Mind-Set Matters In 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters. "1 She recruited female maids2 working in different hotels to participate in her study, and informed maids (randomly chosen) that the work they do satisfies the Surgeon General’s recommendations for an active lifestyle (which is true), giving the maids examples on how their work qualifies as good exercise. The other maids were told nothing. After four weeks, the exercise habits of the two groups had not changed, but the informed group had lost an average of lbs () and the uninformed group had lost an average of lbs (). The data are stored in MindsetMatters. Based on this study, does ‘‘Mind-Set Matter"? In other words, for maids, does simply thinking they are exercising more actually cause them to lose more weight?

The unknown number x = (6.1 ± sqrt(6.

Let's call the two numbers x and y.

We are given:

AM (Arithmetic Mean) between x and y exceeds their GM (Geometric Mean) by 2:

(x + y)/2 - sqrt(xy) = 2

GM between x and y exceeds their HM (Harmonic Mean) by 1.8:

sqrt(xy) - 2xy/(x+y) = 1.8

We can solve for one variable in terms of the other from the second equation and substitute into the first equation to solve for the remaining variable. Let's solve for y in terms of x from the second equation:

sqrt(xy) - 2xy/(x+y) = 1.8

sqrt(xy)(x+y) - 2xy = 1.8(x+y)

sqrt(xy)x + sqrt(xy)y - 2xy = 1.8x + 1.8y

sqrt(xy)(x+y-1.8) = 0.2x + 0.8y

x+y-1.8 = (0.2/0.8)sqrt(xy)(x+y-1.8)

x+y-1.8 = 0.25sqrt(xy)(x+y-1.8)

4x + 4y - 7.2 = sqrt(xy)(x+y)

Now we can substitute this expression for sqrt(xy)(x+y) into the first equation and solve for x:

(x + y)/2 - sqrt(xy) = 2

(x + y)/2 - (4x + 4y - 7.2)/4 = 2

2(x + y) - (4x + 4y - 7.2) = 8

12.2 = 2x + 2y

6.1 = x + y

Now we can substitute x + y = 6.1 into the expression we derived for sqrt(xy)(x+y) to solve for sqrt(xy):

4x + 4y - 7.2 = sqrt(xy)(x+y)

4x + 4y - 7.2 = sqrt(xy)(6.1)

sqrt(xy) = (4x + 4y - 7.2)/6.1

Finally, we can substitute both x + y = 6.1 and sqrt(xy) = (4x + 4y - 7.2)/6.1 into the equation sqrt(xy) - 2xy/(x+y) = 1.8 and solve for y:

sqrt(xy) - 2xy/(x+y) = 1.8

(4x + 4y - 7.2)/6.1 - 2xy/6.1 = 1.8

4x + 4y - 7.2 - 12.2xy = 11.38

4x + 4y - 11.38 = 12.2xy

4x + 4(6.1 - x) - 11.38 = 12.2xy (substituting x + y = 6.1)

xy = 4.08

Now we know that xy = 4.08, and we can use this to solve for x and y:

y = 6.1 - x

xy = 4.08

x(6.1 - x) = 4.08

6.1x - x^2 = 4.08

x^2 - 6.1x + 4.08 = 0

We can solve for x using the quadratic formula:

x = (6.1 ± sqrt(6.

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Decision variables in Doors&Windows linear programming model.

The decision variables in the linear programming model for this problem are the number of windows (W) and the number of tables (T) that Doors&Windows should produce to maximize their profit while meeting the constraints. The objective function to maximize would be the total profit, which can be expressed as 40W + 90T. The constraints include the available linear feet of framing material (6150) and labor hours (600), which can be written as 30W + 120T ≤ 6150 and 6W + 10T ≤ 600, respectively. Additionally, the maximum number of windows that can be produced (W ≤ 70) due to glass availability is also a constraint. These decision variables and constraints can be used to create a linear programming model to optimize Doors&Windows' production and profit.

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Nine ears of sweetcorn will cost $2.25 at this store.

To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:

1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.

2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.

So, nine ears of sweetcorn will cost $2.25 at this store.

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Answer: 5 1/4

Step-by-step explanation: 3/4 times 7/1 equals 5.25

Turn the decimal to a fraction and get 5 1/4

The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.

To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.

Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.

The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:

x² + 52x + 576 - (x² + 16x) = 1600

Simplifying this equation, we get:

36x + 576 = 1600

36x = 1024

x = 28

Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.

The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.

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The volume of the gift bag is given as 1152 cubic inches.

Since it is shaped like a rectangular prism, we can write the formula for its volume as V = l × w × h, where l, w, and h are the length, width, and height of the rectangular prism, respectively.

To determine the dimensions of the gift bag, we need more information such as the ratio of its length, width, and height or any one of its dimensions. If we assume one of the dimensions, say, the length is L inches, then we can write the volume as V = L × w × h. Solving for w × h, we get w × h = V/L = 1152/L.

We can then use this equation along with the fact that the gift bag is a rectangular prism to find the other dimensions. For example, if the width is W inches, then we have h = 1152/(L × W) and the volume can be expressed as V = L × W × 1152/(L × W) = 1152.

Similarly, if the height is H inches, then we have w = 1152/(L × H) and the volume can be expressed as V = L × 1152/(L × H) × H = 1152.

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Answer:

Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:

(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)

1/2^3 = 1/8 (because 2^3 = 8)

So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48

Next, simplify the expression outside the parentheses:

(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576

Now, substitute the simplified terms back into the original expression and simplify:

3x(1/48)x(1/576) = 1/768

So the final answer is 1/768.

The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.

To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.

The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.

The total distance the frog will travel is:

300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm

So here none of the options are correct.

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"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).

To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.

In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.

Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.

Hence the correct option is (c).

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The derivative of the function f(x) = [tex]x^{0,9}[/tex] is f'(x) = [tex]0.9x^{-0.1}[/tex].

To find the derivative of f(x), we use the power rule of differentiation, which states that if f(x) = [tex]x^n[/tex], then f'(x) = [tex]nx^{(n-1)}[/tex].

In this case, we have f(x) = [tex]x^{0,9}[/tex]. Applying the power rule, we get:

f'(x) = [tex]0.9x^{0.9-1} = 0.9x^{-0.1}[/tex]

Note that [tex]x^{-0.1}[/tex] can be rewritten as [tex]1/x^{0.1}[/tex]. So we have:

f'(x) =[tex]0.9/x^{0.1}[/tex]

This expression tells us the slope of the tangent line to the curve of f(x) at any given point. For example, at x = 1, we have:

f'(1) = [tex]0.9/1^{0.1} = 0.9[/tex]

This means that the slope of the tangent line to the curve of f(x) at x = 1 is 0.9. As x increases or decreases from 1, the slope of the tangent line changes accordingly.

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Answer:224cm^2

Step-by-step explanation:

Formula for the area of a parallelogram is base x height (b x h) so we do 14x16 which is 224.

The two triangles shows that an angle opposite the longest side of a triangle is the largest angle

From the question, we have the following parameters that can be used in our computation:

The two triangles

From the triangles we have the largest angles to be

C = 117.3 and E = 93 degrees

The lennths opposite these sides aere

AB = 6 and DF = 11.94

These lengths are the longest segments on their respective triangles

This means that an angle opposite the longest side of a triangle is the largest angle

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In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.

In ΔPQR, given that ∠R=90°, ∠P=26°, and PQ=8.5 feet, you want to find the length of QR to the nearest tenth of a foot.

Step 1: Since ∠R is a right angle (90°), we can use trigonometric ratios to find QR. First, let's find ∠Q. We know that the sum of angles in a triangle is 180°, so ∠Q = 180° - (∠P + ∠R) = 180° - (26° + 90°) = 64°.

Step 2: Now that we have all the angles, we can use the sine formula to find QR. We'll use the sine of ∠P (26°) and the given side PQ (8.5 feet) as our reference. The sine formula is:

QR = (PQ * sin(∠P)) / sin(∠Q)

Step 3: Plug in the known values:

QR = (8.5 * sin(26°)) / sin(64°)

Step 4: Calculate the sine values and the division:

QR = (8.5 * 0.4384) / 0.8988 ≈ 4.1326

Step 5: Round the answer to the nearest tenth of a foot:

QR ≈ 4.1 feet

In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.

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The measure of angle A is given as follows:

m < A = 53.13º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Angle A is opposite to a side of length 4 cm, while the hypotenuse is of 5 cm, hence it's measure is obtained as follows:

sin(A) = 4/5

m < A = arcsin(4/5)

m < A = 53.13º.

We have a right triangle, in which the side length opposite to angle A is BC = 4, while the hypotenuse is CA = 5.

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The coordinates of the fourth vertex is (3.9, 6.3,0).To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

We can find the length and slope of one side of the rectangle and then use that information to find the coordinates of the fourth vertex.

Let's start by finding the length and slope of the side connecting (-1.3, -3.5) and (-1.3, 1.4). The length of this side is the difference between the y-coordinates, which is:

1.4 - (-3.5) = 4.9

Since this side is vertical, its slope is undefined.

Next, let's find the length and slope of the side connecting (-1.3, 1.4) and (3.9, 1.4). The length of this side is the difference between the x-coordinates, which is:

3.9 - (-1.3) = 5.2

Since this side is horizontal, its slope is 0.

Since opposite sides of a rectangle are equal in length, the length of the side connecting (-1.3, 1.4) and (3.9, 1.4) must also be 4.9. We can use this length to find the y-coordinate of the fourth vertex, which is:

1.4 + 4.9 = 6.3

Now we know that the fourth vertex has coordinates (x, 6.3). To find the x-coordinate, we can use the length of the vertical side connecting (-1.3, -3.5) and (-1.3, 1.4), which is also 5.2. The x-coordinate of the fourth vertex is:

-1.3 + 5.2 = 3.9

Therefore, the coordinates of the fourth vertex are (3.9, 6.3,0).

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The given equation on a graph can be described best as C. It will be a line.

The given equation is a linear equation because it has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rewritten as:

y = 3x + 15 - 64

y = 3x - 49

Since it's a linear equation, it will represent a straight line on the graph that can be found by using the equation and some values of x, to find values of y and then plotting them.

In conclusion, the best answer is C. It will be a line.

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The full question is:

An equation is given to be 3x + 15 = 64

What will this be on a graph ?

A. It will be irregular

B. It will be a curve.

C. It will be a line.

D. There is no way to tell.

21. in the figure, provided line n and line m are parallel the values of x and y are

x = 7

y = 24

21. When line m and line n are parallel then using corresponding angle theorem we have that:

7y - 23 + 8x - 21 = 180

7y - 8x = 180 + 23 - 21

7x - 8x = 182

Also

8x - 21 + 23x - 16 = 180

8x + 23x = 180 + 21 + 16

31x = 217

x = 217 / 31

x = 7

using vertical angle theorem we have:

7y - 23 = 23x - 16

plugging in the value of x

7y - 23 = 23 * 7 - 16

7y - 23 = 145

7y = 145 + 23

7y = 168

y = 24

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Answer:

Step-by-step explanation:

you multiply 5 by 50 and that would equal 250

5 x 50 = 250

To use Lagrange multipliers, we need to set up the Lagrangian function, Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.

L(x,y,z,λ) = xyz + λ(x+y+z-6)
Then we need to find the critical points of L by setting its partial derivatives equal to zero:
∂L/∂x = yz + λ = 0
∂L/∂y = xz + λ = 0
∂L/∂z = xy + λ = 0
∂L/∂λ = x + y + z - 6 = 0
Solving this system of equations, we get:
x = y = z = 2
λ = -4
This critical point satisfies the constraint, since 2+2+2-6 = 0. To check whether it is a maximum or minimum, we need to use the second partial derivative test:
∂²L/∂x² = 0, ∂²L/∂y² = 0, ∂²L/∂z² = 0
∂²L/∂x∂y = z, ∂²L/∂x∂z = y, ∂²L/∂y∂z = x
The Hessian matrix is:
| 0  z  y |
| z  0  x |
| y  x  0 |
At the critical point (2,2,2), the Hessian matrix is:
| 0  2  2 |
| 2  0  2 |
| 2  2  0 |
The eigenvalues of this matrix are -4, -4, and 8. Since the eigenvalues are not all positive or all negative, we cannot conclude whether the critical point is a maximum or minimum.
Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.

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First, solve the expression inside the parentheses: (-28) - (+42) = -70

Next, subtract 3 from -70: -70 - (+3) = -73

The given expression can be simplified as follows:

[( -28 )-( +42)]-(+3) = -28 - 42 - 3 = -73

So, the answer to the given expression is -73.

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In a case whereby A bike wheel is 26 inches in diameter  the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters) the  the diameter is  660.4mm

Note; the bike man do not make any calculation, so we can not know mat be he make any mistake.

Since the bike wheel is 26 inches in diameter then we can calculate the diameter of the bike wheel  through the multiplication of the two numbers.

Diameter in milimeters = ( 26.0 x 25.4)

Diameter in milimeters =  660.4 mm.

Hence diameter of the bike wheel in millimeters will be 660.4.

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Answer:

Let's start by assigning some variables to the unknowns:

Let's call the price of one taco "t".

Let's call the price of one burrito "b".

With these variables, we can write two equations based on the information given in the problem:

5t + 2b = 13.25 (equation 1)

3t + 2b = 10.75 (equation 2)

We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:

(5t + 2b) - (3t + 2b) = 13.25 - 10.75

Simplifying this equation, we get:

2t = 2.5

Dividing both sides by 2, we get:

t = 1.25

So the price of one taco is $1.25.

Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:

5t + 2b = 13.25

Substituting t = 1.25, we get:

5(1.25) + 2b = 13.25

Simplifying this equation, we get:

6.25 + 2b = 13.25

Subtracting 6.25 from both sides, we get:

2b = 7

Dividing both sides by 2, we get:

b = 3.5

So the price of one burrito is $3.5.

Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.

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One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.

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Using Rule of thumb,

1) A common rule of thumb is to spend no more than 30% of your income on rent. Therefore, the maximum amount you should spend on rent is:

$2,800 x 0.3 = $840

2) Using the same rule of thumb, the maximum amount you should spend on rent is:

$1,900 x 0.3 = $570

3) To afford an $820/month apartment, you should aim to spend no more than 30% of your income on rent:

$820 = 0.3x

x = $2,733.33

So your monthly income must be at least $2,733.33 to afford the apartment.

4) Following the same reasoning, your monthly income must be at least:

$900 = 0.3x

x = $3,000

5) To start renting, you need to pay first and last month's rent, plus a $650 security deposit, for a total of:

$665 x 2 + $650 = $1,980

So you would need $1,980 to start renting the apartment.

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probability that the next car will turn left, we need to divide the number of cars that turned left by the total number of cars that passed through the intersection in the past 24 hours. This will give us a fraction that represents the likelihood of a car turning left.

Using the numbers provided, the total number of cars that passed through the intersection in the past 24 hours is:
318 (cars turned left) + 557 (cars turned right) + 390 (cars went straight) = 1265
So, the probability of the next car turning left is:

318 (cars turned left) ÷ 1265 (total number of cars) = 0.251 (rounded to three decimal places)

This means that there is a 25.1% chance that the next car will turn left at the intersection.
As a surveyor, it is important to be able to analyze data and calculate probabilities to make informed decisions. Understanding the probability of different outcomes can help to plan for future events and anticipate potential issues.

In this case, knowing the probability of a car turning left can help to inform traffic flow and reduce congestion at the intersection.

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We are given that f is continuous on [1, 5], differentiable on (1, 5), and f'(x) ≤ 23 for all x. We want to find the largest possible value for f(5). the largest possible value for f(5) is found to be 96.

We can apply the Mean Value Theorem (MVT) here, which states that if a function is continuous on [a, b] and differentiable on (a, b), there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a). In this case, a = 1, b = 5, and f(1) = 4.

Since f'(x) ≤ 23 for all x, we know that f'(c) ≤ 23. Plugging into the MVT equation, we have:
[tex]f'(c) = (f(5) - f(1))/(5 - 1) ≤ 23, f'(c) = (f(5) - 4)/4 ≤ 23[/tex]

To find the largest possible value for f(5), we assume f'(c) is equal to its maximum, 23: 23 = (f(5) - 4)/4. Solving for f(5), we get: f(5) = 4 + 4 * 23 = 4 + 92 = 96. So, the largest possible value for f(5) is 96.

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To determine how many gallons of white and maroon paint Frank will need, we need to calculate the total square footage for each color. Here's a step-by-step explanation:

1. Determine the square footage of the floor and ceiling that will be painted white. Since they are the same size, we can calculate the area of one and multiply it by 2.
2. Determine the square footage of all the walls that will be painted maroon. Calculate the area of each wall and sum them up.
3. Determine the square footage of the door that will be painted white. Subtract this value from the total maroon wall area.
4. Divide the total square footage of the white and maroon surfaces by 400 sq ft (coverage of one gallon) to find out how many gallons are needed for each color.

After calculating the areas and the number of gallons needed, compare the results with the given options (A, B, C, or D). Keep in mind that we don't have the specific dimensions for Frank's room, but following these steps will help you solve the problem once you have the necessary measurements.

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The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :

[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]

In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).

Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)

Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.

[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]

Now, substituting the values of (h, k) and

[tex] {r}^{2} [/tex] into the standard form equation to get the equation:

[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

Therefore, the standard form equation of the circle with the given characteristics is

[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]

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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).

In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.

The diameter comprises the midpoints of  the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).

Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.

Then,

(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.

Staging in this equation
h=4,
k=3
r=5

(x - 4)²+ (y - 3)² = 25


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A graph of the function p(x) and the function p(x + 2) is shown below.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

0 = a(-3 - 0)² + 4

0 = 9a + 4

a = -4/9

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

p(x) = y = -4/9(x - 0)² + 4

p(x + 2) = -4/9(x + 2)² + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.