The cheetah is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and is capable of speeds above 72 mph. The accompanying table contains a sample of the top speeds of 35 cheetahs. The sample mean and sample standard deviation of these speeds are 59.53 mph and 4.21 mph, respectively. A histogram of the speeds is bell-shaped Complete parts (a) through (d) below. Click the icon to view the top speeds of cheetahs. a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean? A. It is not reasonable to apply the empirical rule. The data is quantitative, but the value of k takes on values less than 1; therefore, the empirical rule is not appropriate. B. It is reasonable to apply the empirical rule. The data is quantitative and the mean and standard deviation are known; therefore, the empirical rule applies. C. It is not reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped, but this does not imply that the data itself is bell-shaped; therefore, the empirical rule is not appropriate. D. It is reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped; therefore, the empirical rule applies. b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean. Roughly 68% of observations lie within one standard deviation to either side of the mean. Roughly 95 % of observations lie within two standard deviations to either side of the mean. Roughly 99.7% of observations lie within three standard deviations to either side of the mean. (Type integers or decimals. Do not round.) c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean. Using the data.% of observations lie within one standard deviation to either side of the mean, % of observations lie within two standard deviations to either side of the mean, and % of observations lie within three standard deviations to either side of the mean. (Type integers or decimals. Round to one decimal place as needed.)

According to the information we can infer that the triangle and its internal angles are: 76.7°, 125.2°, and 21.9°.

To draw the triangle with the given measures we must take into account the internal angles so that the triangle is correct. Additionally we must take into account that it is a scalene triangle.

In this case, the internal angles are the most important part because it gives the shape of the triangle. These angles are:

So, according to the above, this triangles is scalene and its sides are:

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Answer:

14

Step-by-step explanation:

From the question we are given the first term 8,second term 11 and we are to find the third term.

Using the formula:Tn=a+(n-1)d

Where a=first term=8

n=number of terms =3

d= difference between terms( second term -first term)=11-8=3

T3=8+(3-1)3

=8+2(3)

=8+6

The next term =14

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

i think the answer is infinitely many solutions

i am not sure tho

hope it helps

The value of x in the given equation, 6x + 1.6 = 58, is x = 9.4

From the question, we are to determine the value of x in the given equation.

The given equation is

6x + 1.6 = 58

To determine the value of x in the equation, we will determine the value of the unknown variable.

The unknown variable in the given equation is x.

Thus, we will determine the value of x.

Solving the equation for x

6x + 1.6 = 58

Subtract 1.6 from both sides of the equation

6x + 1.6 - 1.6 = 58 - 1.6

6x = 56.4

Divide both sides of the equation by 6

6x/6 = 56.4/6

x = 9.4

Hence, the equation solved for x gives x = 9.4

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Answer:

Step-by-step explanation:

Standard form of the equation:

y  = \(-\frac{1}{4} (x+3)^2+3\)

Directrix: y=4

Focus: (-3,2)

Points on the parabola (x,y):

(-5,2) (-3,3) (-1,2)

Distance from points to focus:

(-5,2) = (-3,2)

Answer choices:  (x+3)^2+(y−3)^2, (x−2)2+(y+3)2, (x+3)2+(y−2)2

(-5+3)^2+(2-3)^2=5

(-5-2)^2+(2+3)^2=74

(-5+3)^2+(2-2)^2=4

(-1,2)

Answer:

0.2x-0.8

Step-by-step explanation:

In 0.2(x-4), you can multiply 0.2(The number outside of the parentheses) by the numbers inside the parentheses. So, it would be 0.2*x-0.2*4, which is 0.2x-0.2(4), which is 0.2x-0.8.

The probability that no two adjacent people would stand is option C: 49/256, as there are 256 distinct counting rotations.

First, we assume that one person stands up. There are 8 possible ways to select which person does. We can, next, assume that no two adjacent people stand up. There are 4 ways to choose which of the remaining 7 people will stand up (since no two adjacent people can stand up).

Then, we can assume that no two adjacent people stand up again. There are 3 ways to choose which of the remaining 6 people will stand up (since no two adjacent people can stand up).

We continue this process until there is only one person left who can stand up.

The number of arrangements according to the number of people standing.

Therefore, the number of arrangements that no two adjacent people will stand.

n(S) = 1 + 8 + 20 + 16 + 2 + 2 = 49

The total number of possible outcomes is:

2⁸ = 256

So, the probability that no two adjacent people will stand would be:

= 49/256.

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Complete question is:

Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?

(a) 47/256

(b) 3/16

(c) 49/256

(d) 25//128

(e) 51/256

Answer:

A

Step-by-step explanation:

i think this is right tell me if this helps

Answer:

its A

Step-by-step explanation:

i know because i just tested it out and i got it correct

Answer:

d

Step-by-step explanation:

-3(4x+2)-2x

-12x+6-2x

-14x+6

Answer:

*error* error* This account is here to assist CodeName: ELA/ LANGUAGE ARTS/ ENGLISH. Please say RESET in order for me to go back to ELA/ LANGUAGE ARTS/ ENGLISH.

Step-by-step explanation:

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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To ensure that each of the three friends has a fair chance of being selected to drive first on their road trip, they can use the method of flipping a coin. Here's a step-by-step explanation:
1. Mark, Anthony, and Derek can gather together and agree to use a coin flip method to determine who will drive first.
2. They can designate one person to be the flipper, who will toss the coin into the air.
3. Before flipping the coin, they should establish what each side of the coin represents. For example, they can agree that heads means Mark drives first and tails means Anthony drives first.
4. The flipper then tosses the coin into the air, allowing it to spin and fall back down.
5. Once the coin lands, they can check the result and determine who will drive first based on the agreed-upon assignment for each side of the coin.
6. If Mark and Anthony are not selected to drive first, it automatically means that Derek will be the one to drive first.

Using the coin flip method ensures fairness because it provides an equal chance for each friend to be selected. It relies on chance rather than personal preferences or biases, making it an unbiased way to decide who will drive first on their road trip.

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Answer:

I believe the answer is D. a = 3 m/s²

Step-by-step explanation:

In the formula a = \(\frac{F}{m}\) we need F (force) and m (mass) in order to find a.

F = 150 N

m = 50 kg

so put these numbers into the equation.

a = \(\frac{150}{50}\)

Then finally solve for a by dividing.

a = 3

The equation of the trajectory which can be described using the equations for projectile motion is; y(t) = x·tan(θ) - g·x²/(2·v₀²·cos²(θ)), which is a quadratic equation with a path of a parabola

Projectile motion is the motion of an object that is projected in the air under the influence of gravitational attraction.

Let θ represent the angle at which the path of the object makes with the horizontal, and let v₀ represent the velocity of the object. The path of the object can be described using the equations of the motion of a projectile, as follows;

Horizontal component of the velocity, v₀ₓ = v₀ × cos(θ)

Vertical component of the velocity, \(v_{0y}\) = v₀ × sin(θ)

The horizontal motion of the object is therefore;

x(t) = v₀ₓ × t = v₀ × cos(θ) × t

The vertical motion which is under the influence of gravity is; y(t) = \(v_{0y}\)  × t - (1/2) × g × t²

v₀ × sin(θ) × t - (1/2) × g × t²

The horizontal component indicates that we get;

t = x/(v₀ × cos(θ))

Plugging in the above expression for t into the equation for y(t), we get;

y(t) = \(v_{0y}\)  × t - (1/2) × g × t² = \(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

\(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = (v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

(v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = x·tan(θ) - g·x²/(2·v₀×cos(θ))²

The equation, y = x·tan(θ) - g·x²/(2·v₀×cos(θ))², is a quadratic equation, which is an equation of a parabola, therefore, the trajectory of an object thrown at an angle to the horizontal is a parabola.

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Answer:

$0.8 or better known as answer C

Step-by-step explanation:

If the rank of matrix A is equal to the number of columns of A, and the rank of matrix A is equal to the rank of the augmented matrix [A|b], then the system Ax = b will have a unique solution for all choices of b. Otherwise, the system Ax = b will not have a unique solution for all choices of b.

To determine if the system ax = b has a solution for all choices of b, we need to look at the rank of the matrix A and the rank of the matrix formed by appending the vector b to the matrix A.

The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of matrix A is equal to the number of columns in A, then matrix A is full rank and the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the number of columns in A, then matrix A is not full rank, and the system Ax = b will not have a unique solution for all choices of b.

If the rank of matrix A is equal to the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will not have a unique solution for all choices of b.

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The upper and lower 3-sigma control chart limits for this DNA sample data are UCL = 18.53 and LCL = 0

When we are given data on the DNA samples taken over the past 10 days, we can calculate the upper and lower 3-sigma control chart limits. The sample size is 100, and the defective number of DNA samples is given for each of the ten days.

The 3-sigma control limits for a process control chart can be calculated using the following formula: Upper control limit (UCL) = Mean + (3 × Standard Deviation) and Lower control limit (LCL) = Mean - (3 × Standard Deviation),where the mean is the average value of the data, and the standard deviation is the spread of the data around the mean.

Here, we need to calculate the mean and standard deviation of the defective samples for the past 10 days. The average number of defectives per day (mean) is (7+9+9+11+7+8+0+11+13+2) / 10 = 77 / 10 = 7.7

To calculate the standard deviation, firstly, calculate the variance: variance = sum of the squared differences from the mean divided by the number of samples = \([(7-7.7)^2 + (9-7.7)^2 + ... + (2-7.7)^2] / 10\)  ≈ 13.01 2.. Now, take the square root of the variance which gives standard deviation. So, standard deviation = \(\sqrt{13.01\\}\) ≈ 3.61

Using the 3-sigma rule UCL = Mean + (3 * Standard Deviation) = 7.7 + (3 * 3.61) ≈ 18.53    and   LCL = Mean - (3 * Standard Deviation) = 7.7 - (3 * 3.61) ≈ -3.13. However, since the LCL cannot be negative, we set it to 0 in this context. So, the upper and lower 3-sigma control chart limits are: UCL = 18.53 LCL = 0

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Answer: C

Work: So, after you simplify that equation, it's 8/0. You Cannot divide zero like that. You can divide 0/8, but you can't with 8/0. I hope this wasn't to confusing, and Happy Holidays! :)

The type of symmetry it possesses is: Reflection symmetry about the line x = 7

We are given the coordinates of the vertices of the kite as:

(5, 6), (7, 9), (9, 6) and (7, 1)

Now, looking critically at the kite with the vertices, we can tell that it is a reflection symmetry because reflection symmetry is a type of symmetry related to reflection. Reflection symmetry is also called line symmetry or reflection symmetry. It states that there is at least one line dividing a figure in half, and that one half is the mirror image of the other.

Thus, we conclude that the type of symmetry  it possesses is: reflection symmetry about the line x=7

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Answer: I wish to help you but there are question error signs that show the symbol is not valid to be shown. It shows theit shws "�" symbol and I don't know what it means.

Step-by-step explanation:

The measure of the arc KL and MJ in the given attached figure is equal to = 20° and 80°.

Measure of angle MEJ = 30 degrees

Measure of angle MFJ = 50 degrees

In the attached figure apply angle intersecting secant theorem we get,

m∠MEJ = 1/2(MJ - KL)

Substitute the value of m∠MEJ = 30 degrees we get,

⇒30° = 1/2(MJ - KL)

Multiply both the side by 2 we get,

⇒60° = MJ - KL

⇒ KL = MJ - 60°

Now , we have from the attached figure,

m∠MFJ = 1/2(MJ + KL)

⇒50° = 1/2(MJ + MJ - 60°)

⇒100° = 2MJ - 60°

⇒2MJ = 100° + 60°

⇒2MJ = 160°

⇒MJ = 160°/2

⇒MJ = 80°

⇒KL = MJ - 60°

       = 80° - 60°

This implies that,

KL = 20°

Therefore, the measures of the arcs are equal to measure of arc KL = 20° and MJ = 80°.

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The above question is incomplete, the complete question is:

Given: m∠MEJ=30, m∠MFJ=50

Find the measure of the arc KL, MJ.

Attached figure.

The answer, Arianna's battery, as a percentage, 3.75t hours after Arianna left her house.

What is percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.

The initial charge of Arianna's phone = 45%

now the charge remaining in Arianna's battery = 15%

If after 4 hours of leaving her house, the battery had 15% remaining battery life, then the battery is discharging at the rate of ( 15% / 4 hours)

=3.75% per hour.

Thus, the charge remaining in Arianna's battery after she left her house will be, B = 3.75t

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Answer:

Its not a perfect square

Step-by-step explanation:

To solve this problem, we will follow the steps below;

If length of the legs of the triangle are 4 inches and 6 inches, to find the length of the hypotenuse, we will simply use the formula from the hypotenuse triangle;

hypotenuse² = opposite² + adjacent²

                  = 4²  +  6²

                  = 16 + 36

hypotenuse² = 52

hypotenuse = √52

hypotenuse =7.2111025509.........

Therefore hypotenuse is not a rational number because the 52 is not a perfect square and thus √52 has an unending values

The value of the given double integral ∫[0 to 1]∫[x to 1] 8 +\(y^3 dy dx,\)evaluated by switching the order of integration, is 41/20.

a) To find the critical points of the function f(x, y) = xy(2y + xy + \(y^2),\) we need to find the values of x and y where the partial derivatives of f with respect to x and y are equal to zero.

Partial derivative with respect to x:

∂f/∂x = y\((2y + xy + y^2) + xy(0 + y + 2y)\)=\(y(2y + xy + y^2) + 3xy^2 = 0\)

Partial derivative with respect to y:

∂f/∂y = \(x(2y + xy + y^2) + xy(2 + 2y) = x(2y + xy + y^2) + 2xy + 2xy^2 = 0\)

Setting both partial derivatives equal to zero, we have the following system of equations:

\(y(2y + xy + y^2) + 3xy^2 = 0 ...(1)\)

\(x(2y + xy + y^2) + 2xy + 2xy^2 = 0 ...(2)\)

Simplifying equation (1):

\(2y^2 + xy^2 + y^3 + 3xy^2 = 0y^3 + 5xy^2 + xy^2 + 2y^2 = 0y^3 + 6xy^2 + 2y^2 = 0y^2(y + 6x + 2) = 0\)

From this equation, we have two possibilities:

\(y^2 = 0 = > y = 0y + 6x + 2 = 0 = > y = -6x - 2 ...(3)\)

Now, substituting equation (3) into equation (2):

\(x(2(-6x - 2) + x(-6x - 2) + (-6x - 2)^2) + 2x(-6x - 2) + 2x(-6x - 2)^2 = 0x(-12x - 4 - 6x^2 - 2x^2 - 24x - 8 + 12x^2 + 4x + 24x + 8) + 2(-6x - 2) + 2(-6x - 2)^2 = 0-20x - 6x^2 - 48x + 20x^2 + 4x + 2 + 2(-6x - 2) + 2(36x^2 + 24x + 4) = 020x^2 - 6x^2 - 48x + 20x - 20x - 48x + 4x + 12x + 2 + 72x^2 + 48x + 8 = 086x^2 - 12x^2 - 48x + 72x = 074x^2 + 24x = 02x(37x + 12) = 0\)

From this equation, we have two possibilities:

2x = 0 => x = 0

37x + 12 = 0 => x = -12/37 ...(4)

Now, substituting x = 0 into equation (3):

y = -6(0) - 2

y = -2

So one critical point is (0, -2).

Substituting x = -12/37 into equation (3):

y = -6(-12/37) - 2

y = 72/37 - 2

y = (72 - 74)/37

y = -2/37

So another critical point is (-12/37, -2/37).

Therefore, the critical points of the function f(x, y) = \(xy(2y + xy + y^2)\)are (0, -2) and (-12/37, -2/37).

b) To classify the critical points, we need to use the second partial derivative test. Let's calculate the second partial derivatives:

Second partial derivative with respect to x:

∂^2f/∂x^2 = \(0 + y(0 + y + 2) + 3y^2 = y^2 + 2y + 3y^2 = 4y^2 + 2y ...(5)\)

Second partial derivative with respect to y:

∂^2f/∂y^2 = \(x(2 + 2y) + x(2 + 2y) + 2x = 4xy + 4xy + 2x = 8xy + 2x ...(6)\)

Mixed partial derivative:

∂^2f/∂y∂x = ∂^2f/∂x∂y = 2y + x(2 + 2y) + 3xy = 2y + 2xy + 2xy + 3xy = 7xy + 2y ...(7)

Now, let's evaluate the second partial derivatives at each critical point:

For the critical point (0, -2):

∂^2f/∂x^2 = 4(-2)^2 + 2(-2) = 16 - 4 = 12

∂^2f/∂y^2 = 8(0)(-2) + 2(0) = 0

∂^2f/∂y∂x = 7(0)(-2) + 2(-2) = 0 - 4 = -4

For the critical point (-12/37, -2/37):

∂^2f/∂x^2 = 4(-2/37)^2 + 2(-2/37) = 16/37 - 4/37 = 12/37

∂^2f/∂y^2 = 8(-12/37)(-2/37) + 2(-12/37) = 192/1369 + (-24/37) = 192/1369 - 888/1369 = -696/1369

∂^2f/∂y∂x = 7(-2/37)(-2/37) + 2(-2/37) = 28/1369 - 74/37 = 28/1369 - 2666/1369 = -2638/1369

Using the second partial derivative test:

For the critical point (0, -2):

The discriminant D = (∂^2f/∂x^2)(∂^2f/∂y^2) - (∂^2f/∂y∂x)^2 = (12)(0) - (-4)^2 = 0 - 16 = -16

Since D < 0 and ∂^2f/∂x^2 > 0, the critical point (0, -2) is a saddle point.

For the critical point (-12/37, -2/37):

The discriminant D = (∂^2f/∂x^2)(∂^2f/∂y^2) - (∂^2f/∂y∂x)^2 = (12/37)(-696/1369) - (-2638/1369)^2

Simplifying the expression, we find D = -696/1369 + 6944/1369 = 6248/1369 > 0

Since D > 0 and ∂^2f/∂x^2 > 0, the critical point (-12/37, -2/37) is a local minimum.

Therefore, the critical point (0, -2) is a saddle point, and the critical point (-12/37, -2/37) is a local minimum.

c) To evaluate the given double integral ∫[0 to 1]∫[x to 1] 8 + \(y^3 dy\) dx by switching the order of integration, we need to express the limits of integration in terms of the opposite variable.

The original limits of integration are:

x varies from 0 to 1

y varies from x to 1

To switch the order of integration, we need to rewrite these limits in terms of y as the outer integral and x as the inner integral.

The new limits of integration are:

y varies from 0 to 1

x varies from 0 to y

Therefore, the double integral becomes:

∫[0 to 1]∫[0 to y] \(8 + y^3 dx dy\)

Now, let's evaluate the integral:

∫[0 to y] 8 +\(y^3 dx = (8x + (1/4)y^4)[0 to y] = (8y + (1/4)y^4) - (0 + 0) = 8y + (1/4)y^4\)

∫[0 to 1] \((8y + (1/4)y^4) dy = (4y^2/2 + (1/5)y^5/20)[0 to 1] = (2 + 1/20) - (0 + 0) = 41/20\)

Therefore, the value of the given double integral ∫[0 to 1]∫[x to 1] 8 + y^3 dy dx, evaluated by switching the order of integration, is 41/20.

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The person that has a better performance is Puja Limbu.

From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:

= 8/10 × 100

= 80%

Raju Lama did 11 out of 15 similar math problem. This will be:

= 11/15 × 100

= 73%

Therefore, Puja has a better performance.

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The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].

Part I: Effective cost per hour per employee

To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.

Base hourly wage: $12.30 per hour

Number of working hours per day: 8 (1 shift)

Number of holidays: 5

Number of vacation days: 7

First, let's calculate the total fringe benefits per hour:

Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551

Next, let's calculate the paid time off per hour:

Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours

Now, let's calculate the effective cost per hour per employee:

Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)

Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)

Part II: Reduction in labor cost

To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.

Number of working hours needed every year: 306,050

Productivity increase from 70% to 85%: 85% - 70% = 15%

First, let's calculate the initial number of workers needed:

Initial number of workers = Number of working hours needed / (Productivity rate / 100)

Initial number of workers = 306,050 / (70 / 100)

Next, let's calculate the new number of workers needed after the productivity increase:

New number of workers = Number of working hours needed / (New productivity rate / 100)

New number of workers = 306,050 / (85 / 100)

Finally, let's calculate the total dollar change in labor expense:

Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year

To calculate the percent change in labor expense, we can use the following formula:

Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100

Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.

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The standard format for electronic document submission in U.S. federal courts is PDF (Portable Document Format).

PDF, or Portable Document Format, is a widely used file format that allows for the electronic representation of documents. It is designed to be platform-independent, meaning it can be viewed and accessed on different devices and operating systems while retaining its original formatting. In the context of U.S. federal courts, PDF has become the standard format for attorneys to submit documents electronically.

The adoption of PDF as the standard format for electronic document submission in U.S. federal courts brings several advantages. PDF files are generally compact in size, making them easier to transmit and store. They also preserve the interest, fonts, and graphics of the original document, ensuring that the submitted materials are accurately represented.

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Answer:

graph 19 because since it is that means also like the thingy equals that number si then like when the thing is at the highest point it cab maybe actually it will equal that number