How much money does the average professional hockey fan spend on food at a single hockey​ game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $ 18.00 and $ 2.75​, respectively. Use this information to create a 90​% confidence interval for the mean. Express the answer in the form x overbar plus or minus t Subscript alpha divided by 2 Baseline (s divided by StartRoot n EndRoot ).

Answer:

The onject 1/8 of the length of the path 3/4 in second.

Using the ratio and proportion to find the total time does it take the object to travel the entire length of the path as following

Length:time

X:(total time )

Total time x.(3/4)/(1/8x)=(3/4)/(1/8) = 6 seconds

Answer:

Mean = 3x

Step-by-step explanation:

Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]

Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]

Mean = [tex]\frac{15x}{5}[/tex]

Mean = 3x

The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.

To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.

In this case, we have five values.

Mean = (x + 2x + 3x + 4x + 5x) / 5

Simplifying the numerator:

Mean = (15x) / 5

Mean = 3x

Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.

The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.

To learn more about the mean;

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Answer:

The probability that a randomly selected student didn’t take economics but did take statistics is 13%.

Step-by-step explanation:

Let the event that a student offers Economics be E.

The event that a student does NOT offer Economics is E'.

Let the event that a student offers Statistics be S.

The event that a student does NOT offer Statistics be S'.

P(E) = 13.5% = 0.135

P(S) = 24.7% = 0.247

P(E n S) = 11.7% = 0.117

Find the probability that a randomly selected student didn’t take economics but did take statistics

This probability = P(E' n S)

Since E and E' are mutually exclusive events,

P(S) = P(E' n S) + P(E n S)

P(E' n S) = P(S) - P(E n S)

P(E' n S) = 0.247 - 0.117 = 0.13 = 13%

Hope this Helps!!!

Answer:

252

Step-by-step explanation:

The order of the books isn't important, so we'll use combinations.

The number of ways to choose 5 books from 10 is:

₁₀C₅ = 10! / (5! (10 − 5)!)

₁₀C₅ = 10! / (5! 5!)

₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)

₁₀C₅ = 252

Answer:

The question is not clear.

Step-by-step explanation:

Normally it helps to rewrite 8 as

8 = 2 * 2 * 2 = 2³

However the question is not clear.

There are no following expressions given...

By 2X^2 +8,

do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)

or did you perhaps mean 2^(x+8)

Next time, please add a picture.

Answer:

(2x-4i)(x+2i)

Answer:

The probability that at least 13 flights arrive late is 2.5196 [tex]\times 10^{-6}[/tex].

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]

where, n = number of trials (samples) taken = 18 Southwest flights

           r = number of success = at least 13 flights arrive late

          p = probability of success which in our question is probability that

                flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = Number of flights that arrive late.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X [tex]\geq[/tex] 13)

P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

= [tex]\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}[/tex]

= [tex]\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}[/tex]

= 2.5196 [tex]\times 10^{-6}[/tex].

Solution,

Radius=2 m

Area =pi r^2

= 3.142*(2)^2

=12.568 m^2

hope it helps

Good luck on your assignment

Answer:

Step-by-step explanation:

1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...

  g(x) = 2|x|

__

2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.

  g(x) = -2|x|

__

3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.

  g(x) = -2|x| -3

__

4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...

  g(x) = -2|x -1| -3

She will receive a lot more money because she is already retired from work already and will win as bit more money

Answer:

B and A

Step-by-step explanation:

So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.

Answer:

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595

The margin of error is:

M = T*s = 1.8595*2.7 = 5

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 25.3 - 5 = 20.3 milligrams

The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

Answer:

[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]  

The degrees of freedom are given by:

[tex] df =n-1= 12-1=11[/tex]

And the p value would be:

[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4

Step-by-step explanation:

We have the following data given:

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

The sample mean and deviation from these data are:

[tex]\bar X=4.5[/tex] represent the sample mean  

[tex]s=2.680[/tex] represent the sample deviation

[tex]n=10[/tex] sample size  

[tex]\mu_o =4[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to verify if the true mean is equal to 4, the system of hypothesis would be:  

Null hypothesis:[tex]\mu =4[/tex]  

Alternative hypothesis:[tex]\mu \neq 4[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the the info we got:

[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]  

The degrees of freedom are given by:

[tex] df =n-1= 12-1=11[/tex]

And the p value would be:

[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4

Answer:

option 2

Step-by-step explanation:

4^2=16/8=2.  4^2=16/16=1.  2-1=1

Answer:

Dear user,

Answer to your query is provided below

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.

Step-by-step explanation:

Here , It is given that the number is three digit in which units digit is 2 and hundreds digit is 4.

As per rule, the sum of its digits should've divisible by 9. So, Let the unknown digit be X .

Therefore, 2+X+4 =9

This implies, X = 9-2-4 = 3

So, the three digit number will be 432.

Verify - 432/9 = 48

Hence proved

Answer:

$5073.37

Step-by-step explanation:

We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t

Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:

A = 5000(1 + 0.06)^0.25

When you plug that into the calc, you should get 5073.37 as your final answer!

[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

Step-by-step explanation:

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.

Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.

Answer:

a) C. The population must be normally distributed.

b) P(x < 65.8) = 0.8159

c) P(x > 64.2) = 0.3015

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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

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

In this question:

[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me

n < 30, so the distribution of the population must be normal.

The correct answer is:

C. The population must be normally distributed.

(b) Assuming the normal model can be used, determine P(x < 65.8).

This is the pvalue of Z when X = 65.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{65.8 - 62}{4.22}[/tex]

[tex]Z = 0.9[/tex]

[tex]Z = 0.9[/tex] has a pvalue of 0.8159.

So

P(x < 65.8) = 0.8159

(c) Assuming the normal model can be used, determine P(x > 64.2).

This is 1 subtracted by the pvalue of Z when X = 64.2. So

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

[tex]Z = \frac{64.2 - 62}{4.22}[/tex]

[tex]Z = 0.52[/tex]

[tex]Z = 0.52[/tex] has a pvalue of 0.6985.

1 - 0.6985 = 0.3015

So

P(x > 64.2) = 0.3015

Answer:

Step-by-step explanation:

If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5

We would set up the hypothesis test.

For the null hypothesis,

p = 0.5

For the alternative hypothesis,

p < 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 28

n = number of samples = 80

P = 28/80 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68

From the normal distribution table, the area below the test z score in the left tail 0.0037

Therefore,

p value = 0.0037

Assuming a significance level of 0.05, therefore,

Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.

Answer:

[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]

And then we can find the y intercept using one point for example (0,800) and we have:

[tex] 800= -2*0+ b[/tex]

[tex] b= 800[/tex]

And our model would be:

[tex] y = -2x +800[/tex]

And the x intercept would be if y=0 then

[tex] 0 =-2x +800[/tex]

[tex] x =400[/tex]

x intercept =400 represent the value of x when y =0

y intercept = 800 represent the value of y when x =0

Step-by-step explanation:

We have the following points given:

(0, 800) and (400, 0)

If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:

[tex] y=mx +b[/tex]

Where

[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]

And then we can find the y intercept using one point for example (0,800) and we have:

[tex] 800= -2*0+ b[/tex]

[tex] b= 800[/tex]

And our model would be:

[tex] y = -2x +800[/tex]

And the x intercept would be if y=0 then

[tex] 0 =-2x +800[/tex]

[tex] x =400[/tex]

x intercept =400 represent the value of x when y =0

y intercept = 800 represent the value of y when x =0

Answer:

And then we can find the y intercept using one point for example (0,800) and we have:

And our model would be:

And the x intercept would be if y=0 then

x intercept =400 represent the value of x when y =0

y intercept = 800 represent the value of y when x =0

Step-by-step explanation:

We have the following points given:

(0, 800) and (400, 0)

If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:

Where

And then we can find the y intercept using one point for example (0,800) and we have:

And our model would be:

And the x intercept would be if y=0 then

x intercept =400 represent the value of x when y =0

y intercept = 800 represent the value of y when x =0

Step-by-step explanation:

Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

Answer:  b) Each sold the same number of vehicles

Step-by-step explanation:

This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.

Kelly: 8 + 2 + 6 = 16

Scott: 7 + 8 + 1 = 16

Mark: 10 + 4 + 2 = 16

The total number of vehicles sold by each person is the same

Answer:

Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]

Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]

Step-by-step explanation:

This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:

Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:

[tex]A=6\,*\, B\\A=6B[/tex]

Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour​", we write:

[tex]A+B=224\,\,\frac{mi}{h}[/tex]

Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:

[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]

Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:

[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]

Answer:

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Step-by-step explanation:

In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:

probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks

probability that the next customer will request mid-grade gas and fill the tank=  30%*60%

probability that the next customer will request mid-grade gas and fill the tank= 0.1800

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Answer:

answer B [tex]\boxed{ \ 569 \ }\\[/tex]

Step-by-step explanation:

f(8)=-2*8+5=-11

g(8)=9*8*8+4=580

f(8)+g(8)= -11+580=569

Answer:

Step-by-step explanation:

a) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 451

x = 1.5/100 × 451 = 7

p = 7/451 = 0.02

q = 1 - 0.02 = 0.98

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.97 = 0.1

α/2 = 0.01/2 = 0.03

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.03 = 0.97

The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17

Therefore, the 97% confidence interval is

0.02 ± 2.17√(0.02)(0.98)/451

= 0.02 ± 0.014

b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

The distribution that should be used is the normal distribution

Answer:

w || n and n ⊥ m

Step-by-step explanation:

To find out which statement is true, recall the following:

1. 2 lines are said to be parallel to each other if they do not intersect at any given point and are of the same distant apart. Parallel is denoted by ||

2. 2 lines are said to be perpendicular if both lines intersect at a right angle. It is denoted by ⊥

==>From the diagram given, we can see that w and n are of the same distant apart and they do not intersect at any given point.

Also, we can see that n and m intersect at point X to at right angle.

Therefore, we can conclude that w || n and n ⊥ m

Answer:

12

Step-by-step explanation:

1:4 = 3:12

Answer:

12 cups of water

Step-by-step explanation:

The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12

113/32

Step-by-step explanation:

7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.

49 plus 64 is 113 divided by 32

3.53125

Step-by-step explanation:

7^2+4^3/2^5

= 49+64/32

= 113/32

= 3.53125

Answer:

7. [tex]x \leq 5[/tex]

8. [tex]x\geq 4[/tex]

9. x < 5

10. x < -7

11.  x < 45

12. [tex]x\geq -10[/tex]

13. x < -7

14. x < 45

15. [tex]x\leq 50[/tex]

16. [tex]w\geq 16[/tex]

18. q > 4

Step-by-step explanation: