ty suspects are properly judged while, of course, 10% of the guilty suspects are improperly found innocent. on the other hand, innocent suspects are misjudged 1% of the time. if the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocen

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

Answer:
3(a - 1) / (a + 1)

Step-by-step explanation:

I double checked, its right

Razak weighs 16.2 kg. To find Razak's weight, we need to use the information given in the problem that his mother weighs 4 times his weight.

Let's use the variable "R" to represent Razak's weight in kilograms. According to the problem, Razak's mother weighs 4 times Razak's weight, so we can write an equation:

Mother's weight = 4 * Razak's weight

64.8 = 4R

To solve for R, we can divide both sides by 4:

64.8 / 4 = R

16.2 = R

Therefore, Razak weighs 16.2 kg.

It's important to note that in solving this problem, we assumed that the weight of Razak's mother was accurately given in the problem. Additionally, we assumed that the units of measurement were in kilograms. If the problem used different units, we would need to convert them to kilograms before solving the equation.

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Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.

What is interest rate?

Interest rate is the percentage charged by a lender to a borrower for the use of money, usually expressed as an annual percentage of the principal borrowed.

Emily had to pay interest on the remaining balance after making the minimum payment of $30.

Remaining balance = $156 - $30 = $126

The amount of interest to be paid would be calculated as:

interest = (interest rate/12) * remaining balance

Where 12 is the number of months in a year.

So,

interest = (15.5/12) * $126 = $16.41

Therefore, Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.

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The given Fahrenheit temperatures evaluated to their Celsius equivalents are: 68°F = 20°C, 32°F = 0°C, 23°F = -5°C, -4°F = -20°C, and -40°F = -40°C.

The expression C = 5/9(F - 32) is used to convert temperatures in degrees Fahrenheit to degrees Celsius. To evaluate the expression for a given Fahrenheit temperature, we simply substitute the value of F into the formula and perform the necessary calculations.

For example, when F = 68, we substitute the value of F into the formula and simplify as follows:

C = 5/9 (68 - 32)

C = 5/9 * 36

C = 20

Here are the evaluations of the given Fahrenheit temperatures in degrees Celsius using the formula C = 5/9(F - 32):

F= 68: C = 5/9(68-32) = 20

F= 32: C = 5/9(32-32) = 0

F= 23: C = 5/9(23-32) = -5

F= -4: C = 5/9(-4-32) = -20

F= -40: C = 5/9(-40-32) = -40

Matching the correct Celsius temperatures to their respective Fahrenheit temperatures:

F= 68: C = 20

F= 32: C = 0

F= 23: C = -5

F= -4: C = -20

F= -40: C = -40

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Given a temperature F in degrees Fahrenheit, the expression C = 5/9(F - 32) gives the temperature in degrees Celsius. Evaluate the following Expressions and Match the correct answer to each the degrees listed.

1. F= 68  

2. F= 32

3. F = 23

4. F = -4

5. F = -40

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

The range of a number collection or data points in mathematics is the difference here between biggest and smallest values. It is a measurement of the data's dispersion or variability. The range is frequently employed in descriptive statistics and can serve to provide information about the data's distribution.

given

Certainly! The data are shown in a stem-and-leaf plot as follows:

5 | 4

6 | 0 1 2 2

7 | 1 2 4 6 8

8 | 2 3 4 4 6 7

9 | 0 5 5 9

The difference between the largest and smallest values is the data's range.

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

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The scatter plot suggests that there is a relationship between the number of chinups and push-ups, but it is not a perfect relationship

What is Scatter plot ?

A scatter plot is a type of graph that is used to display the relationship between two variables. It is a visual representation of a set of data points, where each point represents the values of two variables for a single observation.

Based on the scatter plot, it appears that there is a positive correlation between the number of chin-ups and push-ups several students did. This means that as the number of chin-ups increase, the number of push-ups also tend to increase.

We can see this trend in the general upward slope of the points in the scatter plot. However, there is also a fair amount of variability in the data, as some students did more push-ups than others even when they did a similar number of chin-ups.

Therefore,  the scatter plot suggests that there is a relationship between the number of chin-ups and push-ups, but it is not a perfect relationship

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Assuming a standard six-sided die and a fair coin, the probability of rolling a composite number (any number that is not a prime number) on the die is 3/6 or 1/2, since there are three composite numbers (4, 6, 8) out of six possible outcomes (1, 2, 3, 4, 5, 6).

The probability of the coin landing on heads is 1/2, and the probability of it landing on tails is also 1/2. Therefore, the probability of both events happening together is:

P(composite number and heads and tails) = P(composite number) x P(heads) x P(tails)

P(composite number and heads and tails) = (1/2) x (1/2) x (1/2)

P(composite number and heads and tails) = 1/8

So the probability of rolling a composite number and the coin landing on heads and tails is 1/8.

Answer: Without the graphs posted in your question, unfortunately it is not possible for me to provide you an answer. Please include the graphs given in your question so that I can provide an accurate response.

If the sum of the height and the perimeter of the square base is 14 in, the maximum possible volume is 54 in³.

Let x represent the square box's rectangular base's side length.

Suppose h is the height.

Volume V should be used.

Considering that the square base's height plus perimeter equals 14 inches.

h + 4x = 18

Subtract 4x on both side, we get

h = 18 - 4x..........(1)

The volume is given as:

V = Area × Height

V = x² × h

Substitute the value of h

V = x² × (18 - 4x)

V = 18x² - 4x³..........(2)

Differentiate the equation 2 with respect to x

dV/dx = 36x - 12x²..........(3)

For the critical numbers,

dV/dx = 0

So, 36x - 12x² = 0

x(36 - 12x) = 0

x(-12x + 36) = 0

Equating equal to 0

x = 0                      -12x + 36 = 0

x = 0                      -12x = -36

x = 0                       x = 3

Differentiate the equation 3 with respect to x

d²V/dx² = 36 - 24x

At x = 3 the value of d²V/dx² is

d²V/dx²  = 36 - 24 × 3

d²V/dx² = 36 - 72

d²V/dx² = -36 < 0

x = 3 corresponds to the maximum of the volume V according to the second derivative test.

Now from the equation 1;

[tex]V_{\text{max}}[/tex] = 18(3)² - 4(3)³

[tex]V_{\text{max}}[/tex] = 18(9) - 4(27)

[tex]V_{\text{max}}[/tex] = 162 - 108

[tex]V_{\text{max}}[/tex] = 54 in³

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The probability of selecting a point

1) in ΔADN is also 1/8.

2) in ΔADM but not in ΔADN is 0.

3) lies neither in ΔADM nor in ΔADN is 3/4.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To solve this problem, we need to use the fact that the diagonals of a square bisect each other and are perpendicular. Let's denote the midpoint of AB as P and the midpoint of BC as Q.

To find the probability that a point selected randomly in the square lies in ΔADM, we need to find the ratio of the area of ΔADM to the area of the square ABCD.

Since M is the midpoint of AD, we have DM = AM = 1/2 * AB. Similarly, since N is the midpoint of CD, we have DN = CN = 1/2 * BC.

Thus, the area of ΔADM is (1/2 * DM * AM) = (1/2 * 1/2 * AB * 1/2 * AB) = 1/8 * AB². The area of the square is AB². Therefore, the probability of selecting a point in ΔADM is (1/8 * AB²) / AB² = 1/8.

To find the probability that a point selected randomly in the square lies in ΔADM but not in ΔADN, we need to subtract the probability of selecting a point in ΔADN from the probability of selecting a point in ΔADM. Since N is the midpoint of CD, we have AN = 1/2 * AB, and therefore DN = 1/2 * BC = 1/2 * AB.

Thus, the area of ΔADN is (1/2 * DN * AN) = (1/2 * 1/2 * AB * 1/2 * AB) = 1/8 * AB², which is the same as the area of ΔADM.

Therefore, the probability of selecting a point in ΔADN is also 1/8.

The probability of selecting a point in ΔADM but not in ΔADN is (1/8 * AB²) - (1/8 * AB²) = 0.

To find the probability that a point selected randomly in the square lies neither in ΔADM nor in ΔADN, we need to subtract the probability of selecting a point in ΔADM from the probability of selecting a point in the square and then subtract the probability of selecting a point in ΔADN from that result.

The probability of selecting a point in the square is 1.

The probability of selecting a point in ΔADM is 1/8, and the probability of selecting a point in ΔADN is also 1/8.

Therefore, the probability of selecting a point that lies neither in ΔADM nor in ΔADN is 1 - (1/8 + 1/8) = 3/4.

Hence, the probability of selecting a point

1) in ΔADN is also 1/8.

2) in ΔADM but not in ΔADN is 0.

3) lies neither in ΔADM nor in ΔADN is 3/4.

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Answer:

10π cm

Step-by-step explanation:

C = πd

First, we find the hypotenuse of the triangle which is the diameter of the circle.

a² + b² = c²

6² + 8² = c²

c² = 100

c = 10

d = 10 cm

C = πd

C = 10π cm

If Tayugineans drink an average of 1.64 cups of coffee per day, then 0.38 percent will drink less than 1 cup-of-coffee per day.

The average number of cups of coffee drink is = 1.64 cups,

The variance is = 0.0576, So, the standard-deviation is = √0.0576 = 0.24,

Let us assume that the variable is normally-distributed with a standard deviation of 0.24 cup.  

We have to find the persons who drink less than 1 cup of coffee,

It is calculated as : P(x < 1) ,

The corresponding z-value is = z = (1 - 1.64)/0.24 = -2.6667 ,

So, P(z < -2.67) = 0.0038 = 0.38%.

Therefore, 0.38% drink less than 1 cup of coffee per day.

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This would give you a z* value of approximately 1.96.

To find the value of z* for a specified confidence level c in a mosaic function, you should use the inverse cumulative

distribution function (also called the quantile function or the z-score function). The parameters you need are the

desired confidence level (c) and the standard normal distribution.

Here are the steps to find the value of z*

1. Determine the desired confidence level (c). This is usually given as a percentage, like 95% or 99%.

2. Calculate the area under the curve corresponding to the confidence level. This is equal to (1 - c)/2.

3. Use the inverse cumulative distribution function (quantile function) with the standard normal distribution to find the z

score corresponding to the calculated area.

4. The resulting value is the z* value for the specified confidence level c.

For example, if you need to find the z* value for a 95% confidence level, you would calculate (1 - 0.95)/2 = 0.025, and

then use the inverse cumulative distribution function with the standard normal distribution to find the z-score

corresponding to 0.025. This would give you a z* value of approximately 1.96.

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The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables. To determine whether F is a function of R, we would need to know the number of foxes for each value of R.

A function in mathematics is a rule that converts each element from one set, known as the domain, into a particular element in another set, known as the range. The domain of a function is the set of all potential inputs, whereas the range is the set of all potential outputs. A graph, a table of values, or an equation can all be used to describe a function. In science, engineering, economics, and other disciplines, functions are used to represent the connections between variables.

Neither R nor F is a function of t because there are multiple values of R and F for some values of t. For example, at t=2, the number of rabbits is 750, and at t=3, the number of rabbits is 567.

From the data in the table, we cannot determine whether F is a function of R or whether R is a function of F. To determine whether F is a function of R, we would need to know the number of foxes for each value of R. Similarly, to determine whether R is a function of F, we would need to know the number of rabbits for each value of F. The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables.

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Answer:

x = 71

Step-by-step explanation:

180 degrees is how many degrees were in a triangle.

Add up the angles then subtract by 180 and there is your answer.

The general equation for a circle with center (a,b) and radius r is:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]. By substituting the values and simplifying the equation, we will get 0.

What is circle ?

In math, a circle is a closed, two-dimensional shape made up of all elements that are spaced uniformly apart from the centre. The radius of something like the circle refers to this distance. Often, the letter "O" or "" is used to represent a circle. The circle is really a fundamental geometric shape and includes a number of significant characteristics, including its radius, which is the distance it around circle, or its area, which is the volume of the circle's interior. A circle's area is equal to 2 times its radius square, and its circumference is equal to 2 times its radius.

To find the equation for the circle that passes through the points (-5,0), (0,4), and (2,4), we need to find the center (a,b) and radius r.

First, we find the midpoint of the line segment between (-5,0) and (0,4), which is:

[tex]((-5+0)/2, (0+4)/2) = (-2.5,2)[/tex]

Next, we find the midpoint of the line segment between (0,4) and (2,4), which is:

[tex]((0+2)/2, 4/2) = (1,2)[/tex]

Since the circle passes through all three points, its center must be equidistant from all three points. Using the distance formula, we can set up three equations:

[tex](-2.5 - a)^2 + (2 - b)^2 = r^2[/tex]

[tex]a^2 + (4 - b)^2 = r^2[/tex]

[tex](1 - a)^2 + (2 - b)^2 = r^2[/tex]

Simplifying the equations and setting them equal to each other, we get:

[tex](-2.5 - a)^2 + (2 - b)^2 = a^2 + (4 - b)^2 = (1 - a)^2 + (2 - b)^2[/tex]

Expanding the squares and simplifying, we get:

[tex]6a - 10 = 0[/tex]

[tex]2b - 12 = 0[/tex]

Solving for a and b, we get:

a = 5/3

b = 6

Now we can find the radius of the circle by plugging in the values of a and b into one of the equations we set up earlier:

[tex]a^2 + (4 - b)^2 = r^2[/tex]

[tex](5/3)^2 + (4 - 6)^2 = r^2[/tex]

[tex]25/9 + 4 = r^2[/tex]

[tex]r^2 = 61/9[/tex]

Therefore, the equation of the circle is:

[tex](x - 5/3)^2 + (y - 6)^2 = 61/9[/tex]

Simplifying, we get:

[tex]4x^2 + 4y^2 - 40x + 48y + 167 = 0.[/tex]

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Answer:

3

Step-by-step explanation:

Once we have the total surface area, we will know how much burlap Dominique needs to buy to cover the flower box.

To determine how much burlap Dominique needs to buy to cover the flower box, we need to calculate the surface area of the box. Unfortunately, without the specific dimensions or a provided diagram,

I cannot give you an exact number.
However, here are the general steps to calculate the surface area of a rectangular flower box:
1. Identify the dimensions: length (L), width (W), and height (H).
2. Calculate the surface area of each face:
  - Top/Bottom: 2 x (L x W)
  - Sides: 2 x (L x H)
  - Front/Back: 2 x (W x H)
3. Add the surface areas of all faces together to get the total surface area.
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Answer:

$245.45

Step-by-step explanation:

.45c = $135, so c = $245.45

.45 × $245.45 = $110.45, a $135 savings.

we have derived the formula T = √(8R/2.5) for the time taken for a rope of length R to be rotated about a central point, made R the subject of the formula, and used the formula to calculate the length of a rope that takes 16 seconds for a single revolution and the time taken for a rope of length 18 metres to complete a revolution.

How to solve questions?

a) To make R the subject of the formula, we need to isolate it on one side of the equation. We start by rearranging the formula:

T = √(8R/2.5)

Squaring both sides of the equation, we get:

T²= 8R/2.5

Multiplying both sides by 2.5, we get:

2.5T²= 8R

Finally, dividing both sides by 8, we get:

R = 2.5T²/8

Therefore, R is given by the formula R = 2.5T²/8.

b) To find the length of rope if it takes 16 seconds for a single revolution, we can substitute T = 16 into the formula we derived in part (a):

R = 2.5T²/8 = 2.5(16)²/8 = 100

Therefore, the length of the rope is 100 metres.

c) To find the time taken for a rope of length 18 metres to complete a revolution, we can again use the formula we derived in part (a), but this time we substitute R = 18:

T = √(8R/2.5) = √(8*18/2.5) = √(115.2) ≈ 10.7 seconds

Therefore, the time taken for a rope of length 18 metres to complete a revolution is approximately 10.7 seconds, rounded to one decimal place.

In summary, we have derived the formula T = √(8R/2.5) for the time taken for a rope of length R to be rotated about a central point, made R the subject of the formula, and used the formula to calculate the length of a rope that takes 16 seconds for a single revolution and the time taken for a rope of length 18 metres to complete a revolution.

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Answer: x=5

Step-by-step explanation:

First you gotta box the variable so you don't get confused. The opposite of adding 2 is subtracting so you subtract 2-2 which gives you 0 and subtract 17-2 which gives 15. THEN, you will have left 3x=15 in order to get rid of the three you have to divide by the 3 on both sides. Lastly, you get your answer! Hope this helps :D

Answer:

V = (l)(w)(h)

Step-by-step explanation:

This is essentially volume equals length times width times height.

V: Volume

L: Length

W: Width

H: Height

This means, that to find the volume of a rectangular prism, you multiply length times width times height. This also works if you have the values of volume and 2 values from length, width, or height, because you can rearrange the equation.

Step-by-step explanation:

Perimeter is the sum of all of the sides

  add all of the    3x + 3  's

3x+3    +   3x +3     +  3x+3    +  3x + 3 = 12x + 12  units

Total surface area of this cylinder, the answer is (C) 163.36 cm².

What is an area ?

The total surface area of a cylinder can be found using the formula:

surface area = 2πr² + 2πrh

where r is the radius and h is the height.

Substituting the given values, we get:

surface area = 2π(4.0)² + 2π(4.0)(2.5)

= 2π(16.0) + 2π(10.0)

= 32π + 20π

= 52π

Using the approximation 3.14 for π and rounding to 2 decimal places, we get:

surface area ≈ 52(3.14) ≈ 163.36 cm²

Therefore, the answer is (C) 163.36 cm².

What is cylinder?

A cylinder is a three-dimensional shape that has two circular bases that are parallel and congruent to each other. The sides of a cylinder are curved, and they connect the bases. A cylinder has a constant cross-sectional area throughout its height, and it is a type of prism. The height of a cylinder is the perpendicular distance between the bases.

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. The surface area of a cylinder can be calculated using the formula A = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. Cylinders are commonly found in everyday objects such as cans, pipes, and containers.

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Step-by-step explanation:

Not sure why you would want this...here is the result using a big number calculator on the internet:

2^2000 =

114,813,069,527,425,452,423,283,320,117,768,198,402,231,770,208,869,520,047,764,273,682,576,626,139,237,031,385,665,948,631,650,626,991,844,596,463,898,746,277,344,711,896,086,305,533,142,593,135,616,665,318,539,129,989,145,312,280,000,688,779,148,240,044,871,428,926,990,063,486,244,781,615,463,646,388,363,947,317,026,040,466,353,970,904,996,558,162,398,808,944,629,605,623,311,649,536,164,221,970,332,681,344,168,908,984,458,505,602,379,484,807,914,058,900,934,776,500,429,002,716,706,625,830,522,008,132,236,281,291,761,267,883,317,206,598,995,396,418,127,021,779,858,404,042,159,853,183,251,540,889,433,902,091,920,554,957,783,589,672,039,160,081,957,216,630,582,755,380,425,583,726,015,528,348,786,419,432,054,508,915,275,783,882,625,175,435,528,800,822,842,770,817,965,453,762,184,851,149,029,376

The possible lowest diameter of Katie's cylinder is approximately 5.26 cm.

To find the possible lowest diameter of Katie's cylinder, we'll use the concepts of normal distribution, mean, and standard deviation.
1. Recall the given information:
- Mean diameter (µ) = 5 cm
- Standard deviation (σ) = 0.2 cm
- Katie's cylinder is in the upper 10% in size (diameter).
2. Determine the z-score that corresponds to the upper 10% of the distribution:
To find the z-score for the upper 10%, you can use a z-table or a calculator with a built-in function to find the inverse of the cumulative distribution function (commonly known as the "inverse CDF" or "quantile" function). The z-score corresponding to the upper 10% is approximately 1.28.
3. Calculate the possible lowest diameter of Katie's cylinder using the z-score formula:
z = (X - µ) / σ
where:
- z is the z-score
- X is the diameter we want to find
- µ is the mean diameter
- σ is the standard deviation
4. Rearrange the formula to solve for X:
X = z * σ + µ
5. Plug in the values and solve for X:
X = (1.28 * 0.2) + 5
X = 0.256 + 5
X ≈ 5.26 cm

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As a result, the horizontal component of velocity has a magnitude of 11.8 m/s\ while the vertical component of velocity has a value of 8.0 m/s.

The pace at which an item changes its position is described by a vector quantity called velocity. It is described as the rate at which displacement changes in relation to time The amount and direction of velocity are both present. Speed refers to the velocity's magnitude.

The football's velocity in this scenario is 32 miles per hour, or around 14.3 meters per second.

We can use trigonometry to determine the sizes of a velocity vector's horizontal and vertical components.

Vₓ = V cos (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the horizontal component of velocity.

Vy = V sin (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the vertical component of velocity.

In this instance, we are aware of the football's velocity, which is 32 miles per hour, or around 14.3 meters per second6. It makes a 34 degree 6 angle with the ground.

Therefore,

Vₓ= V cos (theta) * cos (34 degrees) = 14.3 m/s * 11.8 m/s

Vy = V sin (theta) * sin (34 degrees) = 14.3 m/s * 8.0 m/s

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To find the residual for each data point, we subtract the predicted sales from the actual sales. The residuals for the model are 1, 0, 1, and 1 for x=0, 1, 2, and 3 respectively.

To find the residual for each data point, we need to subtract the predicted sales from the actual sales:

For x=0: Residual = Actual sales - Predicted sales = 22 - 21 = 1

For x=1: Residual = Actual sales - Predicted sales = 33 - 33 = 0

For x=2: Residual = Actual sales - Predicted sales = 36 - 35 = 1

For x=3: Residual = Actual sales - Predicted sales = 28 - 27 = 1

Therefore, the residuals for the model are 1, 0, 1, and 1 for x=0, 1, 2, and 3 respectively.

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Answer:

Step-by-step explanation:

The area of the rectangle garden can be expressed as:

Area = Length × Width

Since one side is 6 feet longer than the other, we can express the length as:

Length = Width + 6

Substituting this expression for length into the area formula, we get:

Area = (Width + 6) × Width

Simplifying this expression, we get:

Area = Width² + 6Width

The cost to install synthetic grass is given as $8 per square foot, so the total cost y can be expressed as:

y = 8(Area)

Substituting the expression for area that we found earlier, we get:

y = 8(Width² + 6Width)

Simplifying this expression, we get:

y = 8Width² + 48Width

Therefore, the equation that correctly shows the relationship between x (the length of the shorter side of the garden) and y (the total cost to install synthetic grass) is:

y = 8x² + 48x