Compute the mean and standard deviation of the random variable with the given discrete probability distribution. P (x) -5 0.14 0.17 0.23 0.30 0.16 -4 3 Skip Part Check Answer Save For Later

Answers

Answer 1

The standard deviation of the random variable is approximately 3.4082.

How to compute the mean and standard deviation of the given discrete probability distribution?

To compute the mean and standard deviation of the given discrete probability distribution, we need to use the following formulas:

Mean (μ) = ∑ [xi * P(xi)]

Variance (σ^2) = ∑ [(xi - μ)^2 * P(xi)]

Standard deviation (σ) = sqrt(σ^2)

where xi represents each possible value of the random variable and P(xi) represents the probability of each value.

Using the given probability distribution, we can compute the mean as:

Mean (μ) = (-5 * 0.14) + (-4 * 0.03) + (0 * 0.17) + (3 * 0.30) + (4 * 0.23) + (5 * 0.16) = 1.39

Therefore, the mean of the random variable is 1.39.

To compute the variance, we first need to compute the squared deviation of each value from the mean. Using the formula for variance, we get:

Variance (σ^2) = (-5 - 1.39)^2 * 0.14 + (-4 - 1.39)^2 * 0.03 + (0 - 1.39)^2 * 0.17 + (3 - 1.39)^2 * 0.30 + (4 - 1.39)^2 * 0.23 + (5 - 1.39)^2 * 0.16 = 11.6109

Finally, we can compute the standard deviation by taking the square root of the variance:

Standard deviation (σ) = sqrt(11.6109) = 3.4082

Therefore, the standard deviation of the random variable is approximately 3.4082.

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Related Questions

(T/F) the matrix a and its transpose, ar, have different sets of eigenvalues.

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The given statement, "The matrix a and its transpose, ar, have different sets of eigenvalues" is False.

The proof for this is that if λ is an eigenvalue of A with corresponding eigenvector x, then we have Ax = λx.

Taking the transpose of both sides, we get x^T A^T = λx^T. Since x^T is a row vector and A^T is a square matrix, we can see that λ is also an eigenvalue of A^T with the corresponding eigenvector x^T. Therefore, A and A^T have the same set of eigenvalues.

This characteristic is significant in many linear algebra applications because it allows us to simplify eigenvalue computations by dealing with the transpose of a matrix, which can be easier to manage in some circumstances. It also offers a valuable link between a matrix's eigenvalues and those of its transpose, which may be used in certain arguments and methods.

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find the margin of error for . the duration of telephone calls directed by a local telephone company: s= 4.5 minutes, n = 420, 98onfident.

Answers

The margin of error for the duration of telephone calls directed by a local telephone company is approximately 0.511 minutes or 30.66 seconds, with a 98% confidence level.

Given the provided information, we can use the following terms to calculate the margin of error:

1. Standard deviation (s) = 4.5 minutes
2. Sample size (n) = 420 calls
3. Confidence level = 98%

First, let's find the critical value (z-score) for a 98% confidence level. Using a standard normal distribution table, we can determine that the critical value is approximately 2.33.

Next, we need to find the standard error. The standard error (SE) is calculated as follows:

SE = s / √n
SE = 4.5 / √420
SE ≈ 0.2195

Now that we have the critical value and standard error, we can calculate the margin of error (ME) using the formula:

ME = z-score * SE
ME = 2.33 * 0.2195
ME ≈ 0.511

Thus, the margin of error for the duration of telephone calls directed by a local telephone company is approximately 0.511 minutes or 30.66 seconds, with a 98% confidence level. This means that the true mean duration of telephone calls is likely to be within 0.511 minutes (or 30.66 seconds) of the sample mean.

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check my work in regression analysis, the standard errors should not always be included along with the estimated coefficients. a. true b. false

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The statement "the standard errors should not always be included along with the estimated coefficients" is false.

How to find if the given statement is True or False?

False

In regression analysis, standard errors are calculated for the estimated coefficients to measure the uncertainty or variability in their values.Standard errors are important because they help to construct confidence intervals and conduct hypothesis tests for the coefficients.Confidence intervals are used to estimate the range of values within which the true population coefficients lie. The standard error is a measure of the precision of the estimated coefficient and is used to calculate the confidence interval for the coefficient.

Therefore, if the standard error is not included, it would not be possible to construct the confidence interval.

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data is sampled from a population for scores that has an original σ=5 points how much error should you expect from samples with the following sizes: a. n=4 b. n=9 c. n=16 d.
Look at #9 answers-note the difference between answers to questions 8 and 9. Explain in a sentence what the difference in SD is doing to the error expected (compare 8 & 9 and also what the increase in sample size (comparing a,b,c) does to the SEM.
9. Data is sampled from a population for IQ scores that has an original σ=10 How much error should you expect from samples with the following sizes: a. n=4 b. n=9 c. n=16

Answers

For a population with an original σ=5, the standard error of the mean (SEM) for a sample size of n=4 is approximately 2.5 points, for a sample size of n=9 it is approximately 1.67 points, and for a sample size of n=16 it is approximately 1.25 points.

In question 9, with a population σ of 10, the SEM for a sample size of n=4 is approximately 5 points, for a sample size of n=9 it is approximately 3.33 points, and for a sample size of n=16 it is approximately 2.5 points. The difference between the SEM in questions 8 and 9 is due to the difference in population σ. A larger population σ will result in a larger SEM, which means more error is expected in the sample mean.

Increasing sample size (comparing a, b, c) will decrease the SEM, resulting in less error expected in the sample mean. This is because as sample size increases, the sample mean becomes a better representation of the population mean.

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HELPP Let f(x) = 4x^2-17x+15/x-3

a. What numerical form does f(3) take? What

name is given to this numerical form?

b. Plot the graph of f using a friendly window

that includes x = 3 as a grid point. Sketch

the graph of f taking into account the fact

that f(3) is undefined because of division by

zero. What graphical feature appears at x = 3?

c. The number 7 is the limit of f(x) as x

approaches 3. How close to 3 would you have to keep x in order for f(x) to be within 0.01 unit of 7? Within 0.0001 unit of 7? How

could you keep f(x) arbitrarily close to 7 just

by keeping x close to 3 but not equal to 3?

Answers

a. Numerical form of f(3): When x=3, the denominator of the function becomes 3-3=0, which makes the function undefined. Therefore, f(3) does not exist. This is known as a "point of discontinuity."

How to explain the function

b. Graph of f(x): To plot the graph of f, we need to find the values of f(x) for different values of x. We can use algebraic techniques to simplify the function:

f(x) = (4x^2-17x+15)/(x-3)

= (4x-3)(x-5)/(x-3) (factoring the numerator)

= 4x - 3 (canceling out the common factor of (x-3))

Now, we can see that the function is undefined at x=3, but for all other values of x, it is equal to 4x-3. Therefore, the graph of f(x) is a straight line with slope 4 and y-intercept -3, except for a hole at x=3. To sketch the graph, we can draw a dotted line at x=3 to indicate the point of discontinuity, and draw the straight line with a break at x=3,

c. Limit of f(x) as x approaches 3:

As x approaches 3, the denominator of the function gets closer and closer to zero, but the numerator also approaches a specific value. We can use algebraic techniques to evaluate the limit:

lim x→3 (4x^2-17x+15)/(x-3)

= lim x→3 [(4x-3)(x-5)/(x-3)] (factoring the numerator)

= lim x→3 (4x-3) (canceling out the common factor of (x-3))

= 7

Therefore, the limit of f(x) as x approaches 3 is 7.

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A sum of money will be doubled if it is deposited at a simple interest rate of r% p.a. for t years. What is the percentage change in its interest rate if the same amount of money will be increased by 25% in t/2 years time?

Answers

The percentage change in the interest rate is -80%. This means that the interest rate needs to be reduced by 80% to achieve an increase in the amount of money by 25% in t/2 years time.

What is simple interest?

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

Let the original sum of money be P.

According to the question, if P is deposited at a simple interest rate of r% p.a. for t years, it will be doubled. This means that the interest earned on P after t years is P, i.e.,

I = P

The formula for simple interest is I = (P * r * t) / 100. Substituting I = P, we get:

P = (P * r * t) / 100

Simplifying, we get:

r = 100 / t

Now, the question states that if the same amount of money (P) is increased by 25% in t/2 years time, the new amount becomes:

P' = P + (0.25P) = 1.25P

Let the new rate of interest be r'.

The formula for simple interest is I' = (P' * r' * t/2) / 100. Substituting P' = 1.25P, we get:

I' = (1.25P * r' * t/2) / 100

The interest earned on P' after t/2 years is 1.25P - P = 0.25P. Therefore, we have:

I' = 0.25P

Substituting the value of I' in the above equation, we get:

0.25P = (1.25P * r' * t/2) / 100

Simplifying, we get:

r' = 20 / t

The percentage change in the interest rate is given by:

((r' - r) / r) * 100%

Substituting the values of r and r', we get:

((20/t - 100/t) / (100/t)) * 100%

= -80%

Therefore, the percentage change in the interest rate is -80%. This means that the interest rate needs to be reduced by 80% to achieve an increase in the amount of money by 25% in t/2 years time.

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Let A = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows:
For all x, y is in A, x R y ⇔ 3|(x − y).
It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R.
[0]=
[1]=
[2]=
[3]=
How many distinct equivalence classes does R have?
List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Answers

The equivalence classes are, [0]={0,3,-3,6,-6}, [1]={1,4,-2,-5}, [2]={2,5,-1,-4}, [3]={3,6,-3,0}, and R has 4 distinct equivalence classes: {[0]}, {[1], [4], [-2], [-5]}, {[2], [5], [-1], [-4]}, and {[3], [6], [-3], [0]}.

An equivalence relation is a mathematical concept that relates objects or elements in a set based on a certain property or characteristic they share. In this case, the relation R on set A relates elements x and y if their difference is divisible by 3. This means that the elements in each equivalence class of R share this same property.

The set-roster notation expresses the equivalence classes of R as sets of elements in A that are related to each other under R. In this case, there are four distinct equivalence classes of R, each containing elements that differ by multiples of 3. This concept is important in various areas of mathematics, including algebra, topology, and geometry.

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Find the length of the curve. The spiral r=4θ^2, 0≤θ≤2√3.

Answers

The length of the curve r = 4θ², 0≤θ≤2√3, is 38.786 units.

To find the length of the curve, we can use the formula for arc length:
[tex]L = \int_{a}^{b}\sqrt{(1 + (dy/dx)^2)} dx[/tex]

In this case, we have the polar equation r = 4θ², which we can convert to Cartesian coordinates using x = r cos(θ) and y = r sin(θ):

x = 4θ² cos(θ)
y = 4θ² sin(θ)

To find dy/dx, we can use the chain rule:

dy/dx = (dy/dθ)/(dx/dθ)

= (4θ² cos(θ) + 8θ sin(θ))/(8θ cos(θ) - 4θ² sin(θ))

Simplifying this expression, we get:

dy/dx =(4θ) (θ cos(θ) + 2 sin(θ))/(2 cos(θ) - θ sin(θ))

Now we can substitute this expression and the expression for x into the arc length formula:
[tex]L = \int_{0}^{2\sqrt{3}}\sqrt{(1 + ((4\theta)(\theta cos(\theta) + 2sin(\theta))/(2cos(\theta) - \theta sin(\theta)))^2)} d\theta[/tex]

This integral is difficult to solve analytically, so we can use numerical methods to approximate the value. Using a calculator or computer program, we get:

L ≈ 38.786

So the length of the curve is approximately 38.786 units.

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A consumer research group examining the relationship between the price of meat grams of fat; $3.00 per pound) is removed, how would the correlation most likely be affected? Click the icon to view the scatterplot. G Scatterplot O A become positive B. become stronger negative oc, become weaker negative O D. become zero Scatterplot of Price/lbvs Fat Grams 15 10 Fat Gr ans 20 Print Done Click to select your answer

Answers

Correct option about "How would the correlation most likely be affected?" is C. Become weaker negative

Explain indetail about why the option C is correct?

If the price of meat ($3.00 per pound) is removed, the correlation between price per pound and grams of fat is likely to become weaker negative.

This is because the price per pound is a factor that influences the amount of fat in meat - typically, cheaper cuts of meat have more fat. Therefore, when this factor is removed, the relationship between price and fat grams may not be as strong.

When meat with $3.00 per pound is removed from the dataset, the correlation will most likely:

C. Become weaker negative

This is because removing data points can affect the overall trend observed in the scatterplot. When a data point with a strong influence on the negative correlation is removed, the remaining data points may show a weaker negative correlation.

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Rewrite the expression 4 to the power of negative 2 times 8 to the power of 0 times 5 to the power of 6 using only positive exponents.

Answers

Recall that any non-zero number raised to the power of 0 is equal to 1. Therefore, 8^0 = 1.

To rewrite the expression using only positive exponents, we can use the following rules of exponents:

a^(-n) = 1 / a^n

a^0 = 1

Using these rules, we can rewrite the expression as:

4^(-2) x 8^0 x 5^6

= (1/4^2) x 1 x 5^6

= 1/16 x 5^6

Therefore, the expression 4 to the power of negative 2 times 8 to the power of 0 times 5 to the power of 6, rewritten using only positive exponents, is 1/16 x 5^6.

Calculate y()(0) for 0≤≤5, where y=7x4+x3+x2+cx+ with , , c, and as constants.
(Use symbolic notation and fractions where needed.)

Answers

y''(0) = 2.

To find y''(0) for the given function y=7x^4+x^3+x^2+cx+, we need to take the second derivative of the function and then evaluate it at x=0.

First, we find the second derivative of y:

y'(x) = 28x^3 + 3x^2 + 2x + c

y''(x) = 84x^2 + 6x + 2

Now, we evaluate y''(x) at x=0:

y''(0) = 84(0)^2 + 6(0) + 2

y''(0) = 2

Therefore, y''(0) = 2.

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The volume of a cone with a height of 10 meters is 20 pi cubic meters. What is the diameter of the cone?

Answers

The cone diameter is 2√6 m.

What is the ∀of the cone??

To find the diameter, we must use the height and volume of a cone to find diameter and then multiply the volume of the cone by 3 and divide the resultant number by pi times the height.

The formula for the vol. of a cone is V = (1/3)(area of base)(height).

20π = 1/3π(r)^2(10)

20π*3/10π = r2

√60π/10π = r

Using our calculator, we will get 2√3.

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Find the Value of X pls!!!!

Answers

Here the length of VT is equal to (x-1) which is equal to 6 and SC is equal to (2x-17) which is equal to 3.

So x=7, VT=6 and SC=3.

Explain length

Length is a fundamental physical quantity used to measure the size of an object or the distance between two points. It is expressed in units such as meters, centimetres, or feet and is used in various fields such as mathematics and physics. The length of a straight line is calculated by finding the distance between its endpoints, while the length of two-dimensional shapes such as rectangles is measured by their perimeter.

According to the given information

We can use the following steps to find x:

Find the length of ST using Pythagoras' theorem as follows:

SV = RV + RS = RV + RT = 6 + (2x - 17) = 2x - 11

UT = UV + VT = 12 + (x - 1) = x + 11

ST² = SV² + UT²

(2x - 11)² + (x + 11)² = ST²

Find the length of VT using Pythagoras' theorem as follows:

TV² = UT² - UV²

TV² = (x + 11)² - 12²

Substitute TV² into the equation in step 1 and solve for x.

After solving for x, we get x=7.

Therefore, VT is equal to (x-1) which is equal to 6 and SC is equal to (2x-17) which is equal to 3.

So x=7, VT=6 and SC=3.

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Unit rate and constant of proportion

Answers

The unit rate of a proportional relationship is the constant of proportion, representing by how much the output variable is added/subtracted when the input variable is added by one.

What is a proportional relationship?

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, also called unit rate, representing the increase in the output variable y when the constant variable x is increased by one.

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first-order regression model (1.1) is appropriate for each region. State the estimated regres- sion functions. b. Are the estimated regression functions similar for the four regions? Discuss. C. Calculate MSE for each region. Is the variability around the fitted regression line approxi- e for the four regions? Discuss.

Answers

The estimated regression functions for the four regions using the first-order regression model (1.1) are appropriate.

a. To estimate the regression functions, the first-order regression model (1.1) is used for each region. This model assumes a linear relationship between the predictor variable and the response variable. The estimated regression functions are obtained by fitting a straight line to the data points in each region that best represents the relationship between the predictor and response variables.

b. The estimated regression functions may or may not be similar for the four regions. This depends on the data and the specific characteristics of each region. The estimated regression functions will differ in terms of the slope and intercept values, which represent the magnitude and direction of the relationship between the predictor and response variables.

c. To calculate the mean squared error (MSE) for each region, the residuals (the differences between the observed response values and the predicted response values from the estimated regression functions) are squared and averaged. MSE is a measure of the variability around the fitted regression line, with a lower value indicating less variability.

d. If the MSE values are similar for the four regions, it indicates that the variability around the fitted regression line is approximately the same across all regions. If the MSE values are different, it suggests that the variability around the fitted regression line varies across the regions.

Therefore, the estimated regression functions are appropriate for each region using the first-order regression model (1.1). The similarity of the estimated regression functions and the variability around the fitted regression line can be determined by calculating the MSE values for each region and comparing them.

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y=-x+9 in standard form

Answers

Therefore, the standard form of the equation Y=-x+9 is -x - Y = -9.

Y=-x+9 in standard form

To write the equation Y=-x+9 in standard form, we need to express it in the form Ax + By = C, where A, B, and C are constants.

First, let's add x to both sides of the equation to get:

x + Y = 9

Now, we need to make sure that the coefficients of x and y are integers with a common factor of 1. To do this, we can multiply both sides of the equation by -1:

-x - Y = -9

Therefore, the standard form of the equation Y=-x+9 is -x - Y = -9.

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Therefore, the standard form of the equation Y=-x+9 is -x - Y = -9.

Y=-x+9 in standard form

To write the equation Y=-x+9 in standard form, we need to express it in the form Ax + By = C, where A, B, and C are constants.

First, let's add x to both sides of the equation to get:

x + Y = 9

Now, we need to make sure that the coefficients of x and y are integers with a common factor of 1. To do this, we can multiply both sides of the equation by -1:

-x - Y = -9

Therefore, the standard form of the equation Y=-x+9 is -x - Y = -9.

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Find the surface area of each prism

Answers

The answer to your question is 6,420

s = {t −t2, t2 −t3, 1 −t t3 } for p3

Answers

The value of p3 for which the set s is linearly dependent is p3 = 1

How to find the value of p3?

To find the value of p3 for which s is linearly dependent, we need to find values of p3 such that at least one of the vectors in the set s can be written as a linear combination of the other vectors in the set.

Let's start by setting up the linear combination equation:

c1(t − t^2) + c2(t^2 − t^3) + c3(1 − t t^3) = 0

where c1, c2, and c3 are constants that represent the coefficients of the linear combination.

Next, we can expand the terms and group them by powers of t:

(c1 − c2)t^2 + (-c1 + c2 + c3)t + (c3) = 0

For this equation to have a non-trivial solution (i.e., not all c1, c2, and c3 are zero), the determinant of the coefficient matrix must be zero:

det

|1 -1 0|

|-1 1 1|

|0 -1 p3|

= 0

Expanding the determinant, we get:

1(1-p3) - (-1)(-p3) + 0(1) = 0

Simplifying this equation, we get:

p3 - 1 = 0

Therefore, the value of p3 for which the set s is linearly dependent is p3 = 1

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Find the area inside the quadrilateral with corners (1, 2), (2,3), (5,1), and (3,-1). Use calculus to do this. With what I am expecting, there will be three definite integrals involved. You should start by sketching this quadrilateral.

Answers

The area inside the quadrilateral with corners (1, 2), (2, 3), (5, 1), and (3, -1) is approximately 4.5 square units.


1. Sketch the quadrilateral with given vertices.


2. Divide the quadrilateral into three triangles:


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


3. For each triangle, find the equation of the line connecting its two points on the same vertical level (either x=1, x=3, or x=5).


4. Calculate the definite integral of each line equation over its respective x range.


5. Subtract the lower line's integral from the upper line's integral for each triangle to find each triangle's area.


6. Add the areas of the three triangles to find the total area of the quadrilateral.

Following these steps, the quadrilateral's area is approximately 4.5 square units.

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what is the missing value in the table ?

Answers

Step-by-step explanation:

f(x)=3x+5

3*6+5=23

f(0)=3*0+5=5

f(1)=3*1+5=8

Height is normally distributed with a mean of 68 inches and a standard deviation of 3 inches. Given the data above, if 9 people were randomly chosen, what is the probability that their average height would be over 70 inches?

Answers

The probability that the average height of 9 randomly chosen people is over 70 inches is approximately 0.0478, or 4.78%.

1. Identify the given values: mean (µ) = 68 inches, standard deviation (σ) = 3 inches, and sample size (n) = 9.


2. Calculate the standard deviation of the sample mean using the formula σ/√n: 3/√9 = 3/3 = 1.


3. Determine the z-score for 70 inches using the formula (X - µ)/(σ/√n): (70 - 68)/1 = 2.


4. Find the probability of a z-score greater than 2 by referring to a z-table or using a calculator, which is approximately 0.0228.


5. Since the question asks for the probability over 70 inches, subtract the probability from 1: 1 - 0.0228 ≈ 0.9772.


6. The probability that the average height is over 70 inches is 1 - 0.9772 = 0.0478, or 4.78%.

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HELPPP DUE IN A HOUR!!+​

Answers

The system of linear functions for the graph below is given as follows:

y = -0.5x + 1.y = -4x - 6.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

For the first line, we have that:

The intercept is of b = 1, as when x = 0, y = 1.The slope is of m = -0.5, as when x increases by 2, y decays by 1.

Hence the equation is:

y = -0.5x + 1.

For the second line, we have that:

The intercept is of b = -6, as when x = 0, y = -6.The slope is of m = -4, as when x increases by 2, y decays by 8.

Hence the equation is:

y = -4x - 6.

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Entered Answer Preview Result ABDFGJ ABDFGJ correct The answer above is correct. (1 point) Check all the statements that are true: A. An integer is divisible by b if the last digit in its base-b expansion is zero. B. Using fast modular exponentiation, we can computer a" mod b in order of log(n) steps. C. The god of p?qand pq is pq4. D. The Icm of two distinct prime numbers is their product. E. There is a way to perform block conversion of binary number into decimal. F. The Euclidean algorithm always terminates because the remainders are integers, get smaller with each step and are bounded below by 0. G. You can block convert a binary number to octal by grouping the binary digits into blocks of 3 and converting each block into an octal digit. H. If p and q are distinct primes, then the lcm of p q and pq2 is pq. 1. If a has n distinct prime factors and b has m distinct prime factors and n>m, then ab has at least m and at most n distinct prime factors. J. If a has n distinct prime factors and b has m distinct prime factors and n>m, then ab has at least n and at most n+m distinct prime factors.

Answers

The correct answers are Using fast modular exponentiation, we can compute a^m mod b in order of log(n) steps, The lcm of two distinct prime numbers is their product, The Euclidean algorithm always terminates because the remainders are integers, get smaller with each step, and are bounded below by 0, You can block convert a binary number to octal by grouping the binary digits into blocks of 3 and converting each block into an octal digit and If p and q are distinct primes, then the lcm of p and q and pq^2 is pq. The correct answers options are  B, D, F, G, and H.

Option B is true because fast modular exponentiation is a technique that can be used to compute a^m mod b in O(log n) time complexity. Option D is true because the LCM of two distinct prime numbers is their product since they do not have any common factors other than 1.

Option F is true because the Euclidean algorithm is guaranteed to terminate because each remainder is smaller than the divisor in each step, and the remainders are non-negative integers. Option G is true because binary numbers can be grouped into blocks of 3 digits, and each block can be converted into a single octal digit.

Option H is true because the LCM of p and q and pq^2 is pq since the prime factors of pq^2 are already included in the prime factorization of pq. So, Statements that are true are B, D, F, G, and H.

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Evaluate 7P6

Help please and thanks

Answers

Answer: 5,040

Step-by-step explanation: The value of 7P6 is 5,040. To evaluate this, you can use the formula for permutations: nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being selected. In this case, n = 7 and r = 6, so 7P6 = 7! / (7 - 6)! = 7! / 1! = 5,040.

Declare three private double instance variables: x, y and radius. The instance variables x and y represent the coordinates of the center of the circle. Note that you should not declare any other instance variables other than these three.

Answers

To declare three private double instance variables x, y, and radius in a class representing a circle, you would include the following code within your class definition:
```java
private double x;
private double y;
private double radius;
```

To declare three private double instance variables x, y, and radius in a class, you can use the following code:

```
private double x;
private double y;
private double radius;
```

Here, the `private` keyword makes sure that these variables are accessible only within the class and not outside it. The `double` data type is used to store decimal values. The variables `x` and `y` represent the coordinates of the center of the circle, while `radius` represents the radius of the circle. It is important to note that no other instance variables other than these three should be declared, as per the instructions given in the question.

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Circle H is shown

What is the measure of angle RWY?

Answers

The measure of <RWY is 60 degree.

We have,

YMX = (YM) + (MX)

YMX = (4x-49) + (3x+4)

(YMX) = 7x - 45

Now, (YMX - TN) /2 = <TKN

(7x- 45 - 43)/2 = <TKN

5x -77 = 7x - 88 /2

10x - 154 = 7x-88

x=22

Now, (RY) = 6x-82 = 50

and, (MX) = 3x+4 = 70

So, the measure of <RWY

= (50+70)/2 = .60

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Find the number of ways to write 24 as the sum of at least three positive integer multiples of 3. For example, count 3+18+3, 18+3+3, and 3+6+3+9+3, but not 18+6 or 24.

help pls

Answers

Okay, here are the steps to solve this problem:

1) 24 is divisible by 3. So any sum of 3 multiples of 3 that adds to 24 will have at least one multiple that is 6 (2 x 3) or 9 (3 x 3).

2) We can represent the multiples as: 3n, 3n+1, 3n+2 where n is an integer.

3) The 3n terms can only be 3, 6, 9, 12, 15, 18, 21. The 3n+1 terms can be 4, 7, 10, 13, 16, 19, 22. And 3n+2 terms can be 5, 8, 11, 14, 17, 20, 23.

4) We need to count the number of combinations of these terms that add to 24. Some options are:

3 + 9 + 12 = 24

6 + 9 + 9 = 24

12 + 6 + 6 = 24

15 + 3 + 6 = 24

18 + 3 + 3 = 24

5) In total, there are 5 options with 3 terms.

6) Additionally, we could have 4 term sums like:

3 + 6 + 9 + 6 = 24

6 + 6 + 6 + 6 = 24

There are 2 four-term options.

7) In total, there are 5 + 2 = 7 number of ways to write 24 as a sum of at least 3 positive integer multiples of 3.

Does this help explain the steps? Let me know if you have any other questions!

find the arc length from (0, 4) clockwise to (3, 7 ) along the circle x^2 + y^2 = 16. (round your answer to four decimal places.)

Answers

The arc length is approximately 20.5744 units.

How to find the arc length from (0, 4) clockwise to (3, 7) along the circle?

To find the arc length from (0, 4) clockwise to (3, 7) along the circle[tex]x^2 + y^2 = 16.[/tex]

We need to first find the angle between the positive x-axis and the line connecting the center of the circle to the point (3, 7), since the arc length is a fraction of the circumference of the circle.

The center of the circle is at (0, 0), and the line connecting (0, 0) to (3, 7) has a slope of (7-0)/(3-0) = 7/3.

Therefore, the angle between the positive x-axis and this line is given by:

θ = arctan(7/3) ≈ 1.1659045 radians

Since we are traveling clockwise from (0, 4) to (3, 7), we are traversing an angle of 2π - θ, which is approximately 5.1766375 radians.

The circumference of the circle is given by 2πr, where r is the radius of the circle. In this case, the radius is 4, so the circumference is 8π.

The fraction of the circumference that we travel along is the ratio of the angle we traverse to the total angle around the circle, which is 2π.

Therefore, the arc length is:

(5.1766375 radians / 2π) × 8π = 20.5744

Rounding to four decimal places, the arc length is approximately 20.5744 units.

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Can anyone help me on this? I’m pretty sue wits base x height

Answers

Answer:

It's 84

Step-by-step explanation:

To calculate the area of a triangule you need to use this formula:

B * H / 2

So:

12 * 14 / 2 = 84

Hope this helps :)

Pls brainliest...

Who can help me
Find the volume of the composite solid. Round your answer to the nearest hundredth.

Answers

By Cavalieri's Principle, the volume of that slanted cylinder will be the same volume of a non-slanted cylinder with the same altitude.

so we have a cylinder with a radius of 3 and a height of 7 and a cone hitching a ride on it, with a radius of 3 and a height of 3, so let's simply get the volume of each.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=7\\ r=3 \end{cases}\implies V=\pi (3)^2(7) \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=3\\ r=3 \end{cases}\implies V=\cfrac{\pi (3)^2(3)}{3} \\\\[-0.35em] ~\dotfill\\\\ \pi (3)^2(7)~~ + ~~\cfrac{\pi (3)^2(3)}{3}\implies 63\pi +9\pi \implies 72\pi ~~ \approx ~~ \text{\LARGE 226.19}~in^3[/tex]

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