Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4

Determine the scale factor used.

2
3
one third
one half

(1) The value of X is equal to 4  (2) The mean age is 3. (3) The probability of randomly selecting  a child under the age of 9  is approximately 0.83.  

The formula for calculating the average of given numbers is equal to the sum of all values ​​divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.

(i). Given that there are a total of 42 children on the birthday, finding the value of x:

2x + 3x (4x-1) + x + (x-2) + (x-3) = 42

11x - 6 = 42

11x = 48

x = 4

Therefore, the value of x is equal to 4.

(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:

Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42

 = (14 + 24 + 27 + 40 + 22 +12) / 42

 = 139/42

 = 3.31

Rounded to the nearest whole number, the average age is 3.  

(iii). The probability of randomly selecting  a child under 9 is obtained by adding  the number of children aged 7, 8 or 9 (because we want children under 9) and  dividing by the total number of children:

Number of children under 9 years  = 2x + 3x + (4x-1)

Number of children under 9 years  = 9x - 1

Number of children under 9  = 9(4)–1

Number of children under 9 years  = 35

Probability of choosing a child under 9  = number of children under 9  / total number of children

Probability of choosing a child under 9 = 35/42

The probability of choosing a child under 9 years old is ≈ 0.83

Thus, the probability of randomly selecting  a child under the age of 9  is approximately 0.83.

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Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.

If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.

We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.

150=200+100sin(2πx)

Subtracting 200 from both sides, we get:

-50 = 100sin(2πx)

Dividing both sides by 100, we get:

-0.5 = sin(2πx)

To find the value of x that satisfies this equation, we can take the inverse sine of both sides:

sin⁻¹(-0.5) = 2πx

Using a calculator, we find that sin⁻¹(-0.5) = -π/6.

-π/6 = 2πx

Solving for x, we get:

x = -1/12

Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:

2000 + 1/12 ≈ 2000.1

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According to the information, the surface area of the solid is 758m² and the volume is 594m³

To find the surface area of the solid we have to perform the following procedure:

12m * 11m = 132m²

132m² * 2 = 264m²

16m * 9m = 144m²

144m² - 18m² = 126m²

126m² * 2 = 252m²

16m * 11m = 176m²

176m² - 66m² = 110m²

3m * 11m = 33m²

33m² * 2 = 66m²

6m * 11m = 66m²

264m² + 66m² + 66m² + 110m² +252m² = 758m²

To find the volume we have to perform the following procedure:

8m * 11m * 9m = 792m³

792m³ - 198m³ = 594m³

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The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.

The total number of ways to develop the complex would be 665, 280 ways.

To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.

Using combinations, we have:

Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)

Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)

Now, we find the probability:

Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members

Probability = (C(28, 6) x C(12, 4)) / C(40, 10)

Probability = 0.3633

To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:

The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:

P(11, 5) = 11! / (11 - 5)!

Total ways to develop the complex = 12 x P(11, 5)

= 12 x 55440 = 665,280 ways

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Answer:

164 Cakes

Step-by-step explanation:

382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.

Jackson's total cost after the discount and before tax would be $24.67.

When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.

To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).

Here we have

Jackson has a 10% discount at his local hardware store.

Let 'x' be the cost before tax

After a 10% discount,

The amount that Jackson could pay 90% of the cost

Given that he wants to buy $ 27.40  

The cost of items after discount = 90% of 27.40

= [ 90/100 ] × 27.40

= [ 0.9 ] × 27.40

= 24.66

Therefore,

Jackson's total cost after the discount and before tax would be $24.67.

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The length of line segment AB is equal to 8 units.

The magnitude of m∠BAQ is equal to 58°.

In Mathematics and Geometry, a perpendicular bisector can be defined as a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, the length of line segment AB can be calculated by using the following mathematical equation;

RP = 2AB

AB = RP/2

AB = 16/2

AB = 8 units.

Since A and B are the midpoints of PQ and RQ respectively, we have the following angles;

m∠P + m∠Q + m∠R = 180° (sum of all interior angles of ∆PQR)

58° + 38° + m∠R = 180°

m∠R = 180° - (58° + 38°)

m∠R = 84°

Since PR || AB, we have;

m∠R = m∠ABQ = 84° (corresponding angles).

m∠Q + m∠ABQ + m∠BAQ = 180° (sum of all interior angles of ∆ABQ).

m∠BAQ = 180° - (84° + 38°)

m∠BAQ = 180° - 122°

m∠BAQ = 58°.

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Complete Question:

In the ΔPQR, A and B are the midpoints of PQ and RQ respectively. If RP = 16, m∠P = 58°, and m∠Q = 38°, obtain AB and m∠BAQ.

Answer:

In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.

If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:

an = a1 + (n-1)d

where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.

If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:

a1 = 3

a2 = 8

a3 = 13

a4 = 18

and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:

a129 = a1 + (129-1)d

a129 = 3 + 128(5)

a129 = 643

Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.

Answer: 30 and 5

Step-by-step explanation:

Therefore , the solution of the given problem of angles comes out to be  the three propositions  m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.

The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.

Here,

Regarding the illustrated diagram, the appropriate statements are:

=> m∠3 + m∠4 + m∠5 = 180°

This is accurate since every triangle's internal angles add up to 180°.

=>  m∠5 + m∠6 = 180°

This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.

=>  m∠2 + m∠3 = m∠6

This is accurate because, based on the information provided,

the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.

Therefore, the three propositions  m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.

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The true statements are:

1. The radius of the circle is 3 units

2. The standard form of the equation is (x-1)^2+y^2=3

3. The center of the circle lies on X-axis

4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9

The given equation is: x^2+y^2-2x-8=0

The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle

The given equation in standard form can be written as

(x^2-2x+1)+y^2-9=0

(x-1)^2+y^2=3^2

Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.

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The area of the remaining portion of the sheet is -4x² + 12x + 6.

Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.

Therefore, the area of the remaining portion can be found as follows:

area of the rectangle = 3(4x + 2)

area of the rectangle = 12x + 6

Therefore,

area of each square cut out = x²

area of the 4 square cut out = 4x²

Therefore,

area of the remaining portion = 12x + 6 - 4x²

area of the remaining portion = -4x² + 12x + 6

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all u got to do is subtract

Answer:

x > 3

Step-by-step explanation:

−8 + x/3 > -7

x/3 > 1

x > 3

We can't simplify anymore, so the answer is x > 3

An image of polygon VWYZ has a line of reflection across the x-axis. So option A is correct.

In geometry, the line of reflection is the line over which a figure is reflected. When a point is reflected over a line, it moves the same distance on the opposite side of the line. The line of reflection is perpendicular to the figure at the point of reflection and is equidistant from the figure and its reflection.

A polygon is a closed two-dimensional shape with straight sides. The sides are line segments that intersect only at their endpoints, called vertices. Polygons can have any number of sides, but they must have at least three. Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and octagons.

The formula for the line of reflection in a Cartesian coordinate system is:

x = a

where a is the equation of the line of reflection.

This formula represents a vertical line that passes through the point (a, 0) and reflects points across the line of reflection to their corresponding images on the other side.

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Answer:

reflection across x=2

Step-by-step explanation:

the picture should be able to explain itself! :)))

The width of the rectangle is 4 units.

What is rectangle?

Rectangle is a four sided polygon or specifically a particular type of parallelogram having two opposite sides are equal and one angle is right angle that is 90°. It has four vertices and two diagonals intersect each other.

Given that,

The length of a rectangle is 2 units more than the width.

Let, the width of the rectangle is w units.

Then the length of the rectangle is w+2 units.

Area of any rectangle is length × width

                                        = (w+2)×w square units

Given that,

The area of the rectangle is   24 square units.

Equating both  the values we get,

                    w(w+2)= 24

We have to solve the equation for w.

    Multiplying the bracket term with w we get,

w²+ 2w = 24

⇒ w² + 2w- 24=0

⇒ (w+6)(w-4)=0

so either w= -6 or w=4

As width cannot be negative so w= 4.

Hence, the width of the rectangle is 4 units.

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Answer:

5.  x = 60

6.  F' (1, 4)

Step-by-step explanation:

5.  The angles shown are same side exterior angles, so they are supplementary (add to 180)

(x + 85) + 35 = 180

x + 120 = 180

x = 180 - 120 = 60

x = 60

6.  The line x = 1 is a vertical line, passing through the x=axis at (1, 0).  All x coordinates on this line equal 1.

The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)

We can use the procedures below to calculate what proportion of the original principal the overall amount of interest represents. This total amount of interest received corresponds to about 5.34% of the initial investment.

Divide the principal even by rate of interest, the time period, and other factors to arrive at simple interest. Simple return Equal principal + interests + hours is the marketing formula.The most typical technique to figure out interest is to use a portion of the principal sum. He would only pay his share of the 100% interest, for example, if somebody borrows $100 from the a partner and pledges to repay the loan with 5% interest. $x (0.05) = $5. When, you must pay interest.when you lend money after borrowing it and adding interest. Interest is often determined as an indicator of the overall of the loan total. The interest rate of the loan is the name given to this percentage.

Determine the total interest that was earned in Step 1.

It states that $33.75 was earned in interest overall.

Step 2: Determine the interest generated before to taxes.

The sum of the interest earned after tax can be determined by dividing the entire sum of the interest by (1 + rate of taxation), where the rate of tax is given as a decimal. Daniela was subject to a tax of 15% on the investment earnings. The tax rate in this instance is 15%, which really is equal to 0.15.

Interest gained before taxes is equal as $33.75 / (1 Plus 0.15), that results in a value of $29.35.

3. Determine the initial principal.

The $550 that Daniela first put into the CD is referred to as the original primary.

Compute the proportion of the initial principle in step four.

By dividing the sum of interest generated after tax by the original principal and multiplying the result by 100 as express it as a percentage, one can determine what proportion of the original principal the entire amount of interest represents.

(Interest paid before taxation / Original principal) / 100 equals the percentage of the original principal.

= ($possess / $550) w x 100

≈ 5.34%

Hence, the total interest earned is equivalent to roughly 5.34% of the initial capital.

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The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.

The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

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The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

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Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

The exponential function is y=5.[tex]2^x[/tex].

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here the exponential function is [tex]y=ab^x[/tex]

Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1

Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2

So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]

=> [tex]b^{3+3}=8\times8[/tex]

=> [tex]b^6=2^6[/tex]

=> b = 2

put b=2 into 2 then,

=> 40= [tex]a\times2^3[/tex]

=> 8a=40

=> a =5

Then the exponential function is y=5.[tex]2^x[/tex].

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Answer:

8.36

Step-by-step explanation:

67 - 1

8. 82

= 2747 - 4

328

=2743

328

= 8.36

Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

We are given two equations:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x + d

and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:

y = 4(-4)² - 3(-4) + 3 = 49

y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d

So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:

49 = 60 + d

Solving for d, we get:

d = -11

Therefore, the two equations become:

y = 4x² - 3x + 3

y = x³ + 7x² - 3x - 11

We can now set them equal to each other:

4x² - 3x + 3 = x³ + 7x² - 3x - 11

Simplifying and rearranging, we get:

x³ + 3x² - 8x - 14 = 0

We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:

2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10

Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:

(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4

This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:

(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6

This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:

x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)

The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:

x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2

= [ -1 ± 3√(7) ] / 2

Therefore, the three intersection points are:

(-2, 0)

( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )

( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )

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Answer: 205.031(nearest thousandth)

or 205.03125

Step-by-step explanation:

From the data in the table, we can conclude that when x = 4, then the residual will equal -1.

To determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.

So, Residual = Gven value - Predicted value.

When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.

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Answer:

The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.

Step-by-step explanation:

In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.

If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.

In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.

The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.

Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.

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The absolute value equation is:

|x - 15| = 0

We want an absolute value equation that only has the solution x = 15.

So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)

So the equation will be something like:

|x - a| = 0

And the solution is 15, so:

|15 - a | = 0

then a = 15

The equation is:

|x - 15| = 0

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The equation that shows how to find a percentage is:

part/whole = percent/100

This equation can be used to solve for any of the three variables, given the values of the other two.

Step-by-step explanation:

y = x and y = 4

(x + y)²

(4 + 4)² = (8)² = 64