For breakfast, Mr. Hill bought a cup of coffee for $1.39 and a bagel for $1.85. What was his total cost?

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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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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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 population in the year 2000 is 1230  students.

The equation for the population, P, of the school t years after 2000 is P = 53t + 1389.

The population of the school in 2015 in 2025 students

The starting population in 2003 is 1389.

average population growth per year = 53

The population in the year 2000 will be:

number of year = 2000 - 2003 = -3  (3 years back)

population in the year 2000 = 1389 -3(53) = 1230

To find an equation for the population, P, of the school t years after 2000. We can write:

P = 53t + 1389

Using your equation, predict the population of the school in 2015:

t = 2015 - 2003 = 12

P = 53t + 1389

P = 53(12) + 1389

P = 2025 students

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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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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:

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 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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An expression that calculates the time in hours a person takes to walk 35 miles at a speed of 5 miles/hour is: T = 35/5 = 7 hours.

In Mathematics, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Making time the subject of formula, we have:

Time = distance/speed

Time = 35/5

Time = 7 hours.

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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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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 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 required ATP singles rankings for tennis players rank is false.

An interval scale is a type of measurement scale that has equal units of measurement and a zero point, meaning that differences between scale values can be meaningfully compared, but there is no meaningful interpretation of the zero point.

In tennis, ranking points are assigned based on a player's performance in a set number of tournaments over a rolling 52-week period, but the actual number of points assigned to a player is not an interval scale.

Thus, it is incorrect to say that the ATP singles rankings for tennis players are an example of an interval scale.

The given statement is false.

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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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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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Step-by-step explanation:

14/16 = 7/8

3/12 = 1/4

16/28 = 4/7

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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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!!!!!!

The area of figure above is a) 6cm²

In addition to the circumference, a square shape also has an area, where the area of a square is calculated by squaring the length of its side.

Formula: Area of square= s²

The question above, the side of square is 1 cm.

so the area of one small square is 1×1= 1cm²

Because the shape is contain of 6 small square, therefore the total area is 6×1cm²=6cm²

A square has the following properties

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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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Years: 2.455 years

Amounts: $843 billions

This can be solved by using equation solving method.

An expense classified as personal is one that is not related to a trade or enterprise, a passive activity, or an investment. Personal consumption spending is often divided into two categories: goods and services. Groceries, automobiles, and fuel are a few examples of products. Rent, medical treatment, and insurance are a few examples of services.

f(x) = 40.74x + 742.65

h(x) = 47.93x +725

For f(x) = h(x),

40.74x + 742.65 = 47.93x +725

47.93x - 40.74x = 742.65 - 725

x (47.93-40.74) = 17.65

x = 17.65 /7.19 = 2.455 years.

2.455 years after 1995, that is in 1998, these expenditures would be equal to each other.

The amount spent on each would be :-

40.74(2.455) + 742.65 = $842.667

= $843 billions.

Years: 2.455 years

Amounts: $843 billions

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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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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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Answer:

Correct option is C)

Given s= 7m, h=9 m

Lateral surface area = Area of the curved surface =2πrh=2×

7

22

×7m×9m=396m

2

Total surface area = Area of curved surface + Area of two circular surfaces

=2πrh+2πr

2

=396m

2

+2×

7

22

×7m×7m=(396+308)m

2

=704m

2

The surface area of cylinder B is 548 square km.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, cylinder B is the image of cylinder A after dilation by a scale factor of 4.

The surface area of cylinder A is 137 km².

Then the surface area of cylinder B is 4×137

= 548 square km.

Therefore, the surface area of cylinder B is 548 square km.

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The total cost to purchase a tarp that is the same size as Keith's tent is given as follows:

$24.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

The dimensions for the tarp in this problem are given as follows:

Hence the area is given as follows:

A = 3 x 8 = 24 square feet.

As the cost is $1.00 per square feet and there are 24 square feet, the total cost is given as follows:

$24.00.

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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 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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Answer: 396

Step-by-step explanation:

length- x+4

width - x

perimeter = 40

40 = x+4+x

40-4=2x

36=2x

x=18

length - 18+4=22

width - 18

area = 22*18 = 396

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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