wen and five friends equally share 1/3 of a pan of snack bars. which expression shows how much of the pan each person gets?

c² + 9 + 6c is the solution by distributive property .

What in mathematics is a distributive property?

This characteristic states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend separately by the number and then combining the products collectively.

                                       When you multiply one value by another, you are using the distributive property of multiplication over addition. When multiplying 5 by the sum of 10 plus 3, for instance, add 3. We typically add the numbers first, then multiply the result by 5, since the terms are similar. However, in accordance with the property, you can first multiply each addend by 5.

= (c+3)^2

= c² + 9 +  2 * c * 3

= c² + 9 + 6c

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Step-by-step explanation:

a)

Arabica coffee = 750a

Robusta coffee = 1200r

The total amount coffee beans 750a + 1200r = 1000000 kg

b)

The total amount of market price

1.42*750a +0.73*1200r 1000000

1065a + 876r = 1000000 dollars

step by step reading

The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while

Robusta yields about 1200 kg per hectare. Suppose that a plantation has a

hectares of Arabica and r hectares of Robusta.

a. Write an equation relating a and r if the plantation yields 1,200,000 kg of coffee.

b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica

and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation

produces coffee worth $1,200.000. what does that answer that means  it would be

ANSWER

a

Arabica coffee = 750a

Robusta coffee = 1200r

The total amount coffee beans

750a + 1200r = 1.200,000 kg

b)

The total amount of market price

1.42*750a + 0.73*1200r = 1,200.000 ⇒

1065a + 876r = 1,200.000 dollar!!!!!!

Answer: Let's call the bill before the tip "x".

The tip was 20.7% of the bill, so the amount of the tip can be expressed as:

tip = 0.207 * x

The total bill, including the tip, was $31.09, so we can write an equation to represent this:

x + tip = 31.09

Substituting the expression for the tip into this equation, we get:

x + 0.207x = 31.09

Expanding and solving for x, we get:

1.207x = 31.09

x = 31.09 / 1.207

x = 25.76

So the bill before adding the tip was $25.76.

Step-by-step explanation:

The number of adults who attended the concert is 824.

Linear Equation:

The equation is said to be linear if the greatest power of a variable always equals 1. It is also known as a one-degree equation. The usual form of a linear equation with one variable is Ax + B = 0. In this case, the variables x and A are variables while the variable B is a constant.

It is given in the question that the number of adults are twice the number of children.

then,

Suppose there were x children present at the concert.

Then number of adults will be 2x.

According to the given question,

x + 2x = 1236

3x = 1236

dividing both sides by 3, we get

x= 412

therefore, number of children who attended the concert is 412.

Then the number of adults will be,

2x = 2 x 412 = 824

therefore, the number of adults who attended the concert is 824.

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According to the information, it can be inferred that US President Nixon's visit to China proved that the communist world was not a single entity and had many different positions.

The visit of the President of the United States Richard Nixon to the People's Republic of China is an important event in the political and foreign relations sphere of the United States because it was a way to establish a formal relationship between the United States and the People's Republic of China.

This was significant because it was the first time a US President had visited the PRC, who at the time considered the US one of his main enemies. Additionally, this allowed him to verify to the other states that there were different ways of proposing communism. In this case, Chinese communist thought was moderated, so the relationship with the United States was allowed.

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The sample size that required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (0.073) is 120.

As per the data given:

The makers of skittles claim that 20% of skittles candies are orange.

20 % = 0.20

Select a random sample of 30 skittles from a large bag.

[tex]\hat p[/tex] = the proportion of orange skittles in the sample.

The standard deviation of the sampling distribution of [tex]\hat p[/tex] = 0.073

The Standard deviation of the Sampling distribution was reduced to [tex]$= \frac{1}{2} \sigma_{\hat{p}}$[/tex].

[tex]$ \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=0.073$[/tex]

Divide both sides by 2

We get:

[tex]$\sqrt{\frac{p(1-p)}{n}}=\frac{0.073}{2}[/tex]............... (1)

Now it should become be one - half.

Let [tex]$n_1[/tex] be the new sample size.

[tex]$\sqrt{\frac{p(1-p)}{n_1}}=\frac{0.073}{2}[/tex] ..................2

From (1) and (2) RHS of both equations is equal.

Then equate both equations

[tex]$\frac{1}{2} \sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{p(1-p)}{n_1}}$[/tex]

Squaring on both sides

We get:

[tex]$\Rightarrow\left(\frac{1}{2}\right)^2 \frac{p(1-p)}{n}=\frac{p(1-p)}{n_1}\end{aligned}$[/tex]

[tex]$\Rightarrow \frac{1}{4 n}=\frac{1}{n_1}$[/tex]

[tex]$\Rightarrow n_1=4 n$[/tex]

[tex]$n_1-[/tex] The new sample size required = 4n

n-The old sample size.

The sample size that required = 4n

= 4 (30)

= 120

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The makers of skittles claim that 20% of skittles candies are orange. Suppose this claim is true. You select a random sample of 30 skittles from a large bag. Let p-hat = the proportion of orange skittles in the sample. The standard deviation of the sampling distribution of p-hat = .073

What sample size would be required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (.073)

Checks, debit cards, and electronic payments are considered forms of cashless payments because they allow for the transfer of funds between individuals or businesses without the need for physical currency, such as bills and coins.

Checks are considered cash because they are legal tender and can be deposited into a bank account, allowing the funds to be transferred between parties. Debit cards and electronic payments work in a similar way by deducting funds directly from a bank account or transferring funds electronically. While these forms of payment may not involve physical currency, they represent a transfer of value and can be used to purchase goods and services in the same way as cash.

In summary, checks, debit cards, and electronic payments are considered forms of cash because they facilitate the transfer of value between parties, even though they do not involve physical currency.

Answer:

Debit cards account for 28% of all payments, and credit cards account for 23% of all payments. For these payments, payment details are entered manually during a checkout process, or the physical card is processed at a point of sale (POS) system. There’s usually a debit or credit card processing fee, which the business owner needs to pay.

Step-by-step explanation:

pls tell me if wrong thank you have a great night or day

Using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.

What is Euler's method?

Ordinary differential equations (ODE) can be solved using the Euler's method, a first-order numerical technique, with a specified beginning value.

We are given an equation y' = f(x,y), a point ([tex]x_{o} ,y_{o}[/tex]) and a step value h.

We have

f(x,y) = (x − y)^2

Point is (0,0.6)

We need to find y(0.5).

So, using Euler's method with step h = 0.1, we get

⇒[tex]x_{1}[/tex] = [tex]x_{o}[/tex] + h

⇒[tex]x_{1}[/tex] = 0 + 0.1 = 0.1

⇒[tex]y_{1}[/tex] = [tex]y_{o}[/tex] + h * f([tex]x_{o} ,y_{o}[/tex])

⇒[tex]y_{1}[/tex] = 0.6 + 0.1 * (0 - 0.6)^2

⇒[tex]y_{1}[/tex] = 0.636

⇒[tex]x_{2}[/tex] = [tex]x_{1}[/tex] + h

⇒[tex]x_{2}[/tex] = 0.1 + 0.1 = 0.2

⇒[tex]y_{2}[/tex] = [tex]y_{1}[/tex] + h * f([tex]x_{1} ,y_{1}[/tex])

⇒[tex]y_{2}[/tex] = 0.636 + 0.1 * (0.1 - 0.636)^2

⇒[tex]y_{2}[/tex] = 0.6647296

⇒[tex]x_{3}[/tex] = [tex]x_{2}[/tex] + h

⇒[tex]x_{3}[/tex] = 0.2 + 0.1 = 0.3

⇒[tex]y_{3}[/tex] = [tex]y_{2}[/tex] + h * f([tex]x_{2} ,y_{2}[/tex])

⇒[tex]y_{3}[/tex] = 0.6647296 + 0.1 * (0.2 - 0.6647296)^2

⇒[tex]y_{3}[/tex] ≈ 0.6863

⇒[tex]x_{4}[/tex] = [tex]x_{3}[/tex] + h

⇒[tex]x_{4}[/tex] = 0.3 + 0.1 = 0.4

⇒[tex]y_{4}[/tex] = [tex]y_{3}[/tex] + h * f([tex]x_{3} ,y_{3}[/tex])

⇒[tex]y_{4}[/tex] ≈ 0.6863 + 0.1 * (0.3 - 0.6863)^2

⇒[tex]y_{4}[/tex] ≈ 0.7012

⇒[tex]x_{5}[/tex] = [tex]x_{4}[/tex] + h

⇒[tex]x_{5}[/tex] = 0.4 + 0.1 = 0.5

⇒[tex]y_{5}[/tex] = [tex]y_{4}[/tex] + h * f([tex]x_{4} ,y_{4}[/tex])

⇒[tex]y_{5}[/tex] ≈ 0.7012 + 0.1 * (0.5 - 0.7012)^2

⇒[tex]y_{5}[/tex] ≈ 0.7052

So, y(0.5) ≈ 0.7052

Similarly, with step h = 0.5, we will calculate the values till [tex]x_{10}[/tex] and [tex]y_{10}[/tex]

On doing this, we get y(0.5) ≈ 0.6803

Hence, using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.

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Answer:

Step-by-step explanation:

We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.

So, if h is the woman's height and L is the length of her shadow, we have:

L/h = d/13

And since h = 6 feet, we can write:

L = (d/13) * 6

So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:

L = (d/13) * 6

The surface area ranges from 0 to 1, and is equal to the integral of the circumference of a circle with a radius of x2x5 times.

An integral can be used to define the surface area gained by rotating the curve y2=x2x5 around the x-axis for y0 and 0x1. This integral represents the circumference, from 0 to 1, of a circle with radius x2x5 multiplied by. This can be expressed as x25x624x3+8 times the integral of from 0 to 1 for. When the given curve is rotated about the x-axis over the specified range of y and x, this integral will evaluate to the surface area achieved. This integral can be expressed in the simplest possible form as 01 x25x624x3+8 dx.

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The team that has the best record when compared to the other teams would be = team High - 5s which has the least number of losses.

The team with the best score can be calculated by finding the difference between the games and the losses.

The difference between games and losses of team Jule's Rules = 36-12 = 24.

The difference between games and losses of Pink Sox= 68-17 = 51

The difference between games and losses Go-Girls =

52-13 = 51

The difference between games and losses High-5s = 72-8 = 64

Therefore the team with the best record = team High - 5s which has the least number of losses.

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the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given The quotient of four is more than a number and seven is ten.

also given Use x for your variable.

In Mathematics, quotient literally means dividing a particular number by another number i.e the division of two (2) numbers.

Next, we would translate the word problem (sentence) into an algebraic expression as follows;

=> (x +4)/7 = 10

In conclusion, the algebraic expression for the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.

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Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.

The set of triangles with the same shape but different sizes are known as similar triangles. For example, all the equilateral triangles are similar triangles.

We can determine similar triangles by using the following conditions

Angle-Angle Similarity condition

Side-Angle-Side Similarity condition

Side-Side-Side Similarity condition

Here we have

Triangle OGD and triangle ATC  

From the given triangles

=> Side OD = Side AC   [ Equal sides ]

=> m ∠O = m ∠ A         [ Equal angles ]

=> m ∠G = m ∠T          [ Equal angles  ]

Hence, By the criteria of Side - Angle - Side given triangles are similar triangles.

Therefore,

Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.

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The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.

The concrete can be considered as in the shape of a cuboid.

Length = 18

Breadth = 24'

Height = 4"

Volume of Cuboid = Length * Breadth * Height

Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³

=5.34 cu.yard.

Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

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Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

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The child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.

A differential equation is an equation that contains one or more functions with its derivatives.

The distance between the kite and the child's hand level "d". Then, using the Pythagorean theorem, we can write:

d² + 105²= (165)²

d² = 165² - 105²

d = 129.1 ft

The length of the cord is increasing at a rate of 6 feet per second

Let us consider the length of the cord "L".

d² + L² = (165)²

Differentiating both sides with respect to time (t), we get:

2d(dd/dt) + 2L (dL/dt) = 0

We want to find (dL/dt) when L = 165 and d = 129.1.

(dL/dt) = -d × (dd/dt) / L

Substituting in the values we found for d and L, we get:

(dL/dt) = -(129.1 ft) × (0 ft/s) / (165 ft) = 0 ft/s

Therefore, the child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.

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The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.

a. P(A) = The probability that the first component drawn is defective = Number of defective components/Total number of components

= 300/1000 = 0.3

b. P(B|A) = The probability that the second component drawn is defective given the first component is defective = Number of defective components remaining/Total number of components remaining

= (300-1)/(1000-1) = 0.299

c. P(A∩B) = The probability that both components are defective = Number of defective components/Total number of components

= 300/1000 = 0.3

d. P(Ac∩B) = The probability that the first component is not defective and the second component is defective = Number of defective components/Total number of components

= 300/1000 = 0.3

e. P(B) = The probability that the second component drawn is defective = Number of defective components/Total number of components

= 300/1000 = 0.3

The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.

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The fair price to pay to play the game of rolling a colored die with three green sides, two red sides, and one blue side is; $2

How to Fair Price?

We are told that in the game of rolling the colored die;

- A roll of a red loses.

- A roll of blue pays 6.00.

- A roll of green pays 2.00.

Now, the best game to get the fairest price is to play; GGGRRB

Fair price = 2(3/6) + 6(1/6) + 0(2/6)

Fair price = $2

The thing that needs to be corrected in the diagram to fix the error is that the third arc should be drawn centered at F.

Given:

Constructing a parallel line to line AB and passing through point P.

To find:

An error occurred in the construction.

The procedure is,

However, the third arc is drawn centered at D. This is wrong.

Therefore, the correct step is that the third arc must be centered at F.

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The ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post, we need to find where should the stake be laced to use the least amount of rope,

Let rope of the 16 ft high pole be at x ft and that of 24 ft high pole at (30-x)

The structure of rope and poles are making a set of similar triangles, (refer to figure attached)

We know that, the corresponding sides of the similar triangle are in same ratio,

Therefore,

16 / x = 24 / (30-x)

2 / x = 3 / (30-x)

60 - 2x = 3x

5x = 60

x = 12

30-12 = 18

Hence, the ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

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The Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].

Any object sent into space with only gravity acting on it is considered a projectile. Gravity is the main force working on a projectile. This doesn't necessary imply that the other troops don't affect it; it merely means that their impact is far less than that of gravity. A projectile's route is known as its trajectory. When a particle is hurled obliquely near the surface of the earth, it flows along a curved route with constant acceleration directed towards the planet's center (we assume that the particle stays close to the surface). Such a particle's motion is referred to as projectile motion, and its route is a projectile.

(A) Time taken by the projectile to reach its maximum height which will be given as -

using the equation of motion (1), we get

Vy= V0 + a*t

So the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex]

And the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex]

Hence the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].

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m = -2, 0.  The function y = xm is a solution when m = -2 or 0.

For the differential equation xy'' + 2y' = 0, the function y = xm is a solution if m = -2 or 0. This can be seen by substitution and solving the resulting equation. When m = -2, the equation simplifies to 0 = 0, which is true. When m = 0, the equation simplifies to 0 = 2y', which is true when y' = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

To solve for m, first substitute the function y = xm into the differential equation, giving xm'' + 2mx' = 0. Then move all terms containing m to one side of the equation, leaving 0 on the other side. This gives m'' + 2m' = 0, which is a second-order linear differential equation. This equation can be solved using the characteristic equation, which is found by setting the discriminant of the equation equal to 0. The discriminant for this equation is 4 - 4(1)(0) = 4, which is greater than 0. Thus, the equation has two distinct real solutions, which are m = -2 and m = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

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The first and second models are linear regression models as it follow the general form, while the third model is not a linear regression model

Linear Regression is a statistical method used to model the relationship between a dependent variable (also known as the response or output variable) and one or more independent variables (also known as predictor or input variables). It assumes that there is a linear relationship between the independent variables and the dependent variable.

A linear regression model takes the form:

Y = β0 + β1X1 + β2X2 + ... + βnXn + ε

Where Y is the dependent variable, X1, X2, ..., Xn are the independent variables, β0, β1, β2, ..., βn are the coefficients that represent the slope of the line for each independent variable, and ε is the error term. The goal of linear regression is to estimate the coefficients β0, β1, β2, ..., βn so that the model can be used to make predictions about the dependent variable.

a. Y₁ = A + B₁X₁ + B₂X₂

This is a linear regression model, as the relationship between Y₁ and X₁, X₂ is linear, with the coefficients A, B₁, and B₂.

b. Y₁ = B₁X₁ + A

This is also a linear regression model, as the relationship between Y₁ and X₁ is linear with the coefficients A and B₁.

c. Y₁ = 1 + exp(-B₁ - B2X₁)

This is not a linear regression model, as the relationship between Y₁ and X₁ is not linear. It is not possible to convert it into a linear regression model by suitable algebraic manipulations.

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The required example of a function with a minimum at a value where its derivative is undefined is f(x) = |x|.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

A function that has a minimum at a point where its derivative is undefined is the absolute value function. The absolute value function is defined as:

f(x) = |x|

At x = 0, the absolute value function has a minimum value of 0. However, the derivative of the absolute value function is undefined at x = 0, because the function is not differentiable there.

At x < 0, the absolute value function is decreasing and therefore has a negative derivative. At x > 0, the absolute value function is increasing and therefore has a positive derivative. At x = 0, the behavior of the function changes abruptly from decreasing to increasing, which makes the derivative undefined. Despite this, the absolute value function still has a minimum value of 0 at x = 0.

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Answer:

12 / 1 and runner B

Step-by-step explanation:

at 13 seconds runner a had only run 156 ft, however runner b had run 200 ft.

The proceeds (discounted value) on the third-party discount note are $4,116.90.

The discounted value of a note is a value that is less than the maturity value.

The maturity value is the face value of the note plus the accumulated interest.

Face value of the note receivable = $4,000

Annual interest rate = 12%

Note issuance date = March 16

Note due date = November 14

The total number of days = 243 days

Discount date = June 11

Discount rate = 11%

March 16 to June 11 = 87 days

Interest on the note = $320 ($4,000 x 243/365 x 0.12)

Maturity value = $4,320 ($4,000 + $320)

Discount period = 156 days (243 - 87)

Discount on the note = $203.10 ($4,320 x 156/365 x 11%)

Discounted value = $4,116.90 ($4,320 - $203.10)

Thus, the man, who holds a note of $4,000 at 12% interest but sells it at a discount rate of 11%, will receive $4,116.90.

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Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data.

It is used to show the frequency of occurrence of different values within a set of data. In a histogram, the data is divided into a set of intervals or "bins," and the height of each bar represents the number of data points that fall within that bin.

The x-axis of a histogram typically represents the range of values in the data, while the y-axis represents the frequency of occurrence of those values. The bars are positioned so that they touch each other, indicating that the data is continuous and that there are no gaps between the bins.

Discrete data refers to data that can only take certain values within a defined range, such as the number of candies sold. Continuous data refers to data that can take any value within a defined range, such as swimming time.

To create a histogram for the swimming times, we first need to determine the range of the data and choose an appropriate interval width. In this case, the lowest value is 87 and the highest value is 136, so the range is 87 to 136. A suitable interval width could be 5. This would give us 11 intervals, from 85 to 90, 90 to 95, and so on, up to 135 to 140.

Next, we would tally the number of swimming times that fall into each interval and plot this information as bars on the histogram. The height of each bar represents the frequency of the interval.

Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data. Based on the shape of the histogram, we can make a guess as to where the average is likely to fall. If the histogram is symmetrical, the average is likely to be in the middle. If it is skewed, the average will be closer to the side with the longer bar. By drawing a vertical line labeled "My Guess" on the histogram, we can see how close our guess was to the actual average.

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Answer: A person who is eligible to use a 1040EZ form when filing a federal income tax return must meet certain criteria:

Must have taxable income of less than $100,000

Must not claim any dependents

Must only have wages, salaries, tips, taxable scholarship or fellowship grants, unemployment compensation, or Alaska Permanent Fund dividends, and your taxable interest is less than $1,500

Given these criteria, the correct answer is:

D. Single person, with no dependents, who made $49,000 last year.

Step-by-step explanation: