Shown are graphs of the position functions of two runners, A and B, who run a 100-m race and finish in a tie. (a) Describe and compare how the runners run the race. (b) At what time is the distance between the runners the greatest? (c) At what time do they have the same velocity?

2 - 2i is the quotient of these complex numbers (6-7i)-(4-5i).

A division is a process of splitting a specific amount into equal parts.

To find the quotient of complex numbers, we need to use the formula:

(a + bi) / (c + di) = [(a + bi) x (c - di)] / (c^2 + d^2)

where a, b, c, and d are real numbers and i is the imaginary unit.

In this case, we are subtracting two complex numbers:

(6-7i) - (4-5i)

= 6 - 7i - 4 + 5i (distribute the negative sign)

= 2 - 2i

Hence,  2 - 2i is the quotient of these complex numbers (6-7i)-(4-5i).

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Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Dylan's father's age is currently the square of Dylan's age. Dylan is 6 years old.

We can write Dylan's father's age as -

A{father} = A{Dylan} x A{Dylan}

A{father} = 6 x 6

A{father} = 36

Therefore, Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.

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{Question in english -
Dylan's father's age is currently the square of Dylan's age. If Dylan is 6 years old, how old is his dad?}

Answer:

This is a function because only one amount of plant food remain each day.

Step-by-step explanation:

A function is a relation where every input has only one output.

A relations is a set of ordered pairs like:

(1,5) (2,4) (3,3) (4,2)

Your input is the days and your output is the amount of food.  Each day the food is going down.  Each day would have a unique amount of food.

Taking into account the definition of a system of linear equations, the number of pennies and nickles that Arianys has is 15 and 6 respectively.

The degrees of systems of linear equations are groupings of linear equations with the same unknowns, of which it is necessary to find a common solution.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y = 21

0.01x + 0.05y = 0.45

There are several methods to solve a system of equations, it is decided to solve it using the graphical method, which consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.

In this case, graphing the system of equations (image attached) it is obtained that the system of intersection between both equations is (x,y)=(15,6). This means that the number of pennies that Arianys has is 15 and the number of nickels that Arianys has is 6.

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Answer:

x = 3, y = -1

Step-by-step explanation:

4x - 3y = 15

x + y = 2 -> y = 2 - x

4x - 3(2 - x) = 15

4x - 6 + 3x = 15

7x = 21

x = 3

y = 2 - x

y = 2 -3

y = -1

Answer: x =3, y = -1

Step-by-step explanation:

[tex]\bf{\underline{We\:solve\:by\:applying\:the\:reduction\:method.}}[/tex]

          [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{The\:exercise\:is \ ---\to \ \left \{ {{4x-3y=15} \atop {x+y=2 \ \ \ \ \ }} \right. } \end{gathered}$}}[/tex]

Multiply the second equation by -4, then add both equations.

  4x - 3y = 15

  -4(x + y = 2)

We add these equations to eliminate x.

    -7y = 7

Then we solve -7y = 7 for y. (We divide by 7)

        [tex]\bf{\dfrac{-7y}{ -7}=\dfrac{7}{-7} } \\ \\ \bf{y=-1}[/tex]

We place the found value of y , in one of the original equations y in order to solve for x:

        4x - 3y = 15

        4x - 3(-1) = 15

        3x + 4 = 15

We add (-3) to both sides.

     4x + 3 + (-3) = 15 + (-3)

      4x = 12

We divide both sides by 4.

         [tex]\bf{\dfrac{4x}{4}=\dfrac{12}{4} } \\ \\ \bf{x=3}[/tex]

Solution: x=3,y=-1

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Answer:

The given probability of Delta mishandling a bag is 1.35 per 1,000 passengers. This means the probability of not mishandling a bag is 1 - 1.35/1000 = 0.99865.

The probability of no mishandled bags in the next 1,000 passengers is:

P(no mishandled bags) = (0.99865)^1000 ≈ 0.716

The probability of at least one mishandled bag in the next 1,000 passengers is the complement of no mishandled bags:

P(at least one mishandled bag) = 1 - P(no mishandled bags) ≈ 0.284

To find the probability of at least two mishandled bags, we can use the binomial distribution formula:

P(at least two mishandled bags) = 1 - P(0 mishandled bags) - P(1 mishandled bag)

where P(0 mishandled bags) and P(1 mishandled bag) can be calculated using the binomial probability formula:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient.

For P(0 mishandled bags), we have n = 1000, k = 0, and p = 0.00135:

P(0 mishandled bags) = (1000 choose 0) * 0.00135^0 * 0.99865^1000 ≈ 0.716

For P(1 mishandled bag), we have n = 1000, k = 1, and p = 0.00135:

P(1 mishandled bag) = (1000 choose 1) * 0.00135^1 * 0.99865^999 ≈ 0.242

Therefore,

P(at least two mishandled bags) = 1 - 0.716 - 0.242 ≈ 0.042

Answer:

x^2+8x+15

x^2-2x+15

x^2-8x+15

2x^2&10x-28

Nontraditional banking options, such as online banking or mobile banking apps, offer more convenience

Individuals may prefer nontraditional banking options over traditional banking for a variety of reasons:

Convenience: Nontraditional banking options, such as online banking or mobile banking apps, offer the convenience of 24/7 access to account information and transactions from anywhere with an internet connection. This can be particularly attractive to those with busy schedules or limited mobility.

Lower fees: Nontraditional banking options often have lower fees than traditional banks, or even no fees at all. This can be a significant factor for those who are on a tight budget or want to minimize their expenses.

Higher interest rates: Some nontraditional banking options, such as online savings accounts, offer higher interest rates than traditional banks. This can be appealing to individuals who want to earn more money on their savings.

Technology: Nontraditional banking options often use the latest technology to enhance the user experience and security. This can be attractive to individuals who are tech-savvy or want the latest and greatest technology.

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The scores are measurements of a discrete variable is 10 and the median is 5.  The scores are measurements of a continuous variable is 10 and the median by locating the precise midpoint of the distribution is 5.

To find the median of a set of data, we first need to put the data in order.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

The median is the middle value when the data is in order. Since there are 10 scores, the middle two scores are the 5th and 6th scores, which are both 5. Therefore, the median is 5.

To find the median of a continuous variable, we also need to put the data in order, but this time we treat the scores as if they are measurements on a continuous scale.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Next, we locate the precise midpoint of the distribution. Since there are 10 scores, the midpoint falls between the 5th and 6th scores. The 5th score is 5 and the 6th score is also 5. Therefore, the midpoint is (5+5)/2 = 5.

So, the median is 5 when we treat the scores as measurements on a continuous scale.

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The equation of line is y = 5x + 3 , where the slope is m = 5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 3 )

Let the second point be Q ( 5 , 28 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 28 - 3 ) / ( 5 - 0 )

Slope m = 25 / 5 = 5

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 3 = 5 ( x - 0 )

On simplifying the equation , we get

y - 3 = 5x

Adding 3 on both sides of the equation ,  we get

y = 5x + 3

Hence , the equation of line is y = 5x + 3

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Assume n is odd. Since n^3 is odd, n^3 + 5 should be even, but it's odd. Therefore, n is even.

The correct ranking of the options is:

As n^3 and 5 are odd, their sum n^3 + 5 should be even, but it is given to be odd. This is a contradiction.

Suppose that n^3 + 5 is odd and that n is odd. We know that the sum of two odd numbers is even. As n is odd, n^3 is odd. Therefore, our supposition was wrong; hence n is even.

The proof by contradiction shows that the assumption that n is odd leads to a contradiction with the given fact that n^3 + 5 is odd. Therefore, the assumption that n is odd must be false, and hence n is even.

The proof begins by assuming that n is odd and showing that this leads to a contradiction with the given fact that n^3 + 5 is odd. Specifically, since the sum of two odd numbers is even, n^3 + 5 should be even if n is odd. However, we know that n^3 + 5 is odd, so our assumption that n is odd must be false, meaning that n is even.

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We can start by using the formula for inverse square law: F = k/d^2. where F is the force, d is the distance between the magnets, and k is a constant.

We can use the given information to solve for k: 4 = k/0.06^2, k = 4 * 0.06^2, k = 0.0144

Now we can use the value of k to find the force when the magnets are 0.03 meters and 0.1 meters apart: F1 = 0.0144/0.03^2 = 16, F2 = 0.0144/0.1^2 = 0.144

The work required to move the magnets is equal to the change in potential energy between the initial and final positions.

We can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy plus its change in potential energy. Since the magnets are not moving, their kinetic energy is constant, so the work done on them is equal to their change in potential energy: W = Uf - Ui

where W is the work, Uf is the final potential energy, and Ui is the initial potential energy. The potential energy of the magnets is given by: U = -k/d

where k is the constant we found earlier and d is the distance between the magnets.

Therefore, the initial potential energy is: Ui = -0.0144/0.03 = -0.48

And the final potential energy is: Uf = -0.0144/0.1 = -0.144

So the work required to move the magnets is: W = -0.144 - (-0.48) = 0.336 Joules

Therefore, the work required to move the magnets from 0.03 meters apart to 0.1 meters apart is 0.336 Joules (rounded to three decimal places).

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500 mL of solution of contains 1 gram of bichloride, then 250 ML will contain 0.5 gram of bichloride.

The mean and median of given data of population change for the ten most populous counties in the US from 2000 to 2010 is 7.2% and 6.25%.

To find the mean of the data, we need to add up all the percent changes and divide by the total number of counties:

Mean = (3.1 - 3.4 + 20.3 + 24.2 + 10.0 + 5.8 + 1.6 + 10.8 + 6.7 + 0.1) / 10 = 7.2%

Therefore, the mean percent change for the ten most populous counties in the US from 2000 to 2010 is 7.2%.

To find the median of the data, we first need to order the percent changes from smallest to largest:

-3.4, 0.1, 1.6, 3.1, 5.8, 6.7, 10.0, 10.8, 20.3, 24.2

Since there are an even number of values, the median is the average of the two middle values, which in this case are 5.8 and 6.7. Therefore, the median percent change for the ten most populous counties in the US from 2000 to 2010 is (5.8 + 6.7) / 2 = 6.25%.

The better description of the center of this data is the median, because it is less affected by outliers than the mean. In this case, the percent change for Maricopa County, AZ (24.2%) is much larger than the other values, and it pulls the mean upward. The median, on the other hand, is not affected by outliers, and it gives a better representation of the typical percent change for these counties.

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The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

X X^2

95 9025

96 9216

98 9604

Sum = 289 27845

n 3

The sample mean 96.33333333 SUM/n

Population mean 96.33333333 SUM/n

Sample standard dev [tex]1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population standard dev [tex]1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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Answer:

decrease by 21.04%

Step-by-step explanation:

18.82" - 14.86" = 3.96

percentage = 3.96/18.82

= 0.21041445271(100)

=21.04%

By solving an expression, we can find that the number of packs of paper that each classroom should get is 10/3.

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations. An example is the expression x + y, which combines the terms x and y with an addition operator. In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

Given,

Number of classrooms= 3

Number of packs of paper= 10

Now let the number of packs of paper per class be x.

x= Number of packs of paper/Number of classrooms

 = 10/3.

Therefore, each classroom will get 10/3 packs of paper.

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Answer:

A2 x average range

Step-by-step explanation:

Answer: [tex]x=3.5[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the number, then

[tex]\frac{1}{2}x=x-7\\\frac{1}{2}x-x=-7\\-\frac{1}{2}x=-7\\x=3.5[/tex]

a. n is 100 and p = 2 when we generate the simulated data set.

b. By generating a scatterplot we found a quadratic function. Y from -9 to 3 and x from -2 to 2.

c. Yes the result is the same as we got in question c.

d. Report of d is exactly the same because LOOCV will be the same since it evaluates n folds of a single observation.

e. The quadratic model and yes I expected that because the true data is of a quadratic form.

a. Generate a simulated data set.

set.seed(1)

Y <- rnorm(100)

X <- rnorm(100)

Y <- X - 2 × X² + rnorm(100)

n=100, p=2.

y=x−2x2+ϵ,ϵ∼N(0,1)

b. Create a scatterplot of X against Y . Comment on what you find.

ggplot(data.table(X=X, Y=Y), aes(x=X,y=Y)) + geom_point()

We can see a clear quadratic function. Y from -9 to 3 and x from -2 to 2.

c. Set a random seed, and then compute the LOOCV errors that result from fitting the following four models using least squares:

dt = data.table(X, Y)

# i

glm.fit1 <- glm(Y ~ X)

cv.glm(dt, glm.fit1)$delta

## [1] 5.890979 5.888812

# ii

glm.fit2 <- glm(Y ~ poly(X,2))

cv.glm(dt, glm.fit2)$delta

## [1] 1.086596 1.086326

# iii

glm.fit3 <- glm(Y ~ poly(X,3))

cv.glm(dt, glm.fit3)$delta

## [1] 1.102585 1.102227

# iv

glm.fit4 <- glm(Y ~ poly(X,4))

cv.glm(dt, glm.fit4)$delta

## [1] 1.114772 1.114334

d. Repeat (c) using another random seed, and report your results. Are your results the same as what you got in (c)? Why?

dt = data.table(X, Y)

set.seed(2)

# i

glm.fit1 <- glm(Y ~ X)

cv.glm(dt, glm.fit1)$delta

## [1] 5.890979 5.888812

# ii

glm.fit2 <- glm(Y ~ poly(X,2))

cv.glm(dt, glm.fit2)$delta

## [1] 1.086596 1.086326

# iii

glm.fit3 <- glm(Y ~ poly(X,3))

cv.glm(dt, glm.fit3)$delta

## [1] 1.102585 1.102227

# iv

glm.fit4 <- glm(Y ~ poly(X,4))

cv.glm(dt, glm.fit4)$delta

## [1] 1.114772 1.114334

Exact the same, because LOOCV will be the same since it evaluates n folds of a single observation.

e. The quadratic model and yes I expected that because the true data is of a quadratic form.

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When comparing exponential functions, the one with the bigger base expands more quickly. A logarithmic function grows more quickly if its argument is bigger.

Compared to polynomial functions, which in turn expand more quickly than logarithmic functions, exponential functions grow more quickly.

When comparing exponential functions, the one with the bigger base expands more quickly.

A logarithmic function grows more quickly if its argument is bigger.

We can arrange the provided functions in this manner by applying these rules:

log n, n, n log n, n, n2, n!, nn

Taking the function with the fastest rate of growth first: log n n n log n n 2

Each of these variables has a polynomial or logarithmic growth rate. The exponential functions will now be discussed:

2^n > n^2

Since polynomial functions increase more slowly than exponential functions, n2 grows more slowly than 2n.

The two categories with the fastest growth are: n! > n^2

n! grows more quickly than 2n and n2, as factorial functions expand even more quickly than exponential functions do. Finally:

n^n > n!

Therefore, nn grows more quickly than n! because exponential functions with bigger bases scale up more quickly than those with smaller bases.

Consequently, the following functions are listed in ascending order of growth rate:

log n n n log n n n log n n n! n n.

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The two transformations that can be applied are a horizontal translation of 2 units to the left or a vertical translation of 10 units up.

A general linear equation is written as:

f(x) = a*x + b

Here we can see that the two lines are parallel, so the transformations that can be applied are a vertical or an horizontal translation of N units.

The vertical translation is written as:

g(x) = f(x) + N

The horizontal one is:

g(x) = f(x + N).

B) now we need to solve this for both both of the transformations.

i) We can see that f(0) = -2 and g(0) = 8

For the first transformation we have:

g(0) =f(0) + N = 8

       = -2 + N = 8

                  N = 8 +2 = 10

For the second transformation:

g(0) = f(0 + N) = 8

We can see that f(x) = 8 for x = 2, then in this case N = 2.

Then we can have a translation of 2 units to the left or 10 units up.

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The correct statement regarding the function [tex]f(x) = \sqrt{-x}[/tex] is given as follows:

The domain of the graph is all real numbers less than or equal to zero.

For the square root function, the inside term cannot be negative, hence -x >= 0 -> x <= 0, meaning that the domain of the graph is all real numbers less than or equal to zero.

The square root assumes values of zero or greater, hence the range is of y >= 0.

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a) The probability P(X = 3) = 0.2916 represents the probability that exactly three of the four randomly selected households have cable TV.

b) The probability that all four selected households have cable TV is: 0.6561

c) P(x ≤ 3) = 0.9477

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability. The formula is:

P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)

where:

n = the number of trials.

x = number of times a particular outcome is attained.

p = probability of success.

a) We are given to calculate p(X = 3).

p = 0.90

n = 4

Thus:

P(X = 3) = ⁴C₃ * 0.9³ * (1 - 0.9)⁴⁻³

= 0.2916

This represents the probability that exactly three of the four randomly selected households have cable TV.

b) The probability p(4) is:

P(X = 4) = ⁴C₄ * 0.9⁴ * (1 - 0.9)⁴⁻⁴

= 0.6561

c) P(x ≤ 3)= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.9477

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The complete statement is 14 tires is 5.6% of 250 tires.

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

14 tires is% of 250 tires.

As an equation, we have

14 = x% * 250

Divide both sides of the equation by 250

So, we have the following representation

x% = 14/250

Evaluate

x% = 0.056

Multiply by 100

x = 5.6

Hence, the expression in the blank is 5.6

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Answer: V = 493.19

Step-by-step explanation:

V=1/3bh

7.6*12.4=94

94*15.7=1479.568

1479.568*1/3=493.19

Answer:

The formula to find the area of a regular pentagon (a polygon with five sides of equal length and equal interior angles) is:

Area = (1/4) * sqrt(5(5+2sqrt(5))) * s^2

Where s is the length of one side of the pentagon.

Step-by-step explanation: