How do you calculate the arc length of a circle?

An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.

Examples of interval variables include temperature (in Celsius or Fahrenheit), time (in seconds, minutes, hours, etc.), and dates. You can calculate the difference in temperature between two points, the length of time between two events, or the number of days between two dates. For example, let's say that the temperature outside is 25°C at noon and 29°C at 4 pm. The interval variable is the temperature, and the difference between the two temperatures is 4°C (29°C - 25°C = 4°C). Another example is the length of time between two events. Let's say that Event A began at 1 pm and Event B began at 2 pm. The interval variable is the length of time between the two events and the difference between the two times is 1 hour (2 pm - 1 pm = 1 hour). Finally, let's say that Date A is January 1, 2020 and Date B is January 10, 2020. The interval variable is the number of days between the two dates, and the difference between the two dates is 9 days (January 10,)An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.

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The solution to the radical equation is given as follows:

x = 1.

The radical equation for this problem is defined as follows:

1/x + (x - 1)/9x = 1.

To leave the left side with a common denominator, we can multiply 1/x by 9 in the numerator and in the denominator, hence:

9/9x + (x - 1)/9x = 1.

As the left side has a common denominator, we can add the numerators and keep the denominator constant, as follows:

(9 + x - 1)/9x = 1

(8 + x)/9x = 1.

Applying cross multiplication, the value of x is obtained as follows:

9x = 8 + x

8x = 8

x = 8/8

x = 1.

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Jimmy’s total income is $91838.61

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period

The given parameters that will help us to determine the income are

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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The expression to represent how much more Elena spent is 4.1 + p.

Two friends shop for fresh fruit. Elena buys a watermelon for ​$8.55 and 5 pounds of cherries. Taniya buys a pineapple for ​$4.45 and 4 pounds of cherries.

Therefore, the expression to represent how much more Elena spent can be represented as follows:

hence,

p = price in​ dollars, per pound of cherries.

Hence,

amount Elena spent more = 8.55 + 5p - (4.45 + 4p)

amount Elena spent more = 8.55 + 5p - 4.45 - 4p

amount Elena spent more = 8.55 - 4.45 + 5p - 4p

Therefore,

amount Elena spent more = 4.1 + p

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Answer: Infinite solutions.

Step-by-step explanation:

To graph both these equations, you need to make them slope intercept form (which is y = mx + b):

x + 2y = -2 in slope intercept form is y = -1/2x - 1 (subtract x from both sides then divide both sides by 2).

-3x - 6y = 6 in slope intercept form is y = -1/2x - 1. (add 3x to both sides then divide both sides by -6).

These are the same lines, so there are an infinite number of solutions when you graph.

Hope this helps!

Based on the amount deposited into the account every month, the amount that Andrew will deposit in the account is $72,548.64. The interest earned will be $17,451.36.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

What amount does Andrew deposit?

This can be found by the formula:

= Amount deposited every month x Number of years x Number of months in a year

= 503.81 x 12 x 12

= $72,548.64

What amount of interest is earned?

This can be found as:

= Future value of amount - Amount deposited

= 90,000 - 72,548.64

= $17,451.36

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The mean income, of people who worked full-time in 2001 and had at least a bachelor's degree, was $53,054. while the median income was $72,674.

The mean is the average value.  The mean is computed as the quotient of the total value divided by the number of values.

The median is the middle value of the data set in an ordered list.

Both the mean and the median are described as measures of central tendency.

Thus, we can identify the mean value as $53,054 since it was the first to be mentioned, followed by the median income as $72,674.

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Which of these numbers is the mean and which is the median? Explain your reasoning.

Is this a right triangle: C. Yes, because 6² + 8² = 10².

In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < n < b + c

Where:

n, b, and c represent the side lengths of this triangle.

By applying Pythagorean theorem, the possible side lengths of the triangle's third side is given by:

10² = 6² + 8²

100 = 36 + 64

100 = 100 (True).

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The slope of the function is equal to: C. 3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (4 - 1)/(0 - (-1))

Slope, m = 3/4=1

Slope, m = 3.

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The relation which are function is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x.The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

We know that a relation is said to be function if one input have only one output.

1. The relation is not function because the input 6 have two output values

5 and 10.

2. The relation is a function because the each input have one output values.

3. The relation is a function because the each input have one output values.

4. The relation is not function because the input 4 have two output values .

5. The relation is a function because the each input have one output values.

6. The relation is not function because the input have two output values.

7. The relation is a function because the each input have one output values.

8. The relation is not function because the input have two output values.

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The formulas for the rigid transformations of the figures are listed below:

Case 1: (x, y) → (x - 10, y + 9)

Case 2: (x, y) → (- y, x)

Case 3: (x, y) → (- x, y)

Case 4: (x, y) → (- y, x)

Case 5: (x, y) → (x, - y)

Case 6: (x, y) → (x, y + 10)

In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:

Then, by direct inspection, we derive the following rigid transformations:

Case 1 (Translation)

(x, y) → (x - 10, y + 9)

Case 2 (Rotation)

(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))

(x, y) → (- y, x)

Case 3 (Reflection about y-axis)

(x, y) → (- x, y)

Case 4 (Rotation)

(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)

(x, y) → (- y, x)

Case 5 (Reflection about x-axis)

(x, y) → (x, - y)

Case 6 (Translation)

(x, y) → (x, y + 10)

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Answer:

4x+2

Step-by-step explanation:

Add common numbers together.

3x + x = 4x

Therefore, the answer is 4x+2.

Hope this helps ^_^

Answer:

[tex]x=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]2x=9 \implies x=\frac{9}{2}[/tex]

Option A is correct.

Selecting eight members randomly and recording whether each member is wearing a blue shirt.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Here, in 8 members the person wearing blue will be a success others will be a failure outcome.

Answer:

a

Step-by-step explanation:

In this situation, Allison's insurance company will pay a total of $400,000.

First, we need to add up the total amount awarded to the people injured in the accident. This is $40,000 x 4 + $80,000 x 2 + $160,000 x 1 = $400,000.

Next, we need to look at Allison's insurance policy. She has 50/250 bodily injury insurance, which means that the insurance company will pay up to $50,000 per person and up to $250,000 per accident.

Since the total amount awarded is $400,000, the insurance company will only pay the maximum amount allowed per accident, which is $250,000.

Therefore, the insurance company will pay $250,000 and Allison will be responsible for the remaining $150,000.

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Answer: 15

Step-by-step explanation:

Base x Height = Area

Answer:

(6x+8y)(6x-8y)

Step-by-step explanation:

See attached worksheet.

Answer:

Step-by-step explanation:

You're welcome

Answer:

x=17

Step-by-step explanation:

132 + (-30) = (6x+30) + (-30)

132 - 30 =6x + 30 - 30

102 =6x

6x/6 = 102/6

(This step has a picture)
x=17

Answer:

[tex]\mbox{\large \boxed{\textsf{5, 849 \;feet}}}[/tex]

Step-by-step explanation:

See figure for information pertaining to this explanation

The figure is self explanatory

The triangle ABC forms a right triangle with the vertical leg of length 14000-h and horizontal length of 58000

The angle opposite side 14000 - h = 8°

By the tangent formula

[tex]\tan 8^\circ = \dfrac{AB}{AC} = \dfrac{14000-h}{58000}[/tex]

Switching sides,

[tex]\dfrac{14000-h}{58000} = \tan 8^\circ[/tex]

[tex]14,000 - h = 58,000 \times \tan 8^\circ\\\\14,000 - h = 8,151.36 \approx 8,151[/tex]

h = 14,000 - 8,151 = 5,849 feet

So the altitude of Colorado Springs is roughly 5,849 feet

This is close to the published value of 6,035 feet. The differences are due to estimate errors in horizontal distance, peak height and angle of depression

1. Another point on the graph p(x) is (5, 9)

2. the vertex of the q(x) is (4, 10).

The other two points on the q(x) are (0, 2) and (2, 8).

Parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus ) and a fixed straight line (the directrix ).

Given:

The two equations of the quadratic functions are;

p(x) = -(x - 1)² + 10

q(x) = 1/2(x - 4)² + 10.,

The graph of p(x) and q(x) is given in the image below.

1. Another point on the graph p(x) is (5, 9)

2. the vertex of the q(x) is (4, 10).

The other two points on the q(x) are (0, 2) and (2, 8).

3. Yes the assumption is correct.

Therefore, all the required values are given above.

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Answer:

There is exactly one solution: (3, 1)

Step-by-step explanation:

To graph these equations, you need to change them to slope intercept form:

x + y = 4 in slope intercept form is y = -x + 4 (subtract x frok both sides).

x - y = 2 in slope intercept form is y = x - 2 (subtract x from both sides then divide both sides by -1)*.

Now, all you have to do is graph both and find the point they cross at (the solution) which is (3, 1).

* = y can never be negative, which is why you divide by a -1 after subtracting x.

Hope this helps!

One liter is equal to 33.814 ounces, so 2.7 liters is equal to 90.772 ounces. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.

To calculate the number of ounces in a given amount of liters, this formula can be used. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.This is useful for quickly and accurately converting between liters and ounces, which can come in handy when measuring liquids or other substances. For example, if a recipe calls for 2.7 liters of a certain ingredient, you can easily convert that to ounces using the formula.

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To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics

In 1947, George Dantzig invented an algorithm that allows us to take a system of equations and find its maximum or minimum values that make the equations most efficient. This method is used in linear programming to determine optimization.

If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.

Maximization of n = 30x + 32y + 33z

The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;

The answer is 644 because x = 0, y = 16, z = 4.

To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.

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The amount of money Company A charge more for x miles,  35 - 0.05x dollars

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Let's call the number of miles the family wants to travel "x".

The cost for Company A is $30.50 plus 8 cents per mile, so the total cost for Company A is,

30.50 + 0.08x.

The cost for Company B is $65.50 plus 13 cents per mile, so the total cost for Company B is,

65.50 + 0.13x.

To find out how much more Company A charges, we can subtract the cost for Company B from the cost for Company A:

= (30.50 + 0.08x) - (65.50 + 0.13x)

= 35 - 0.05x

So, Company A charges 35 - 0.05x dollars more than Company B for x miles.

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The required cost to lay carpet for her entire bedroom is 45,000.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.

To calculate the cost of carpeting Linda's bedroom, we need to find the area of the rectangle:

Area = length x width

Area = 75m x 50m

Area = 3750 square meters

Then, we can multiply the area by the cost per square meter of carpeting:

Cost = Area x Cost per square meter

Cost = 3750 square meters x AED 12/square meter

Cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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Answer:

8n^3 + 3n^2 + 8

Step-by-step explanation:

If a bag has 28 orange marbles, then it contain 49 red marbles.

A ratio is a comparison of two quantities or values, expressed in the form of a fraction or a division. Ratios are used to compare the size, magnitude, or quantity of two or more quantities or values.

For example, if there are 10 apples and 5 oranges, we can write the ratio of apples to oranges as 10:5 or 2:1, since there are two times as many apples as oranges. Similarly, if a recipe calls for 3 cups of flour and 1 cup of sugar, we can write the ratio of flour to sugar as 3:1, indicating that there are three times as much flour as sugar.

Ratios can be simplified, converted to equivalent fractions or decimals, or used to solve problems involving proportional relationships between different quantities. They are widely used in many areas of mathematics, science, and everyday life, such as in finance, engineering, and statistics.

We can start by using the given ratio of 7 red marbles for every 4 orange marbles to find the ratio of red marbles to orange marbles in the bag.

For every 4 orange marbles, there are 7 red marbles, so we can write:

7 red marbles / 4 orange marbles

We can simplify this ratio by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. This gives:

7/4

So the bag contains 7 red marbles for every 4 orange marbles.

If the bag has 28 orange marbles, we can use this ratio to find the number of red marbles in the bag. We can set up a proportion:

7/4 = x/28

where x is the number of red marbles in the bag.

To solve for x, we can cross-multiply:

7 × 28 = 4 × x

196 = 4x

Dividing both sides by 4, we get:

x = 49

Therefore, the bag contains 49 red marbles.

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