤x≤ 600.

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All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Congruent Figures :

Those figures which covers each other/one another exactly then they are congruent Figures.

There are 4 ways by which we can prove any 2 triangles as congruent :

If they are having -

Three pairs of side are equal then the triangles are congruent.

If any 2 pairs of angles and 1 side are equal then the triangles are congruent.

If any two pairs of sides and the included angle are equal then the triangles are congruent.

If any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.

So, all three pairs of corresponding sides are equal then are congruent to each other.

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The measure of the angle m∠COD is 20 degrees

From the question, we have the following parameters that can be used in our computation:

The measures of the angles:

m∠BOD = 46 and m∠BOC = 26.

The measure of the angle m∠COD is the difference between of the above angles

Using the above as a guide, we have the following:

Measure of the angle m∠COD = Difference of angles m∠BOD and m∠BOC

Mathematically, this is represented as

Measure of the angle m∠COD =  m∠BOD - m∠BOC

Substitute the known values in the above equation, so, we have the following representation

Measure of the angle m∠COD =  46 - 26

Evaluate the difference

Measure of the angle m∠COD =  20

Hence, the angle is 20 degrees

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Answer:

the approximate sample proportion is 87%, which means that 13% of the people surveyed do not participate in the city’s recycling program.

Answer: see below

Step-by-step explanation:

The domain of a graph consists of all the input values shown on the x-axis

We want to find the left-most x value and the right-most x value.

-8, 3

since there is a hole at the point where x=3 we will use a paratensesis

D:xE[-8,3)