an average bus speed between cape Town to east London was 108 km/h Due to the bad weather, the average speed on the trip back was 72 km/h. Determine how long the outward trip took if the return trip takes 12 hours​

The value of the quadratic equation when simplified gives 2x+7

We should understand that Quadratic equations are second-degree algebraic expressions and are of the form ax2 + bx + c = 0

The given quadratic expression is given as

[(x²+5x+20) + (x²+6x-6)]/(x+2)

Opening the brackets we have

[x²+5x+20+x²+6x-6]/x+2

Collecting like terms we have

(x²+x²+5x+6x+20-6)/x+2

⇒(2x²+11x+14)/x+2

Factorizing the expression to have

[(2x²+4x)+(7x+14)]/x+2

⇒ [2x(x+2) +7(x+2)]/x+2

Regrouping to have

[(2x+7)(x+2)]/x/2

Dividing through by x+2 to have

2x+7

Therefore the value of the expression [(x²+5x+20) + (x²+6x-6)]/(x+2) is 2x+7

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P(inside larger square and outside smaller) = [tex]\dfrac{16}{100}[/tex]

Probability is the result of the division of the number of possible outcome by the number of an event.

In the question, for a point chosen, the point can be in the small square only or in the area or region between the small square and the big square as such,

Area of larger square = area of region between both squares + area of smaller square

Where the area of a square is S × S where S is the side of a square

Area of larger square = 5 × 5

                                   = 25 cm square

Area of smaller square = 3 × 3

                                     = 9 cm square

Area of the region between  both squares

                                     = 25 - 9

                                     = 16 cm square

The probability that a dot selected is inside the larger square and outside the smaller is

P(inside larger square and outside smaller) = Area of region between both square/ Area of larger square

P(inside larger square and outside smaller) = [tex]\dfrac{16}{100}[/tex]

The answers are:

3 a). 02:25 is time when aircraft arrives

b). The lower bound of the distance is 3150 km

4). The bottle weight is 200 g

3 a). Aircraft leaves at 22:35

As per the given,

From 22:35 and takes 3h 50min is 02:25 will time when aircraft arrive

b). Because the distance is corrected to the nearest 100 km

The lower bound of the distance is = 3200 - 100/2

                                                           = 3150 km

4). Assume that the container weighs "x" and the honey weighs "y."

We are aware that a 1000 g container of honey weighs in total.

So Equation 1 is x + y = 1000 g

We can calculate the overall weight to be 600g by using half of the honey.

Equation 2: x + (y/2) = 600 g

y/2=600 - x

y= 2 (600 - x)

y= 1200 - 2x

We can replace “y” with 1200 - 2x in Equation 1:

x + 1200 - 2x = 1000

x = 200 g

The container weighs 200 grammes.

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Therefore, the range of the function is all real numbers except for 0. In interval notation, this can be written as (-∞, 0) U (0, ∞).

In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the range). Formally, a function f from a set A to a set B is a rule that assigns to each element a in A a unique element b in B, denoted by f(a). The set A is called the domain of the function, and the set B is called the range.

Here,

The given function is y = x/(8-x).

To find the range of this function, we need to determine the possible values of y for all possible values of x.

First, we note that the function is undefined when the denominator (8-x) equals zero. Therefore, x cannot be equal to 8.

Next, we consider the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the value of y approaches zero. This is because the x term in the numerator grows much more slowly than the 8-x term in the denominator, causing the overall value of the function to approach zero.

As x approaches negative infinity, the value of y approaches negative infinity. This is because the x term in the numerator becomes very negative while the 8-x term in the denominator approaches 8, causing the overall value of the function to become very negative.

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1. The rational expression representing the charge each attendee will have to pay is 300 + 55x.

2. Each attendee will have to pay $65 in order to cover the total cost.

The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be adequately explained by the four basic operations, sometimes known as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

1. We are given that it costs $300 plus $55 per person attending to host an event.

Let the number of attendees be x.

We get the expression as 300 + 55x.

2. We are given that 30 people are attending the event.

So, substituting x = 30 in the expression, we get

⇒ Total cost = 300 + (55 * 30)

⇒ Total cost = 300 + 1650

⇒ Total cost = $1950

Now, using the division operation, we get

⇒ Per person charge = 1950 ÷ 30

⇒ Per person charge = $65

Hence, the required solutions have been obtained.

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Question: To host an event at a popular convention center, it costs $300 plus $55 per person attending.

1. Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.

2. In the previous step you determined that for x number of people, the total cost for hosting the event is 300+55x. Now, adjust the expression to represent what each attendee would need to be charged to cover the total cost if 30 people were attending.

Answer:

As a result, the first pair of hikers is around 0.15 miles further away from camp than the second pair.

Step-by-step explanation:

Let's designate "x" for the distance travelled directly east or west and "y" for the distance directly north or south. Then, using the method below, determine how far each pair of hikers is from camp:

Distance is equal to sqrt(2xy*cos(angle) - xy + yy).

where "angle" is the angle at which the hikers veer away from their original path.

The first group of hikers includes:

Distance is equal to sqrt(((2cos(50°) + 1.2sin(50°))).

(1.2cos(50°) + 2 sin(50°))

(1.2sin(50°) + 2cos(50°)) = 2 - 2*

(1.25*cos(50°) + 1.2*cos(50°)*cos(130°))

approximately 2.53 miles.

The second group of hikers includes:

Distance is equal to sqrt(((2cos(40°) + 1.2sin(40°))).

-2sin(40°) + 1.2cos(40°) = 2

(1.2sin(40°) + 2cos(40°)) = 2 - 2*

(-2sin(40°) plus 1.2*cos(40°)*cos(140°))

about 2.38 miles.

As a result, the first pair of hikers is around 0.15 miles further away from camp than the second pair.

The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Let's call the length of the rectangle "l" and the width "w".

We can write two equations based on the given information -

Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)

Area equation: A = 3lw (since the field is divided into 3 equal parts)

We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.

We can use the perimeter equation to solve for one of the variables in terms of the other -

2l + 4w = 600

2l = 600 - 4w

l = 300 - 2w

Now we can substitute this expression for "l" into the area equation -

A = 3lw

A = 3(300 - 2w)w

A = 900w - 6w²

To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -

dA/dw = 900 - 12w = 0

12w = 900

w = 75

So the width of each of the smaller rectangular plots is 75 feet. We can use the perimeter equation to find the length -

2l + 4w = 600

2l + 4(75) = 600

2l = 300

l = 150

Therefore, the dimensions value are obtained as 150 feet by 75 feet.

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Answer:

y - 1 = 2(x + 2)

Step-by-step explanation:

Point-slope form is y - y₁ = m(x - x₁)

y - 1 = 2(x - -2)

=> y - 1 = 2(x + 2)

The equation that represents the total cost of the TV is Option B: 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's represent the total cost of the TV with the variable x.

According to the problem, Adam's first payment was 1/4 of the total price, so he still owed 3/4 of the price.

His second payment was 1/3 of the remaining amount, which is 1/3 × 3/4x = 1/4x, leaving him with 3/4x - 1/4x = 1/2x to pay.

His third payment was $20 more than the first payment, so it was 1/4x + 20, leaving him with 1/2x - (1/4x + 20) = 1/4x - 20 to pay.

Finally, his last payment was $120, so the remaining amount he owed was 1/4x - 20 - 120 = 1/4x - 140.

Adding up all of these payments, we get -

1/4x + 1/4x + 20 + 1/4x - 140 + 120 = x

Simplifying this equation, we get -

3/4x = 100

Multiplying both sides by 4/3, we get -

x = 400/3

Therefore, the equation is obtained as 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x.

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Adam bought a TV and paid it in four payments. His first payment was 1/4 of the total price. His second payment was 1/3 of the remaining amount. His third payment was $20 more than the first payment. His last payment was $120. Which equation represents the total cost of the TV?

a. 1/4x + 1/3x + 20 + 120 = x

b. 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x

c. 1/4x + 1/3 × 1/4x + 20 + 120 = x

d. 1/4x + 1/3x + 20 = 120

The inequality that compares Tara's height to Jeff's height is: ℎ > 120

An inequality is a mathematical statement that shows a relationship between two values that are not necessarily equal. It uses symbols such as <, >, ≤, or ≥ to indicate that one value is less than, greater than, less than or equal to, or greater than or equal to another value.

Let ℎ be Tara's height in centimeters. Since Tara is taller than Jeff, her height must be greater than 120 centimeters.

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Z decreased by 15% can be expressed as Z x 0.85.

Expression in math is a combination of numbers, symbols, and operations that represent a value or a mathematical concept. Expressions can be used to calculate a numerical result, solve equations, and evaluate logical statements. Expressions can also be used to express abstract ideas and concepts.

Mathematically, this is written as Z x (1 - 0.15).
This expression shows that Z is multiplied by a number that is less than 1, which results in a decrease.

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Z decreased by 15% can be expressed as Z x 0.85.

Expression in math is a combination of numbers, symbols, and operations that represent a value or a mathematical concept. Expressions can be used to calculate a numerical result, solve equations, and evaluate logical statements. Expressions can also be used to express abstract ideas and concepts.

Mathematically, this is written as Z x (1 - 0.15).
This expression shows that Z is multiplied by a number that is less than 1, which results in a decrease.

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complete questions as follows-

Express Using algebra Z deacresed by 15%. show your all work.

The prοbability that the mean gain fοr the sample was between 400 and 800 is apprοximately 0.603.

The distributiοn οf sample means apprοaches a nοrmal distributiοn with mean equal tο the pοpulatiοn mean and standard deviatiοn equal tο the pοpulatiοn standard deviatiοn divided by the square rοοt οf the sample size.

standard errοr οf the mean = standard deviatiοn / square rοοt οf sample size

[tex]s = 1539 / \sqrt{(34)}\\\\s = 263.8[/tex]

we can standardize the sample mean using the fοrmula:

z = (sample mean - pοpulatiοn mean) / standard errοr οf the mean

z1 = (400 - 651) / 263.8 ≈ -0.953

z2 = (800 - 651) / 263.8 ≈ 0.564

P(-0.953 < z < 0.564) ≈ 0.603

Therefοre, the prοbability that the mean gain fοr the sample was between 400 and 800 is apprοximately 0.603.

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Based on the information provided, it can be concluded that the length of the two shorter sides combined is half the length of the longest side.

The longest side, which is the green bar is 10 centimeters long. On the other hand, by adding the two shortest sides (orange bar 3 centimeters + blue bar 2 centimeters) the total length would be 5 centimeters.

Considering the longest side is 10 centimeters and the shortest side is 5 centimeters then the length of the two shorter sides combined is half the length of the longest side.

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Answer:

The probability of grabbing a tile other than a "B" is approximately 0.818 or 81.8%.

Answer:

Let's use "d" to represent the time the team spent on each drill.

Since the team spent the same amount of time on each drill, and they worked on 5 drills, the total time spent at practice before Jayla arrived can be represented as:

5d

We know that Jayla was 15 minutes late, so when she arrived, the team had already been practicing for 15 minutes. Therefore, the total time she spent practicing is:

40 minutes = 5d - 15

Now we can solve for "d":

5d - 15 = 40

5d = 55

d = 11

So the team spent 11 minutes on each drill.

The equation we used is:

5d - 15 = 40

The statement "Given any two numbers x, y, there is a third number w between them" can be expressed using symbolic logic and quantifiers as follows:

∀x∀y∃w (w is between x and y)

Here, the universal quantifier ∀x∀y indicates that the statement is true for any two numbers x and y. The existential quantifier ∃w indicates that there exists a third number w that is between x and y.

the examination of the links between statements that are used to express precise mathematical concepts. Formal logic is another name for symbolic logic.

Given any two digits x, y, there exists a third integer w between them. This proposition can be expressed in symbolic logic as follows:

∀x∀y(x<y → ∃w(x<w<y))

Where ∀x means "for all x", ∀y means "for all y", → means "implies", ∃w means "there exists a w", and (x<y → ∃w(x<w<y)) means "if x is less than y, then there exists a w such that w is between x and y".

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The statement can be expressed using symbοlic lοgic and quantifiers as in ∀x∀y∃w (w is between x and y)

The examinatiοn οf the links between statements that are used tο express precise mathematical cοncepts. Fοrmal lοgic is anοther name fοr symbοlic lοgic.

Given any twο digits x, y, there exists a third integer w between them. This prοpοsitiοn can be expressed in symbοlic lοgic as fοllοws:

∀x∀y(x<y → ∃w(x<w<y))

Where ∀x means "fοr all x", ∀y means "fοr all y", → means "implies", ∃w means "there exists a w", and (x<y → ∃w(x<w<y)) means "if x is less than y, then there exists a w such that w is between x and y".

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Monique needs to invest $50,354.37 today to have $500,000 in 30 years at an annual interest rate of 7.8% compounded half-yearly. Option D

We can use the formula for future value of an annuity to solve this problem:

FV = P * [(1 + r/n)^(n*t) - 1]/(r/n)

Where:

FV = future value (desired amount) = $500,000

P = the amount invested today

r = annual interest rate = 7.8%

n = number of compounding periods per year = 2 (half-yearly)

t = number of years = 30

Substituting the values:

$500,000 = P * [(1 + 0.078/2)^(2*30) - 1]/(0.078/2)

Solving for P using a financial calculator or an online TVM calculator, we get:

P = $50,354.37

Therefore, Monique needs to invest $50,354.37 today to have $500,000 in 30 years at an annual interest rate of 7.8% compounded half-yearly.

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Answer:

please specify

Step-by-step explanation:

Based on the information provided, the value of x in this triangle will be 0.9646 if solved by this letter.

In this case, we are required to calculate the base of the triangle by using the angle provided 16° and the length of the hypotenuse which is 3.5. Based on this, a possible equation considering the law of the sinuses would be:

Sin 16° = x/3.5

Now using this equation, let's solve it by x to find the x value:

x = Sin 16° × 3.5

x = 0.2756 × 3.5

x = 0.9646

This means that the value of x is 0.9646

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For the Venn Diagram with the code 0000, the 7-bit Hamming code extended is 0011000.

What is a Venn Diagram?

In order to solve problems based on the sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

To extend the four-bit code word "0000" to a seven-bit Hamming code word, we need to add three parity bits to the code word.

These parity bits are calculated based on the positions of the 1's in the code word.

To determine which subset of the Venn Diagram to put each parity bit in, we can use the following rules -

Parity bit 1 covers all bit positions that have an odd index (i.e., 1, 3, 5, 7, etc.).

Parity bit 2 covers all bit positions that have a "2" bit in their binary representation (i.e., 2, 3, 6, 7, etc.).

Parity bit 3 covers all bit positions that have a "4" bit in their binary representation (i.e., 4, 5, 6, 7, etc.).

Using these rules, we can fill in the Venn Diagram as follows -

Subset 1: 0 (bit position 1)

Subset 2: 00 (bit positions 2, 3)

Subset 3: 000 (bit positions 4, 5, 6)

Subset 4: 0000 (bit positions 7, 8, 9, 10)

Parity bit 1: 1 (covers bit positions 1, 3, 5, 7, 9, 11, 13)

Parity bit 2: 1 (covers bit positions 2, 3, 6, 7, 10, 11, 14)

Parity bit 3: 0 (covers bit positions 4, 5, 6, 7, 12, 13, 14)

So, the seven-bit Hamming code word that extends the four-bit code word "0000" is -

0011000

The first three bits (001) represent Subset 3, which contains the original code word "0000".

The next three bits (100) are the parity bits, and the last bit (0) represents Subset 4.

Therefore, the 7-bit code is obtained as 0011000.

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The distance from the sun to Canopus in parsecs is approximately 229.4 parsecs.

Absolute magnitude is a measure of the intrinsic brightness of a celestial object, such as a star or a galaxy, as it would be seen from a standard distance of 10 parsecs (about 32.6 light-years) away. It is defined as the magnitude (brightness) that the object would have if it were located at this standard distance, and it is determined by the object's luminosity, or total amount of energy radiated per unit time.

We are given that the absolute magnitude of Canopus is M = -3.1, and its apparent brightness is m = -0.72. We can use the formula (m - M) = 5log(d/10) to find the distance, d, from the Sun to Canopus in parsecs.

Substituting the given values, we get:

-0.72 - (-3.1) = 5log(d/10)

Simplifying:

2.38 = 5log(d/10)

log(d/10) = 2.38/5 = 0.476

Taking antilogarithm on both sides, we get:

d/10 = 10^(0.476)

d = 10^(0.476) * 10 = 229.4 parsecs

Therefore, the distance from the Sun to Canopus is approximately 229.4 parsecs.

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The graph of the function with asymptotes at x = -2, and x = 3, and x-intercept of (3, 0), indicates that the possible equation graphed is of the form;

[tex]f(x) = \frac{-6\cdot (x -2)}{(x + 2)\cdot (x -3)}[/tex]

An asymptote is the line which the graph of the function approaches when the input value of the function approaches infinity or minus infinity.

The asymptotes of the graph of the function are; x = -2, and x = 3

The possible denominators of the function are therefore; (x + 2) and (x - 3)

The value of the function when x = 0 is -2, therefore;

Numerator ÷ ((0 + 2)×(0 - 3)) = -2

When x = 0, the numerator = ((0 + 2)×(0 - 3)) × -2 = 12

The expressions in the denominator of the function, (x + 2), and (x - 3), and the shape of the graph with a x-intercept of 2, indicates that we get;

The possible numerator is; 6·(x - 2)

The equation for the function graphed is; f(x) = (6·(x - 2))/((x + 2)·(x - 3))

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An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch or cross.

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Answer:

We can expect the town to have a population of approximately 32,413 in the 2030 census if the growth rate remains at 1.8% per year.

Step-by-step explanation:

To calculate how long it will take for the town to double in size, we can use the Rule of 70, which states that the time it takes for a quantity to double is approximately 70 divided by the annual growth rate as a percentage.

So in this case, the annual growth rate is 1.8%, and therefore the doubling time is approximately 70/1.8 = 38.89 years (rounded to two decimal places).

To estimate the population in the 2030 census, we can use the same growth rate of 1.8% per year. Starting with the 2020 population of 27,370, we can use the formula:

Population = Initial population x (1 + growth rate)^number of years

Plugging in the numbers, we get:

Population = 27,370 x (1 + 0.018)^10 = 32,413 (rounded to the nearest whole number)

Therefore, we can expect the town to have a population of approximately 32,413 in the 2030 census if the growth rate remains at 1.8% per year.

The largest conceivable rectangular enclosure has dimensions of x = 40 feet, w = 40 feet, and area = 1600 square feet.

Assume the rectangular enclosure has dimensions of x feet in length and w feet in width.

The needed length of fence is 40 feet for the stone wall, plus 2 feet for each of the two ends and sides, for a total of 6 feet. This results in:

[tex]40 + 2w + 2x = 200[/tex]

Using a simplified formula and x in terms of w, we get at:

[tex]x = 80 - w[/tex]

A = xw, which has the following textual form, determines the area of the rectangular enclosure:

Solving for w:

w = 40

When we enter this value of w in place of x in the equation, we obtain:

[tex]x = 80 - w = 40[/tex]

As a result, the rectangular enclosure with the largest available area is 40 feet long and 40 feet wide. This enclosure's area is:

1600 square feet are equal to [tex]A = x*w = 40 * 40[/tex]

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The chromosomes are made up of DNA.

A chromosome is a structure in the nucleus of a cell that carries genetic information in the form of genes. Chromosomes are made up of DNA (deoxyribonucleic acid) and proteins called histones. They play a critical role in the transmission of genetic information from one generation to the next during cell division.

The relationship between a chromosome and DNA is that chromosomes are made up of DNA. DNA (deoxyribonucleic acid) is the genetic material that carries the information for the development, functioning, and reproduction of living organisms. DNA is packaged into structures called chromosomes, which are found in the nucleus of a cell. Each chromosome contains a long, linear strand of DNA that is tightly coiled around proteins called histones. The combination of DNA and proteins form the chromatin, which further condenses into the characteristic shape of a chromosome during cell division. Therefore, while DNA contains the genetic information, chromosomes are the structures that package and organize DNA.

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Chromosomes are the structures that bundle and organize DNA, while DNA holds genetic information.

A chromosome is a structure in a cell's nucleus that contains genetic data in the form of genes. The chromosome is made up of DNA and proteins known as histones. They are crucial in the transmission of genetic data from this generation to the next during cell division.

A chromosome and DNA are related in that chromosomes are built up of DNA. DNA (deoxyribonucleic acid) is the genetic substance that conveys information for the development, function, and reproduction of living organisms.

DNA is bundled into structures known as chromosomes, which are present in the nucleus of a cell. Each chromosome comprises a long, linear strand of DNA that is tightly wrapped around proteins called histones.

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The area of the rectangle would be = 4,522.14cm²

The perimeter for the rectangle = 9044.28 cm

To calculate the area of a rectangle the formula given below is used. Such as;

Area = length× width

Where length= 87.3cm

width = 51.8cm

Area = 87.3×51.8 = 4,522.14cm²

To calculate the perimeter of a rectangle the formula given below is used. Such as;

perimeter = 2 (length× width)

= 2 ( 87.3×51.8)

= 2 (4,522.14)

= 9044.28 cm

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The answer of the given question based on finding the surface area of a rectangular prism  the answer is ,60 square inches.

A prism is  polyhedron with two parallel, congruent faces called the bases, which are typically polygons, and rectangular sides connecting  corresponding sides of  bases.

To find the surface area of the rectangular prism shown in the net, we need to find the area of each of its six faces and then add them together.

Looking at the net, we can see that the rectangular prism has three pairs of identical faces. The dimensions of the rectangular prism are given by the labels on the net as follows:

The length of the rectangular prism is 6 inches (labeled L on the net).

The width of the rectangular prism is 3 inches (labeled W on the net).

The height of the rectangular prism is 2 inches (labeled H on the net).

The six faces of the rectangular prism and their areas are:

Front face: 3 x 2 = 6 square inches

Back face: 3 x 2 = 6 square inches

Top face: 6 x 2 = 12 square inches

Bottom face: 6 x 2 = 12 square inches

Left face: 6 x 2 = 12 square inches

Right face: 6 x 2 = 12 square inches

To find the total surface area, we add the areas of all six faces:

Total surface area = 6 + 6 + 12 + 12 + 12 + 12 = 60 square inches

Therefore, the surface area of the rectangular prism shown in the net is 60 square inches.

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An equation for the linear function that best fits this data is equal to y = 17.83x + 53.6.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the x-values would be plotted on the x-axis of the scatter plot while the y-values would be plotted on the y-axis of the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit and correlation coefficient are as follows:

Equation: y = 17.83x + 53.6

Correlation coefficient, r = 0.9926.

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