A study is conducted comparing a student's height versus the height of their father. The correlation between father's heights and student's heights for 79 male students was r = 0.72. What is the proportion of variation in son's heights explained by the linear relationship with father's heights?

Answer:

0

Step-by-step explanation:

The equation if I read this correctly is:

(7 / 7x⁶+4) / 7x⁶

Using x = 0 you would have:

[7 / (7(0)⁶+4)] / 7(0)⁶

(7 / 0 +4) / 0

(7/4) / 0 which is the same as 7/4 x 0  = 0

Answer: 55

Step-by-step explanation:

90+x+15+3x-5=180

Combine like terms

100+4x=180

Subtract 100 from both sides

4x=180

Divide by 4

X=20

Insert into equation

3(20)-5

=55

As the sample size increases, the standard deviation decreases, and the distribution of the sample mean becomes more concentrated around the population mean.

Increasing the sample size has a significant effect on the mean and standard deviation of all possible sample mean hours worked per week at home. The sample size is the number of observations in the sample, and the sample mean is the average of those observations.

When the sample size is large, the sample mean becomes a better estimate of the population mean. This is because a large sample size reduces the sampling error, which is the difference between the sample mean and the population mean.Standard deviation is a measure of how spread out the data is.

When the sample size is large, the standard deviation becomes a better estimate of the population standard deviation. This is because a large sample size reduces the standard error, which is the difference between the sample standard deviation and the population standard deviation.

Increasing the sample size makes the mean more accurate and reduces the variability of the sample mean. As the sample size increases, the standard deviation decreases, and the distribution of the sample mean becomes more concentrated around the population mean.

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Answer:

\(-2x^2y+3xy^2\)

Step-by-step explanation:

The terms \(5x^2y \text{ and } -7x^y\) are like terms.

The terms \(2xy^2 \text{ and } xy^2\) are like terms.

Remember, \(xy^2\) means \(1x^2y\).

The constant of proportionality is comes out to be 3.

When two variables are proportional to one another, their relationship can be expressed as y = kx or y = k/x, where k defines how the 2 factors are related to one another. The above k is recognized as the proportionality constant.

Now according to the question.

The proportionality constant denotes the ratio of the words x and y.

It is found by dividing Δy by Δx.

Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

Consider two values from the table;

y₂ = 39 ; x₂ = 13

y₁ = 30 ; x₁ = 10

Substituting the values in the formula;

Δy/Δx = (39 - 30)/(13 - 10)

Δy/Δx = 9/3

Δy/Δx = 3

Therefore, the value of constant of proportionality is 3.

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The complete question is -

Washington high school's head tennis coach, Ms. racket, runs a tennis camp for middle school students every summer. the students bring their own lunches, but Ms. racket provides them with snacks. there is a proportional relationship between the number of students who enroll in Ms. racket's tennis camp, x, and the total number of snacks she buys, y. what is the constant of proportionality? write your answer as a whole number or decimal. snacks per student.

X      Y

10     30

13     39

14     42

21     63

Answer:

a. x = 10

b. x = 3/5

c. x = 16

d. x = 21/32

Step-by-step explanation:

a - 2x/3 + (x+3)/3 = 11

b - 3/x + 6/x = 15

c - x/2 + x/8 = 10

d - 4/x + 5/4x = 8

Apologies for the long explanations--it's not something I do very well.

Answer:

  D.  the length of the quarter

Step-by-step explanation:

Given Patrick started playing 4 minutes into the 2nd quarter, and played until the end of the 3rd quarter, you want to know how long Patrick played.

If q is the length of a quarter, Patrick's playing time is ...

  2q -4 . . . . minutes

In order to give this a numerical value, we need to know the value of q.

The most important variable to the problem is ...

  D.  the length of a quarter.

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The coordinates of D' are (1, 5).

On a coordinate plane, a triangle has points D (-2.5, 5), E (0, -1), and F (-5, -1). We need to find the coordinates of point D' which is the image of point D after a translation.
To find the coordinates of D', we need to know the amount and direction of the translation. Since we don't have that information, we can't determine the exact coordinates of D'. However, we can still calculate the general formula for the translation and find the y-coordinate of D'.
Let's assume that the translation moves point D horizontally by a distance of 3.5 units to the right. We can add 3.5 to the x-coordinate of D to find the x-coordinate of D'.
D' will have the coordinates (x', y'). Given that D has the coordinates (-2.5, 5) and D' has the coordinates (3.5, y'), we can set up the following equation:
x' = -2.5 + 3.5
Simplifying, we find that x' = 1
Now, we need to find the y-coordinate of D'. Since D' is the image of D after a translation, the y-coordinate of D' will be the same as the y-coordinate of D.
In summary, the coordinates of point D' are (1, 5).

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Answer:

3

Step-by-step explanation:

speed is distance divided by time

Answer:

20 minutes

Step-by-step explanation:

Answer:

So it will take the stone 1 (one) second to reach its maximum height.

Step-by-step explanation:

Notice that the mathematical quadratic expression given is that of a parabola with branches pointing down. This means that the maximum value for that parabola is at the vertex. Your expression is also given in vertex form:

\(f(x)=a\,(x-x_v)^2+y_v\)

where the pair of coordinates \((x_v,y_v)\) are the x coordinate of the vertex and the y coordinate of the vertex.

Since x in your case is the time the stone is on the air, then the maximum (vertex) is at the point (1, 45) where "1" is the time in seconds and 45 is the height of the stone in meters.

So it will take the stone 1 (one) second to reach its maximum height.

The negation of the statement "Not all cats dislike having their belly rubbed" is "Some cats dislike having their belly rubbed". Therefore, the correct answer is "Some cats dislike having their belly rubbed."

a) To show that the composition of two univalent relations is also univalent, let's assume we have three sets A, B, and C, and two univalent relations R1 ⊆ A × B and R2 ⊆ B × C. We need to prove that the composition R1∘R2 ⊆ A × C is univalent.

Let's suppose a ∈ A, and suppose (a, c1) ∈ R1∘R2 and (a, c2) ∈ R1∘R2 for c1, c2 ∈ C. Then, there exist b1, b2 ∈ B such that (a, b1) ∈ R1, (b1, c1) ∈ R2 and (a, b2) ∈ R1, (b2, c2) ∈ R2. Since R1 is univalent, we have b1 = b2. Now, since R2 is also univalent, we have c1 = c2. Thus, (a, c1) = (a, c2), proving that the composition R1∘R2 is univalent.

b) To show that the composition of two total relations is also total, let's assume we have three sets A, B, and C, and two total relations R1 ⊆ A × B and R2 ⊆ B × C. We need to prove that for every a ∈ A, there exists c ∈ C such that (a, c) ∈ R1∘R2.

Let a ∈ A be arbitrary. Since R1 is total, there exists b ∈ B such that (a, b) ∈ R1. Similarly, since R2 is total, there exists c ∈ C such that (b, c) ∈ R2. Therefore, we have (a, c) ∈ R1∘R2, satisfying the condition for the composition R1∘R2 to be total.

In summary, the composition of two univalent relations is univalent, and the composition of two total relations is total.

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There is a very small chance (less than 1%) that a randomly selected baby from this sample was born on Tuesday OR on Friday.

To find the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday, we need to add the number of babies born on Tuesday to the number of babies born on Friday, and then divide by the total number of babies in the sample.

The number of babies born on Tuesday is 202020, and the number of babies born on Friday is 151515. Therefore, the total number of babies born on Tuesday or on Friday is 202020 + 151515 = 353535.

The total number of babies in the sample is 500500500. Therefore, the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday is:

353535 / 500500500 = 0.0007061

It is interesting to note that the number of babies born on different days of the week varies in this sample. For example, there are more babies born on weekdays (Monday-Friday) than on weekends (Saturday and Sunday), and there are more babies born on Tuesday than on Wednesday or Thursday.

The number of scheduled deliveries is higher than the number of unscheduled deliveries overall, but there are some days (e.g., Friday and Saturday) where there are more unscheduled deliveries than scheduled deliveries. These patterns could be explored further to understand the factors that influence the timing and scheduling of deliveries.

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Answer:

8 lines

Step-by-step explanation:

5 yards = 4.572 meters

40 m /4.572 = 8.7489063867

8 lines

The student 3's numeric grade percentage is 95.6%.

The final grade for the students is calculated based on the test scores and the class project score.

The test is worth 80% and the project is worth 20% of the grade. To calculate the final grade percentage, the individual percentages of test and project are computed, then added together.

The result cannot exceed 100%.Let us calculate the weighted test score for student 3.

There were three tests each worth 100 points. The scores of student 3 are 91, 78, and 83.

We have to add up the test scores; then divide by the total number of test points and then multiply by the weighted percentage.

The weighted test score is:(91+78+83)/300 * 80% = 76.6%

We can now calculate the percentage for the project. Student 3 received a grade of 95%.

Therefore, the percentage for the project is: 95% * 20% = 19%.

Now, we add the weighted test score to the weighted project score to find the final grade for student 3. 76.6% + 19% = 95.6%.

Therefore, The final grade of student 3 is 95.6%

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Answer:

126 mm / 3 = 42 mm

The length of each side of this equilateral triangle is 42 mm.

Answer:

2\(\sqrt{58}\)

Step-by-step explanation:

Use the distance formula.

The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

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C. The parabola does not have a tangent whose slope is – 2 because y' does not have the value - 2 for any x-value in the domain of the curve.

To find the slope of the tangent line at any point on the parabola, we need to find the derivative of the equation y = 2x^2 - 14x + 3. The derivative of this equation is y' = 4x - 14. To find the slope of the tangent line at any point on the parabola, we need to set y' equal to - 2 and solve for x:

- 2 = 4x - 14

16 = 4x

x = 4

Now we can plug x = 4 back into the equation y = 2x^2 - 14x + 3 to find the y-value of the point of tangency:

y = 2(4)^2 - 14(4) + 3

y = - 29

So the point of tangency is (4, - 29). However, when we plug x = 4 back into the derivative equation y' = 4x - 14, we get y' = 2, not - 2. This means that the slope of the tangent line at the point (4, - 29) is not - 2, and therefore the parabola does not have a tangent whose slope is - 2.

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Answer:

1798 and 32798

Step-by-step explanation:

31000/100=310

310x5.8=1798

Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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The woman has €123,750 left after paying taxes.

To calculate how much the woman has left after paying taxes, we need to determine her taxable income and then subtract the tax amount.

The woman earns €150,000 per annum and is allowed a tax-free pay of €45,000. This means that her taxable income is the difference between her total income and the tax-free allowance:

Taxable Income = Total Income - Tax-Free Pay

= €150,000 - €45,000

= €105,000

Next, we need to calculate the tax amount based on the taxable income. The woman pays 25 cents per euro as tax on her taxable income, which can be expressed as a tax rate of 25%.

Tax Amount = Tax Rate * Taxable Income

= 0.25 * €105,000

= €26,250

Finally, we can determine the amount the woman has left after paying taxes by subtracting the tax amount from her total income:

Amount Left = Total Income - Tax Amount

= €150,000 - €26,250

= €123,750

Therefore, the woman has €123,750 left after paying taxes.

It is important to note that tax calculations can vary depending on the specific tax laws and regulations in a particular jurisdiction. The above calculation assumes a tax rate of 25% and does not take into account any additional deductions or credits that may apply.

It is always advisable to consult with a tax professional or refer to the tax laws in the relevant jurisdiction for accurate and up-to-date information regarding tax calculations.

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Answer:

Yesterday a lady on the subway asked me what my favorite subject was. I said math and she looked at me weird.So I was trying to think of a way to properly explain it to her. I wanted to provide her with so many details. So since I work at a company of calculaters I used how the manager makes them as an example. She was surprised with all the details I game her and told me that my manager needs to give me a promotion...I agree with her.

For the hole in the above triangular, the area that we need is the area of the rectangular hole i.e length times breadth that is 3 × 2 = 6

Hence, 6 sq. ft. carpet will be needed

Answer:

58.1 m²

Step-by-step explanation:

d = 8.6 m

r = d/2 = 4.3 m

A = πr²

A = 3.14159 × (4.3 m)²

A = 58.1 m²

Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.

How to solve the question?

To find out how much Saanvi paid for the boat, we can use the concept of depreciation. Depreciation is the reduction in value of an asset over time. In this case, the boat has depreciated at a rate of 2.5% per year.

Let the initial value of the boat be 'P'. After one year, the value of the boat would be 97.5% of P. After two years, it would be 95% of P, and so on. We can write this mathematically as:

Value of the boat after n years = P x (0.975)^n

We are given that the value of the boat after 13 years is £3115. Therefore, we can write:

3115 = P x (0.975)^13

Solving this equation for P, we get:

P = 3115 / (0.975)^13

P = 5329.39

Therefore, Saanvi paid £5329.39 for the boat.

In conclusion, Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.  

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Step-by-step explanation:

To make your answer concrete, suppose there will be 30 guests and the genie will tell you either x-bar= 5 cans or M=3 cans. Which of these two measures would best help you determine how many can you should have on hand?

Answer:the mean proportional of 5 and 15 is 5sqrt(3)

Given that a = 5 and b = 15. We are to find the mean proportional of 5 and 15.

To find the mean proportional of 5 and 15, we will substitute the given values in the formula below:

a/x = x/bWe get, 5/x = x/15

We can then cross multiply to get:x^2 = 5 × 15

Simplifying, we get:x^2 = 75Then, x = sqrt(75

)We can simplify x as follows: x = sqrt(25 × 3)

Taking the square root of 25, we get:x = 5sqrt(3)

Therefore, the mean proportional of 5 and 15 is 5sqrt(3).

Given that a and b are two non-zero numbers, the mean proportional of a and b is defined as the value x which satisfies the following condition: a/x = x/b.

This can also be written as "a is to x, as x is to b".

If we cross-multiply, we get:x^2 = ab

Taking the square root of both sides,

we get:x = sqrt(ab)Therefore, the mean proportional of any two non-zero numbers a and b is given by sqrt(ab).

In the given problem, we have a = 5 and b = 15.

Therefore, the mean proportional of 5 and 15 is:x = sqrt(ab) = sqrt(5 × 15) = sqrt(75) = sqrt(25 × 3) = 5sqrt(3)

Therefore, the mean proportional of 5 and 15 is 5sqrt(3).

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