An input-output machine generates the information below

a- Find the values to fill in the table for variables a and b
b- write up a rule that describes the relationship between the input output.
c- what is the value of the output and input in 20?
d- what is the value of the input when the output is 77.

Answer:

B).150ft

Explanation:

The distance from homeplate to 1st Base = 90 feet

Therefore: distance from homeplate to point P is:

The distance from homeplate to 3rd base is 90 feet.

We see that the problem forms a right-triangle where the distance from point P to 3rd Base is the Hypotenuse.

Using Pythagoras Theorem:

The player threw the ball a distance of 150 feet.

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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Two triangles are congruent if corresponding sides and corresponding angles are congruent. The correct option is A.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.

Therefore, two triangles are congruent if corresponding sides and corresponding angles are congruent. The correct option is A.

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The amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

We should know that we have to deduct the tip for excellent driving g before adding up the tax to the total first.

The given parameters are

Bill =$65

Tax rate= 7%

Tip for excellent driving =20%

First deduct 0.2*65

=13

Balance = $(65-13)

Balance= $52.00

Tax = 0.07*65

Tax = 4.55

Then $(52.00+4.55)

= $56.55

In conclusion, the amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

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Answer:

18in of rapping paper

Step-by-step explanation:

a rubics cube has 6 sides so 6x3=18

Answer: imaginary axis

Step-by-step explanation:

The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.

The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.

In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.

Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.

The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .

The given question is incomplete , the complete question is

What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?

(a) Descriptive

(b) Inferential

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Answer:

23

Step-by-step explanation:

Since Jungkook's birthday is on September 1, 1997, that makes him 22 for now. When September 1st, 2020 occurs, he will be 23.

Answer:d=7

Step-by-step explanation:

Easy math

Answer:

d

Step-by-step explanation:

527 / 17 = 31

Steps to calculate the area are shown below and the figure is attached below.

The steps of calculating the area of the given figure are,

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Answer:64

Step-by-step explanation:

1/2 of 6 = 3

his brother was 3 years older than him when he was 3. meaning his brother was 6.

67 (his brothers age) - 3 = 64

he is 64 years old

Answer:

275 * 0.03 = accrued interest

accrued interest + initial deposit = total after one year

Step-by-step explanation:

The optima of the Lagrangian objective function is minimized at z = 54,000. Also the Lagrange multiplier solution corresponds to a minimum.

The optimal values for the Lagrangian objective function can be determined by solving the given optimization problem using Lagrange multipliers. We have the objective function z = 6x₁² + 12x₂² and the constraint g(x₁, x₂) = 90 = x₁ + x₂.

To find the optimal values, we form the Lagrangian function L(x₁, x₂, λ) = f(x₁, x₂) - λ(g(x₁, x₂) - 90). Here, λ is the Lagrange multiplier.

Taking the partial derivatives with respect to x₁, x₂, and λ, and setting them to zero, we obtain the following equations:

∂L/∂x₁ = 12x₁ - λ = 0

∂L/∂x₂ = 24x₂ - λ = 0

∂L/∂λ = x₁ + x₂ - 90 = 0

Solving these equations simultaneously, we find x₁ = 30, x₂ = 60, and λ = 360. Substituting these values back into the objective function, we get z = 6(30)² + 12(60)² = 54,000.

To determine whether this is a maximum or minimum, we can examine the second partial derivatives of the Lagrangian. Calculating the second partial derivatives, we have:

∂²L/∂x₁² = 12

∂²L/∂x₂² = 24

Since both second partial derivatives are positive, we can conclude that the Lagrange multiplier solution corresponds to a minimum. Therefore, the optima of the Lagrangian objective function is minimized at z = 54,000.

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Thus, the volume of Pyramid with the given base and height is found as:  

2342.925 sq. km.

A pyramid is just a polyhedron with a polygonal base and triangles on all of its lateral faces. In this lesson, we will only focus on pyramids with lateral faces that are congruent, or identical in size and shape.

Given data:

Volume of Pyramid:

V = base area * height

Base area = 1/2*base*height

Base area = 1/2*26.7*11.7

Base area =  156.195 sq.km.

Now,

Volume of Pyramid =  156.195 * 15

Volume of Pyramid =  2342.925 sq. km.

Thus, the volume of Pyramid with the given base and height is found as:  

2342.925 sq. km.

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Complete question:

find the Volume of Pyramid:

Base length = 26.7 km

base width = 11.7 km

Height = 15 km

Answer:

d. 60m=w

Step-by-step explanation:

because in 1 minute he writes 60 words

in 2 mins he will write 60*2= 120 words

and so on

The correct option is 20.

The score found for the sample is 20.

A standard error is a statistic that is applied to test the distribution of data. This metric is comparable to standard deviation. We can calculate the standard error if we know the sample size & standard deviation. It assesses the mean's precision.

Now, according to the question;

Sample mean; \(\bar{x}=40\)

Sample variance; \(s^{2}=20\)

Thus, \(s=\sqrt{20}=4.47\)

Standard error SE = 1

The amount of scores with in sample must be determined here.

The standard error formula is as follows:

\(S E=\frac{s}{\sqrt{n}}\)

We might rearrange the formula as follows:

\(\begin{aligned}\sqrt{n} &=\frac{s}{S E} \\n &=\left(\frac{s}{S E}\right)^{2}\end{aligned}\)

Substituting the values;

\(\begin{aligned}&n=\left(\frac{4.47}{1}\right)^{2} \\&n=19.98\end{aligned}\)

The sample's number of scores n = 19.98 = 20 (round up)

Therefore, the scores are in the sample is 20.

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Using a system of equations, it is found that Sana's mother bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

She bought one more pound of peaches than pounds of tomatoes, hence:

x = y + 1.

y = x - 1.

She bought 3 times as many pounds of tomatoes as pounds of mushrooms, hence:

x = 3z.

y = x - 1 = 3z - 1.

She spent a total of $80, hence considering the cost per pound of each product we have that:

6x + 3y + 10z = 80.

Considering the values of x and y as function of z and replacing in the equation, we have that:

6(3z) + 3(3z - 1) + 10z = 80

18z + 9z - 3 + 10z = 80.

37z = 83.

z = 83/37

z = 2.24.

Then:

x = 3z = 3 x 2.24 = 6.72.

y = x - 1 = 3z - 1 = 6.72 - 1 = 5.72.

Hence, she bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.

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7 lbs peaches, 6 lbs tomatoes, 2 lbs mushrooms

yum!

The equation of the line that lies entirely in the set defined by the equation x²y² - z² = 1 is 2x²y² - 2x² - 2y² + 2 = 0.

A line that lies entirely in the set defined by the equation x²y² - z² = 1 can be found using the following steps:1. Choose an arbitrary point on the surface defined by the equation, such as (1, 0, 0).2.

Take the partial derivative of the equation with respect to x, y, and z. In this case, we get:2x * y² - 2z * dz/dx = 02y * x² + 2z * dz/dy = 02z * -1 = -2z3. Evaluate the partial derivatives at the point chosen in step 1.

For our point (1, 0, 0), the partial derivatives are:-2 * 0 = 0-2 * 0 = 02 * -1 = -24. Use the partial derivatives to find the equation of the tangent plane to the surface at the chosen point.

The equation of the tangent plane is:0(x - 1) + 0(y - 0) - 2z(z - 0) = 0-2z² = 05. Solve for z in terms of x and y using the equation of the surface:x²y² - z² = 1z = ±√(x²y² - 1)6.

Substitute z in the equation of the tangent plane with the expression obtained in step 5:-2(x - 1)²y² + 2(x²y² - 1) = 07.

Simplify the resulting equation to obtain the equation of the line that lies entirely in the set defined by the original equation:2x²y² - 2x² - 2y² + 2 = 0.

Given the equation x²y² - z² = 1, the task is to find a line that lies entirely in the set defined by this equation.

This can be done by finding the equation of the tangent plane to the surface at a chosen point and then intersecting it with the surface to obtain the equation of the line.

We start by choosing an arbitrary point on the surface, such as (1, 0, 0). We then take the partial derivative of the equation with respect to x, y, and z, and evaluate them at the chosen point. This gives us the normal vector to the tangent plane to the surface at that point.

Using the point-normal form of the equation of a plane, we obtain the equation of the tangent plane.

We then solve for z in terms of x and y using the equation of the surface and substitute it into the equation of the tangent plane.

This gives us a simplified equation that describes the intersection of the tangent plane and the surface.

This equation can be further simplified to obtain the equation of the line that lies entirely in the set defined by the original equation. In this case, we get the equation 2x²y² - 2x² - 2y² + 2 = 0. This is the equation of a hyperbola that lies entirely in the set defined by x²y² - z² = 1.

Therefore, the equation of the line that lies entirely in the set defined by the equation x²y² - z² = 1 is 2x²y² - 2x² - 2y² + 2 = 0.

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Answer:

t = 14.82 and 2.72secs

Step-by-step explanation:

Given the function of the rocket height expressed as;

h(t) = -4.9t^2+ 86t + 2.1

if the rocket height is at 200m, then;

200 = -4.9t^2+ 86t + 2.1

multiplying through by 10

2000 = -49t^2 + 860t + 21

49t^2 - 860t - 21 + 2000 = 0

49t^2 - 860t + 1979 = 0

Factorize

t = 860±√(860)²-4(49)(1979)/2(49)

t = 860±√739,600-387,884/98

t = 860±√351,716/98

t = 860±593.06/98

t = 860+593.05/98 and 860-593.05/98

t = 1,453.05/98 and 266.94/98

t = 14.82 and 2.72secs

These are the times

To approximate the surface area of one slipcover for Davea's topiaries, we need more information regarding the shape and dimensions of the topiaries.

To calculate the surface area of a slipcover, we need information about the shape and dimensions of the topiary. Depending on the specific shape, whether it is a cone, cylinder, or other geometric form, the surface area formula will differ. For example, if the topiary is a cone, the surface area formula would involve the radius and slant height of the cone. If it is a cylinder, the surface area formula would involve the radius and height of the cylinder. Without these details, it is impossible to provide an accurate estimate of the surface area of the slipcover. However, in general, the slipcover would cover the entire surface of the topiary, excluding the base, to provide adequate protection against frost.

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The probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board is 0.031.

Mean = 196 × 43

Mean = 8428

Std. Dev. = 63 × √(43)

Std. Dev. = 63 × 6.56

Std. Dev. = 413.28

Here, μ = 8428, σ = 413.1186 and x = 9200. We must calculate P(X ≥ 9200).

he central limit theorem states that, for a sufficiently large sample size, the sample mean of all observations will be approximately normally distributed, regardless of the distribution of the population from which it was sampled.

The Central Limit Theorem is used to get the associated z-value.

z = (x - μ)/σ

z = (9200 - 8428)/413.28

z = 772/413.28

z = 1.87

Therefore,

P(X ≥ 9200) = P(z ≤ (9200 - 8428)/413.1186)

P(X ≥ 9200) = P(z ≤ 772/413.1186)

P(X ≥ 9200) = P(z ≥ 1.87)

P(X ≥ 9200) = 1 - 0.9693

P(X ≥ 9200) = 0.031

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The complete question is:

A small jet can carry up to 40 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 196 pounds, with a standard deviation of 63 pounds. What is the probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

\(\stackrel{\textit{area of the great circle}}{A=\pi r^2}\hspace{5em}81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies 9=r \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{surface area of the sphere}}{SA=4\pi r^2}\hspace{5em}SA=4\pi (9)^2\implies SA=324\pi ~in^2\)

Answer:

\(y=\frac{5}{2}x-13\)

Step-by-step explanation:

Given the equation

\(y=-\frac{2}{5}x-1\)

comparing the equation with the slope-intercept form\(y=mx+b\)

Here,

so the slope of the line is m = -2/5

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,

so  the slope of the perpendicular line will be: 5/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-8\right)=\frac{5}{2}\left(x-2\right)\)

\(y+8=\frac{5}{2}\left(x-2\right)\)

subtract 8 from both sides

\(y+8-8=\frac{5}{2}\left(x-2\right)-8\)

\(y=\frac{5}{2}x-13\)

Answer:

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

y=4x+2

Step-by-step explanation:

Answer:

y=4x+4

Step-by-step explanation:

move 8x to the left side than divide 2y by 8x and 4 to give u that answer. hope it helps