3.6.16. Let X1, X2, and X3 be three independent chi-square variables with ri, r2, and r3 degrees of freedom, respectively. = X1/X2 and Y2 = X1 + X2 are independent and that Y2 is = (a) Show that Y x?(rı +r2) (b) Deduce that Xi/rı X2/r2 and *3/r3 (X1 + X2)/(ri+r2) are independent F-variables.

Step-by-step explanation:

= (c - 4) ( c - 5)

= c ( c- 5 ) -4 (c - 5)

= c² - 5c - 4c + 20

Grouping of like terms since it have already been arranged.

=c² - 9c + 20

since we're finding for the coefficient of c

than we will square both sides or value

given as

\( \sqrt{c {}^{2} } - \sqrt{9c} + \sqrt{20} = 0 \\ c - \sqrt[3]{3c} + \sqrt[2]{10} = 0 \\ c - c + 5 = 0 \\ 0 = 0 - 5 \\ 0 = - 5\)

sorry but I tried.

The equation of the circle with in the graph with center at (-1, 1) passing through the point (2, 1) is x² + y² + 2x - 2y - 7 = 0.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

From the image, the center of the circle is (-1,1) and it passes through point (2,1).

Hence:

h = -1

k = 1

Next, we find the radius r using the distance formula.

We can calculate the distance between the center (-1, 1) and the point (2, 1):

\(r = \sqrt{( x_2 - x_1 )^2+( y_2 - y_1 )^2} \\\\r = \sqrt{( 2 - (-1) )^2+( 1 -1 )^2} \\\\r = \sqrt{( 2 + 1 )^2+( 0 )^2} \\\\r = \sqrt{( 3)^2+( 0 )^2} \\\\r = \sqrt{9} \\\\r = 3\)

Plugging the radius (r = 3) and center (-1,1) into the equation, we have:

(x - h)² + (y - k)² = r²

(x - (-1) )² + (y - 1)² = 3²

(x + 1)² + (y - 1)² = 9

Convert to general form:

x² + 2x + 1 + y² - 2y + 1 = 9

x² + y² + 2x - 2y + 1 + 1 = 9

x² + y² + 2x - 2y + 2 = 9

x² + y² + 2x - 2y + 2 - 9 = 0

x² + y² + 2x - 2y - 7 = 0

Therefore, the equation of the circle is x² + y² + 2x - 2y - 7 = 0.

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Answer:

11

Step-by-step explanation:

Answer: x = 8, y = 2, coordinates (8,2)

Step-by-step explanation:

2x = 4y + 8 (divide by 2 to get value of x)

x = 2y + 4

(now substitute x into the second equation to find value of y)

2y + 4 - 2y = 4

2y - 2y = 4 - 4 (divide by 2 to get value of y)

y - y = 2 - 2

y = 2

Now plug in value of "y" to get value of "x".

x - 2(2) = 4

x - 4 = 4

x = 8

Coordinates (8,2)

1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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This is a one-tailed or right-tailed hypothesis test.

In a hypothesis test, we have a null hypothesis and an alternative hypothesis. The null hypothesis is usually the hypothesis that there is no significant difference between two variables or no effect of a treatment. The alternative hypothesis is the hypothesis that there is a significant difference between two variables or an effect of a treatment.

When the null hypothesis is that the mean is equal to a specific value and the alternative hypothesis is that the mean is greater than that value, we are conducting a one-tailed right-sided test.

This means that we are interested in finding evidence to support the claim that the mean is larger than the specific value, rather than just testing if the mean is different from the specific value.

In a one-tailed right-sided test, the rejection region is located entirely in the right tail of the sampling distribution of the test statistic. The level of significance or alpha is split between the rejection region and the non-rejection region on the right side of the distribution.

If the calculated test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis that the mean is greater than the specific value.

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Answer:

If 1 m/s is 1 meter per second, then it would take 5 seconds.

add it and you will get 24 so pick D

Given:

The lines l and m are parallel lines and x=40 degrees.

To find the angle:

We know that alternate angles are equal.

So that,

And then, using the angle sum property of a triangle,

Thus, the measure of angle DEF is 100 degrees.

The dimensions of the photograph are found as 13 in and 6 in.

Let length = x.

So, width = x - 7

Area = length x width

A = x (x -7)

and A = 78 inches squared.

Thus,

78 = x (x -7)

On solving.

x² - 7x - 78 = 0

Find the factors of the quadratic equation,

x² - 7x - 78 = 0

(x - 13)(x + 6) = 0

Thus,

x = 13 and x = -6 but (x > 0)

Thus, when x = 13 in,

Width = x + 7

Width = 13 - 7

Width = 6 in

Thus, the dimensions of the photograph are found as 13 in and 6 in.

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Answer: -11.75

Step-by-step explanation: The distance is 11.75 units close to 0, compared to the 2nd closest which is A (12)

Answer:

\(\frac{1}{27000}\) or \(3.703\) × \(10^{-5} \\\)

Step-by-step explanation:

\(3^{-3} \\\) is the same as \(\frac{1}{3}^{3}\) or \(\frac{1}{27}\).

\(10^{-3}\) is the same as \(\frac{1}{10}^3\) or \(\frac{1}{1000}\).

So, \(3^{-3}\) × \(10^{-3}\) is basically \(\frac{1}{3}^{3}\)× \(\frac{1}{10}^3\) or \(\frac{1}{27}\) × \(\frac{1}{1000}\), which both are simplified to \(\frac{1}{27000}\) .

\(\frac{1}{27000}\) can also be written as \(3.703\) × \(10^{-5} \\\) in scientific notation in decimal form.

(a) The expected number of times the frisbee is thrown through the course of the game is n-1. (b) The expected number of people that never got the frisbee during the game is 1.

(a) In this game, each time the frisbee is thrown, it moves to a different person in the circle, excluding Ben. Since there are n-1 people in the circle other than Ben, the frisbee is expected to be thrown n-1 times before it reaches Ben again. (b) Since the game ends when someone throws the frisbee back to Ben, there will always be one person who never gets the frisbee throughout the game. Therefore, the expected number of people that never got the frisbee during the game is 1.

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Answer:

-59

Step-by-step explanation:

3(3)+2(2)-6(12)

Answer: -59

Step-by-step explanation:

3a + 2b - 6c

a = 3  b = 2  c = 12

Substitute

3 (3) + 2 (2) - 6 (12)

9 + 4 - 72

13 - 72

-59

Answer:

C) x = 12

Step-by-step explanation:

We can calculate the value of x using similarity ratio

x/8 = 9/6 cross multiply expressions

6x = 72 divide both sides by 6

x = 12

Answer:

B

Step-by-step explanation:

4.598  4.599  4.603

The middle number is 0.001 larger than the first number and 0.004 smaller than the second number.

Answer: A 4.597

Step-by-step explanation:

It is one one thousandth more than 4.598 and is less the 4.603.

Answer:

nothing

Step-by-step explanation:

a product of 2 positive numbers always shows a positive value if we add them

The mean amount dispensed by the machine should be set to approximately 0.50 ounces in order to achieve a desired probability of 0.006 for a cup overflowing.

Identify the given information:

Desired probability of cup overflowing (P) = 0.006

Standard deviation (σ) = 0.39 ounces

Use the Z-score formula:

Z = (X - μ) / σ

Rearrange the formula to solve for the mean (μ):

X = Z * σ + μ

Look up the Z-score value that corresponds to a cumulative probability of 0.006 in a standard normal distribution table. In this case, the Z-score is approximately -2.69.

Substitute the values into the formula:

μ = Z * σ + X

μ = -2.69 * 0.39 + X

Solve the equation P(X > X) = 0.006 using the given probability of overflowing.

Using a statistical software or calculator, find that X is approximately 0.50 ounces.

Therefore, based on the calculations, the mean amount that the dispenser should be set to in order to achieve a desired probability of 0.006 for a cup overflowing is approximately 0.50 ounces. This means that by setting the mean amount to 0.50 ounces, the probability of a cup overflowing will be approximately 0.006 or 0.6%.

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Answer:

lklklkj

Step-by-step explanation:

67890-

Angles in 59 non-similar triangles having degree measures that are integers via arithmetic progression.

Let the summation of the angle values be: Using arithmetic progression & triangle knowledge, letting the sum of the angle values be:

∑degree = 180

For an odd arithmetic progression with a strange number of words, the median term is equivalent to the average of both the sum of all terms:

An arithmetic sequence's nth term,

Let the initial triangle angle =a

Let d be a common difference.

Because the angles' measurements follow an arithmetic progression \(T_{n}\) = a + (n - 1) × d

a + (a + d) + (a + 2d) = 180

3a+3d=180

a+d=60

Because an or d cannot be identical to zero, the minimum and maximum possible values for a and d are 1 and 59, respectively.

As a result, there are 59 distinct triangles.

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Answer:

n = 3

Step-by-step explanation:

\(3^{5}\) x \(3^{n}\) = \(3^{8}\)

5 + n = 8

n = 3

\(3^{5}\) x \(3^{3}\) = \(3^{8}\)

The median of the data is 5 if the all class widths are 1, option (C) is correct.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

In the histogram, 15 data values are given:

1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9

The mid-value is 5 which is on the 8th place

Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.

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Answer:

$4,208.5

Step-by-step explanation:

The simple interest rate of the college savings account, R = 5.5%

The amount with which the account was opened, P = $500

The amount added each month to her account = $50

The amount in her account after 4 years = Required

The interest on each added $50 is given as follows;

50  × 0.055/12 × (1 + 2 + 3 + ... + 47) = 50  × 0.055/12 × (47/2)(1 + 47) = 258.5

The total amount deposited = 500 + 50 × 47 = $2,850

The total interest = 500×0.55×4 + 50  × 0.055/12 × (47/2)(1 + 47) = 1,358.5

The amount in her account at the end of 4 years, A, is given as follows

A = $2,850 + $1,358.5 = $4,208.5

Answer:

36

Step-by-step explanation:

7/6 u=42

7u =42×6

u=252/7

u=36

\(-2(-1+2w)\)

distribute

\(2-4w\)

put in standard form

\(-4w+2\)

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The number of possibilities for Jane for making the four letter password (either upper case or lower case) with first letter being a vowel is 1406080

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in \(p \times q\) ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

We need to find the number of ways a four letter password can be made The first letter is fixed to be a vowel.

There are 10 vowels (5 of lowercase and 5 of upper case).

Thus, 10 ways of choosing the first letter.

Second letter can be any of the 52 letters(26 of lowercase and 26 of uppercase).

Similarly, third and fourth letter can be any of the 52 letters.

Thus, using the product rule, the number of ways of making the four letter password is:

\(N = 10 \times 52 \times 52 \times 52 = 1406080\)

(the answer can be different if we consider only either lowercase letters or only upper case letters. In those cases, there would be \(5 \times 26^3 = 87880\) ways to make such passwords).

We used product rule, since we wanted to do the choosing of all the four letters for password, and we knew the number of ways each of them can be done individually.

Thus,  the number of possibilities for Jane for making the four letter password (either upper case or lower case) with first letter being a vowel is 1406080

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Answer:

20%

Step-by-step explanation:

Profit = 24000 - 20000 = 4000

\(Profit \: percent = \frac{4000 \times 100}{20000} \\ = \frac{400000}{20000} \\ = 20\%\)

Answer:

8 units

Step-by-step explanation: