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The scale factor used to create the image is given as follows:

4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

In the context of this problem, we have that each vertex of A'B'C'D' is obtained with the multiplication of each of the coordinates of ABCD by four.

For example, we have that vertex A has the coordinates A(1, -2), while the equivalent vertex A' has the coordinates of A'(4, -8).

Hence the scale factor used to create the image is given as follows:

4.

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Michelle pays $1365 in total.

Option D is the correct answer.

We have,

To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.

The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:

= $6.50 x 200

= $1300

The shipping fee is 5% of the total order, which is:

= 5% x $1300

= $65

To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:

= $1300 + $65 = $1365

Therefore,

Michelle pays $1365 in total.

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The area of triangle ABC is given as follows:

A = 5.5 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The base AB has the length given as follows:

[tex]AB = \sqrt{(-4  - (-8))^2 + (-7 - (-8))^2}[/tex]

b = 4.12.

The midpoint of the base AB is given by the mean of the coordinates, hence:

M = (-6, -7.5).

The height is given by the distance MC, as follows:

[tex]h = \sqrt{(-6 - (-5))^2 + (-7.5 - (-5))^2}[/tex]

h = 2.69.

Hence the area of the triangle is given as follows:

A = 0.5 x 4.12 x 2.69

A = 5.5 square units.

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The rate of change of y with respect to x for the given linear relationship is 10.

To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:

slope = (change in y) / (change in x)

Given the values in the table:

x: -8.5, -6.5, -2.5, -1

y: -92, -72, -32, -17

We can calculate the change in y and change in x between any two points.

For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:

change in y = -72 - (-92) = -72 + 92 = 20

And the change in x is

change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2

Using the formula for slope:

slope = (change in y) / (change in x) = 20 / 2 = 10.

Therefore, the rate of change of y with respect to x is 10.

This means that for every unit increase in x, y increases by 10 units.

We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.

Hence, the rate of change of y with respect to x for the given linear relationship is 10.

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Answer: 6 years

Step-by-step explanation:

75,000*15% = 11,250

11,250*6 = 67,500

75,000-67,500 = 7500

7500 is worth less than 15,000

5 years would have been 18,750; more than 15,000

Answer:

d

Step-by-step explanation:

To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:

Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5

Next year's estimated budget is £6,032 per quarter.

To calculate the percentage difference, we can use the following formula:

Percentage difference = (new value - old value) / old value x 100%

Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%

Therefore, the answer is (d) 3.9%.

Answer:

9 + x ≥ -23

Step-by-step explanation:

'At least' here means the lowest possibility of the sum 9 + x can equal -23, which means 9 + x can also be greater than -23. So the sum is either equal to -23 or greater than -23.

Answer:

30% increase

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = $35.10 - $27 = $8.10 , then

percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%

Answer:

Step-by-step explanation:

step 1:       35.10-27 =8.1

step 2:       8.1/27 x 100 = 30%

so therefore = 30% increase

The equation for the parabola in the graph is the one in option C:

y = (-1/4)x² -2x - 7

Remember that a parabola with leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)² + k

Here the vertx is at (-4, -3), then:

y = a*(x + 4)² - 3

And we can see that it passes through the point (0, -7), replacing that we will get:

-7 = a*(0 + 4)² - 3

-7 = a*16 - 3

-7 + 3 = a*16

-4 = a*16

-4/16 = a

-1/4 = a

The quadratic is:

y = (-1/4)*(x + 4)² - 3

Expanding that, we will get:

y = (-1/4)x² -2x - 4 - 3

y = (-1/4)x² -2x - 7

The correct option is C.

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There were 172 children and 165 adults admitted to the amusement park.

Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.

Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.

We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:

c + a = 337

The total admission fees collected is $918.

1.5c + 4a = 918

Now we have a system of two equations.

From the first equation, we can express 'c' in terms of 'a':

c = 337 - a

Substituting this value of 'c' into the second equation:

1.5(337 - a) + 4a = 918

505.5 - 1.5a + 4a = 918

2.5a = 918 - 505.5

2.5a = 412.5

a = 412.5 / 2.5

a = 165

Substituting the value of 'a' back into the first equation:

c + 165 = 337

c = 337 - 165

c = 172

Therefore, there were 172 children and 165 adults admitted to the amusement park.

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Answer:

subsidiaries hi sus

Step-by-step explanation:

scientific 2 is the answer

b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x

c) The domain of ƒ⁻¹(x) is all real numbers except for 1.

d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):

f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))

f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))

f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)

f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)

f(x) = (x - 3) / (x - 3)(x + 1)

f(x) = 1 / (x + 1)

Therefore, we have shown that f(x) = 1 / (x + 1).

(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:

x = 1 / (y + 1)

xy + x = 1

xy = 1 - x

y = (1 - x) / x

Therefore, the inverse function of ƒ(x) is given by:

ƒ⁻¹(x) = (1 - x) / x

(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.

For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).

Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.

(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.

(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):

ƒ(g(x)) = 1 / (g(x) + 1)

Substituting g(x) = 2x² - 3:

ƒ(2x² - 3) = 1 / (2x² - 3 + 1)

ƒ(2x² - 3) = 1 / (2x² - 2)

1 / (2x² - 2) = 1 / 8

8 = 2x² - 2

2x² = 10

x² = 5

x = ±√5

Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

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Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

[tex]A = P \times e^{rt}[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

[tex]3P = P \times e^{rt}[/tex]

Dividing both sides by P, we get:

[tex]3 = e^{rt}[/tex]

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

[tex]A = P \times (1 + r)^t[/tex]

[tex]A = $8,000 \times (1 + 0.0275)^{22.313}[/tex]

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

Answer:

  f(x)=40(2.25)^x

Step-by-step explanation:

You want the equation of the exponential function that goes through points (0, 40) and (1, 90).

The exponential function can be written ...

  f(x) = a·b^x

When x = 0, this is ...

  f(0) = a·b^0 = a·1 = a

Using the given point, we have a = 40.

When x = 1, this is ...

  f(1) = 40·b^1 = 40b

Using the given point, we have ...

  90 = 40b

  b = 90/40 = 2.25

The function equation is ...

  f(x) = 40(2.25^x)

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Answer:

Is the relation a function?

no

Step-by-step explanation:

please make brainlist

Answer: I think question two is Adjacent angles and complimentary angles.

Step-by-step explanation: Complementary angles are two acute angles that add to form a right angle.
Adjacent angles are two angles that share a common side.

Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA

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The data set with the greater range is greater for girls. The median is greater for girls.

The range of a dataset is the difference between the maximum and minimum values in the set.

The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.

To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.

To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).

The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.

Hence, the data set with the greater range is greater for girls. The median is greater for girls.

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The required sign that makes the statement true is "||".

The given options are 7, 22, 64, and V.

To express a percentage in mathematical notation, we divide the number by 100. In this case, 67.18% can be written as 0.6718.

Using the "||" symbol, we can write the equation as: 0.6718 || 7 = 22.

This equation represents the statement "0.6718 is to 7 as 22 is to 100." The vertical bar "||" signifies the ratio or proportion between the numbers. The double vertical bars "||" typically represent the symbol for "is equivalent to" or "is parallel to" in various contexts.

Therefore, the sign "||" makes the statement true.

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Note that the   curvature of the curve defined by the function y = 3x² - 2x +4   at point x = 2 is approximately 0.0002.

To find the curvature   of the curve defined by the function, we need to first find the second derivative of the function.

y = 3x² - 2x + 4

Taking the first derivative of y with respect to x

y' = 6x - 2

Taking the second derivative of y with respect to x:

y'' = 6

So the second derivative of y is a constant 6.

To find the curvature of the curve at point x = 2, we need to evaluate the following formula:

k = |y''| / [1 + (y')²][tex]^{(3/2)}[/tex]

Substituting x = 2 and y'' = 6, we get:

k = |6| / [1 + (6x2 - 2)²][tex]^{(3/2)}[/tex]

= 6 / [1 + (22)²][tex]^{(3/2)}[/tex]

= 6 / [1 + 484][tex]^{(3/2)}[/tex]

= 6 / 485[tex]^{(3/2)}[/tex]

k ≈ 0.0002

Hence,  the curvature of the curve defined by the function y = 3x² - 2x + 4 at point x = 2 is approximately 0.0002.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Find the curvature of the curve defined by the function

y=3x^2 -2x + 4

at point x =2

As it only told interest i asume its simple interest for compound interest the answer would be different

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

1 calculate the Expected values for opening a sample of 100 cards

The volume of the figure is 704 cubic centimeters.The correct option is B. 704 cubic centimeters.

The volume of the figure, need to calculate the volumes of the cube and the right triangular prism separately, and then add them together.

Volume of the cube:

The length of each side of the cube is given as 8 cm. The formula for the volume of a cube is V_cube = [tex]side^3.[/tex] Substituting the given value, we have V_cube = [tex]8^3[/tex] = 512 cubic centimeters.

Volume of the right triangular prism:

The base of the right triangular prism is a right triangle with one side measuring 8 cm and the other side measuring 6 cm. The height of the prism is given as 8 cm.

The formula for the volume of a right triangular prism is V_prism = base area * height. The base area of a right triangle is  [tex](1/2) * base * height[/tex]Substituting the given values, we have V_prism = [tex](1/2) * 8 cm * 6 cm * 8[/tex]cm = 192 cubic centimeters.

Add the volumes of the cube and the right triangular prism:

V_figure = V_cube + V_prism = 512 cubic centimeters + 192 cubic centimeters = 704 cubic centimeters.

The volume of the figure is 704 cubic centimeters.

The correct option is B. 704 cubic centimeters.

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The number of ways of selecting a committee of 4 women and 3 men from  8 women and 5 men is 700 ways

First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(8, 4) = 8! / [4!(8 - 4)!]

C(8, 4) = 70 ways

Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(5, 3) = 5! / [3!(5 - 3)!]

C(5, 3) = 10 ways

Finally, we shall determine the Total ways of selecting the committee. Details below:

Total ways of selecting = [C(8, 4)] × C(5, 3)]

Total ways of selecting = 70 × 10

Total ways of selecting = 700 ways

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The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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

y < 1/2x + 5

y ≤ -3x - 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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Answer:

(-5, -5)

Step-by-step explanation:

Given system of linear inequalities:

[tex]\begin{cases}y < \dfrac{1}{2}x+5\\\\y\leq-3x-2\end{case}[/tex]

When graphing inequalities:

To graph linear inequalities, treat them as equations (swap the inequality sign for an "equals" sign). Plug in two values of x to find two points on the line to help draw the lines.  

Substitute x = 0 and x = 6 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+5\\y&=5\end{aligned}[/tex]               [tex]\begin{aligned}x=6 \implies y&=\dfrac{1}{2}(6)+5\\y&=8\end{aligned}[/tex]

Plots points (0, 5) and (6, 8).

As the inequality sign is <, draw a dashed line through the plotted points and shade below the line.

Substitute x = 0 and x = 2 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=-3(0)-2\\y&=-2\end{aligned}[/tex]               [tex]\begin{aligned}x=2 \implies y&=-3(2)-2\\y&=-8\end{aligned}[/tex]

Plots points (0, -2) and (2, -8).

As the inequality sign is ≤, draw a solid line through the plotted points and shade below the line.

The solution set is the set of points contained within the overlapping shaded region and on the solid line.

Therefore, a point in the solution set is (-5, -5).

Answer:

FE = 12

DE = 20

Step-by-step explanation:

Part A

We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.

[tex]HE : GH = FE : DF[/tex]

↓ plugging in the given values

[tex]9 : 12 = FE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{9}{12} = \dfrac{FE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{FE = 12}[/tex]

Part B

We can solve for DE using the same technique.

[tex]GE : GH = DE : DF[/tex]

↓ plugging in the given values

[tex]15 : 12 = DE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{15}{12}= \dfrac{DE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{DE = 20}[/tex]

The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.

To find P(G|N), which represents the probability of event G given event N, we can use the formula:

P(G|N) = P(G∩N) / P(N)

Given that P(G∩N) = 0.24 and P(N) = 0.41

we can substitute these values into the formula:

P(G|N) = 0.24 / 0.41

Calculating the division:

P(G|N) = 0.585

Therefore, the value of P(G|N) is 0.585.

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