According to the key of a park map, every 5 inches-
on the map represents 3 miles of trails in the park.
How many inches on the map represents 12 miles on
the park trails?

The required equivalent expression using the distributive property is: [tex]$$\boxed{21r + 49s - 28}$$[/tex]

This principle states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Using the distributive property, we can distribute the factor of 7 to each term inside the parentheses:

7(3r + 7s - 4) = 7(3r) + 7(7s) - 7(4)

Simplifying each term:

= 21r + 49s - 28

Therefore, the equivalent expression using the distributive property is:

[tex]$$\boxed{21r + 49s - 28}$$[/tex]

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The value of the median of the data is 35.

Algebraic expression can be defined as combination of variables and constants.

A box plot is a graphical representation of a data set that shows the distribution of the data, as well as the central tendency and the variability of the data. In this case, the box plot displays the number of push-ups completed by 9 students in a PE class.

The box plot has a number line from 9 to 56 with tick marks every 2 units. The box extends from 20 to 42.5 on the number line, which means that the middle 50% of the data (i.e., the interquartile range) lies between 20 and 42.5. The line in the box represents the median of the data, which is the value that separates the data set into two equal halves.

In this case, the line in the box is at 35, which means that half of the students completed more than 35 push-ups, while the other half completed fewer than 35 push-ups.

Therefore, the value of the median of the data is 35.

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To solve problems with integers, first, you must identify which operation you need to  first then, you need to think about which mathematical operations you need to use.

What is integers ?

Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. Integers can be represented on a number line that extends infinitely in both directions.

To solve problems with integers, you need to understand the basic operations such as addition, subtraction, multiplication, and division. You also need to know the rules and properties of integers, such as the commutative, associative, and distributive properties, as well as the rules for adding, subtracting, multiplying, and dividing positive and negative integers.

When solving a problem with integers, you should first identify which operation you need to perform first based on the order of operations. This order is typically remembered with the acronym PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). Once you have identified the operation, you can use the appropriate mathematical technique to solve the problem.

Therefore, to solve problems with integers, first, you must identify which operation you need to  first then, you need to think about which mathematical operations you need to use.

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Using the altitude or leg rule, we have:

x ≈ 42.7  

y = 40

z ≈ 53.4

The leg rule is given as:

hypotenuse/leg = leg/part.

The altitude rule is:

left/altitude = altitude/right

To find the value of x, apply the altitude rule:

left = x

right = 24

altitude = 32

Substitute:

x/32 = 32/24

Cross multiply:

24x = 32²

24x = 1,024

x ≈ 42.7  

To find y, apply the leg rule:

leg = y

part = 24

hypotenuse = x + 24 = 42.7 + 24 = 66.7

Substitute:

66.7/y = y/24

y² = 1,600.8

y = √1x00.8

y = 40

To find z, apply the leg rule:

leg = z

part = x = 42.7  

Hypotenuse = 66.7

Substitute:

66.7/z = z/42.7

z² = 2,848.09

z = √2,848.09

z ≈ 53.4

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The triangle AEC is similar to triangle BDC.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

Given:

5. ΔAEC is a triangle.

Assuming BD is parallel to AE.

The ratio of the corresponding sides,

10/5 = 2

8/4 = 2

The ratio is constant.

A similar triangle is made by drawing a line parallel to one of the triangle's sides.

Therefore, triangle AEC ~ triangle BDC.

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Answer:7

Step-by-step explanation:

The sample size οf 50 might nοt be large οr randοm enοugh, and there might be sοme systematic bias οr errοr in the data sοurces, leading tο a large difference between the sample mean (38) and Admissiοns and Recοrds data (25) in estimating the average class size οf Basic Statistics classes at the cοllege.

Statistics is a branch οf mathematics that deals with the cοllectiοn, analysis, interpretatiοn, presentatiοn, and οrganizatiοn οf data. It invοlves the use οf mathematical tοοls and techniques tο extract useful infοrmatiοn frοm data, and tο make decisiοns οr predictiοns based οn that infοrmatiοn.

In the given scenariο, it seems that there might be an issue with the methοd used tο cοllect the data, οr the data sοurces might be different. The sample size οf 50 students is nοt large enοugh tο represent the whοle pοpulatiοn οf Basic Statistics classes at the cοllege, especially if the cοllege has many sectiοns οf the class οr the class size varies widely between sectiοns. Mοreοver, the sample might nοt be truly randοm, as there cοuld be sοme bias in hοw the sample was selected, such as selecting οnly students frοm a particular sectiοn οr time slοt.

Alsο, the difference between the average class size οbtained frοm the sample (38) and the οne οbtained frοm Admissiοns and Recοrds (25) is tοο large tο attribute tο randοm variatiοn, which suggests that there might be sοme systematic bias οr errοr in either the sample οr the Admissiοns and Recοrds data.

Tο get a mοre accurate estimate οf the average class size οf Basic Statistics classes at the cοllege, a larger and mοre representative sample might be needed, οr the data cοllectiοn methοd might need tο be revised.

Hence, The sample size οf 50 might nοt be large οr randοm enοugh, and there might be sοme systematic bias οr errοr in the data sοurces, leading tο a large difference between the sample mean (38) and Admissiοns and Recοrds data (25) in estimating the average class size οf Basic Statistics classes at the cοllege.

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Answer:

$585 dollars will be used for cleaning supplies out of the total of $900 that was collected over the six days.

Step-by-step explanation:

$150.00 (money each day) * 6 (number of days) = $ (total)

[tex]150*6=900[/tex]

$900 in 6 days

100% (total amount) - 35% (pet food) = % (cleaning supplies)

[tex]100-35=65[/tex]

65% of his money will be used for cleaning supplied

Change the percentage into a decimal

65% = [tex]0.65[/tex]

Multiply the total amount of money by the decimal

[tex]900*0.65=585[/tex]

Out of the total $900 dollars he collected over 6 days, $585 dollars will be used for cleaning supplies and the rest ($315) will be used on pet food.

The coordinates of point A′ are (4.5, 3), the answer is A′(4.5, 3).

A triangle is a polygon with three sides and three angles. It is a two-dimensional figure that is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees, and the side opposite to the largest angle is the longest side of the triangle, while the side opposite to the smallest angle is the shortest side.

In this problem, we are given a triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1), and we are asked to dilate it using a scale factor of 1.5 to create triangle A′B′C′.

Dilation is a transformation that changes the size of a figure but not its shape. To dilate a figure, we multiply the coordinates of each point by a scale factor. In this case, we are given a scale factor of 1.5, so we will multiply each coordinate of triangle ABC by 1.5 to get the coordinates of triangle A′B′C′.

To find the vertex of point A′, we need to apply the dilation to the coordinates of point A(3, 2). Multiplying the x-coordinate by 1.5, we get 1.5 × 3 = 4.5. Multiplying the y-coordinate by 1.5, we get 1.5 × 2 = 3.

Therefore,  the coordinates of point A′ are (4.5, 3), the answer is A′(4.5, 3).

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The linear equation on the graph is written as:

y = 20x + 10

Remember that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

By looking at the graph, we can see that the line intercepts the y-axis at y = 10, then the y-intercept is b = 10.

We can write:

y = a*x + 10

Now we can also identify the point (1, 30), replacing the values of that point in the equation above we will get:

30 = a*1 + 10

30 = a + 10

30 - 10  =a

20  =a

Then the linear equation is:

y = 20x + 10

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The area of the sector is 37.68ft²

The region inside the portion of the circle formed by two radii and an arc is known as the area of a sector. It just covers a small portion of the circle's total area.

Area of a sector

The area of a sector can be gotten using the expression (θ/360º) × π r ² where

Using the expression we will get,(270/360) x 3.14 x 4²

From the solution, we will find the area to be 37.68ft²

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Answer:

Julia should buy at least 5 sets of glasses.

Step-by-step explanation:

The inequality will be

286 +6s ≥ 316

Solve for s to get s ≥ 5

We can write the expression in the simplest form as -

[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex].

An expression is a term made up of both constants and variables.

Given is the expression as -

[tex]$(8x^{7} y^{4} )^{2/3} \\[/tex]

We can solve as -

[tex]$(8x^{7} y^{4} )^{2/3} \\[/tex]

[tex](8^{2/3} x^{7\times\frac{2}{3} } y^{4\times\frac{x}{y} 2/3})[/tex]

[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex]

Therefore, we can write the expression in the simplest form as -

[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex].

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Answer:

Step-by-step explanation:

95 hours

B] Ans ~

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \small{ \star{ \boxed{ \rm{ \red{Volume \: of \: solid \: = lwh}}}}}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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hope it helps! :)

Answer:

0.0166666666666666666666666666666666666666666667

Step-by-step explanation:

USE CALCULATORRRRRR

Answer:

I'd say edges

Sarah's age using the equation of the situation is 60 years.

A mathematical statement that establishes the equality of two expressions is known as an equation. Variables are elements in equations that can change or have different values assigned to them. Finding the value or values of the variable that make the equation true is the aim of equation solving. Several branches of mathematics and science employ equations to simulate real-world scenarios and examine the interactions between different variables.

Equations come in a variety of forms, including differential, quadratic, and linear equations. Algebraic methods can be used to solve some problems analytically, while numerical approaches or computer simulations may be necessary for others.

Let us suppose Sarah's age =a.

From the given situation we have:

64 = 4(a - 44)

64/4 = a - 44

16 = a - 44

a = 60

Hence, Sarah's age using the equation of the situation is 60 years.

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The next number in the sequence is 47, 1, and 27.

A series of numbers is called a number series. We must identify the rules that lead to the formation of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.

One possible pattern in this sequence is that each number is the reverse of the sum of the digits of the previous number, followed by the next odd number. Applying this pattern to the given sequence, we have:

The reverse of 63 is 36. The sum of the digits of 63 is 6 + 3 = 9. Therefore, the next number is 36 + 9 = 45, followed by the next odd number, which is 47. So the next number is 47.

The reverse of 00 is 00. The sum of the digits of 00 is 0 + 0 = 0. Therefore, the next number is 00 + 0 = 0, followed by the next odd number, which is 1. So the next number is 1.

The reverse of 22 is 22. The sum of the digits of 22 is 2 + 2 = 4. Therefore, the next number is 22 + 4 = 26, followed by the next odd number, which is 27. So the next number is 27.

Therefore, the next number in the sequence is 47, 1, 27.

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Answer:

1: 2.097,2: 1000,3: 1.4282,4: 10000,5: 2.774546,6: 10,7: 2.00141,8: 1000,9: 100,10: 10

Step-by-step explanation:

Multiplication and division I don't know how to explain it lol

Solution of equation 16x - 22 = 20x + 14 is x = -8

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given equation

16x - 22 = 20x + 14

Moving like terms to same side

- 20x + 16x = 14 + 22

Adding like terms

-4x = 36

Dividing by -4 on both sides

x = 36/-4

x = -8

Hence, x = -8 is the solution of equation 16x - 22 = 20x + 14.

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Complete question is:

Find the value of x, in equation 16x - 22 = 20x + 14

Answer:

Rectangle pyramid

What is a rectangle pyramid ?

A rectangular pyramid is a pyramid, which has a rectangular-shaped base. If we look at the bottom view of this pyramid, it looks like a rectangle. Hence, the base has two parallel sides equal.

A pyramid crowns at a point on top of the base, which is known as the apex. A rectangular pyramid can be a right pyramid or oblique pyramid. If it is a right rectangular pyramid, then the apex lies right over the center of the base and if it is an oblique rectangular pyramid, the apex is not directly over the center of the base, but at some angle from the center.

Apart from the rectangular pyramid, there are other types of pyramids based on the shape of their bases, such as:

1) Triangular Pyramid

2) Square Pyramid

3) Pentagonal Pyramid

4) Hexagonal Pyramid

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The converse of the [tex]H[/tex]inge theorem indicates that the angle subtended by the segment [tex]\overline{LM}[/tex], (∠K) which is less than the length of the segment [tex]\overline{OP}[/tex], will be less than the measure of the angle subtended by the segment [tex]\overline{OP}[/tex], which is 90°

The h-i-n-g-e theorem, which is also known as the open mouth theorem states that two triangles that have a pair of corresponding congruent sides and which have different measure of the included angle between the sides, then the third side of the triangle with the larger included angle will be longer.

The h-i-n-g-e theorem can be deduced from the triangle inequality theorem.

The corresponding congruent sides in the two triangles are;

[tex]\overline{KL}[/tex] is congruent to [tex]\overline{ON}[/tex], [tex]\overline{KM}[/tex] is congruent to [tex]\overline{NP}[/tex]

[tex]\overline{LM}[/tex] = 7 is less than [tex]\overline{OP}[/tex] = 9

Therefore;

[tex]\overline{LM}[/tex] < [tex]\overline{OP}[/tex]

m∠N = 90°, therefore, the converse of the h-i-n-g-e theorem, indicates that the angle subtended by the segment [tex]\overline{LM}[/tex] is less than the angle subtended by the angle [tex]\overline{OP}[/tex], which is 90°

The angle ∠K is less than the angle ∠N

m∠K < m∠N = 90°

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Answer:

2. x-10=24

Step-by-step explanation:

x is the unknown amount of candy that Charlie has.

He gives ten away (-10).

Now he has 24 pieces.

x-10 = 24

The probability of drawing a vowel, replacing it, and then drawing a Z is 5/676.

The alphabet consists of 26 letters, and 5 of them are vowels (A, E, I, O, U). Hence, 5/26 of the time, a vowel will be drawn in the initial draw.

The likelihood of drawing a Z on the second draw is also 1/26, due to the fact that the card is changed after the first draw.

We can multiply the probabilities to determine the likelihood that both of these occurrences will occur:

P(Draw a Z after a vowel is drawn) = P(Draw a vowel) P(Draw a Z after the vowel is replaced) = (5/26) (1/26) = 5/676

As a result, the likelihood of drawing a Z after substituting a vowel is 5/676.

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Answer: 80 ft squared

Step-by-step explanation:

For the square, the formula is base times height which, in this case, are both 8. 8 x 8 = 64. Next, the triangle below is (8 x 4)/2 because the formula for a triangle is base x height divided by 2. 8  x 4 = 32 divided by 2 is 16.

64 + 16 = 80

So, your answer will be 80ft squared

Hope this helped!

The word or phrase that describes the probability that Charlotte will win a prize, with a probability of 12%, is D. likely.

Probability refers to the likelihood of an expected outcome occurring, given the many possible chances.

Probability lies between zero and one, depending on the level of certainty or otherwise of the successful outcomes.

In this situation, Charlotte's chances of winning cannot be described as impossible, zero percent, or unlikely.

Charlotte does not have an equal chance or 50-50 odds of winning because the probability is not up to 50%.

Thus, we can conclude that Charlotte has a D. likely opportunity of winning.

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Answer:

43 degrees

Step-by-step explanation:

85 degrees + 25 = 110 and the angle sum for a right triangle will always equal 180 degrees. The outside angle is 62 degrees, so 62 +70= 132. 180-132 is 48. Now you want to solve the angle sum for the shorter wider triangle. We know one angle is 89 degrees, plus the 48 degrees= 137. Now to find ? do 180-137=43. The missing angle for ? is 43 degrees.

I hope this helps :)

If the base triangle has a base of 8 meters and a height of 6.9 meters. the surface area of the pyramid is 139.6 square meters.

First, let's find the area of the base triangle:

Area of base triangle = (1/2) * base * height

Area of base triangle = (1/2) * 8 * 6.9

Area of base triangle = 27.6 square meters

Now, let's find the area of one of the triangular faces:

Area of triangular face = (1/2) * base * height

Area of triangular face = (1/2) * 8 * 7

Area of triangular face = 28 square meters

Since the pyramid has four triangular faces, the total area of the triangular faces is 4 times the area of one triangular face, which is:

4 * 28 = 112 square meters

Total surface area = area of base triangle + area of triangular faces

Total surface area = 27.6 + 112

Total surface area = 139.6 square meters

Therefore, the surface area of the pyramid is 139.6 square meters.

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