if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?

Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.

The correct circle graph representing the data in the table is:

circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 25 percent, auto supplies 20 percent, and beverages 40 percent.

This graph accurately represents the proportion of each item's purchases out of the total number of purchases. Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.

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For given trapezoid, the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.

A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The legs may be of equal length, or they may be different lengths.

Since trapezoid ABCD has two parallel sides, we know that angle A + angle D = 180 degrees. Similarly, angle B + angle C = 180 degrees.

Therefore, we can write:

angle A + angle B + angle C + angle D = 360 degrees

Substituting angle A = angle B and angle C = angle D, we get:

2(angle A) + 2(angle C) = 360 degrees

Simplifying:

2(angle A) + 2(50)= 180 degrees

2(angle A) = 180 degree-100 degree

2(angle A) = 80 degree

angle A= 80 degree/2

angle A = 40 degree

Since we know that angle A = angle B

angle B= 40 degree

Therefore,

angle A = angle B = 40 degrees

angle D = angle C = 50 degrees

So the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.

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Since triangle D has been dilated to create triangle D', the scale factor used include the following: A. 1/2.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given parameters into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = 2.4/4.8

Scale factor = 1/2.

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The empty set (also known as the null set) is a subset of every set because it does not contain any elements that are not in the set. In other words, if A is any set, then every element of the empty set is also an element of A, since the empty set contains no elements. This satisfies the definition of a subset, which states that for any two sets A and B, A is a subset of B if every element of A is also an element of B. Therefore, the empty set is a subset of every set.

~~~Harsha~~~

The length of the side of the square with the same area as the trapezoid is [tex]$12\sqrt{2}$[/tex] cm.

The area of a trapezoid is given by the formula:

[tex]$A = \frac{1}{2}(b_1 + b_2)h$[/tex]

where [tex]$b_1$[/tex] and [tex]$b_2$[/tex] are the lengths of the bases and h is the altitude.

Substituting the given values, we have:

[tex]$A = \frac{1}{2}(12+36)(12) = 288\text{ cm}^2$[/tex]

Since a square has all sides equal in length, the area of a square is given by:

[tex]$A = s^2$[/tex]

where s is the length of each side.

Substituting the area of the trapezoid, we get:

[tex]$s^2 = 288$[/tex]

Taking the square root of both sides, we have:

[tex]$s = \sqrt{288} = 12\sqrt{2}$[/tex]

Therefore, the length of the side of the square with the same area as the trapezoid is [tex]$12\sqrt{2}$[/tex] cm.

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Therefore, the exponential function showing the relationship between y and t is:

[tex]y = 230,000 *{ (1.063)^{t}[/tex]

The population of the city is growing at a constant rate of 6.3% per year. This means that the population is increasing by a factor of 1.063 each year.

Let y0 be the initial population in 1997, which is 230,000. The population in year t can be represented as:

[tex]y = y_0 * (1.063)^t[/tex]

where t is the number of years since 1997.

Therefore, the exponential function showing the relationship between y and t is:

[tex]y = 230,000 * (1.063)^{t}[/tex]

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the answer to the equation 112+18*14/14-19 is 111.

How to solve the question?

To solve this equation, we need to follow the order of operations (also known as PEMDAS), which is as follows: parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).

So let's break down the equation step by step:

18*14 = 252 (multiplication)

252/14 = 18 (division)

112+18 = 130 (addition)

130-19 = 111 (subtraction)

Therefore, the answer to the equation 112+18*14/14-19 is 111.

It's important to note that if we had performed the operations in a different order, we would have gotten a different answer. That's why following the order of operations is crucial in solving mathematical equations.

In general, it's important to have a good understanding of basic arithmetic and algebraic concepts to solve equations like this one. This includes knowing the order of operations, how to perform operations with fractions and decimals, and how to use variables and solve for unknowns. Practicing these skills regularly can help improve your problem-solving abilities in math and other subjects.

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Answer:

below

Step-by-step explanation:

To find out how many bunches of each flower the shop should order, we need to calculate the percentage of customers who preferred each flower, and then use that percentage to estimate the number of bunches needed for each flower.

First, we need to calculate the total number of customers who were surveyed:

Total customers surveyed = 8 + 4 + 8 + 20 = 40

Next, we can calculate the percentage of customers who preferred each flower:

Percentage of customers who preferred daisy = (8/40) x 100% = 20%

Percentage of customers who preferred gardenia = (4/40) x 100% = 10%

Percentage of customers who preferred mum = (8/40) x 100% = 20%

Percentage of customers who preferred rose = (20/40) x 100% = 50%

Now, we can use these percentages to estimate how many bunches of each flower to order.

Let's assume that each bunch contains 10 flowers (this is just an example, the actual number may vary):

Number of bunches of daisy to order = 20% of 50 bunches = 10 bunches

Number of bunches of gardenia to order = 10% of 50 bunches = 5 bunches

Number of bunches of mum to order = 20% of 50 bunches = 10 bunches

Number of bunches of rose to order = 50% of 50 bunches = 25 bunches

So, the shop should order 10 bunches of daisy, 5 bunches of gardenia, 10 bunches of mum, and 25 bunches of rose to meet the expected demand on Sunday.

According to the information, we know that the term 125x^5y^4 appears in the expansion when n = 6 and the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.

We know that the binomial expansion of (x-y)^n is given by the formula:

where nCk represents the binomial coefficient "n choose k".

We are given that the term 125x^5y^4 appears in the expansion, so we can set up an equation using the binomial coefficient for that term:

Simplifying this equation, we get:

We can solve for n by finding the smallest value of n for which nC5 is greater than or equal to 125. We can use the formula for binomial coefficients:

to calculate the values of nCk for different values of n and k. However, it is easier to use Pascal's triangle to find the binomial coefficients quickly. The fifth row of Pascal's triangle is:

We see that the sixth term of this row is 10C5 = 252, which is greater than 125. Therefore, we know that the term 125x^5y^4 appears in the expansion when n = 6.

To find the x^6y^7 term in the expansion, we need to find the coefficient of x^6y^7 in the expansion. We can use the same formula as before, but with k = 7 instead of k = 5:

We can simplify this expression using the fact that (-1)^7 = -1:

We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:

We see that 6C7 is zero because we cannot choose 7 items from a set of 6. Therefore, the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.

To find the x^7y^2 term in the expansion, we can use the same formula as before, but with k = 2:

We can simplify this expression using the fact that (-1)^2 = 1:

We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:

We can use Pascal's triangle to find that 6C2 = 15. Therefore, the coefficient of x^7y^2 in the expansion is 15, and the x^7y^2 term appears in the expansion as:

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Answer:

The maximum length of the poster that can be put in the box is 28 in.

Step-by-step explanation:

Answer:

M ≈ $933.24

Step-by-step explanation:

To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal (in this case, $45,000)

r is the annual interest rate (in this case, 8.5%)

n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)

Substituting the given values, we get:

M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)

Using a calculator, we get:

M ≈ $933.24

Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.

Answer: 5 were triangles :)

The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.

Using the formula:

Interest = Principal x Rate x Time

where Principal = $10,000,

Rate = 12.59% per year,

Time = 51/12 years (since the interest is compounded monthly):

Interest = $10,000 x 0.1259 x (51/12)

= $5,307.13

So the total amount owed after 51 months would be:

Total amount owed = Principal + Interest

= $10,000 + $5,307.13

= $15,307.13

Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States.  Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.

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The derivative of L(x) with respect to x is: d/dx [L(x)] = cosx + sinx

Given that

L(x) = sin(x) - cos(x)

To find dy/dx for the function L(x) = sinx - cosx, we need to take the derivative of L(x) with respect to x:

d/dx [L(x)] = d/dx [sinx - cosx]

Using the derivative rules, we can find the derivative of sinx and cosx:

d/dx [sinx] = cosx

d/dx [cosx] = -sinx

Therefore, the derivative of L(x) with respect to x is:

d/dx [L(x)] = cosx + sinx

So, dy/dx for L(x) is cosx + sinx.

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Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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The fraction that has been given illustrates that the person who ran further is Lisa and Jane.

Your information isn't complete. Therefore, an overview of the fraction will given.

Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/6 of a mile. In order to know who ran more, you can convert the fraction to percentage.

This will be

[tex]\text{Lisa} = \dfrac{1}{2} \times 100 = \bold{50\%}[/tex]

[tex]\text{Jane} = \dfrac{3}{6} \times 100 = \bold{50\%}[/tex]

Therefore, both Lisa and Jane ran more.

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The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:

Most students found a pine tree.

More students found a pine tree than a birch tree. That is option A and D respectively.

The quantity of students that found birch tree = 1/7 = 0.14

The quantity of students that found pine tree = 7/9 = 0.8

The quantity of students that found maple tree = 1/4 = 0.25

The quantity of students that found oak tree = 11/23 = 0.48

Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:

Most students found a pine tree.

More students found a pine tree than a birch tree.

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The range of the function in the graph is  6≤e≤12. So correct option is A.

In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.

For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.

The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.

Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.

The range of the function in the graph is  6≤e≤12. So correct option is A.

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The percentage of adults who preferred soccer or basketball is 25%.

The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.

From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.

Thus,

11% + 14% = 25%

Hence, the percentage of adults who preferred soccer or basketball is 25%.

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The two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.

Therefore, the two equations that can be solved using the zero product property are:

3x² - 6x = 0

This equation can be factored as:

3x(x - 2) = 0

Using the zero product property, we get:

3x = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = 2

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

This equation can be factored using the difference of squares:

-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0

Using the zero product property, we get:

x - 1 = 0 or x + 9 = 0

Solving for x, we get:

x = 1 or x = -9

Therefore, the two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

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Answer: B

Step-by-step explanation:

subtract 3 from both sides to get

4x > 27

divide both sides by 4 to get

x > 27/4 or 6 3/4

Using the formula for the area of a rectangle, the area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

From the question, we are to calculate the area of the cellphone shown in the diagram

From the given information,

We have a diagram that shows a cellphone which is rectangular in shape.

Thus,

We will use the formula for finding the area of a rectangle to calculate the area of the cellphone.

Area of a rectangle = Length * Width

From the given information,

Length of the cellphone = 6x²y⁶

Width of the cellphone = 3x⁻³y²

Thus,

Area of the cellphone = 6x²y⁶ × 3x⁻³y²

Area of the cellphone = 6 × 3 × x² × x⁻³ × y⁶ × y²

Area of the cellphone = 18 × x⁻¹ × y⁸

Area of the cellphone = 18x⁻¹y⁸ OR 18y⁸/x

Hence,

The area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

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Answer:

To find the set (AUB)' n C, we first need to find the union of sets A and B, which is the set of all elements that belong to either A or B or both:

AUB = {1, 2, 3, 5, 6}

The complement of AUB, denoted by (AUB)', is the set of all elements in U that do not belong to AUB:

(AUB)' = {4, 7, 8}

Next, we need to find the intersection of (AUB)' and C, which is the set of all elements that belong to both (AUB)' and C:

(AUB)' n C = {1}

Therefore, the set (AUB)' n C contains only the element 1.

The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

Using the formula A = P(1 + r/n)^(nt), where:

A = the amount in the account after t years

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

a) If interest is compounded annually:

A = 2000(1 + 0.05/1)^(1*7) = $2,835.08

b) If interest is compounded quarterly:

A = 2000(1 + 0.05/4)^(4*7) = $2,888.95

c) If interest is compounded monthly:

A = 2000(1 + 0.05/12)^(12*7) = $2,905.03

d) If interest is compounded continuously:

A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36

Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

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Answer:

The answer is x<8

Step-by-step explanation:

x/2<4

x<8

Answer:

Step-by-step explanation:

a) The probability that the customer is a good risk is given by the ratio of the number of good risks to the total number of customers. Therefore:

P(customer is a good risk) = 7751/11124 = 0.6968 (rounded to four decimal places)

b) The probability that the customer is not a poor risk is equal to the probability that the customer is a good risk or a medium risk. Therefore:

P(customer is not a poor risk) = P(customer is a good risk or a medium risk)

= P(customer is a good risk) + P(customer is a medium risk)

= (7751 + 2426) / 11124

= 0.9239 (rounded to four decimal places)

A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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Answer: 1

Step-by-step explanation:

x=1

A graph of the points is shown in the image below.

If ABCD is rotated 90° clockwise (U) about the origin to form A'B'C'D', the coordinates of the vertices of A'B'C'D'

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Additionally, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

Next, we would apply a rotation of 90° clockwise to the coordinate of quadrilateral ABCD as follows;

(x, y)                               →            (y, -x)

Coordinate A = (-3, 4) → Coordinate A' = (4, -(-3)) = (4, 3)

Coordinate B = (1, 6) → Coordinate B' = (6, -(1)) = (6, -1)

Coordinate C = (5, -2) → Coordinate C' = (-2, -(5)) = (-2, -5)

Coordinate D = (1, -4) → Coordinate D' = (-4, -(1)) = (-4, -1)

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