Astronomers estimate that the diameter of the Andromeda galaxy is approximately 2.2 X 10^5 light-year. A light-year is the distance light travels in a vacuum in 1 year. One light-year is approximately 5.9 X 10^12 miles. What is the diameter of the Andromeda galaxy in miles? Write your answer in scientific notation.

The best function to use to identify the lowest-paid representative who was elected after 11/1/2024 from the given dataset would be a filter function.

A filter function is used to extract a subset of data from a larger dataset based on specific criteria. In this case, the criteria would be the governor being elected after 11/1/2024 and having the lowest salary.

The filter function would first be used to extract only the governors who were elected after 11/1/2024. Then, the minimum salary among these governors can be identified using a min function. Finally, the filter function can be used again to extract the governor with the minimum salary.

Here's an example of how this can be done in Python:

governors = [

   {'name': 'John', 'state': 'CA', 'year_elected': '11/15/2024', 'salary': 100000},

   {'name': 'Jane', 'state': 'NY', 'year_elected': '1/1/2025', 'salary': 90000},

   {'name': 'Bob', 'state': 'TX', 'year_elected': '6/1/2025', 'salary': 80000},

]

lowest_paid_gov = min(filter(lambda x: x['year_elected'] > '11/1/2024', governors), key=lambda x: x['salary'])

print(lowest_paid_gov['name']) # Output: 'Bob'

In the example above, the filter function extracts only the governors who were elected after 11/1/2024, and then the min function identifies the governor with the lowest salary among them. Finally, the filter function is used again to extract the governor with the minimum salary, which is 'Bob'.

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Answer:

Mr Ellis has 9 cookies left

Step-by-step explanation:

12 × 4 = 48

12 × 3 = 36

12× 5 = 60

48+36+60= 144 cookies

144 - 135 = 9 cookies left

The length of the rectangular kitchen with a width of 12 feet and holes in opposite corners, 15 feet apart, is 9 feet.

To solve this problem, we need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).

Therefore, we can use the Pythagorean theorem to solve for the length of the kitchen, which is the unknown side of the right triangle.

Let's call the length "L". We know that the width is 12 feet and the distance between the mouse's holes (which is the hypotenuse of a right triangle) is 15 feet. So, we have:

[tex]L^2 + 12^2 = 15^2[/tex]

Simplifying:

[tex]L^2 + 144 = 225[/tex]

Subtracting 144 from both sides:

[tex]L^2 = 81[/tex]

Taking the square root of both sides:

L = 9

Therefore, the length of the kitchen is 9 feet.

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The lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

When two straight lines or beams intersect at a single endpoint, an angle is created.

The vertex of an arc is the location where two points come together. The Latin term "angulus," which means "corner," is where the word "angle" originates.

There are, however, a few fundamental perspectives.

Your camera options expand tremendously when combined with various shots.

This angle, which entails shooting a scene from directly overhead, is the most perplexing of the five.

So, according to the given situation:

= r║s

= Pair of angles are supplementary angles

Therefore, the lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

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Correct questions:

in the given figure, can you conclude r ∥ s? Use the drop-down menus to explain your answer.

The lines-------------parallel because the given angles are----------angles and they -----------have equal angle measures.

(A) first line: (A) are (B) are not

second line: (C) same side interior (D) corresponding (E) alternate (F) supplemental

third line: (G) do (H) do not

Here is the graph of the point (-4, -6) with a slope of 7/3.

To create the graph, start at the point (-4,-6) and plot it on the coordinate axis. From there, use the slope of 7/3 to find another point on the same line. To do this, you can move 7 units up and 3 units to the right from the point (-4,-6) to get to the point ( -1, -1). Plot this point on the graph as well. Finally, draw a straight line passing through both points to get the line representing the equation of the given point and slope.

After answering the presented question, we can conclude that it contains  inequality the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

The interquartile range is the most acceptable measure of variability for Terri's data (IQR).

The IQR is an acceptable measure of variability in this example because it focuses on the middle 50% of the data, which is where Terri spends the majority of her time at the fitness club. The mean and median are measures of central tendency rather than variability, and the range would be less useful in this situation because it contains the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

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As a result, we have demonstrated: 1 / (cos(x) - cot(x)) = cos (x) + cot(x) as the right side of the equation .

Trig ratios are ratios between the sides and angles of a right triangle. The sine, cosine, and tangent are the three main trigonometric ratios (tan). These are their definitions: The ratio of a right triangle's hypotenuse's length to the height of the opposite end is known as the sine (sin) of an angle. The ratio of a right triangle's neighbouring side to hypotenuse length is known as the cosine (cos) of an angle. The ratio of a right triangle's adjacent side's length to its opposite side's length is the angle's tangent (tan).

given

cot + csc(x) (x)

= cos(x)/sin(x) 1/sin(x) (x) [using the csc(x) and cot(x) definitions]

= (cos(x) + 1) / sin (x) [combining the phrases by reducing them to a single value]

The right side of the equation will then be made simpler:

(csc(x) - cot(x)) = 1

= 1 / (1/cos(x)/sin(x) - sin(x)) [using the csc(x) and cot(x) definitions]

= Sin(x) / Cos(x) [using the reciprocal and a denominator that is simpler]

We shall now demonstrate that the left and right sides are equal:

Sine (1 + cos(x)) (x)

= [(1 + cos(x))] / [(1 + sin(x)] *[1 - cos(x)] / (1 - cos(x)] [by adding 1 - cos(x) to the numerator and denominator]

= sin(x) * (1 - cos(x) / (1 - cos2(x)) [reduce the numerator]

= sin2(x)/sin(x)*(1 - cos(x)) [by applying the formula sin2(x) = 1 - cos2(x)]

= Sin(x) / Cos(x) [removing the common sin(x) factor]

As a result, we have demonstrated: 1 / (csc(x) - cot(x)) = csc(x) + cot(x) as the right side of the equation .

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Answer:

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

Step-by-step explanation:

First, we can represent 3/8 in decimal form:

0.375

Next, we can show the numerator using multiplication:

0.375 × a² × b³ × c⁵

Then, we can individually divide by each factor in the denominator using the principle:

[tex]\dfrac{A}{B \times C} = A \div (B \times C) = A \div B \div C[/tex]

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

The group of friends spent $477 on equipment.

A number can be expressed as a fraction of 100 using the word "percent." The Latin term "per centum," which means "by the hundred," is where the word "percent" originates. With "20 percent," we mean that something is 20 out of 100, or 0.2 in decimal form.

The expression of ratios, proportions, and changes through time is frequently done using percentages. We may discuss the proportion of

pupils who pass an exam, the percentage growth in sales from one year to the next, or the proportion of a population that has received a disease-prevention vaccine, for instance.

Given, they use 53% of their budget of $900.

Thus,

900 x 0.53 = 477

Hence, the group of friends spent $477 on equipment.

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Suppose a basketball player has made 215 out of 322 free throws. If the player makes the next 2 free throws, you will be paid $32, otherwise, you pay $24. To find out how much you would expect to win or lose if this game is played 590 times, the first thing to do is to find the probability that the player will make the next two free throws.In order to find the probability that the player makes the next 2 free throws, the total number of free throws attempted is 322 + 2 = 324.

The probability that the player makes each free throw is equal to the ratio of the number of successful free throws to the total number of free throws attempted.Therefore, the probability that the player makes each free throw is215/322 = 0.6667 (rounded to four decimal places)The probability that the player will make the next 2 free throws is:0.6667 × 0.6667 = 0.4445 (rounded to four decimal places).

This means that the probability that the player misses at least one free throw is:1 − 0.4445 = 0.5555 (rounded to four decimal places)If you win, you get $32, while if you lose, you have to pay $24. This means that your expected value is given by the formula:E(X) = $32(0.4445) − $24(0.5555) = −$0.22Therefore, if you played this game 590 times, you would expect to lose a total of:$0.22 × 590 = -$129.80 (rounded to two decimal places)Note that since you are expected to lose, the value is negative.

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[tex]\begin{bmatrix} 5&2\\ 3&x \end{bmatrix}~~ = ~~x^2\implies \stackrel{ \textit{determinant of a }2\times 2 ~matrix}{(5)(x)~~ - ~~(3)(2)}~~ = ~~x^2\implies 5x-6=x^2 \\\\\\ 0=x^2-5x+6\implies 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]

Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.

Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as  shown in the table.

Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.

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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

Colleges and Universities

School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %

Amherst Lib Arts 1315 22% $26,636 85 93

Barnard Lib Arts 1220 53% $17,653 69 80

Bates Lib Arts 1240 36% $17,554 58 88

Berkeley Univ 1176 37% $23,665 95 68

Bowdoin Lib Arts 1300 24% $25,703 78 90

Brown Univ 1281 24% $24,201 80 90

Bryn MawrLib Arts1255 56% $18,847 70 84

Cal Tech Univ 1400 31% $102,262 98 75

Carleton Lib Arts 1300 40% $15,904 75 80

Carnegie University1225 64% $33,607 52 77

Claremont Lib Arts1260 36% $20,377 68 74

Colby Lib Arts 1200 46% $18,872 52 84

Colgate Lib Arts 1258 38% $17,520 61 85

ColumbiaUniversity1268 29% $45,879 78 90

Cornell University1280 30% $37,137 85 83

DavisdsonLib Arts 1230 36% $17,721 77 89

Duke University 1310 25% $39,504 91 91

GeorgetownUniv 1278 24% $23,115 79 89

Grinnell Lib Arts 1244 67% $22,301 65 73

HamiltonLib Arts 1215 38% $20,722 51 85

Harvard Univ 1370 18% $46,918 90 90

HaverfordLib Arts 1285 35% $19,418 71 87

Johns Hop. Univ 1290 48% $45,460 69 86

MiddleburyLib Arts 1255 25% $24,718 65 92

MIT University 1357 30% $56,766 95 86

Mount Lib Arts 1200 61% $23,358 47 83

NWrn University 1230 47% $28,851 77 82

Oberlin Lib Arts 1247 54% $23,591 64 77

Occidental Lib Arts 1170 49% $20,192 54 72

Pomona Lib Arts 1320 33% $26,668 79 80

Princeton University 1340 17% $48,123 89 93

Rice University 1327 24% $26,730 85 88

Smith Lib Arts 1195 57% $25,271 65 87

Stanford University 1370 18% $61,921 92 88

Swarthnore Lib Arts 1310 24% $27,487 78 88

U of MI University 1195 60% $21,853 71 77

U of Chi University 1300 45% $38,937 74 73

U of Roc University 1155 56% $38,597 52 73

U PA University 1280 41% $30,882 87 86

U Va University 1218 37% $19,365 77 88

UCLA University 1142 43% $26,859 96 61

UNC University 1109 32% $19,684 82 73

Vassar Lib Arts 1287 43% $20,179 53 84

Wash U University 1225 54% $39,883 71 76

Wash & Lee Lib Arts 1234 29% $17,998 61 78

Wellesley Lib Arts 1250 49% $27,879 76 86

Wesleyan Lib Arts 1290 35% $19,948 73 91

Williams Lib Arts 1336 28% $23,772 86 93

Yale University 1350 19% $52,468 90 93--

The required values of angles are 1) 90° 2) 180° 3) 45° 4) 135° 5) 135°.

An angle is a figure in Euclidean geometry that is made up of two rays that share a common endpoint, called the vertex of the angle. These rays are called the sides of the angle. The plane containing the rays is where the angles created by two rays are located. Points are additionally shaped by the convergence of two planes. The term for these is dihedral angles.

We have a circle in which angles are vertically equal.

1) So, ∠AB is 90°.

2) BE is half of the circle,

∠BE is 180°

3) BC is half of quadrant,

∠BC is 45°

4) DF is combined of quadrant and half of quadrant,

∠DF is 90 + 45 = 135°

5) EAC contain half circle and half of quadrant,

∠EAC is 180 + 45 = 135°

Thus, required values of angles are 1) 90° 2) 180° 3) 45° 4) 135° 5) 135°.

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The condition that must be satisfied to use a chi-square goodness-of-fit test is D. The expected count for each category is at least 5.

A chi-square goodness-of-fit test is a statistical test used to determine whether the observed frequencies of categorical data match the expected frequencies. This test is often used to analyze categorical data, such as determining if the distribution of colors in a bag of candies matches the expected proportions.

The reason behind this condition is that the chi-square test is based on the assumption that the data follow a specific distribution. When the expected count for each category is less than 5, the test might not accurately represent the true distribution, and the results may be misleading. By having an expected count of at least 5 in each category, the test can better approximate the true distribution and provide more reliable results. Therefore, option D is correct.

The Question was Incomplete, Find the full content below :

which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?

A. The sample size is greater than 30.

B. The number of categories is less than 10% of the number of observations.

C. The expected count is the same for each category. the population distribution is approximately normal.

D. The expected count for each category is at least 5.

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Answer:

Let's call the number of nuts "n", the number of bolts "b", and the number of screws "s".

From the problem, we know:

s = 3n (Since there are 3 times as many screws as nuts)

b = n + 32 (Since there are 32 more bolts than nuts)

n + s + b = 782 (Since the total number of nuts, screws, and bolts is 782)

Now we can use substitution to solve for one of the variables in terms of the others. Let's solve for "n":

n + 3n + (n + 32) = 782

5n + 32 = 782

5n = 750

n = 150

Now we know there are 150 nuts. We can use this information to find the number of bolts:

b = n + 32

b = 150 + 32

b = 182

Finally, we can use the information we have about the screws to find their number:

s = 3n

s = 3(150)

s = 450

Therefore, there are 450 screws in the box.

Step-by-step explanation:

38%  X  78 894.24

  = .38 X 78 894.24 =  $ 29,979.81  tax

[tex]9^(-6)[/tex] is the reciprocal of [tex]9^6[/tex], which is a positive number, and has the same value as [tex](1/9)^6[/tex] based on exponent.

A mathematical procedure known as an exponent entails elevating a number or variable to a specific power or degree. The base number or variable's exponent specifies how many times it has been multiplied by itself.

An exponent's basic form is as follows:

[tex]a^n[/tex]

where "n": the exponent or power and "a": the base number or variable. To the right of the base number "a," a superscript denotes the exponent "n."

Using the following rule, we can make [tex]9^(-6)[/tex] a positive exponent:

[tex]a^(-n) = 1 / a^n[/tex]

A is 9 and n is 6 in this instance. Thus, it can now be written as:

[tex]9^-6 = 1 / 9^6[/tex]

We must now simplify 1/96. To accomplish this, we can apply the following rule:

[tex]a^n / a^m = a^ (n-m)[/tex]

A is 9 and n is 6 in this instance. Rewriting 1/9/6 results in:

[tex]1/9^6 = 9^(-6) (-6)[/tex]

Once more using the method above, we may express 9(-6) as follows:

[tex]9^(-6) = 9^(0 - 6) = 9^0 / 9^6 = 1/9^6[/tex]

Hence, we have demonstrated that 1/9/9/6 = 9/-6. Thus, we only need to rewrite 9-6 as follows to make it a positive exponent:

[tex]9^(-6) = 1 / 9^6[/tex]

This indicates that the reciprocal of the positive number 96, which has the same value as [tex](1/9)^6[/tex], is [tex]9^(-6)[/tex].

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If Legolas shoots 3 arrows at once from his bow which consist of 177 arrows, then Legolas can shoot 59 times before he needs more-arrows.

We know that, if Legolas shoots 3 arrows at once, so he uses 3 arrows each time he shoots his bow,

To find the number of times he can shoot his bow, we divide the total number of arrows by the number of arrows that can be shoot at once.

The total number of arrows is = 177,

The number of arrows that can be shoot at once is = 3 arrows.

So, Legolas can shoot his bow = (177/3) = 59 times before he needs more arrows.

Therefore, Legolas can shoot his bow 59 times before running out of arrows.

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The given question is incomplete, the complete question is

Legolas shoots 3 arrows at once from his bow. He has 177 arrows. How many times can Legolas shoot his bow before he needs more arrows?

Answer:

after 80 years, approximately 2.15 grams of the initial 16 grams of cesium-137 would remain. This means that about 13.4 grams would have decayed during this time period.

Answer:

Step-by-step explanation:

You add the 7x2

The statement that represents the expression 4 x (3 + 2) - 6 is:

"Four times the sum of three and two, minus six."

To write a statement for an expression, you need to describe the expression using words in a clear and concise manner. The statement should convey what the expression means or represents. Here are the steps to follow:

Identify the expression you want to represent with a statement.

Read the expression carefully and determine what mathematical operations are being performed, such as addition, subtraction, multiplication, or division.

Write out the operations in words, such as "add," "subtract," "multiply," or "divide."

Identify any constants or variables in the expression and describe them in words. For example, if the expression is 2x + 5, you would say "two times a number plus five."

Use parentheses to clarify the order of operations. For example, if the expression is 4 x (3 + 2) - 6, you would say "four times the sum of three and two, minus six."

Proofread your statement to make sure it accurately represents the original expression and is clear and concise.

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the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

How to solve angles?

To solve for the angles of a triangle, we need to use the fact that the sum of the angles of a triangle is equal to 180 degrees. We can use this fact to set up equations based on the given information.

Let's start by assigning variables to the angles of the triangle. Let A be the measure of angle A, B be the measure of angle B, and C be the measure of angle C.

We are given that angle B is 5 times angle A, which we can express as B = 5A. We are also given that angle C is 4 times less than angle A, which we can express as C = A - 4.

Using the fact that the sum of the angles of a triangle is 180 degrees, we can write the following equation:

A + B + C = 180

Substituting the expressions we found for B and C, we get:

A + 5A + (A-4) = 180

Simplifying the equation, we get:

7A - 4 = 180

Adding 4 to both sides of the equation, we get:

7A = 184

Dividing both sides by 7, we get:

A = 26.29

Now that we know the measure of angle A, we can use the expressions we found for B and C to find their measures:

B = 5A = 131.45

C = A - 4 = 22.29

Therefore, the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

In summary, we used the fact that the sum of the angles of a triangle is 180 degrees and the given information about the relationship between the angles to set up an equation and solve for the measure of angle A. We then used the expressions we found for angles B and C to find their measures.

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The rate of change using the table that is provided, can be found to be 45 miles per hour.

The rate of change can be found by the formula :

= Change in y / Change in x

Change in x is Hours

Change in y is distance

The rate of change is :
= ( 270 - 135 ) / ( 6 - 3 )

= 135 / 3

= 45

The rate of change as shown by the data on the table, is 45 miles per hour .

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Answer:

1) 24

2) 25

Step-by-step explanation:

Given:

2a + 3b = 8

4x + 10y = 50

.

1)

[tex] \frac{6a + 9b}{2a + 3b} = \frac{3(2a + 3b)}{2a + 3b} = 3[/tex]

Since the second expression is 3 times greater then the previous one, the product will also be 3 times greater:

6a + 9b = 3 × 8 = 24

.

2)

[tex] \frac{2x + 5y}{4x + 10y} = \frac{2x + 5y}{2(2x + 5y)} = \frac{1}{2} = 0.5[/tex]

The second expression's value is two times smaller than the first one's, so the product will also be two times smaller:

2x + 5y = 0,5 × 50 = 25

The amοunt οf prize mοney each winner received can be represented by the expressiοn: $480 / x

A linear equatiοn is a mathematical equatiοn that represents a straight line when graphed, and is in the fοrm οf y = mx + b, where m represents the slοpe οf the line and b represents the y-intercept.

The amοunt οf prize mοney each winner received can be represented by the expressiοn:

$480 / x

This is because the prize mοney οf $480 was split equally amοng x winners, sο dividing the tοtal prize mοney by the number οf winners (x) gives the amοunt each winner received. This expressiοn calculates the quοtient οf $480 divided by the number οf winners (x), resulting in the amοunt οf prize mοney each winner received.

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The figure here is a rectangle.

Using the formula for perimeter and area:

Part a. Fencing that will be used more = 24ft.

Part b. Area of proposed space greater than area of current space

= 276ft²

A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of each rectangle serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

In the given question,

Length of current space, l = 24ft.

Breadth of current space, b = 16 ft.

Length of proposed space = 24 + 3 + 3 = 30ft.

Breadth of proposed space = 16 + 3 + 3 = 22ft.

Part a.

Perimeter of current space = 2 (l + b)

= 2 × (24 + 16)

= 2× 40

= 80ft.

Perimeter of proposed space = 2 × (30+22)

= 2 × 52

= 104ft.

So, fencing that will be used more = 104 - 80

= 24ft.

Part b.

Area of current space = l × b

= 24 × 16

= 384ft².

Area of proposed space = 30 × 22

= 660ft².

Area of proposed space greater than area of current space = 660 - 384

= 276ft²

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The figure's area is calculated by subtracting the entire rectangle from the empty rectangle.

The area of a rectangle in a two-dimensional plane is the space that it occupies. A rectangle is a quadrilateral, a kind of two-dimensional object with four sides and four vertices. The rectangle's four sides are all right angles or exactly 90 degrees. The rectangle's opposing edges are equal and parallel to one another. It should be observed that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.

The following is the solution for the figure's area:

9 (x+3) - 6x.

The entire figure's area has been described as 9 (x+3).

where 9 is the length of the rectangle and (x+3) = (x+1.5+1.5) is the width of the rectangle.

Currently, the empty space between has been assigned the value 6x.

where the rectangle's edges are 6 and x.

Therefore, the size of the figure is the entire rectangle less the empty rectangle.

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The complete question is:

Look at the figure at the right. Explain one thing that representing the area of the figure as 9(X+3)-6x tells you about the situation. Then write an equivalent expression for the area. Explain what information is in your expression that is not in 9(x+3)-6x.

Answer:

68/100

Step-by-step explanation:

first change 6/10 to have an LCD with 8/100

factors of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120

factors of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200

LCD: 100

6/10 · 10/ 10 = 60/ 100 + 8/ 100 = 68/100

Answer:

First, we can simplify the coefficients:

(24/50) * (30/8) = (6/25) * (15/2) = 9/5

Then we can simplify the variables:

x^3 / x^2 = x^(3-2) = x

Therefore, the simplified expression is:

9/5 * x

So answer will be as follows:

(24x^(3))/(50x)*(30)/(8x^(2)) = 9/5 * x

Answer: 8.06 feet

Step-by-step explanation: