Type the expressions as radicals.

Answer:

  0.0833

Step-by-step explanation:

There are 7C6 = 7 ways to choose 6 hazelnuts from the 7 present.

There are 9C6 = 84 ways to choose 6 nuts from the 9 present.

The probability of choosing 6 hazelnuts from the 9 present is ...

  7/84 = 1/12 = 0.0833...(repeating)

The probability of interest is 0.0833.

____

Comment on the notation

The notation nCk means n!/(k!(n-k)!). It is the number of ways k items can be chosen from n items without regard to order. It can be pronounced "n choose k."

Answer:

The standard error of the mean (SE) is of 0.326lb.

Step-by-step explanation:

The standard error of the mean is given by the following formula:

[tex]SE = \frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

In this problem, we have that:

[tex]s = 4.3, n = 174[/tex]

Then

[tex]SE = \frac{s}{\sqrt{n}} = \frac{4.3}{\sqrt{174}} = 0.326[/tex]

The standard error of the mean (SE) is of 0.326lb.

Answer:

y²-3y+2=0

=> y²-(2+1)y +2=0

=> y²-2y-y+2=0

=> y(y-2)-1(y-2)=0

=> (y-2)(y-1)=0

=> y = 2 or y= 1

Answer:

We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.

Step-by-step explanation:

From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.

Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;

Number of single boots = 7 x 2 = 14

Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.

Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.

To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.

The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.

Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.

The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.

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Answer:

$5

Step-by-step explanation:

Using algebra to solve this problem.

Let 'x' be Timmy’s amount.

->Mara has 3 times as many dollars as her brother i.e 3x dollars

->If Mara is given $20 by their mother, then expression would be

3x + 20

Since Mara’s new amount is supposed to be seven times Timmy’s

current amount, this forms an equation

3x + 20 = 7x

Solving for 'x'

7x -3x=20

4x = 20

x=20/4

x=5

Timmy has an amount of $5

Final answer:

By setting up two equations based on the given information and solving for T, we find that Timmy has $5.

Explanation:

Let's denote the amount of dollars Timmy has as T. According to the question, Mara has 3 times as many dollars as Timmy, so we can write this as M = 3T, where M is the amount Mara has. Now, we are told that if Mara is given an additional $20, she will have 7 times the amount Timmy has. We can express this as M + 20 = 7T. Using the two equations, we can solve for the value of T.

First, substitute the value of M from the first equation into the second equation:

3T + 20 = 7T

20 = 7T - 3T

20 = 4T

T = 20 / 4

T = $5

Therefore, Timmy has $5.

Answer:

D = 24

Step-by-step explanation:

The given quadratic equation is [tex]y=x^2-8x+10[/tex].

It is required to find the value of the discriminant. The value of discriminant  of any quadratic equation is given by :

[tex]D=b^2-4ac[/tex]

Here, a = 1, b = -8 and c = 10

On plugging all the values, we get :

[tex]D=(-8)^2-4\times 1\times 10\\\\D=24[/tex]

So, the value of discriminant for y is 24.

Answer:

a) The company should expect to replace 11.51% of its batteries.

b) 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using 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.

In this problem, we have that:

[tex]\mu = 43.8, \sigma = 6.5[/tex]

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. Then

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

[tex]Z = \frac{36 - 43.8}{6.5}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151.

The company should expect to replace 11.51% of its batteries.

(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 43.8}{6.5}[/tex]

[tex]X - 43.8 = -1.28*6.5[/tex]

[tex]X = 35.48[/tex]

To the nearest month, 35 months.

Final answer:

To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36.

Explanation:

In this question, we are given information about the average life of a Quick Start car battery, which follows a normal distribution with a mean of 43.8 months and a standard deviation of 6.5 months.

(a) To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36. We can use the z-score formula to standardize the value of 36 and then use a standard normal distribution table to find the corresponding area. The percentage of batteries that will be expected to be replaced is the same as the percentage of batteries that fall within the range of 0 to 36 months.

Answer:

The point estimate for this problem is 0.48.

Step-by-step explanation:

We are given that a University wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.

A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no".

Let [tex]\hat p[/tex] = proportion of students who felt comfortable reporting cheating by their fellow students

Now,  point estimate ([tex]\hat p[/tex]) is calculated as;

                               [tex]\hat p=\frac{X}{n}[/tex]

where, X = number of students who answered yes = 1,344

            n = number of students surveyed = 2,800

So, Point estimate ([tex]\hat p[/tex])  =  [tex]\frac{1,344}{2,800}[/tex]

                                     =  0.48 or 48%

Final answer:

The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students is 48%.

Explanation:

The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students can be calculated by dividing the number of students who answered 'Yes' by the total number of students surveyed, and then multiplying by 100%. In this case, the point estimate is:

Point estimate = (Number of 'Yes' responses / Total number of students surveyed) * 100% = (1344 / 2800) * 100% = 48%

Answer:

a = 6.3mm

Step-by-step explanation:

Use Pythagoras theorem here

[tex]a^{2} + b^{2} = c^{2}[/tex]

Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation

[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]

Simplify

[tex]a^{2} = c^{2} -b^{2}[/tex]

Substitute in our numbers and solve for a

[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]

[tex]a^{2}[/tex] = 68.89 - 29.16

[tex]a^{2}[/tex] = 39.73

a = [tex]\sqrt{39.73}[/tex]

a = 6.3mm

Final answer:

To find the length of leg a when b = 5.4 mm and c = 8.3 mm in a right triangle, we use the Pythagorean theorem a^2 + b^2 = c^2. We solve for a, yielding a ≈ 6.3 mm (rounded to the nearest tenth).

Explanation:

The student is asking how to find the length of leg a in a right triangle where the lengths of leg b and the hypotenuse c are given. Since b = 5.4 millimeters and c = 8.3 millimeters, we can use the Pythagorean theorem to find leg a.

First, we'll apply the theorem: a2 + b2 = c2. To solve for a, we rearrange it: a2 = c2 - b2.

Substitute the given values:

a2 = c2 - b2
= 8.32 - 5.42
= 68.89 - 29.16
= 39.73

Now, we take the square root of both sides to find a:

a =
√39.73

≈ 6.3 millimeters (rounded to the nearest tenth)

Therefore, the length of leg a is approximately 6.3 millimeters.

Answer:

Step-by-step explanation:

1) point slope form is:

y-y1=m(x-x1)

y1=8

x1=4

m=(slope)

to find m:  y2-y1/x2-x1

hence

-2-8/2-4=-10/-2=5

m=5:

y-8=5(x+4)

This question is incomplete. I got the complete part (the boldened part) of it from google as:

The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:

4.90 hrs < μ1 - μ2 < 17.50 hrs.

Answer:

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A​ (the original​ paint) and 9 cans of type B​ (the modified​ paint) were selected and applied to similar surfaces. The drying​ times, in​ hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following​ 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2​, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population​ means?

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Step-by-step explanation:

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.

Answer:

[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans

[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation

And replacing this into the formula we got:

[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]

So then the best answer for this case would be:

O 50 Db

Step-by-step explanation:

For this case we can use the following equation for decibels:

[tex] dB = 10 log_{10} (\frac{I}{I_o})[/tex]

Where:

[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans

[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation

And replacing this into the formula we got:

[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]

So then the best answer for this case would be:

O 50 Db

The approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db

Given the general expression for calculating the  loudness, L, measured in decibels (Db), of sound intensity, I as:

L = 10log(I0/I)

Given the following parameters

I0 = 10^-12 Wb/m²

I = 10^-7 Wb/m²

Substitute

L = 10log(10^-12/10^-7)
L = 10log(10^-5)
L = -5(10)log10
L = -50Db

Hence the approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db

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Answer:

B. The x-value is between 3 and 4.

C. The y-value is between –2 and –1.

D. The x-value is positive.

Step-by-step explanation:

I did the Assignment on Edg.

The true options are: The x-value is between 3 and 4, the y-value is between –2 and –1 and the x-value is positive.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the graph, we have the following highlights

The point of intersection of the two lines is in the fourth quadrant.

The value of x is between 3 and 4.

The value of y is between -1 and -2.

x is positive, and y is negative.

x is not an integer.

x is between 3 and 4, while y is between -1 and -2

Hence, the true options are: The x-value is between 3 and 4.

the y-value is between –2 and –1 and the x-value is positive.

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Answer:

The null and alternative hypothesis are:

[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]

The test statistic for this hypothesis test is z=-1.15.

The​ P-value for this hypothesis test is P-value=0.124.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that less than 10 percent of the test results are wrong.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]

The significance level is 0.05.

The sample has a size n=317.

The sample proportion is p=0.079.

[tex]p=X/n=25/317=0.079[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{317}}\\\\\\ \sigma_p=\sqrt{0.000284}=0.017[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.079-0.1+0.5/317}{0.017}=\dfrac{-0.019}{0.017}=-1.153[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]P-value=P(z<-1.153)=0.124[/tex]

As the P-value (0.124) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.

a. The velocity function is v(t) = 14 - 2t. b. The particle is moving in a positive direction on the interval (0, 7). c. The particle is moving in a negative direction on the interval (7, infinity). d. The particle changes direction at t = 7.

a. The velocity function can be found by taking the derivative of the position function, s(t). The derivative of s(t) with respect to t is v(t) = 14 - 2t.

b. To determine the time interval on which the particle is moving in a positive direction, we need to find the values of t that make v(t) > 0. Solving the inequality 14 - 2t > 0, we get t < 7. Therefore, the particle is moving in a positive direction on the interval (0, 7).

c. Similarly, to determine the time interval on which the particle is moving in a negative direction, we need to find the values of t that make v(t) < 0. Solving the inequality 14 - 2t < 0, we get t > 7. Therefore, the particle is moving in a negative direction on the interval (7, infinity).

d. The particle changes direction at the time t = 7. This can be determined from the fact that v(t) changes sign at this time.

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Answer:

40.65% of these mothers are between the ages of 32 to 40

23.27% of these mothers are less than 30 years old

37.07% of these mothers are more than 38 years old

Step-by-step explanation:

Problems of normally distributed samples can be solved using 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.

In this problem, we have that:

[tex]\mu = 35.5, \sigma = 7.5[/tex]

What percent of these mothers are between the ages of 32 to 40?

This is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 32.

X = 40

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

[tex]Z = \frac{40 - 35.5}{7.5}[/tex]

[tex]Z = 0.6[/tex]

[tex]Z = 0.6[/tex] has a pvalue of 0.7257

X = 32

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

[tex]Z = \frac{32 - 35.5}{7.5}[/tex]

[tex]Z = -0.47[/tex]

[tex]Z = -0.47[/tex] has a pvalue of 0.3192

0.7257 - 0.3192 = 0.4065

40.65% of these mothers are between the ages of 32 to 40

What percent of these mothers are less than 30 years old?

This is the pvalue of Z when X = 30.

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

[tex]Z = \frac{30 - 35.5}{7.5}[/tex]

[tex]Z = -0.73[/tex]

[tex]Z = -0.73[/tex] has a pvalue of 0.2327

23.27% of these mothers are less than 30 years old

What percent of these mothers are more than 38 years old?

This is 1 subtracted by the pvalue of Z when X = 38.

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

[tex]Z = \frac{38 - 35.5}{7.5}[/tex]

[tex]Z = 0.33[/tex]

[tex]Z = 0.33[/tex] has a pvalue of 0.6293

1 - 0.6293 = 0.3707

37.07% of these mothers are more than 38 years old

Answer:

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.

Step-by-step explanation:

We have the sample standard deviation, 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 = 40 - 1 = 39

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7079

The margin of error is:

M = T*s = 2.7079*15 = 40.62

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 93.43 - 40.62 = $52.81.

The upper end of the interval is the sample mean added to M. So it is 93.43 + 40.62 = $134.05

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.

Answer:

The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Step-by-step explanation:

Let the random variable X be defined as the height of chimneys in factories.

The mean height is, μ = 100 meters.

The standard deviation of heights is, σ = 12 meters.

It is provided that a random sample of n = 40 chimney heights is obtained.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.

[tex]\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})[/tex]

Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:

[tex]P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})[/tex]

                    [tex]=P(Z>1.05)\\=1-P(Z<1.05)\\=1-0.85314\\=0.14686\\\approx 0.1469[/tex]

*Use a z-table fr the probability.

Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Answer :The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1400 after 1&#8203; day

Step-by-step explanation:

Answer:

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1600 after 1 day, what is the size of the colony after 4 days

Step-by-step explanation:

The measure of the portion of Earth that can be seen from an airplane 5.7 miles above the ground is approximately 0.163 degrees, when rounded to the nearest tenth. This is found using the formula for the angle subtended by an arc, and then converting from radians to degrees.

To solve this problem, we can use the properties of a circle, since the Earth is approximately spherical in shape. The formula to calculate the angle subtended by an arc (BD⌢) on the Earth's surface is as follows: θ = 2 * arcsin((distance_to_object)/(2 * radius_of_earth)).

So inserting the given values:

We get: θ = 2 * arcsin((5.7)/(2 * 4000)). This will give you an answer in radians, to convert this to degrees multiply by 180/π. In this case, the answer is approximately 0.163 degrees, rounded to the nearest tenth.

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Answer:

Eldest brother = 18 camels

2nd brother = 12 camels

Youngest brother = 4 camels

Step-by-step explanation:

Question posted:

How could we know how many camels actually correspond to each brother?

It is from "the man who calculated":

The question is incomplete without the background information.

Based on the question, It has to do with sharing an inheritance of 35 camels among 3 brothers.

"The man who calculated", by Malba Tahan.

Since the complete question isn't available, we are going to look at the following question to understand how to do the calculation.

Question:

How can an inheritance of 35 camels be divided among three brothers in such a way that the eldest brother gets half of them, the second one gets 1/3 of the total and the youngest brother gets 1/9 of the total camels?

Solution:

Total number of camels= 35

Eldest brother gets half: 1/2 of 35 gives a fraction and not an whole number

2nd brother = 1/3 of 35 (gives a fraction)

3rd brother = 1/9 of 35 (gives a fraction)

Since we can't have a camel in fraction except in whole number, we would look for the closest number to 35 that would be divided by 2, 3 and 9 respectively without giving a fraction.

Number 36 is the closest number to 35 that satisfies this condition.

1st brother = 1/2 × 36 = 18 camels

2nd brother = 1/3 × 36 = 12 camels

3rd brother = 1/9 × 36 = 4 camels

Now let's add the camels the 3 brother got together = 18 + 12 + 4 = 34 camels

Total camels - amount shared = 35 -34 = 1

Meaning one camel is remaining. The distributor would keep the remaining one as that's the way such distributions could be achieved.

Answer:

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

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 normally distributed samples are solved using 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 [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.

In this problem, we have that:

[tex]\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]

What is the probability that a sample of 100 steady smokers spend between $19 and $21

This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So

X = 21

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

By the Central Limit Theorem

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

[tex]Z = \frac{21 - 20}{0.5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 19

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

[tex]Z = \frac{19 - 20}{0.5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

To find the probability that a sample of 100 steady smokers spend between $19 and $21, calculate the Z-score and use a standard normal distribution table or calculator. The probability is approximately 0.3413.

To find the probability that a sample of 100 steady smokers spend between $19 and $21, we can use the Z-score formula. The Z-score is calculated as the difference between the sample mean and the desired value (in this case, $20), divided by the population standard deviation, multiplied by the square root of the sample size.

Z = (x - μ) / (σ / √n)

Plugging in the values we have:

Z = (21 - 20) / (5 / √100) = 1

We can then use a standard normal distribution table or a calculator to find the probability associated with a Z-score of 1. The probability of obtaining a Z-score of 1 or less is approximately 0.8413. Since we want the probability between $19 and $21, we subtract the probability of getting a Z-score of less than 1 from the probability of getting a Z-score of less than or equal to 0. This gives us:

Probability = 0.8413 - 0.5000 = 0.3413

Answer:

Both are true statements

Step-by-step explanation:

By definition of an angle, an angle is a union of two rays at a common endpoint  and lines can contain rays.

A full circle measures 360 degrees.

Answer:

Question7:true

Question8:true

Step-by-step explanation:

Question 7: an angle is made when two lines or rays come together

Question 8:an angle that has 360° is a circle

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

  f(u +6) = u

Step-by-step explanation:

Put (u+6) in place of t and simplify:

  f(u+6) = (u+6) -6

  f(u+6) = u

Answer:

2^-84

Step-by-step explanation:

First simplify inside the parentheses

2^-10 / 4^2

Rewriting 4 as 2^2

2^-10 / 4^2^2

We know that a^b^c = a^(b*c)

2^-10 / 2^(2*2) = 2^-10 / 2^4

We know that a^b / a^c = a^(b-c)

2^-10 / 2^4 = 2^(-10-4) = 2^-14

Replace the term in side the parentheses with 2^-14

2^-14 ^7

We know that a^b^c = a^(b*c)

2^(-14*7)

2^-84

Answer:

The null hypothesis is H0; u1 - u2 = 0

The mean age of each audience is the same.

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

Let u1 represent the mean age of audience for American idol and

u2 represent the mean age of audience for 60 minutes.

The null hypothesis is H0; u1 - u2 = 0

The mean age of each audience is the same.

Answer:

It measures the probability of observing your test statistic, assuming the null hypothesis is true.

Step-by-step explanation:

The p-value, also known as the probability value measures the probability of observing your test statistic, assuming the null hypothesis is true.

A low p-value means a higher chance of the null hypothesis to be true.

It lies between 0 and 1. A small p-value indicates fewer chances of the null hypothesis to be true.

Answer:

The answer is 2000 yuan.

Step-by-step explanation:

Devise a proportion for this, and then cross-multiply. I believe that is the easiest way.

[tex] \frac{1}{0.15} = \frac{x}{300} \\ 0.15x = 300 \\ x = \frac{300}{0.15} \\ x = \frac{30000}{15} \\ x = \frac{10000}{5} \\ x = 2000[/tex]

Using the given exchange rate of $0.15 for 1 Yuan, Torres will receive 2000 yuan when he exchanges his $300.

Torres plans to go to China and wants to exchange his money into the Chinese currency, known as the Yuan. The exchange rate he finds is $0.15 for 1 Yuan. This means for every 1 yuan, he needs to supply $0.15. Because he wants to exchange $300, the number of Yuan he will receive can be calculated by the formula Amount_in_dollars / Exchange_rate.

Here, the Amount_in_dollars is $300 and the Exchange_rate is $0.15. So, the calculation will be $300 / $0.15 = 2000 yuan. Therefore, Torres will receive 2000 yuan when he exchanges his $300.

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