Cristian purchased a t-shirt for $25.50 and a pair of pants for $32.75. he received $1.75 back from the sales clerk. how much did Cristian give the sales clerk?

Using the equation, the center is (-2,5) and the radius is 12 units.

Use the formula (x-a) ² + (y-b) ² = r² to determine a circle's equation when you are aware of its radius and center.

Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.

The given question is:

(x - 2) ² + (y + 5) ² = 144.

Now this can be written as:

(x - 2) ² + (y + 5) ² = 12²

The circle of center (x₁, y₁) and radius r is written as:

(x - x₁) ² + (y - y₁) ² = r²

Hence, the center is (-2,5) and the radius is 12 units.

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Answer:

4

Step-by-step explanation:

the distance around the field is the perimeter, which is 2(length) + 2(width)

2(150) + 2(100) = 500

2 kilometres = 2000 metres, and 2000/500 = 4

Answer: 4 times

Step-by-step explanation:

Step 1: find the Perimeter

Perimeter = 2L + 2W

= 2(150 meters) + 2(100 meters)

= 500 meters.

Step 2: find how many times the runner would have to run around the perimeter.

2 kilometers = 2000 meters

2000/500=4

The runner would need to go around the field 4 times to run 2km.

After 2013 "changesums", the list {20, 1, 3} becomes {x, x, x}. The maximum difference between two numbers is 0 since all numbers are equal.

We can start by applying the "changesum" procedure to the list {20, 1, 3} repeatedly, until we have done it 2013 times.

After the first application, we get the list {4, 23, 21}. After the second application, we get {44, 25, 27}. We can continue applying the procedure to get the following list of values:

{44, 25, 27}

{69, 71, 52}

{142, 120, 140}

{262, 282, 262}

{524, 524, 544}

{1048, 1068, 1048}

{2116, 2096, 2116}

{4212, 4232, 4212}

After 2013 consecutive "changesums", the list will have the form {x, x, x} for some value x. The maximum difference between two numbers in the list will be 0 in this case, since all the numbers are equal.

Therefore, the maximum difference between two numbers of the list after 2013 consecutive "changesums" is 0.

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Using the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

It seems like you have given me information about the distribution of typing speed for Mes Fuller's 120 keyboarding students. The distribution is normally distributed with a mean (μ) of 45 words per minute and a standard deviation (σ) of 6 words per minute.

A normal distribution is a continuous probability distribution that is symmetric around the mean value. The mean value is the center of the distribution, and the standard deviation measures the amount of variability or spread of the data.

With this information, we can calculate probabilities for different values of typing speed using the standard normal distribution table or a statistical software program.

For example, if we want to know the probability of a student typing more than 50 words per minute, we can calculate the z-score as follows:

z = (x - μ) / σ = (50 - 45) / 6 = 0.83

therefore, the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

Similarly, we can calculate probabilities for other values of typing speed using the same method.

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Answer:

Question #3 *I need help*

Step-by-step explanation:

Students need to be in the top 2% in order to be eligible for the national typing competition, if Carla can type 56 wpm, is she eligible?

(2x10^n)+(4.02x10^5), what is n?

Step-by-step explanation:

To determine the value of n, we need to rewrite the expression as a number in scientific notation, in the form a x 10^n, where 1 ≤ a < 10.

We can start by factoring out 10^n from both terms:

(2 x 10^n) + (4.02 x 10^5) = 10^n (2 + 4.02 x 10^-5)

Now we need to divide both sides of the equation by (2 + 4.02 x 10^-5):

(2 x 10^n) + (4.02 x 10^5) / (2 + 4.02 x 10^-5) = 10^n

We can simplify the expression on the left side by multiplying the numerator and denominator by 10^5:

(2 x 10^n x 10^5 + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Simplifying the numerator:

(2 x 10^(n+5) + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Now we can cross-multiply to eliminate the fraction:

(2 x 10^(n+5) + 4.02 x 10^5) = 10^n (2 x 10^5 + 4.02)

Expanding both sides:

2 x 10^(n+5) + 4.02 x 10^5 = 2 x 10^(n+5) + 4.02 x 10^n

Subtracting 2 x 10^(n+5) from both sides:

4.02 x 10^5 = 4.02 x 10^n

Dividing both sides by 4.02:

10^5 = 10^n

Therefore, n = 5.

The volume of the sphere is 1372 cubic cm for the given radius.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Many forms have various volumes. We have examined the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these forms.

The volume of the sphere is given by the formula:

V = 4/3πr³

Substituting the value of π = 3 and r = 7 we have:

V = 4/3(3)(7)³

V = 1372 cubic cm.

Hence, the volume of the sphere is 1372 cubic cm for the given radius.

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Answer:

Step-by-step explanation:

1

Step-by-step explanation:

The three internal angles of a triangle sum to 180 °

x + 23      +      4x+17     +   80    = 180

5x + 120 = 180

5x = 60

x = 12 °

Answer:

Step-by-step explanation:

t=0

If you replace t with zero -9=-9(0+1)

0+1=1 and -9(1)=-9

so t=0

Here's a visual representation of the lines connecting each value to 10.56:

In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.

by the question.

sure, I can help you with that!

To join 10.56 to all the equivalent values, you can draw lines connecting each value to 10.56. Here's how:

105 tenths and 6 hundredths:

To convert 105 tenths and 6 hundredths to a decimal, you can add the two values together: 105/10 + 6/100 = 10.56.

Draw a line connecting "105 tenths and 6 hundredths" to "10.56".

10 ones and 56 tenths:

To convert 10 ones and 56 tenths to a decimal, you can add the two values together: 10 + 56/10 = 10.56.

Draw a line connecting "10 ones and 56 tenths" to "10.56".

1 ten and 56 hundredths:

To convert 1 ten and 56 hundredths to a decimal, you can add the two values together: 10 + 56/100 = 10.56.

Draw a line connecting "1 ten and 56 hundredths" to "10.56".

156 hundredths:

To convert 156 hundredths to a decimal, you can divide the value by 100: 156/100 = 1.56.

Add 1 to the whole number part to get 10.56: 1 + 0.56 = 10.56.

Draw a line connecting "156 hundredths" to "10.56".

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The area of the shape given above which is the addition of area of semi circle and the area of the triangle prism =660.48 ft²

To calculate the area of a triangular prism the formula given below is used:

Area of a triangular prism = ab+ 3bh

where;

a = side = 20ft

b= base = 10 ft

h = height = 12 ft

Area = 20×10 + 3×10×12

= 200 + 360

= 560ft²

The area is semi circle = πr²/2

π = 3.14

R = 16/2 = 8ft

area = 3.14× 8²/2

= 200.96/2

= 100.48 ft²

Area of the shape = 560+100.48 = 660.48 ft²

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The term used for discovery sampling is statistical random sampling.

What is statistical random sampling?

A simple random sample is a subset of individuals chosen at random, all with the same probability, from a larger set of individuals. It is a method of choosing a sample at random.

Here,

We have to find another term for discovery sampling.

We concluded that another term that is used for discovery sampling is statistical random sampling.

Hence, the term used for discovery sampling is statistical random sampling.

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Answer:

Let the fraction be represented by "a/b".

According to the problem statement, we can create two equations:

Equation 1: (a-1)/(b+2) = 1/2

Equation 2: (a+3)/(b-2) = 1 1/4 = 5/4

We can simplify Equation 1 by cross-multiplying to get:

2(a-1) = b+2

2a - 4 = b + 2

2a = b + 6 --- (Equation A)

Similarly, we can simplify Equation 2 by converting 1 1/4 to an improper fraction:

5/4 = 1 + 1/4 = 4/4 + 1/4 = (4+1)/4 = 5/4

So, Equation 2 becomes:

5(a+3) = 4(b-2)

5a + 15 = 4b - 8

5a = 4b - 23 --- (Equation B)

Now, we have two equations (Equation A and B) with two unknowns (a and b). We can solve for one variable in terms of the other and substitute in either equation to find the value of the other variable. Here, we will solve for 'b' in Equation A:

2a = b + 6

b = 2a - 6

Substitute this value of 'b' in Equation B:

5a = 4b - 23

5a = 4(2a - 6) - 23

5a = 8a - 47

3a = 47

a = 47/3

Substitute this value of 'a' in Equation A to find 'b':

2a = b + 6

2(47/3) = b + 6

94/3 - 6 = b

b = 76/3

Therefore, the fraction is (a/b) = 47/76.

The planet will travel a distance of 17.088 x 106 miles in 8 days.

Distance is a numerical measurement of how far apart two or more objects, people, or locations are from one another. It is a fundamental concept in geometry, physics, and mathematics. Distance can be measured in a variety of ways, such as kilometers, miles, feet, inches, and light years. Distance can also refer to the physical separation between two points, such as the length of a line or the circumference of a circle. Distance can also refer to the emotional or psychological divide between two people. Distance can be both positive and negative, as it can bring people together or drive them apart.

To calculate how far the planet will travel in 8 days, we must first calculate the distance the planet will travel in one day. To do this, we must multiply the speed of the planet (8.9 x 104 mph) by 24 hours, which represents one day:

Distance in 1 day = 8.9 x 104 mph x 24 hours
Distance in 1 day = 2.136 x 106 miles

Now that we know the distance in one day, we can calculate the distance the planet will travel in 8 days. To do this, we must multiply the distance in one day (2.136 x 106 miles) by 8 days:

Distance in 8 days = 2.136 x 106 miles x 8 days
Distance in 8 days = 17.088 x 106 miles

Therefore, the planet will travel a distance of 17.088 x 106 miles in 8 days.

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Answer:

look in explanation

Step-by-step explanation:

In this equation, y can only be equal to 5 if x is labeled as 3.

Why? Because when you input the numbers into the equation, y=5 and x=3 then it will make sense.  5=3+2  If you put y as any other number the equation will not be true.

The scale factor after dilation is 2 in.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here in the given figure QRST , the length of QT = 2in.

Now after dilation the figure Q'R'S'T' , the length of Q'T'= 4in

Then scale factor is,

=> Q'T'/QT = 4/2 = 2in.

Hence the scale factor after dilation is 2 in.

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The two random variables from this list that are continuous are: a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO.

A continuous random variable is a variable whose values are any member of an uncountable set or any uncountable combination of such members. A continuous random variable has an infinite number of possible values, which are represented by an interval (a,b), where a and b can be any value on the real number line. A continuous random variable cannot take on individual values because there are an infinite number of values between any two points.For example, temperature, length, and weight are examples of continuous random variables.

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The value of x that makes the equation true is -1.

To obtain the value of x, we must first express the equation as seen in the diagram. This gives us:

5x + 6 = 1

Five x was obtained by counting the number of x's that we have in the boxes and the sum of figure 1.

Now, when we solve this, we will have

5x = 1 - 6

5x = -5

x = -1.

This then means that if we are to sum -1 five times and add 6 to it, the final value that we will have is 1.

Complete Question:

The diagram shows five boxes with the x initials and 6 boxes with figure 1. All of these are represented on the left-hand side and equated to 1.

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We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using this formula, we can find the distance between (16, 0) and (0, 12) as:

d = sqrt((0 - 16)^2 + (12 - 0)^2)

d = sqrt((-16)^2 + 12^2)

d = sqrt(256 + 144)

d = sqrt(400)

d = 20

Therefore, the distance between (16, 0) and (0, 12) is 20 units.

The horizontal distance covered by Viola is approximately 1282.6 meters.

The height of the plane is approximately 461.7 meters

The height of the pole is approximately 159.8 feet.

The perimeter is 44.2.

The horizontal distance covered by Viola can be calculated by using trigonometry. The angle of inclination is 9°, and the distance traveled up the hill is 200 meters.

Let x be the horizontal distance covered. Then we have:

tan(9°) = 200/x

x = 200/tan(9°) ≈ 1282.6 meters

Therefore, the horizontal distance covered by Viola is approximately 1282.6 meters.

We can use trigonometry to find the height of the plane. Let h be the height of the plane above the atoll, and let d be the horizontal distance from the airplane to the atoll. Then we have:

tan(7°) = h/d

h = d * tan(7°) ≈ 461.7 meters

Therefore, the height of the plane is approximately 461.7 meters.

We can use trigonometry to find the height of the pole. Let h be the height of the pole, and let d be the distance from the surveyor to the base of the pole. Then we have:

tan(44°) = h/(d + 4)

h = (d + 4) * tan(44°)

h = (140 + 4) * tan(44°) ≈ 159.8 feet

Therefore, the height of the pole is approximately 159.8 feet.

In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg and √3 times as long as the longer leg. Therefore, the shorter leg has length 18/2 = 9, and the longer leg has length 18√3/2 = 9√3.

The perimeter of the triangle is the sum of the lengths of the three sides, which are 9, 9√3, and 18. Therefore, the perimeter is:

9 + 9√3 + 18 = 27 + 9√3 ≈ 44.2

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To accumulate $100,000 over 20 years at a 10% annual interest rate compound annually, you would need to make annual payments of $8,218.64.

You can use the formula for the future value of an annuity to accumulate $100,000 over 20 years at a 10% annual interest rate compound on a yearly basis:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

Where:

FV is future value, which is $100,000 in that case

Pmt: annual payment

r: annual interest rate, which is 10%

n: number of payment periods, which is 20

By plugging in values:

[tex]$100,000 = Pmt * [(1 + 0.1)^(20) - 1] / 0.1[/tex]

Solving for Pmt, we get:

[tex]Pmt = $100,000 / [(1 + 0.1)^(20) - 1] / 0.1\\Pmt = $100,000 / 12.167\\Pmt = $8,218.64[/tex]

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Yes we can say that Liam's interpretation of the algebraic expression is correct because it has two variables, coefficients of 6 and 3, and two terms.

In Mathematics, an algebraic expression is defined as an expression that is normally made up of variables, constants, coefficients, and then arithmetic operations. These mentioned items are the different parts that make up the algebraic expression.

Let us consider an expression, 3x + 5y - 8

Here, the parts of the expression are:

Coefficients are 3 and 5

Constant is 8

Variables are x and y

Terms are 3x, 5y

Mathematical operators used are plus (+) and minus (-).

We are given the algebraic equation 6x + (-4) = 3y

Thus, it has:

Two coefficients which are 6 and 3

Two variables which are x and y

Two terms which are 6x and 3y

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The relative frequency is 8/25.

Relative frequency is a statistical concept that refers to the proportion of times that an event occurs in a given sample or population. It is calculated by dividing the number of times the event occurs by the total number of observations in the sample or population.

Relative frequency is an important concept in probability theory and statistics because it provides a way to estimate the probability of an event occurring based on the observed data. As the sample size increases, the relative frequency becomes a more accurate estimate of the true probability of the event.

Relative frequency is also used in hypothesis testing, where it is used to test whether a particular hypothesis is supported by the data. In this case, the observed relative frequency is compared to the expected relative frequency under the null hypothesis to determine whether the difference between the two is statistically significant.

The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

Therefore, the relative frequency for the event "spin a 3" is:

24/75 = 8/25

So, the relative frequency is 8/25.

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The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

The "spin a 3" occurrence has a relative frequency of [tex]\frac{8}{25}[/tex].

A statistical concept known as "relative frequency" describes the percentage of times an event happens in a given sample or population. It is calculated by dividing the total number of observations in the sample or group by the frequency of the event.

Because it offers a method to calculate the probability of an event occurring based on the observed data, relative frequency is a crucial concept in probability theory and statistics. The relative frequency becomes a more precise indicator of the actual probability of the event as sample size rises.

In order to determine whether a specific hypothesis is backed by the data, relative frequency is also used in hypothesis testing. To determine

whether the difference between the two is statistically significant, the observed relative frequency is in this instance compared to the expected relative frequency under the null hypothesis.

There were 75 total spins, and 3 appeared 24 times during those rotations.

As a consequence, the proportional frequency of "spin a 3" is as follows:

[tex]\frac{24}{75} =\frac{8}{25}[/tex]

So, the relative frequency is [tex]\frac{8}{25}[/tex].

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The value of the given integral by converting it into polar coordinates is [a⁴ / 4] (1 - (-1)) = [a⁴ / 2].Hence, the correct option is (d) [a⁴ / 2].

To evaluate the iterated integral by converting to polar coordinates,

we need to change the limits of the integral into polar coordinates.

So the given integral in polar form is ∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0)[tex]4r^3cos(θ)sin(θ)dr dθ.[/tex]

The polar coordinate conversion is given by x = r cos(θ) and y = r sin(θ).Given integral ∫a0∫0−√a2−y24x2y dx dy can be expressed in the form of polar coordinates as follows:

∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr dθ

Where, x = r cos(θ) and y = r sin(θ)

Now, we can evaluate this integral using the polar coordinate conversion.

∫(from θ = 0 to θ = π/2)

∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr

dθ=∫(from θ = 0 to θ = π/2) [cos(θ)sin(θ) ∫(from r = a to r = 0) 4r³ dr ]

dθ= ∫(from θ = 0 to θ = π/2) [ cos(θ) sin(θ) (r⁴) / 4] (from r = a to r = 0)

dθ=∫(from θ = 0 to θ = π/2) [cos(θ) sin(θ) (a⁴) / 4]

dθ= [a⁴ / 4] ∫(from θ = 0 to θ = π/2) sin(2θ)

dθ= [a⁴ / 4] ([- cos(2θ)] from θ = 0 to θ = π/2)

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Answer:

18.5

Step-by-step explanation:

25-6.5=18.5

x=18.5

Answer:

1.11111111

Step-by-step explanation:

Answer: 1/0.9

Step-by-step explanation:

Simply put 1 as the numerator of the given number to get the reciprocal.

If Person A and Person B are playing archery together. the probability that A gets more targets than B is 0.5, or 50%.

The number of targets hit by A and B follows a binomial distribution with parameters n = 201 and n = 200, respectively, and p = 0.5.

To find the probability that A gets more targets than B, we need to find the probability that A hits more than 100 targets (since 100 is the average number of targets hit by each player). We can use the normal approximation to the binomial distribution to do this.

The mean of the difference in the number of targets hit by A and B is:

E(A - B) = E(A) - E(B) = np - np = 0

The variance of the difference in the number of targets hit by A and B is:

Var(A - B) = Var(A) + Var(B) = np(1-p) + np(1-p) = 100

The standard deviation of the difference is then:

SD(A - B) = sqrt(Var(A - B)) = 10

Using the normal distribution approximation, we can standardize the difference in number of targets:

Z = (X - E(A - B)) / SD(A - B)

where X is the number of targets that A hits.

P(A hits more targets than B) = P(A - B > 0)

= P(Z > (0 - 0) / 10)

= P(Z > 0)

= 0.5

Therefore, the probability that A gets more targets than B is 0.5, or 50%. This means that there is an equal chance that A will hit more targets than B as there is that B will hit more targets than A.

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