A dilation with a scale factor of 2 maps ΔABC to ΔDEF. Which best compares m∠B to m∠E?

The equation y = 2(kx - 1)^5 represents a curve. To find the equation of the curve, we need to determine the value of the constant k. To do this, we can use the two points given, (0,1) and (1,8), to find two equations and solve for k.

First, we'll substitute the x-coordinate and y-coordinate of the first point, (0,1), into the equation:

1 = 2(k * 0 - 1)^5

Expanding the right-hand side:

1 = 2(-1)^5

1 = -32

This equation is clearly false, so the point (0,1) does not lie on the curve represented by y = 2(kx - 1)^5.

Next, we'll substitute the x-coordinate and y-coordinate of the second point, (1,8), into the equation:

8 = 2(k * 1 - 1)^5

Expanding the right-hand side:

8 = 2(k - 1)^5

Dividing both sides by 2:

4 = (k - 1)^5

Taking the fifth root of both sides:

2 = k - 1

Adding 1 to both sides:

3 = k

Now that we have the value of k, we can write the equation of the curve:

y = 2(kx - 1)^5

= 2(3x - 1)^5

This is the equation of the curve that passes through the points (0,1) and (1,8).

It's important to note that the original equation y = 2(kx - 1)^5 is only one of an infinite number of curves that can pass through the points (0,1) and (1,8). The process of finding the equation of a curve that passes through specific points is known as curve fitting. The specific equation found in this case is just one possible representation of the curve that passes through the given points.

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Answer: 12

Step-by-step explanation: So, if 6 is 50% of x, x must be 12. Why? Because 50% is also equal to 1/2, so if 6 is only half of x, the other half must also be 6 - so its 6 + 6 = 12.

Step-by-step explanation:

I can explain what each item is, but I don't know exactly what it's asking

5 is a coefficient. The number attached to the left of the variable/term is always called the coefficient

x is the term/variable. Can always change the outcome, it just depends on the value inputed at that place

3 is a constant, since there's no term attached to it, it will always stay 3

Hope this helps in some way

The solution to the equation cos(x + 2π/3) = √2/2 over the interval

(0, 2π) is [7π/12, 3π/4]

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

The given function is cos(x + 2π/3) = √2/2 over the interval (0, 2π).

(x + 2π/3) = cos⁻1(√2/2).

x + 2π/3 = π/4  or 21π/12   (As cos is +ve on I and IV)

Now,

x + 2π/3 = π/4.

x = π/4 - 2π/3.

x = (3π - 8π)/12.

x = - 5π/12.

x = π - 5π/12.

x = (12π - 5π)/12.

x = 7π/12.

And,

x + 2π/3 = 21π/12.

x = 21π/12 - 2π/2.

x = (21π - 12π)/12.

x = 9π/12.

x = 3π/4.

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Answer: x=6

Step-by-step explanation :

4x+10=34

Subtract 10 on both sides :

4x=24

Divide by 4 on both sides

X=6

Answer:

x = 6

Step-by-step explanation:

4x + 10  =   34

    -  10  = - 10

        4x  =  24

         /4      /4

          x  =  6

Answer:

8/5

Step-by-step explanation:

divide numerator and denominator by 8 (GCF)

Answer:

8/5

Step-by-step explanation:

Divide into halves (3 steps):

[tex]\frac{64}{40} =\frac{32}{20} =\frac{16}{10} =\frac{8}{5}[/tex]

Or divide by eight (1 step):

[tex]\frac{64}{40} =\frac{8}{5}[/tex]

Hope this helps

The markup is $6.47 and the selling price is $31.87

percentage, a relative value indicating hundredth parts of any quantity.

A markup is the amount added to the cost price of a product to determine the selling price.

Let the cost price of a box of copy paper is $25.4 and the markup is 25.4%

Now let us find the selling price by given formula.

Selling price = Cost price + (Cost price x Markup percentage)

Selling price = $25.4 + ($25.4 x 25.4%)

Selling price = $25.4 + ($25.4 x 0.254)

Selling price = $25.4 + $6.47

Selling price = $31.87

So, the markup is $6.47 and the selling price is $31.87.

Hence,  the markup is $6.47 and the selling price is $31.87

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Edwin run 1.48 kilometers on  tuesday  as he run 4 lap for 370 meter as given in question.

As given in question that edwin usually does laps on a 370 meter indoor track

its means the total distance he cover on 1 round is 370 meter

and we have to find it on kilometers so to convert meter to kilometer we will do

1  kilometers = 1000 meter

so 370 meter = 370 /1000 km

= 0.37 km in 1 round

and he completer 4 round as given in question so

for 4 round = 0.37 * 4 = 1.48 kilometers

in this Question we already given the total distance which is 1480 meter which he run on tuesday and we just convert it on kilometers only

= 1480 meter = 1480/1000

= 1.48 kilometers

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Answer: For this version of the question its  1.48 kilometers

but for the people on study island or the other version of the question it will be 2.25 km

Step-by-step explanation:

The number of possibilities are 20,160. Therefore, the option A is the correct answer.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The number of specialty pizzas that is being offered by pizza parlor = 8

The number of specialty that Almeida's family wants to order = 2

To calculate the number of possibilities;

= 8!/2!

= 8×7×6×5×4×3×2×1/2×1

= 20,160.

Therefore, the option A is the correct answer.

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a function means that for every input (value of x), there is only one output (value of y)

y can repeat, x cannot (unless it's with the same y value)

eg:

{(1,2), (1,3), (3,2)} is not a function because 1 has two outputs

but if it was

{(1,2), (2,3), (3,2)} it would be a function. It doesn't matter that 2 repeats in the y coordinate

lmk if you still have questions, I'm happy to help!

Answer:

4. 175

5. 2

6. 72

7. 48

8. 45

9. 5

10. 18

11. 3

12. 10

13. 30

14. 12

15. 1

16. 2

17. 2

18. 8

The value of x is 38.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

EB = x - 7

DE = 31

From the figure, we see that,

(1/2)BD = EB = DE

Since the diagonal of a parallelogram bisects each other at its midpoint.

Now,

x - 7 = 31

Adding 7 on both sides.

x = 31 + 7

x = 38

Thus,

x = 38.

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The ribbon needs to be 25.12 inches.

The distance along a circle's perimeter is referred to as its circumference.

Given:

She is putting ribbon around a cake tray that has a diameter of 8 inches.

The diameter = 8 inches.

The circumference = 8 x 3.14

                                = 25.12 inches.

The ribbon needs to be 25.12 inches.

Hence, ribbon should be 25.12 inches.

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Answer:

On xy axis draw the line x+y=10  (slope -1; y-intercept 10)

Draw a vertical line at x=6

Draw a horizontal line y=7

The area will be all that above or on x+y=10, but on or below x=6 and y=7

A mathematical puzzle, where the rational numbers are used is attached with the answer.

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle.

Given is to investigate a mathematical puzzle where rational numbers are used.

Refer to the image attached. It shows a mathematical puzzle attached where the rational numbers are used.

Therefore, a mathematical puzzle, where the rational numbers are used is attached with the answer.

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{Question in english -

Investigate a mathematical puzzle where rational numbers are used.}

The exponential function is [tex]y = 1505.88(0.85)^x[/tex].

The monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To model the monthly number of defective parts, we can use an exponential equation of the form:

[tex]y=a(b)^x[/tex]

Where y is the number of defective parts, x is the number of months after Jane was hired, a is the initial number of defective parts, and b is the common ratio between consecutive months.

To find the values of a and b, use the two data points given -

In the first month, there were 1,280 defective parts, which means that y = 1280 when x = 1.

In the second month, there were 1,088 defective parts, which means that y = 1088 when x = 2.

Substituting these values into the exponential equation -

1280 = a(b)

1088 = a(b)²

Dividing the second equation by the first equation -

1088/1280 = (a(b)²)/(a(b))

0.85 = b

Substituting b = 0.85 into the first equation -

1280 = a(0.85)

1280 = 0.85a

a = 1505.88 (rounded to two decimal places)

So the exponential equation that models the monthly number of defective parts is -

[tex]y = 1505.88(0.85)^x[/tex]

To find when the monthly number of defective parts will be less than 500, we can set y = 500 and solve for x -

[tex]500 = 1505.88(0.85)^x[/tex]

Dividing both sides by 1505.88 -

[tex]0.332 = (0.85)^x[/tex]

Taking the logarithm of both sides (with any base) -

log(0.332) = x log(0.85)

Dividing both sides by log(0.85) -

x = log(0.332) / log(0.85)

x ≈ 6.87

Therefore,  the monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

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The least possible number of coins in the treasure chest Jack found is 29.

In Mathematics, the Lowest Common Multiple (LCM) of any two or more natural numbers is the number that is the lowest of their common multiples.

For a minute put 1 coin aside from the collection.

Then, the number of remaining coins is a multiple of both 4 and 7.

So, the smallest such an integer number of coins

= 7 x 4

= 28.

Now, return 1 coins back.

= 28 + 1

= 29 coins.

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Refer to the attached image.

The probability that a student is in 4th grade given that they did not choose popular as the most important trait is 0.5 or 50%.

The probability is a concept used in statistics that measures the likelihood of an event occurring.

Let's call the event of a student being in 4th grade as A and the event of a student not choosing popular as the most important trait as B. We can find the probability of A and B happening together by dividing the number of students who are in 4th grade and did not choose popular by the total number of students. This can be represented as

P(A and B) = P(A | B) = (75 / 250) = 0.3.

Next, we can find the probability of B happening by dividing the number of students who did not choose popular by the total number of students. This can be represented as

P(B) = (150 / 250) = 0.6.

Finally, we can use Bayes' theorem to find the probability of A given B. Bayes' theorem states that

=> P(A | B) = P(A and B) / P(B).

Therefore,

=> P(A | B) = (75 / 250) / (150 / 250) = 0.3 / 0.6 = 0.5.

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The chance of observing Mississippi after permuting the letters of it and randomly picking a word from that set is 1 in 34032.

The number of words that can be constructed from the letters of the word "Mississippi" is given by the number of permutations of those letters. Since the letters are not unique, we use the formula for permutations with repetition:

n! / (n₁! ×  n₂! ×  ... × nk!)

where n is the total number of letters, and n₁, n₂, ..., nk are the number of times each letter is repeated.

In this case, n = 11 and n₁ = 4, n₂ = 4, n₃ = 2, n₄ = 1.

So, the number of words that can be constructed is 11! / (4! × 4! × 2! × 1!) = 34, 032.

Thus, the chance of observing "Mississippi" is 1 in 34, 032 or approximately 1/34.

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[tex]90 \sqrt{72} [/tex]

which is equal to 763.6753236815

The numbers have been matched accordingly as below.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

√30 is not a perfect square. So it is real, irrational root.

-26 is a negative real integer. So it is a real rational integer.

√64 is actually a perfect square root, 8, which is a whole number. So it is a real, rational root, whole number.

1/4 is of the form a/b. So it is also real, rational.

0.363363336.... is a real irrational decimal.

0.424242..... is a real rational decimal, since it is repeating in nature.

[tex]\sqrt{-7}[/tex] or [tex]7i[/tex] is an imaginary number.

Hence the numbers has been matched according to the properties.

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Answer:

Table 3

Step-by-step explanation:

A linear relationship will have constant rate of change(slope) for all x values

Rate of change = Δf(x)/Δx

where Δf(x) = change in values of f(x)

and Δx = corresponding change in values of x

Only table 3 has this constant rate of change:

This slope of 2 is the same if you take any two pairs of x, f(x) values in that table

Hence constant slope = linear relation

Answer:

5.3

Step-by-step explanation:

sin24 = x/13

x = sin24(13) = 5.3

The probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.

The probability of being dealt two aces and one of them being the ace of spades is 1/221. This is because the chance of the first card being the ace of spades is 1/52 and the chance of the second card being an ace, given that the first card is an ace, is 3/51. Thus, the probability of both cards being aces and one of them being the ace of spades is 1/221.

Mathematically, this can be expressed as P(Ace of Spades, Ace) = P(Ace of Spades) x P(Ace|Ace of Spades) = (1/52) x (3/51) = 1/221.

This means that the probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.

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Answer: x = 18

Step-by-step explanation:

Rearrange the terms

70 = 7 + 3.5 × x

Calculate

-3.5x = 7 -70

Divide Both Sides

-3.5x = -63

x = [tex]\frac{-63}{-3.5}[/tex]

x = 18

Faults are planar features in rocks where the two sides move past each other due to tectonic forces. However, not all planar features in rocks are faults, as there are other types of planar features that do not involve movement. A planar feature that does not involve movement is called a joint.

A planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. These features can be caused by a variety of geological processes, such as deformation, metamorphism, or sedimentation. Some examples of planar features in rocks include bedding planes, foliation, and cleavage.

A fault, in particular, is a type of planar feature that forms when tectonic forces cause two sides of a rock to move past each other. This movement can be horizontal, vertical, or a combination of both. Faults can range in size from small fractures in the rock to large features that extend for kilometers. They are a common feature in regions where tectonic forces are actively shaping the Earth's crust, such as along plate boundaries or in areas with active volcanism.

On the other hand, a planar feature that does not involve movement is called a joint. Joints are fractures in rocks that do not result in any significant displacement of the rock on either side of the fracture. They can be caused by a variety of factors, such as cooling and contraction of magma or shrinkage of sediments. Joints can be important in geology because they can influence the way that rocks weather and erode over time.

In summary, a planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. While faults are a type of planar feature that involves movement between two sides of a rock, joints are planar features that do not involve any significant displacement of the rock on either side of the fracture. Understanding these different planar features is important in geology, as they can provide insight into the geological history of a region and can be used to predict future geological activity.

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The equation of line that passes through (3,2) and has a slope of 1/3 in point-slope form is y - 2 = (1/3)( x - 2 ).

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

Where x and y are the coordinates and m is the slope.

Given the data in the question;

Point (3,2)

Plug the values into the point-slope formula.

y - y₁ = m( x - x₁ )

y - 2 = (1/3)( x - 2 )

Therefore, the equation in point slope form is y - 2 = (1/3)( x - 2 ).

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The ratios of vegetarian and meat recipes to all recipes should be in Bradley’s cookbook is 75:50

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Total Recipes= 150

Books have three section: vegetarian dishes, meat dishes, and desserts.

So, vegetarians

= 150 x 1/2

= 75

and, Non vegetarians

= 150 x 1/3

= 50

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