Justify the last two steps of the proof.

Fraction is a part of whole.Fractions are written in the form of two numbers, one on top of the other, separated by a horizontal line. The number on the top is called the numerator, and the number at the bottom is called the denominator.

What is fraction?

A fraction is a mathematical concept that represents a part of a whole or a group. It is a way of expressing a number that is less than one and greater than zero.

The numerator represents the part of the whole or group that is being referred to, and the denominator represents the total number of parts in the whole or group. For example, if we have a pizza that is cut into eight equal slices, and we eat three slices, we can represent the amount of pizza we ate as the fraction 3/8. In this case, the numerator is 3, which represents the number of slices we ate, and the denominator is 8, which represents the total number of slices in the pizza.

Fractions can be used in a variety of mathematical operations, including addition, subtraction, multiplication, and division. To add or subtract fractions, the denominators must be the same. If they are not, the fractions must be converted into equivalent fractions with the same denominator before they can be added or subtracted.

Multiplying fractions involves multiplying the numerators together and the denominators together. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction, which is obtained by switching the numerator and denominator of the second fraction.

Fractions are commonly used in everyday life, such as when cooking or measuring ingredients, calculating percentages, and dealing with money. For example, if a store is having a sale with a discount of 20%, we can represent the sale price as the fraction 4/5, since the price after the discount is 80% of the original price.

It is important to note that fractions can also be expressed as decimals or percentages. To convert a fraction to a decimal, we divide the numerator by the denominator. To convert a fraction to a percentage, we multiply the fraction by 100.

In conclusion, fractions are an important concept in mathematics and are used in many different areas of our daily lives. They represent a part of a whole or group and are written in the form of a numerator over a denominator. Fractions can be used in a variety of mathematical operations and can be expressed as decimals or percentages.

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Correct question is "What is fraction? Write 358 words about it "

Answer:

(what is your question)

A regression model can be created to predict selling price based on square footage and number of bedrooms using available data. The model equation includes coefficients that can be estimated to predict the selling price of a house. The number of bedrooms is a significant predictor of selling price and should be included in the model.

To develop the regression model to predict selling price based on the square footage and number of bedrooms, the following steps can be taken:

Collect data on the selling price, square footage, and number of bedrooms for a sample of houses.

Create a scatter plot to visually inspect the relationship between selling price and square footage, and between selling price and number of bedrooms.

Use regression analysis to create a model that predicts selling price based on square footage and number of bedrooms. The model equation will be:

Selling price = b0 + b1(Square footage) + b2(Number of bedrooms)

where b0, b1, and b2 are coefficients to be estimated from the data.

To predict the selling price of a 2,000-square-foot house with three bedrooms, substitute the values into the model equation and solve for selling price:

Selling price = b0 + b1(2000) + b2(3)

Comparing the performance of this model with the models in problem 4-22. The number of bedrooms should be included in the model because it is a significant predictor of selling price. However, further analysis could be conducted to determine if other variables could improve the model's predictive power.

Overall, this regression model can provide a useful estimate of the selling price of a house based on its square footage and number of bedrooms.

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Answer:

Step-by-step explanation:

18 tickets cost $10 and 52 tickets cost $12.

Answer:

Step-by-step explanation:

Because the lines are perpendicular the slopes will be negtive

reciprocals of each other.  Thus slope of 3/8 becomes -8/3.

Using point slope formula:   y - y1 = m(x - x1)

Substitute the point given with the new slope and solve.

y - 5 = -8/3(x - 4)

y - 5 = -8/3x - - 32/3

y - 5 = -8/3x + 32/3

y - 5 + 5 = -8/3x + 32/3 + 5

y = -8/3x + 47/3

or

y = -8/3x + 15 2/3

Answer:

d.  x² + 5x - 104 = 0

Step-by-step explanation:

(x+5)x = 104

x² + 5x = 104

x² + 5x - 104 = 0

Answer:

5(x - 5)(x + 2)

Step-by-step explanation:

5x² - 15x - 50

5(x² - 3x - 10)

5(x - 5)(x + 2)

The correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.

What is a polynomial?

In mathematics, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which involves only the operations of addition, subtraction, and multiplication. Polynomials can have one or more terms, and each term can have one or more variables with non-negative integer exponents.

Chen's error is in the second line where they added the terms -(-2p²-mp+1) without distributing the negative sign to each term inside the bracket. The correct way to subtract a polynomial is to change the sign of each term inside the bracket and then add them to the other polynomial. So, the correct simplification would be:

P²+7mp+4-(-2p²-mp+1)

= P²+7mp+4+2p²+mp-1 (Distributing the negative sign)

= 3p²+8mp+3

Therefore, the correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.

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Answer:

1.yes it's a function

a.1,2,3,4,5

b.40,80,120,160,200

Answer: For the triangle area you do= base*height what gives you 198in

For the rectangle area you do= side*lenght what gives you 756in

An for the shaded area you do triangle area-rectangle area, what gives you 558 in

The set of points and lines when named are listed below

Using the figure as a guide, we have the following:

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The water level is rising at a rate of 0.0075 ft/min when the depth at the deepest point is 5 ft.

Let's call the depth at the deepest point of the pool "y" and the volume of

the water in the pool "V".

We want to find the rate at which the water level is rising, which is the

rate of change of "y" with respect to time.

We know the rate at which the pool is being filled, which is 0.9 ft3/min,

and we can find the rate at which the volume of the water is increasing

using the formula for the volume of a rectangular prism:

V = lwh

where l is the length, w is the width, and h is the height.

Since the pool is not rectangular, we can find the volume of the water as

a function of "y" using similar triangles:

h/y = (9 - 3)/(40 - 20) = 0.3

where h is the height of the pool at the deepest point. Solving for h, we get:

h = 0.3y

Substituting this expression for h into the formula for the volume, we get:

V = lw(3 + 0.6y)

Taking the derivative with respect to time, we get:

dV/dt = lw(0.6 dy/dt)

Now we need to find the values of l and w. The width is given as 20 ft,

and the length is a function of "y":

l = 40 - 2(40 - y) = 2y

Substituting these values into the expression for dV/dt, we get:

dV/dt = 40y(0.6 dy/dt)

Finally, we can find the rate at which the water level is rising when y = 5 ft

by plugging in the values:

0.9 = 40(5)(0.6 dy/dt)

Solving for dy/dt, we get:

dy/dt = 0.9/(4050.6) = 0.0075 ft/min

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The quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.

The quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass.

Since the actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable, the specialist should use a t-distribution.
1. The sample size (n) is 18, which is relatively small.
2. The population standard deviation (σ) is unknown.
In such cases, the t-distribution is more appropriate than the z-distribution, chi-square distribution, or f distribution.

The t-distribution is a statistical distribution that is used when the sample size is small, and the population standard deviation is unknown.
The z-distribution is used when the population standard deviation is known, and the sample size is large enough (typically, n > 30).
The chi-square distribution is used for testing the goodness-of-fit of a distribution or for testing the independence between two categorical variables.
The f distribution is used for comparing the variances of two populations.

It is not suitable for estimating the mean clarity rating in this case.
In conclusion, the quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.

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The percentage of the people between the ages of 35 and 54 that prefer baseball is 17.14%.

A preferences means the certain characteristics that any person wants to have in a good/service to make it preferable to him.

In the table, the total number of people between the ages of 35 and 54 is 35. Out of the 35 people, the people that prefer baseball is known to be 6.

Now, the percentage between the ages of 35 and 54 that prefer baseball will be:

= Baseball preference / Total number of people aged 35 and 54

= 6/35

= 0.17142857142

= 17.14%

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Answer: f(x)

Step-by-step explanation: It goes from the lowest elevation to the highest.

The ratio between their radii of cylinder is therefore 1:4.

The distance between a circle's or sphere's centre and its edge is referred to in geometry as its radius1. It is known as "r" and is a crucial component of spheres and circles3.

For instance, if a circle has a radius of 5 cm, that indicates that the circle's center to edge distance is 5 cm3.

When two cylinders have 1:16 ratios for their volumes and heights, it is possible to calculate their radii as follows:

Assume that one cylinder has a radius of r and a height of h. The other cylinder will have a radius of R and a height of 16h.

As the volumes of both cylinders are equal, we may write:

πr²h = πR²(16h) (16h)

r²/R² = 1/16

r/R = √(1/16) = 1/4

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Rounding to four decimal places, the probability is (a) 0.3273 (b) 0.8423, and (c) 0.0446.

We can model this problem using a binomial distribution, where the probability of success (having the disease) is p = 0.84, and the number of trials (people tested) is n = 10.

(a) To find the probability that all 10 people have the disease, we can calculate the:

P(X = 10) = (10 choose 10) * (0.84)^10 * (1-0.84)^(10-10) = 0.3273

Rounding to four decimal places, the probability is 0.3273.

(b) To find the probability that at least 8 people have the disease, we can calculate the:

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

We can find each term using the binomial probability formula and then add them up:

P(X = 8) = (10 choose 8) * (0.84)^8 * (1-0.84)^(10-8) = 0.2018

P(X = 9) = (10 choose 9) * (0.84)^9 * (1-0.84)^(10-9) = 0.3132

P(X = 10) = (10 choose 10) * (0.84)^10 * (1-0.84)^(10-10) = 0.3273

P(X ≥ 8) = 0.2018 + 0.3132 + 0.3273 = 0.8423

Rounding to four decimal places, the probability is 0.8423.

(c) To find the probability that at most 4 people have the disease, we can calculate:

[tex]P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

We can find each term using the binomial probability formula and then add them up:

P(X = 0) = (10 choose 0) * (0.84)^0 * (1-0.84)^(10-0) = 0.000004

P(X = 1) = (10 choose 1) * (0.84)^1 * (1-0.84)^(10-1) = 0.0001

P(X = 2) = (10 choose 2) * (0.84)^2 * (1-0.84)^(10-2) = 0.0012

P(X = 3) = (10 choose 3) * (0.84)^3 * (1-0.84)^(10-3) = 0.0084

P(X = 4) = (10 choose 4) * (0.84)^4 * (1-0.84)^(10-4) = 0.0348

P(X ≤ 4) = 0.000004 + 0.0001 + 0.0012 + 0.0084 + 0.0348 = 0.0446

Rounding to four decimal places, the probability is 0.0446.

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So the equation that represents the function F is F(x) = 2^(x-3) + 1.

None of the above equations represent the function given in the table. To find the equation, we need to look for a pattern in the outputs (f(x)) based on the inputs (x).

Starting with x=3, we see that f(x)=9. Moving to x=4, we see that f(x) increases by 8 to equal 17. Moving to x=6, we see that f(x) increases by 48 to equal 65. Each time we move to the next input value, the output increases by double the previous increase plus 1. This pattern can be written as:

f(x) = 2^(x-3) + 1

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The angle of depression of the boat from the top of the cliff = 51.78 degrees

To calculate the angle of depression of the boat from the top of the cliff, we need to draw a diagram to visualize the situation.

In this instance, we can draw a right-angled triangle with one side representing the cliff's height (94m) and the other representing the horizontal distance between the boat and the cliff's foot. (74m). This triangle's hypotenuse depicts the line of sight from the top of the cliff to the boat.

The angle of depression is defined as the angle formed by the horizontal line and the line of sight from the cliff's summit to the boat.

We can use the tan function to determine this angle.

tan(angle of depression) = (height of cliff) / (horizontal distance from the boat to the foot of the cliff)

tan(∅) = (h/x)

tan(angle of depression) = 94 / 74

angle of depression = [tex]tanx^{-1} (94/74)[/tex]

angle of depression = 51.788974574 degrees

Therefore, the angle of depression of the boat from the top of the cliff is approximately 51.78 degrees.

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The angle of depression of the boat from the top of the cliff is approximately 50.67 degrees.

To calculate the angle of depression of the boat from the top of the cliff, we can use trigonometry. The angle of depression is the angle formed between the horizontal line (parallel to the ground) and the line of sight from the top of the cliff to the boat.

In this scenario, we have a right triangle formed by the cliff, the boat, and the horizontal line connecting them.

Let's denote the angle of depression as θ.

Using trigonometric ratios, we can use the tangent function to calculate the angle of depression:

tan(θ) = opposite/adjacent

In this case, the opposite side is the height of the cliff (94 meters) and the adjacent side is the horizontal distance from the foot of the cliff to the boat (74 meters).

tan(θ) = 94/74

To find θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(94/74)

Using a calculator or trigonometric table, we can find that θ is approximately 50.67 degrees.

Therefore, the angle of depression of the boat from the top of the cliff is approximately 50.67 degrees.

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Answer:

The answer would be 28.96

Step-by-step explanation:

Sorry I was'nt to explain step by step But I know the answer

The quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point (5,-42) is:

f(x) = -2(x - 7)(x + 2)

The quadratic function has x-intercepts of (-2,0) and (7,0).

The function passes through the point (5,-42).Let's try to find the quadratic equation using the above information:

Since the quadratic function has x-intercepts of (-2,0) and (7,0), the function can be written as:

f(x) = a(x + 2)(x - 7)

Since the quadratic function passes through the point (5,-42), we can substitute the x and y coordinates into the above

equation to get the value of 'a':-

42 = a(5 + 2)(5 - 7)-42 = a(7)(-2)-42 = -14a => a = 3

So, the quadratic equation for the given function is:

f(x) = 3(x + 2)(x - 7)

Simplifying the equation:

f(x) = 3(x² - 5x - 14)f(x) = 3x² - 15x - 42

Therefore, the quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point

(5,-42) is: f(x) = -2(x - 7)(x + 2)

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The interquartile range (IQR) of the data is 70 and the third and the first quartile of the data is (90, 20).

The second and third quartiles, or the middle half of your data collection, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data collection.

The given plot shows the number of days on the market for single-family homes in the city.

The figure shows the first quartile = 20 and the third quartile 90

Therefore the interquartile range of the data is equal to the difference between the third quartile and the first quartile i.

The interquartile range = Q3 - Q1

                                       = 90 - 20

                                       = 70

The third and first quartiles of the data are (90, 20).

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Answer:

Let the number of marbles in the large bag be L. Then we have: 25 : 7S = 7S : L Multiplying both sides by 7S, we get: 25(7S) = (7S)^2 : L 175S = 49S^2 : L L = (49S^2) / 175 L = (7S^2) / 25 Therefore, the number of marbles in the large bag is (7/25) times the number of marbles in the medium bag.

Answer: A | 12² + b² = 37²

Step-by-step explanation:

The height can be found by using the Pythagoras Theorem
h² = b² + p²

The gradient of the line segment AB is -4/3.

What is the gradient?

The gradient is a measure of the steepness of a curve or surface at a particular point. It is a vector quantity that points in the direction of the greatest increase in the function value and whose magnitude gives the rate of change of the function in that direction.

The coordinates of point A are (0, 6), and the coordinates of point B are (3, 2). We can find the gradient of the line connecting these two points using the formula:

gradient = rise/run

where "rise" is the difference in the y-coordinates of the two points, and "run" is the difference in the x-coordinates.

So, we have:

rise = 2 - 6 = -4

run = 3 - 0 = 3

Plugging these values into the formula, we get:

gradient = -4 / 3

Therefore, the gradient of the line segment AB is -4/3.

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The Average rate of growth is 28589 per year

The Slope of the line connecting is m = 28589 pee year.

The average rate of growth is a measure of how much a quantity or variable changes on average over a certain period of time. It is calculated by dividing the total change in the quantity by the length of the time period. The formula for the average rate of growth is:

Average Rate of Growth = (Final Value - Initial Value) / Time Interval

Average rate of growth = 1611,589-210733 / 2009-1960

= 28589 per year

Slope of the line connecting ( 1960, 210, 733) 4 (2009, 1,611, 589) will be:

m = У2 - y1 / x2 - x1

m = 28589 per year

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Answer:

Therefore, there are 27.04 cubic feet of sand in the container.

Step-by-step explanation:

We can start by calculating the volume of the rectangular container:

Volume = length x width x height

Volume = 6.5 ft x 3.2 ft x 2 ft

Volume = 41.6 cubic feet

Since the sand fills the container to a depth of 1.3 feet, we can calculate the volume of the sand as follows:

Volume of sand = length x width x depth of sand

Volume of sand = 6.5 ft x 3.2 ft x 1.3 ft

Volume of sand = 27.04 cubic feet

Therefore, there are 27.04 cubic feet of sand in the container.

Answer:

whitney

Step-by-step explanation:

so amir in term 2 has 40+20=60

and whitney has 55+11=66

11 because 20% of 55 is 11 and when you add that two numbers you got the answer that whitney have higher mark

10% of 55=5.5

20% = 10%×2

5.5×2=11

Answer:

Therefore, the surface area of the composite figure is 368 cm².

Step-by-step explanation:

To find the surface area of the composite figure, we need to find the areas of each individual face and add them together.

The triangular prism has two triangular faces and three rectangular faces.

The area of each triangular face is 1/2(base × height).

Area of each triangular face = 1/2(10 × 5) = 25 cm²

The area of each rectangular face is length × width.

Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²

Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²

Area of the rectangular face with dimensions 10 cm by 8 cm = 10 × 8 = 80 cm²

Total area of the triangular prism = 2 × 25 + 3 × 50 + 80 = 280 cm²

The rectangular prism has two rectangular faces and four square faces.

The area of each rectangular face is length × width.

Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²

Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²

The area of each square face is side × side.

Area of each square face with side length 4 cm = 4 × 4 = 16 cm²

Total area of the rectangular prism = 2 × 20 + 4 × 16 = 88 cm²

The total surface area of the composite figure is the sum of the surface areas of the triangular prism and the rectangular prism.

Total surface area = surface area of triangular prism + surface area of rectangular prism

= 280 cm² + 88 cm²

= 368 cm²