ons
Write the equation for this relationship and identify the constant of proportionality (or k value).
X
Y
28 36 40
21
27
30
56
42

Answer:

It depends on the amount of slices.

Step-by-step explanation:

The diameter of the pie is 10 inches. Multiply this by π and we get approximately 31.4. Basically just divide it by the number of slices. For example, if there were six slices, 31.4/6=5.23, so that's the arc length of one slice.

A circle graph representing the data presented will show half of the students prefer apple juice; while grape, orange juice, and fruit punch are preferred by a lower ratio of students.

A circle graph also known as a pie graph is a visual representation of data based on a circle and its fractions of it. In this way, if 20 out of the 40 students prefer apple juice this means in the circle graph half of it would be for students preferring apple juice.

Based on this, a possible circle graph that represents the data is shown below:

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Approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

A logarithmic equation is an equation that involves a logarithmic function. A logarithmic function is the inverse of an exponential function, and it represents the exponent to which a given base must be raised to obtain a given number.

The formula that relates the energy released by an earthquake to its magnitude is given by:

logE = 5.24 + 1.44M

To find the amount of energy released by a magnitude 5 earthquake, we can substitute M = 5 into the formula and solve for E.

logE = 5.24 + 1.44(5)

logE = 5.24 + 7.2

logE = 12.44

Now we need to convert this logarithmic value to a regular value of E. We can do this by taking the antilogarithm (or exponentiating) both sides of the equation.

10⁽ˡᵒᵍᴱ⁾ = 10⁽¹²ॱ⁴⁴⁾

E = 2.51 x 10¹² joules

Therefore, approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

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Answer:

Rowan collects

3x + 4

Step-by-step explanation:

Maribel collects x sea shells.

Rowan collects 4 more (this is the +4)

than 3 times Maribels (this is the 3x)



Maribel = x

Rowan = 3x + 4

Answer:

its actually 4x + 3

Step-by-step explanation:

Answer:

41 inches

Step-by-step explanation:

to find the perimeter of any shape, add the length of all the sides together

Answer: the answer is C just did it

Answer:

Step-by-step explanation:

a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:

     (1)

    /   \

 (H)     (T)

/   \   /   \

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

b) There are four stages in the tree diagram.

c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTTT

d) There are 2^4 = 16 outcomes in the sample space.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1)

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4)

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1).

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4).

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.

The compound interest is $348,966.97 and the future value is $464,966.97.

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

We can use the formula for compound interest to calculate the future value of the investment:

[tex]FV=P(a1+r/n)^{nt}[/tex]

where:

P = the principal amount (the initial investment)$116,000

r = the annual interest rate (as a decimal)=0.0429

n = the number of times the interest is compounded per year=52

t = the number of years=34

Plugging in these values, we get:

FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸

FV = $464,966.97

So the future value of the investment after 34 years is $464,966.97.

Compound interest = $464,966.97 - $116,000 = $348,966.97

Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.

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Answer: The result when the number 45 is increased by 57% is approximately 70.65.

Step-by-step explanation:

To find the result when the number 45 is increased by 57%, we need to calculate 45 * (1 + 0.57), where 0.57 represents 57% as a decimal.

Performing the calculation, we get:

45 * (1 + 0.57) = 45 * 1.57 = 70.65

So, the result when the number 45 is increased by 57% is approximately 70.65.

Answer:

70.65

Step-by-step explanation:

The new value =

45 + The value of the percentage increase =

45 + (57% × 45) =

45 + 57% × 45 =

(1 + 57%) × 45 =

(100% + 57%) × 45 =

157% × 45 =

157 ÷ 100 × 45 =

157 × 45 ÷ 100 =

7,065 ÷ 100 =

70.65

Answer:

295>_ 39x+11.50

Step-by-step explanation:

the >_ means less than or equal to.

Based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

The reading specialist is trying to estimate the population mean word length of an elementary school history textbook, but it is not practical or possible to measure the word length of every single word in the book. So, instead, the specialist takes repeated random samples of 100 words from the book and calculates the mean word length of each sample. Based on these repeated samples, the specialist estimates that the mean word length of the book is 4.9 letters. This means that, on average, the words in the book are about 4.9 letters long. The specialist also calculated the standard deviation of the sampling distribution, which is a measure of the variability of the sample means. In this case, the standard deviation of the sampling distribution is estimated to be 0.15 letters. This means that the mean word length of each random sample is expected to vary by about 0.15 letters from the population mean. It is important to note that these estimates are based on a specific set of samples and are subject to sampling variability. If the specialist were to take different random samples, the estimates may be slightly different. However, based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

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The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;

A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.

The coordinates of the vertices of the triangle are;

X(0, 5), Y(10, 3), Z(4, -1)

The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;

The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;

Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))

The coordinates of the point Y(4, -1) following the composite transformation is therefore;

Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)

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Answer:

A and C are the correct answers

Step-by-step explanation:

Answer:

And C is the answer to the question

Y = (1/x-3) has been moved 3 units to the right and up one unit. If it is moved to the right, it should look like this: (x-3). It should show up as (x+3) if it were moved to the left. If the result were moved ahead, the outcome would be (1/x-3).

The original function f is horizontally shifted into the new function g(x)=f(xh), where h is a constant. Given a function f. The graph will shift to the right in a positive h situation. If h is negative, the graph will slide to the left.

To move a function left in function notation, add within the function's argument: f(x + b) moves f(x) b units left. In the same way, shifting to the right moves f(x) b units to the right.

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The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.

Answer:

Pole Vault, Discus, 200m, Long Jump

Step-by-step explanation:

Once putting them all as decimals can’t you just sort it our from there? From what I can see, your answers are incorrect, but they might have reset.

Answer:

= (4x^2 + y^2)(2x + y)(2x - y).

Step-by-step explanation:

16x^4 - y^4

= (4x2)^2 - (y^2)^2

= (4x^2 +y^2)(4x^2 - y^2)

=(4x^2 + y^2)( (2x)^2 -y^2)

= (4x^2 + y^2)(2x + y)(2x - y).

Answer:

Step-by-step explanation: [tex]16x^{4} -4y^{4} = (4x^{2} )^{2} -(2y^{2} )^{2}= (4x^{2} + 2y^{2} )(4x^{2} - 2y^{2})[/tex]

identity used =

[tex](a^{2} -b^{2} ) = (a+b)(a-b)[/tex]

In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen

The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

The total  dozen = 8 dozen eggs

The total price of the 8 dozen eggs $2,800.00

The price per dozen = $2,800.00/ 8 dozen

=$350 per dozen

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C

The answer to the question is C

Answer:

D is the answer cuz 2x-1=5

2x=5-1

2x=4

X=2

We divide both side by two

The equation of line is y = 1.5x + 5.5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

We have the reference point as (-2, 2.5) and (-1, 4)

so, slope

= (4- 2.5)/ (-1 + 2)

= 1.5

and, the equation of line is

y- 2.5 = 1.5 (x+ 2)

y- 2.5 = 1.5x + 3

y = 1.5x + 5.5

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Answer:     [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300} } } )[/tex]

Step-by-step explanation:

[tex]P=\frac{22}{100} =0.22, n=300[/tex]     [tex]q=1-p=0.78[/tex]

[tex]p' = \frac{27}{100}=0.27[/tex]

[tex]p(z > \frac{p'-p}{\sqrt{\frac{p*q}{n} } } )[/tex]

 [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300}} }[/tex]

The two lengths that Bottom 7%: L= 6.04 cm

Top 7%: L= 6.22 cm

What does "z-score" mean?

The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.

                                       The level of variability within a particular data collection is effectively reflected in the standard deviation.

Mean length of the population (μ) = 6.13 cm

Standard deviation (σ) = 0.06 cm

The z-score for any given length 'X' is

        Z = X - μ/σ

     What we want to know is the length at the 7-th percentile and at the 93-rd percentile.

According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths

      Z(Xb) = Xb - μ/σ

  - 1.476 = Xb - 6.13/0.06

      Xb = 6.04

  z(Xt ) = Xt - μ/σ

   1.476 = Xt - 6.13/0.06

     Xt = 6.22

Bottom 7%: L= 6.04 cm.

Top 7%: L= 6.22 cm.

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1. Area of the figure = 702 square feet.

Perimeter = 114 feet

2. Area of the figure = 20 square inches.

Perimeter = 24 inches.

Area of a rectangle = length * width

Perimeter of a shape = length of all the surrounding of a figure.

1. Area = area of rectangle 1 + area of rectangle 2 = 27 * 24 + 9 * 6

= 702 square feet.

Perimeter = 30 + 27 + 24 + 18 + 6 + 9 = 114 feet

2. Area = area of rectangle 1 + area of rectangle 2 = 7 * 2 + 3 * 2

= 20 square inches.

Perimeter = 7 + 2 + 3 + 3 + 2 + 3 + 2 + 2

= 24 inches.

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Answer:

689.85 liters

Step-by-step explanation:

1 gallon =  about 3.78 liters

182.5 gallon = ? liter

We take  

182.5 times 3.78 = 689.85 liters

So, 182.5 gallons is about 689.85 liters

Answer:

A. 513 cubic units

Step-by-step explanation:

trust me bro.

The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 12 - (-3)

Common difference, d = 12 + 3

Common difference, d = 15

Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;

a₅₂ = a₁ + (52 - 1)d

a₅₂ = -3 + (51)(15)

a₅₂ = -3 + 765

a₅₂ = 762.

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Answer:

See the explanation below