The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the x-test statistic, and use the x-distribution to find the p-value of the test. Category Observed (Expected) A 25 (20) B 35(40) C 50(60) D 90(80) Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places. chi-square statistic = p-value = i

Answer:

5

Step-by-step explanation:

took the test

The coordinates of the point that divides the line segment from J to K into a ratio of 2:3 are P(-5,7), and the y-coordinate is 7, the correct option is D.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Ratio= 2:3

Now,

Let the point we are looking for be denoted as P(x,y), and let the ratio be 2:3, which means that the distance from J to P is 2/5 times the distance from J to K.

Using the distance formula, we can find the distance between J and K as:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

= sqrt((-8 - (-3))^2 + (11 - 1)^2)

= sqrt(25 + 100)

= sqrt(125)

The distance from J to P is 2/5 of the total distance, which is:

(2/5)d = (2/5)sqrt(125) = 2sqrt(5)

Using the ratio formula, we get:

x = (3* (-3) + 2 * (-8)) / (3+2) = -5

y = (31 + 211) / (3+2) = 7

Therefore, by the given ratio answer will be 7.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ7

Answer:

22 mi

Step-by-step explanation:

From the question given above, the distance from E to F is 6 in.

Thus, we can obtain the distance from E to F (i.e mi) by using the scale provided in the question. This is illustrated below:

3 in = 11 mi

Therefore,

6 in = 6 in × 11 mi / 3 in

6 in = 22 mi

Therefore, the distance from E to F is 22 mi

Answer:

[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]

Answer:

8 + 30 ÷ 2 + 4  = 27

8 + 30 ÷ (2 + 4 ) = 13

(8 + 30) ÷ 2 + 4  = 23

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

when you change the mixed numbers to improper fractions, you get 4/5 * 10/9 ÷ 8/3. you can flip the 8/3 to 3/8 and change the division sign to multiplication, because dividing by a fraction is the same as multiplying by its reciprocal. you can cancel some things and ultimately you get 1/3

Answer:

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A carpet expert believes that 9% of Persian carpets are counterfeits.

This means that [tex]p = 0.09[/tex]

Sample of 686:

This means that [tex]n = 686[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{0.09*0.91}{686}} = 0.0109[/tex]

What is the probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%?

Proportion lower than 9% - 3% = 6% or higher than 9% + 3% = 12%. The normal distribution is symmetric, thus these probabilities are equal, so we can find one of them and multiply by 2.

Probability it is lower than 6%

p-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0109}[/tex]

[tex]Z = -2.75[/tex]

[tex]Z = -2.75[/tex] has a p-value of 0.0030

2*0.0030 = 0.0060

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Answer:

≤ y ≤ 70 and 0 ≤ x ≤ 500

Step-by-step explanation:

In this relation we have two things to analyze, the number of gallons of water in the heater, that is 500 gallons, and the time that it took to empty the heater.

Let's count the time.

First, there are 20 minutes in wich 100 gallons are drained.

then, another drain valve is opened, so in 20 minutes they drain 200 gallons of water.

now, the wait for 10 minutes.

Now there are 200 gallons remaining, so the workers must wait for the other 20 minutes to drain the 200 gallons remaining.

The total amount of time is 70 minutes.

So if we have a relationship of water in the heater vs time, where X is the water remaining and Y is the time, the correct domains are:

Y from 0 minutes to 70 minutes

X from 0 gallons to 500 gallons  

So the correct options are C and E.

0 ≤ y ≤ 70 and 0 ≤ x ≤ 500

Step-by-step explanation:

Let us take a nominal square of area 25 cm².

So, in this question, we can say that:-

a. The length of one of its sides will be less than 5 cm.

b. Its perimeter will be less than 20 cm.

Hope it helps :)

Step-by-step explanation:

area= 25cm squared

length of one side = 5cm as 5*5 =25

perimeter= 5*4= 20cm

But since the area is less than 25cm squared

we can say that the length of one side is less than 5cm and we can also say that the length of the perimeter is less than 20cm.

Hope this helps.

Answer: I do not know what you mean, but you could do burpees, and sit ups.

Answer:

A: x = 0

B: x = All real numbers

Step-by-step explanation:

A.

Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;

[tex](6^2)^x=1[/tex]

Simplifying that will result in;

[tex]36^x=1[/tex]

As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.

[tex]36^0=1\\x=0[/tex]

B.

As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;

[tex](6^0)^x=1[/tex]

One can simplify that;

[tex]1^x=1[/tex]

However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.

[tex]x=All\ real \ numbers[/tex]

Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

=1/3×π×5²×11

=275/3 ×3.14

≈287.33 in³

Answer

$0.1346

Explanation:

Find probability of each card and the value of each card and then add them together.

Probability of getting a heart = 13/52

Price of one heart =$0.30

Pay for one heart = 13/52×0.30=$0.075

Probability of getting a queen =4/52

Price of one queen =$0.55

Pay for one queen =4/52×$0.55=$0.0423

Probability of getting a queen of hearts =1/52

Price of one queen =$0.90

Pay for one queen =1/52×$0.90=$0.0173

Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346

Answer:

0.2952

Step-by-step explanation:

Not enough seats will be available if 23 or 24 people show up.

Required probability = 24C24(0.9005)24 + 24C23(0.9005)23*0.0995 = 0.2952

Answer:

0.9484 = 94.84% probability that the sample proportion of girls will be greater than 41%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 44% of the children in a school are girls.

This means that [tex]p = 0.44[/tex]

Sample of 727 children

This means that [tex]n = 727[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.44[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.44*0.56}{727}} = 0.0184[/tex]

What is the probability that the sample proportion of girls will be greater than 41%?

This is 1 subtracted by the p-value of Z when X = 0.41. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.41 - 0.44}{0.0184}[/tex]

[tex]Z = -1.63[/tex]

[tex]Z = -1.63[/tex] has a p-value of 0.0516

1 - 0.0516 = 0.9884

0.9484 = 94.84% probability that the sample proportion of girls will be greater than 41%

Step-by-step explanation

n^3-n.

Hope this will help you :) <3

Answer:

1 mile per 10 minutes

Step-by-step explanation:

Answer:

Freezers made up [tex]\frac{6}{25}[/tex] = 24% of the appliances sold in January.

Step-by-step explanation:

We have that:

10 + 8 + 12 + 12 + 8 = 50 parts were sold in January.

Freezers made up what part of the appliances sold in January?

12 of those were freezers, so:

[tex]\frac{12}{50} = \frac{6}{25} = 0.24[/tex]

Freezers made up [tex]\frac{6}{25}[/tex] = 24% of the appliances sold in January.

Answer:

7 miles

Step-by-step explanation:

* means multiply

7/10 * 10 = 7

Answer:

The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

An experimenter flips a coin 100 times and gets 59 heads.

This means that [tex]n = 100, \pi = \frac{59}{100} = 0.59[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 - 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.4756[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 + 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.7044[/tex]

The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).

Answer:

HEY THERE!

Step-by-step explanation:

the correct answer for your question is 90°

Answer:

The answer is c :)

Step-by-step explanation:

90 degrees

Answer:

[tex]4 {x}^{2} - 4x - 8 - (2 {x}^{2} + 3x - 6) = 4 {x}^{2} - 4x - 8 - 2 {x}^{2} - 3x + 6 = 2 {x}^{2} - 7x - 2[/tex]

Answer:

is 22

Step-by-step explanation:

Answer:

It doesn't have a slope?

Step-by-step explanation:

Knowing that the slope equation is y2-y1/x2-x1

9-4       5

----- = ------   = 0

4-4       0

this means that the slope is 0...

Step-by-step explanation:

x intercept=(-1,0) because the graph is passing this point on the x axis

y intercept=(0,-3)

Answer:

4th option

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis.

This is at (- 1, 0 )

The y- intercept is where the graph crosses the y- axis.

This is at (0, - 3 )

9514 1404 393

Answer:

Step-by-step explanation:

Consecutive interior angles are supplementary.

  (x -20)° +(4x +15)° = 180°

  5x = 185 . . . . . . . . . . . . . . divide by °, add 5

  x = 37 . . . . . . . . . . . . divide by 5

__

  74° +(5y -4)° = 180°

  5y = 110 . . . . . . . . . . . divide by °, subtract 70

  y = 22 . . . . . . . . . . divide by 5

Step-by-step explanation:

x²-xy-xy+y²

x²+2xy+y²

hope it helps

Answer:

ai) 5pi

aii) 4.5pi

aiii) 4.1pi

b) 4pi

Step-by-step explanation:

a) Area of a circle is given by pi×r^2.

The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).

Let's simplify this.

Factor pi from the terms in the numerator:

pi(b^2-a^2)/(b-a)

Factor the difference of squares in the numerator:

pi(b-a)(b+a)/(b-a)

"Cancel" common factor (b-a):

pi(b+a).

So let's write a conclusive statement about what we just came up with:

The average rate of change of the area of a circle from r=b to r=a is pi(b+a).

i) from 2 to 3 the average rate of change is pi(2+3)=5pi.

ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.

from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.

b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.

Let's confirm by differentiating and then plugging in 2 for r.

A=pi×r^2

A'=pi×2r

At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.

Hi there I hope you are having a great day :) I am pretty sure that you do 280 degrees around angle so i would say you would add 63 + 73 + 83 = 219 then you would take away it 280 - 219 =  61 so y must equal to 61 this is because we can see a z shape and a z shape adds up to 280.

Hopefully that helps you.

Answer:

(a): The conditional pmf of Y when X = 1

[tex]p_{Y|X}(0|1) = 0.2353[/tex]

[tex]p_{Y|X}(1|1) = 0.5882[/tex]

[tex]p_{Y|X}(2|1) = 0.1765[/tex]

(b): The conditional pmf of Y when X = 2

[tex]p_{Y|X}(0|2) = 0.0962[/tex]

[tex]p_{Y|X}(1|2) = 0.2692[/tex]

[tex]p_{Y|X}(2|2) = 0.6346[/tex]

(c): From (b) calculate P(Y<=1 | X =2)

[tex]P(Y\le1 | X =2) = 0.3654[/tex]

(d): The conditional pmf of X when Y = 2

[tex]p_{X|Y}(0|2) = 0.025[/tex]

[tex]p_{X|Y}(1|2) = 0.150[/tex]

[tex]p_{X|Y}(2|2) = 0.825[/tex]

Step-by-step explanation:

Given

The above table

Solving (a): The conditional pmf of Y when X = 1

This implies that we calculate

[tex]p_{Y|X}(0|1), p_{Y|X}(1|1), p_{Y|X}(2|1)[/tex]

So, we have:

[tex]p_{Y|X}(0|1) = \frac{p(y = 0\ n\ x = 1)}{p(x = 1)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{Y|X}(0|1) = \frac{0.08}{0.08+0.20+0.06}[/tex]

[tex]p_{Y|X}(0|1) = \frac{0.08}{0.34}[/tex]

[tex]p_{Y|X}(0|1) = 0.2353[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{Y|X}(1|1) = \frac{0.20}{0.34}[/tex]

[tex]p_{Y|X}(1|1) = 0.5882[/tex]

[tex]p_{Y|X}(2|1) = \frac{0.06}{0.34}[/tex]

[tex]p_{Y|X}(2|1) = 0.1765[/tex]

Solving (b): The conditional pmf of Y when X = 2

This implies that we calculate

[tex]p_{Y|X}(0|2), p_{Y|X}(1|2), p_{Y|X}(2|2)[/tex]

So, we have:

[tex]p_{Y|X}(0|2) = \frac{p(y = 0\ n\ x = 2)}{p(x = 2)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{Y|X}(0|2) = \frac{0.05}{0.05+0.14+0.33}[/tex]

[tex]p_{Y|X}(0|2) = \frac{0.05}{0.52}[/tex]

[tex]p_{Y|X}(0|2) = 0.0962[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{Y|X}(1|2) = \frac{0.14}{0.52}[/tex]

[tex]p_{Y|X}(1|2) = 0.2692[/tex]

[tex]p_{Y|X}(2|2) = \frac{0.33}{0.52}[/tex]

[tex]p_{Y|X}(2|2) = 0.6346[/tex]

Solving (c): From (b) calculate P(Y<=1 | X =2)

To do this, where Y = 0 or 1

So, we have:

[tex]P(Y\le1 | X =2) = P_{Y|X}(0|2) + P_{Y|X}(1|2)[/tex]

[tex]P(Y\le1 | X =2) = 0.0962 + 0.2692[/tex]

[tex]P(Y\le1 | X =2) = 0.3654[/tex]

Solving (d): The conditional pmf of X when Y = 2

This implies that we calculate

[tex]p_{X|Y}(0|2), p_{X|Y}(1|2), p_{X|Y}(2|2)[/tex]

So, we have:

[tex]p_{X|Y}(0|2) = \frac{p(x = 0\ n\ y = 2)}{p(y = 2)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{X|Y}(0|2) = \frac{0.01}{0.01+0.06+0.33}[/tex]

[tex]p_{X|Y}(0|2) = \frac{0.01}{0.40}[/tex]

[tex]p_{X|Y}(0|2) = 0.025[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{X|Y}(1|2) = \frac{0.06}{0.40}[/tex]

[tex]p_{X|Y}(1|2) = 0.150[/tex]

[tex]p_{X|Y}(2|2) = \frac{0.33}{0.40}[/tex]

[tex]p_{X|Y}(2|2) = 0.825[/tex]

Answer:

Median: 7.5

Mean: 8.6

Step-by-step explanation:

Median = the average of the 2 middle numbers of the set in ascending order, 6, 6, 6, 7, 8, 10, 12, 14

(7+8)/2 = 2

Mean = the sum of the numbers divided by the number of values

6 + 6+ 6+ 7 +8 +10 +12 +14/8

69/8

8.625