find the following probabilities, where χ 2 has a chi-squared distribution with ν degrees of freedom. (a) ν = 30 : p ( χ 2 ≥ 18.493 ) = (b) ν = 10 : p ( χ 2 ≤ 7.267 )

Answers

Answer 1

The probability of getting a value of χ2 less than or equal to 7.267 when ν = 10 is 0.05. Therefore, the correct option is: (b) ν = 10 : p ( χ 2 ≤ 7.267 )

To find the probabilities, we need to use the chi-squared distribution. The chi-squared distribution is a probability distribution that is used to test whether an observed distribution differs significantly from an expected distribution. It is commonly used in hypothesis testing and confidence interval estimation.

(a) For ν = 30 and p ( χ 2 ≥ 18.493 ), we can use a chi-squared table or a calculator to find the probability. Using a calculator, we get:

P(χ2 ≥ 18.493) = 0.0775

Therefore, the probability of getting a value of χ2 greater than or equal to 18.493 when ν = 30 is 0.0775.

(b) For ν = 10 and p ( χ 2 ≤ 7.267 ), we can use a chi-squared table or a calculator to find the probability. Using a calculator, we get:

P(χ2 ≤ 7.267) = 0.05

Therefore, the probability of getting a value of χ2 less than or equal to 7.267 when ν = 10 is 0.05.

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Find The Following Probabilities, Where 2 Has A Chi-squared Distribution With Degrees Of Freedom. (a)

Related Questions

You are building a ramp that must cover a horizontal distance of exactly 13 feet. The angle of the ramp from the ground is 26 degrees. Determine the length of the ramp, in feet.

Answers

Answer: 18.6 feet

Step-by-step explanation: Horizontal distance = 17 feet and the angle

of elevation = 24°

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. Assume the underlying population of unoccupied seats is normally distributed. Using a t- statistic, construct a 95% confidence interval for the population mean number of unoccupied seats per flight.

Answers

The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.

How to find the confidence interval?

To find the confidence interval C.I,

Determine the mean(μ) of the sampleDetermine the standard deviation(σ)Determine the z-score for the given confidence level using the z-score tableUsing all these, the confidence interval is calculated by the formula,  C. I = μ ± z(σ/√n) where n is the sample size and z(σ/√n) gives the margin error. So, we can also write C. I = mean ± margin error.

Calculation:

It is given that,

Sample size n = 225

Sample mean μ = 11.6

Standard deviation σ = 4.1

Since 95% confidence interval, z-score is 1.96

So, the required confidence interval is calculated by,

C. I = μ ± z(σ/√n) or mean ± margin error

On substituting,

C. I = 11.6 ± 1.96(4.1/√225)

     = 11.6 ± 1.96 × 0.2733

     = 11.6 ± 0.5357

So, the lower bound = 11.6 - 0.5357 = 11.065 and

the upper bound = 11.6 + 0.5357 = 12.135.

Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.

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someone please help me with question #14 !!!

Answers

Answer: a, c, e

Step-by-step explanation:

a) True. If x=0, f(0)=c.

b) False. Considering the quadratic formula, we know the solutions are not always x=c.

c) True. This is a standard fact.

d) False. If the discriminant is not positive, there are less than two x-intercepts.

e) True. If you plug into the formula [tex]x=-\frac{b}{2a}[/tex], if b=0, then obviously the x-coordinate of the vertex is also 0.

The length of side ab is units. the length of side bc is units. the length of side ac is units.

Answers

The length of side AC = 5 units

Solving missing sides of right triangles

Missing sides of a right triangle can be solved using the Pythagoras theorem

From the given question

Length of side AB = 3 units

Length of side BC = 4 units

The length of side AC is calculated below

[tex]AC^2=AB^2+BC^2\\\\AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25\\\\AC=\sqrt{25}\\\\AC=5[/tex]

Therefore, the length of side AC = 5 units

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Complete Question

The length of side ab is 3 units. the length of side bc is 4 units. the length of side ac is .......... units.

Find the greatest common factor of the
following monomials:
33c 27c^4

Answers

The greatest Common factor of monomials  [tex]33c[/tex]  and  [tex]27c^4[/tex] is  [tex]3c[/tex]

How we can find the GCF of monomials ?

Monomials are [tex]33c[/tex] and [tex]27c^4[/tex]

We can write the monomials in fraction form

[tex]33c=11*3*c[/tex]

[tex]27c^4=3*9*c*c*c*c[/tex]

----------------------------------

So we can see the common factor is [tex]3c[/tex]

The Greatest Common Factor of [tex]33c ,27c^4[/tex] is [tex]3c[/tex]

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Select the correct answer.
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?
OA 2+2-4x+2y+1=0
OB. ++4x-2y+1=0
OC. 2+2+4x-2y+9=0
OD. -+2x+y+1=0
entum. All rights reserved.
Reset
C
Next
C

Answers

The equation of a circle, with its center (a,b) and radius R is
(x-a)^2 + (y-b)^2 = R^2

For this circle,
(x+2)^2 + (y-1)^2 = R^2

We also know that (-4,1) is a part of the circle, so we replace:
(-4+2)^2 + (1-1)^2 =R^2
4= R^2

The equation of the circle is:
(x+2)^2 + (y-1)^2 = 4
x^2 +4x+4 + y^2 -2x+1 =4
x^2 + 4x + y^2 -2y +1 =0

Please answer questions three to five!

Answers

The computation shows that the amount that will be charged will be $5.00 and $9.00 respectively.

How to illustrate the information?

When the customer has a 6 pound Chihuahua, the amount that will be charged will be $5.00.

When a customer has a 65 pound Labrador, the amount that will be charged is $9.00.

This is illustrated as the cost is based on the weights given.

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Quick algebra 1 questions for 50 points!

Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!

Answers

The cost per person if number of students is 100 given the inverse variation is $46.75

Inverse variation

Cost per person = CNumber of students = n

C = k / n

where,

k = constant of proportionality

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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Answer:

C = $46.75

Step-by-step explanation:

85 × 55 = k

4,675 = k

4675/100=46.75

therefore the answer is 46.75

Find the area of each of these rectangles

Answers

a) 5 square root (2) units square
b) 6 units square
c) 36 units square

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to
finish his breakfast and 39 minutes to commute to school. At what time did he
reach the school?

Answers

Answer:

[tex]\huge\boxed{\sf 8:32\ AM}[/tex]

Step-by-step explanation:

Woke up = 7:30 AM

Time to:

Get ready = 14 minFinish breakfast = 9 minCommute to school = 39 min

Altogether:

= 14 + 9 + 39 min

= 62 minutes

(As we know that, 1 hour = 60 minutes)

So,

62 minutes = 1 hour 2 minutes

Time he reached the school:

7 hr 30 min + 1 hr 2 min

Combine like terms

7 hr + 1 hr + 30 min + 2 min

8 hr + 32 min

OR

8:32 AM

[tex]\rule[225]{225}{2}[/tex]

❍ Question -:

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?

❍ Explanation -:

In this question we are asked to calculate the time paul reach the school.

Altogether time paul took to get ready, to finish his breakfast and to commute to school.

(14 + 9 + 39) minutes

→ (23 + 39) minutes

→ 62 minutes

Now we will convert minutes into hour.

62 ÷ 60

→ 1 hr 2 min

Now we will calculate the time he reached his school.

7 hr + 30 + 1 hr 2 min

[tex]\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}[/tex]

He will reach the school at 8:32 AM.

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. what is the probability that the lock code consists of all even digits?

Answers

Probability that the lock code consists of all even digits is [tex]1344[/tex] if we choose the [tex]4[/tex] digit lock is randomly from numbers [tex]1,2,3,4,5,6,7,8,9[/tex]

How can we find the probability that the lock code consists of all even digits?

Total numbers are [tex]1,2,3,4,5,6,7,8,9[/tex]

And we choose [tex]4[/tex] digit code

So probability of choosing [tex]4[/tex] numbers from [tex]9[/tex] numbers without reapitation is

[tex]9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024[/tex]

For All numbers are even , probability the last digit of number is even.

So we have [tex]4[/tex]  even number and if we fix one on last digit and can change other [tex]3[/tex] then the probability is

[tex]4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344[/tex]

So the total probability of code lock having all even number is [tex]1344[/tex]

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If rick has 35 oranges and he divide them into equally into 7 bags. what fraction represents the number of oranges rick puts in each bag?

Answers

the answer for this question is 35/7

You and a friend are playing a game of chance. Every time you roll a 1 or 2 you are successful, and your friend will pay you $1. Every time you roll (using a fair die) a 3, 4, 5 or 6, you must pay your friend $2. If 71% of your rolls are successful and 29% of your rolls are unsuccessful, how much money do you expect to have earned/owed by the end of the game

Answers

Considering the mean of a discrete distribution, you are expected to earn $0.13 by the end of the game.

What is the mean of a discrete distribution?

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Since 71% of your rolls are successful and 29% of your rolls are unsuccessful, the distribution of your earnings is:

P(X = 1) = 0.71.P(X = -2) = 0.29

Hence the expected value is:

E(X) = 1 x 0.71 - 2 x 0.29 = 0.71 - 0.58 = 0.13

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The reciprocals of what three different positive integers have sum equal to 1?

Answers

Answer:

1/a + 1/b + 1/c = 1 , a,b,c is nonzero

Step-by-step explanation:

bc +ac +ab /abc = 1

bc + ac + ab = abc

a = b = c = 1

Can you plssss help !!!

Answers

The parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.

Parts of the circle shown in the image

The following are the parts of the circle shown;

Chord: the length DC and DG represent the chord of the circleDiameter: the length HF represent the diameter of the circleRadius: the length HA and FA represents the radius of the circletangent: the line JB represents a tangent to the circleCenter: point A represents the center of the circle

Thus, the parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.

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The ratio of dogs to cats is 3 to 8. if there are 294 dogs, how many cats are there?

Answers

Answer:

784 cats      Yikes !

Step-by-step explanation:

d/c = 3/8  

              3/8 = 294/c

                        c = 294 * 8/3 = 784 cats

help me!!!
please I am in a rush

Answers

Answer:

A= 54

B=3

Step-by-step explanation:

I hope this helps!

The length of a rectangle is 3 less than twice the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by 2. Show your work.

Answers

The change in the area is represented by the expression ΔA = 9 · x + 4, where x is the original width of the rectangle.

What is the change in the area of the rectangle if side lengths are changed?

By geometry we know that the area of a rectangle is equal to the product of its width (x) and length (y). Based on the statement, the original rectangle is equal to:

A = x · y

A = x · (2 · x - 3)

And the change in the area is:

A + ΔA = (x + Δx) · (y + Δy)

A + ΔA = x · y + Δx · y + Δy · x + Δx · Δy

ΔA = Δx · y + Δy · x + Δx · Δy

ΔA = (2 · x - 3) · Δx + Δy · x + Δx · Δy

ΔA = 2 · (2 · x - 3) + 5 · x + 10

ΔA = 9 · x + 4

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Which value is not part of the five-number summary for the following data set?
35, 23, 24, 30, 28, 23, 27, 33, 27, 34, 30, 30

A. 29
B. 23
C. 31.5
D. 24

Answers

Answer:

  D. 24

Step-by-step explanation:

The 5-number summary of a data set includes ...

minimum1st quartilemedian (2nd quartile)3rd quartilemaximum

Summary values

When the data are written in increasing order, they are ...

  23 23 24  27 27 28  30 30 30  33 34 35

The minimum is the first value on the list, 23.

The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.

The median is the average of the two middle values: (28+30)/2 = 29.

The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.

The maximum is the last value on the list: 35.

Answer choices

A. 29 is the median

B. 23 is the minimum

C. 31.5 is the 3rd quartile

D. 24 is not part of the 5-number summary

It cost Cai $1,80 to send 12 text messages, How much would it cost to send 90 text
messages?

Answers

Answer:

$13.5

Step-by-step explanation:

cost of 1 text message= $1.80÷12 =$0.15

cost of 90 messages = $0.15×90 = $13.5

Answer: $13.50 for 90 text messages

Step-by-step explanation:

$0.15×90 = $13.5

$0.15 is the unit rate for 1 text message cost.

Find the other endpoint of the line segment with the given endpoint -5, 2 and midpoint 2, -5

Answers

Answer:

( 9, -12 )

Step-by-step explanation:

Mario's Math Tutoring

you have the midpoint

2, -5

use the midpoint formula

(x1+x2)/2 , (y1+y2)/2

to get the endpoint

x :

(-5+x2)/2 = 2

(-5+x2) = 4

-5+x2 = 4

x2 = 9

y:

(2+y2)/2 = -5

(2+y2) = -10

2+y2 = -10

y2 = -12

Thank you Mario!

Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).

Answers

The area of the convex polygon is 43/2 square units

How to determine the area of the convex polygon?

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]

So, we have:

[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]

Evaluate

[tex]A = \frac12 * (|-43|)[/tex]

Remove the absolute bracket

[tex]A = \frac12 * 43[/tex]

This gives

[tex]A = \frac{43}2[/tex]

Hence, the area of the convex polygon is 43/2 square units

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To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?

Answers

The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.

According to the statement

we have given that the to form a ellipse we use the base and angle of the cone, And we have to tell the relationship between them.

So, For this purpose, We know that the

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

And to make a ellipse the relationship between the base of triangle and the angle of the cone is that the

The plane must be at a 45 degree angle to the base of the cone.

By this way we make a ellipse with the help of the cone.

So, The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?

A. The plane is parallel to the base of the cone..

B. The plane may be perpendicular to the base of the cone..

C. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.

D. The plane must be at a  angle to the base of the cone.

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Answer:

The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.

Step-by-step explanation:

The plane doesn't need to be at an exact angle of 45 degrees. The most important thing is that the angle isn't parallel or perpendicular to the base of the cone, but it has to be non-zero without intersecting the base itself. It also only intersects one of the cones when looking at a double-cone.

Which of the following is not considered an action that would interfere with the airflow patterns at the front opening of the biosafety cabinet

Answers

An action that would not interfere with the airflow patterns at the front opening of the biosafety cabinet is a researcher discarding waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening.

What is biosafety?

It should be noted that biosafety simply means the use of safety equipment as specifically designs tools to ensure that people are protected from hazards.

In this case, when a researcher discards waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening, it won't interfere with the airflow pattern.

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HELP pleeeeease, will give brainliest

Answers

Answer:The answer is A

Step-by-step explanation:

Almost done!!! Appreciate the help

Answers

Using the formula for the distance between two points to find the side lengths, the perimeter of the polygon is of 25 units.

What is the perimeter of a figure?

The perimeter of a figure is given by the sum of the side lengths of it's outside dimensions.

What is the distance between two points?

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For this problem, the distances are given as follows:

[tex]D_1 = \sqrt{(-1 -(-1))^2 + (6 - 3)^2} = 3[/tex].[tex]D_2 = \sqrt{(2 -(-1))^2 + (10 - 6)^2} = 5[/tex].[tex]D_3 = \sqrt{(5 - 2)^2 + (6 - 10)^2} = 5[/tex].[tex]D_4 = \sqrt{(5 - 5)^2 + (3 - 6)^2} = 6[/tex].[tex]D_5 = \sqrt{(5 - (-1))^2 + (3 - 3)^2} = 6[/tex].

Hence the perimeter is given by:

P = 3 + 2 x 5 + 2 x 6 = 25 units.

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The length of a rectangle is 8 inches more than the width. the perimeter is 44 inches. find the length and width of the rectangle

Answers

Answer: Width is 7 inches, length is 15 inches.

Step-by-step explanation:

Let the width be w. Then, the length is w+8.

[tex]2(w+w+8)=44\\\\w+w+8=22\\\\2w+8=22\\\\2w=14\\\\w=7\\\\\implies l=15[/tex]

A group of 31 friends gets together to play a sport. First, people
must be divided into teams. Each team has to have exactly 3
players, and no one can be on more than one team. How many
teams can they make? (It is possible that not everyone can be on a
team.)
(Do not include units in your answer.)

Answers

The number of teams she can make is 10.

How many teams can she make?

Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.

The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.

Number of teams she can make = total number of friends / number of people in each group

31 / 3 = 10 remainder 1

So, only 10 teams can be made. one person would not be on any team.

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A group of students consists of four people in all; two women and two men. They agree to take turns taking notes in lecture. One person at a time will be selected at random from the group (without replacement) until everyone has had a turn. The expected value of the number of people selected before and including the first time a woman has a turn is (Q17)______ .
The standard error of the number of people selected before and including the first time a woman has a turn is (Q18)______ .

Answers

The expected value of the number of people selected before and including the first time a woman has a turn is 1.6667 and the standard error is 0.7454.

How to illustrate the information?

It should be noted that the expected value will be:

1[p(x = 1)] + 2[p(x = 2)] + 3[p(x = 3)]

= 1(0.5) + 2(0.3333) + 3(0.1667)

= 1.6667

Var(X) = E(X²) - E(X)2

= 3.3335 & (1.6667)²

= 0.555611

The standard error will be:

= ✓0.555611

= 0.7454

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In apirl is rained 1/4 of a inch on 15 diffret day how many inches of rain fell

Answers

In [tex]15[/tex] diffret days [tex]15/4[/tex] inches of rain fell in April month if every day rained [tex]1/4[/tex] of a inch .

How to find the rain fell in [tex]15[/tex] diffret days ?

We know that rain in every day is [tex]1/4[/tex] of a inch

So for [tex]15[/tex] days

[tex]1/4+1/4+1/4+......15times\\=15/4[/tex]

So in [tex]15[/tex] diffret days in April rain fell is [tex]15/4[/tex] inches.

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