Find the point estimate for the true difference between the given population means. Round your answer to three decimal places.

(HINT: The point estimate for the difference between the population means is found by simply subtracting one sample mean from the other.)


Sample 1: Weights (in Grams) of Soap Bar A:

129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127

_____________________________________________________________

Sample 2: Weights (in Grams) of Soap Bar B:

131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

x=10

Step-by-step explanation:

7x - 5=65

+5 +5 so the 5's cancel so add 5 to 65

7x =70 because you add 5 to 65 to get 70

7x 7

7 x cancels out so you answer will be

x=10

Answer:

Step-by-step explanation:

7 x -5  = 65

7 times what? (x) - 5 equals 65

Well we know that x has to be less than 65 and more than 7 and -5.

So 7 must be multiplied by numbers 8, and up.

7 * 8 -5  = 51, NOT 65.

7 * 9 -5  = 58, NOT 65.

7 * 10 -5  = Does equal 65.

Therefore, x is equivalent to 10.

Answer:

The median of this set is 45.

Step-by-step explanation:

Step-by-step explanation:

15.4% of the nuts are pecans.

0.154x = 77

x = 500

There are 500 pounds of mixed nuts in the batch.

Answer: 40in²

Step-by-step explanation:

To find the area of the shade region, considering the diagram, the diagonal of the rectangle has divided the figure into two equal half. So, one is shaded and the other not shaded. So the shaded region is a right angled triangle,. So the formula for finding the area of a triangle need to be applied.

Area. = 1/2 × b × h

= 1/2 × 10 × 8

= 40in²

Answer:

[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]

[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]

And the confidence interval for the difference of the two means is given by (74.54, 127.46)

Step-by-step explanation:

Information given:

[tex]\bar X_1 = 759[/tex] the sample mean for construction workers

[tex] s_1 =73[/tex] the sample standard deviation for construction workers

[tex]n_1 =30[/tex] sample size of construction workers

[tex]\bar X_2 = 658[/tex] the sample mean for manufacturing workers

[tex] s_2 =65[/tex] the sample standard deviation for manufacturing workers

[tex]n_2 =28[/tex] sample size of construction workers

Confidence interval

The confidence interval for the difference of means are given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We need to find the degrees of freedom given by:

[tex] df = n_1 +n_2 -2= 30+28-2=56[/tex]

The confidence is 0.85 and the significance level would be [tex]1-0.85=0.15[/tex] and [tex]\alpha/2 = 0.075[/tex]. We need to find a critical value in the t distribution who accumulates 0.075 of the area on each tail and we got:

[tex] t_{\alpha/2}= \pm 1.46[/tex]

And then we can replace and we got:

[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]

[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]

And the confidence interval for the difference of the two means is given by (74.54, 127.46)

Part (a): The 80% confidence interval for the earnings difference is $77.51 to $124.49.

Part (b): The interval suggests 80% confidence in the true earnings difference falling within $77.51 to $124.49.

Part (c): Since zero isn't in the interval, there's a significant pay difference between construction and manufacturing workers.

Part (a): Construct an 80% confidence interval for the difference between the mean weekly earnings

Step 1: Identify the given data

- Construction workers:

 - Mean [tex](\(\bar{X_1}\)) = \$759[/tex]

 - Standard deviation [tex](\(s_1\)) = \$73[/tex]

 - Sample size [tex](\(n_1\))[/tex] = 30

- Manufacturing workers:

 - Mean [tex](\(\bar{X_2}\)) = \$658[/tex]

 - Standard deviation [tex](\(s_2\)) = \$65[/tex]

 - Sample size [tex](\(n_2\)) = 28[/tex]

Step 2: Determine the formula for the confidence interval

We use the formula for the confidence interval of the difference between two independent means:

[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]

Step 3: Calculate the standard error (SE) of the difference

[tex]\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]

[tex]\[ SE = \sqrt{\frac{73^2}{30} + \frac{65^2}{28}} \][/tex]

[tex]\[ SE = \sqrt{\frac{5329}{30} + \frac{4225}{28}} \][/tex]

[tex]\[ SE = \sqrt{177.63 + 150.89} \][/tex]

[tex]\[ SE = \sqrt{328.52} \approx 18.12 \][/tex]

Step 4: Determine the degrees of freedom (df) using the Welch-Satterthwaite equation

[tex]\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1-1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}} \][/tex]

[tex]\[ df \approx \frac{328.52^2}{\frac{(177.63)^2}{29} + \frac{(150.89)^2}{27}} \][/tex]

[tex]\[ df \approx \frac{107,922.4}{1090.15 + 843.48} \][/tex]

[tex]\[ df \approx \frac{107,922.4}{1933.63} \approx 55.83 \approx 56 \][/tex]

Step 5: Find the t-value for an 80% confidence interval

For df ≈ 56 and [tex]\(\alpha/2 = 0.10\),[/tex] the t-value [tex](\(t_{0.10}\))[/tex] is approximately 1.296.

Step 6: Construct the confidence interval

[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot SE \][/tex]

[tex]\[ (759 - 658) \pm 1.296 \cdot 18.12 \][/tex]

[tex]\[ 101 \pm 23.49 \][/tex]

[tex]\[ (77.51, 124.49) \][/tex]

So, the 80% confidence interval for the difference between the mean weekly earnings is [tex]\((77.51, 124.49)\).[/tex]

Part (b): Explanation of the Confidence Interval

The 80% confidence interval [tex]\((77.51, 124.49)\)[/tex] means that we are 80% confident that the true difference between the mean weekly earnings of construction workers and manufacturing workers lies between [tex]\$77.51[/tex] and [tex]\$124.49[/tex]. In other words, if we were to take many samples and compute the confidence interval for each, about 80% of those intervals would contain the true difference in mean earnings.

Part (c): Is there a significant difference in pay?

To determine if there is a significant difference in pay, we look at whether the confidence interval includes zero. Since the 80% confidence interval for the difference in mean earnings (\(77.51, 124.49\)) does not include zero, we can conclude that there is a statistically significant difference in pay between construction workers and manufacturing workers at the 80% confidence level.

Complete Question:

Answer:

[tex]x = p( m - n)[/tex]

Step-by-step explanation:

[tex]m = n + \frac{x}{p} \\ m - n = \frac{x}{p} \\ p(m - n) = \frac{x}{p} \times p \\ \\ x = p(m - n)[/tex]

Answer:

S = 85cm^2

Step-by-step explanation:

The surface area of a square pyramid is given by the following formula:

[tex]S=2hb+b^2[/tex]

where it has taken into account the sum of the area of a square and four triangles:

[tex]4(\frac{hb}{2})+b*b=2bh+b^2[/tex]

h: slant height = 6cm

b: base = 5cm

By replacing in the formula you obtain:

[tex]S=2(5cm)(6cm)+(5cm)^2=85cm^2[/tex]

hence, the surface area is 85cm^2

Answer:

89 units

Step-by-step explanation:

-The population's mean point estimate is equivalent to the sample mean.

Given the 5 month units sold is 94,80,85,94 and 92

-Mean is the average of the units sold over the 5 month period:

[tex]\bar X=\frac{\sum {x_i}}{n}\\\\=\frac{94+80+85+84+92}{5}\\\\=89[/tex]

Hence, the point estimate for the population mean is 89 units

Answer:

$1.9

Step-by-step explanation:

2 pound bag (when he bought) =.30×2=$0.6

when he sells, price is $2.50.

Profit for each bag= $2.5-$0.6=$1.9

Answer:

the answer is B,C,F

Step-by-step explanation:

The correct options are,
1. Add 3.4 to both sides of the equation.
2. 12.7 + 3.4 = 16.1, so j = 16.1.
3. Substitute 16.1 for j to check the solution.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The steps to solve the equation: 12.7 = j - 3.4 are as follows,

Add 3.4 to both sides of the equation,

12.7 + 3.4 = j

Solve for j,

16.1 = j

So the solution is j = 16.1

To check the solution, you would substitute 16.1 for j in the original equation and see if both sides are equal.

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Answer:

V≈4188.79in³    

Step-by-step explanation:

4.188.79in3

6 3/4 = 27/4

27/4 * 1/3 = 27/12

27/12 = 9/4

Answer: 9/4 cups

To find out how much fruit salad was eaten, convert the mixed number to an improper fraction and multiply by the fraction representing the amount eaten.

To calculate how much fruit salad was eaten, we need to find 1/3 of 6 3/4 cups. First, we convert the mixed number 6 3/4 to an improper fraction by multiplying the whole part (6) by the denominator (4) and adding the numerator (3) to it. This gives us 27/4 cups. Next, we multiply 27/4 by 1/3, which can be simplified to 9/4. So, they ate 9/4 cups of fruit salad.

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Answer:

42%

Step-by-step explanation:

Answer:

Since the events are independent, 30% of his customers have neither a foreign car nor a dog.

Step-by-step explanation:

Let the total number of his customers = 100.

Since the events are independent,

customers with foreign cars + customers that own dogs + customers that have neither a foreign car nor a dog = 100.

But,

Customers with foreign cars = 30% = 30

Customers that own dogs = 40% = 40

Customers with neither foreign car nor dog  = x%

So that,

     30 + 40 + x = 100

       70 + x = 100

      x = 100 - 70

      x = 30

Customers with neither foreign car nor dog  = 30.

Converting this value to percentage,

             =  [tex]\frac{30}{100}[/tex] × 100                      

             = 30%.

Therefore, 30% of his customers have neither a foreign car nor a dog.

Answer:

2931 + 51.4n/7 degrees where n is the number of animal from the lion to the zebra in the clockwise direction.

Step-by-step explanation:

We don't have details on the positions of the lion and the zebra prior to revolution but suppose the zebra is n animal away from the lion where n could be in the range of 0 to 6 in the clockwise direction. If n = 0, the zebra is next to the lion in line, and if n = 6, the zebra is right behind the lion.

In angular term, since all 8 animals are evenly spaced, there are 7 space in between them, each of them would span an angle of 360/7 degrees

Then the angular distance between the zebra and the lion is (n+1)360/7 degrees

If the carousel makes between 8 and 9 revolutions then the total angular distance is 8*360 + (n+1)360/7 = 2931 + 51.4n/7 degrees

Answer:

-2970, -3320

Step-by-step explanation:

The carousel makes between 8 and 9 clockwise revolutions

the position of the lion rotated to that of the zebra is two steps

now,

1 revolution = 360 degrees accomplished in 8 steps

1 step = 360/8 = 45 deg

=> position of  lion rotated to zebra = 2 × 45 = 90 deg

if 1 revolution = 360 accomplished in 9 steps

then

1 step = 360/9 = 40 deg

=> position of  lion rotated to zebra = 2 × 40 = 80 deg

since the rotation is in clockwise direction, a negative sign is required

FOR 8 Revolutions

in total the carousel rotates

-[8(360) + 90] degrees

= -2970 degrees

FOR 9 revolution

in total the carousel rotates

-[9(360) + 80] degrees

= -3320 degrees

7.  tails, odd, 4

P(tails) = 1/2

P(odd) = 3/6 = 1/2

P(4) = 1/6

P(tails then odd then 4) = (1/2)×(1/2)×(1/6) = 1/24 ≈ 0.041666

Answer: 1/24, 4.2%

8.  tails, 6 or 1, 3

P(6 or 1) = 2/6 = 1/3

P(3) = 1/6

P( tails, 6 or 1, 3) = (1/2)(1/3)(1/6) = 1/36 ≈ 0.027777

Answer: 1/36, 2.8%

9.  heads, not 2, even

P(heads) = 1/2

P(not 2) = 5/6

P(even) = 1/2

P(heads, not 2, even) = (1/2)(5/6)(1/2) = 5/24 ≈ 0.208333

Answer: 5/24, 20.8%

Answer:

7. 1/24  = 4.2%

8. 1/36  = 2.8%

9. 1/6 = 16.67%

All percentages are rounded

Answer:

Step-by-step explanation:

Answer:

In my opinion I think the answer is C.12/33

Step-by-step explanation:

this would be the answer because...

1. First, add up the amount of boys and girls

21 girls+ 12 boys= 33 total

2. Next, since its asking for the probability for a boys name to de drawn at random, your going to divide 12 by 33

Answer:

it is c i took test good luck

Step-by-step explanation:

sike i lied your a is mine lol

Answer:

The first one is matched with 700,000

The second one is matched with 7

The third one is matched with 70

The fourth one is matched with 70,000

Step-by-step explanation:

Look at where the 7 is in the number, and replace all the digits to the right of it with 0's. Get rid of the digits to the left of the 7, if any

Answer:

1-->1

2-->3

3-->2

4-->4

Step-by-step explanation:

In the first number the 7 is in the the hundred thousands place. In the second the 7 is in the ones place. In the third the 7 is in the tens place. In the fourth the 7 is in the ten thousands place.

Answer:

94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 50, p = 0.6[/tex]

So

[tex]\mu = E(X) = np = 50*0.6 = 30[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.6*0.4} = 3.46[/tex]

What is the probability that at least 25 employees in the sample will participate in the optional retirement plan?

Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5

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

[tex]Z = \frac{24.5 - 30}{3.46}[/tex]

[tex]Z = -1.59[/tex]

[tex]Z = -1.59[/tex] has a pvalue of 0.0559

1 - 0.0559 = 0.9441

94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan

Answer:

$99.44 + $1.99 = $101.47

Delivery fee: $6.95

Final bill: $101.47 + 6.95 = $108.42

The final bill will be either $109.43 or $108.42, depending on whether the last-minute item is included in the order.

To calculate the final bill, we need to consider two scenarios: the order without the last-minute item and the order with the last-minute item. First, let's calculate the delivery fee for an order without the last-minute item. Since the order total is $99.48, which is less than $100, the delivery fee will be $9.95. Now, let's calculate the final bill by adding the delivery fee to the order total: $99.48 + $9.95 = $109.43.

Next, let's calculate the delivery fee for an order with the last-minute item. Since the order total will be $101.47 ($99.48 + $1.99), which is more than $100, the delivery fee will be $6.95. To calculate the final bill, we need to add the delivery fee to the updated order total: $101.47 + $6.95 = $108.42.

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Answer:

Work done by george = 35.28J

Step-by-step explanation:

We are given;

Mass; m = 2 kg

Height;h = 1.8 m

Now, we want to find how much work does George do on a 2-kg package at the height of 1.8m.

This is a potential energy problem.

The formula for work done is therefore;

W = mgh

Where;

m is mass

g is acceleration due to gravity which has a constant value of 9.8 m/s²

h is height

Thus, plugging in relevant values;

W = 2 x 9.8 x 1.8

W = 35.28 J

Final answer:

The work done by George on the 2-kg package when he lifts it to a height of 1.8 meters is calculated using the equation W = mgh, which results in 35.28 joules.

Explanation:

The question How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m? requires the calculation of the work done against the force of gravity. To find the work done, the equation W = mgh is used, where W is the work done in joules, m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2), and h is the height in meters.

To solve for the work done in this case: W = (2 kg)(9.8 m/s2)(1.8 m).

When you calculate this, it gives you the work done by George as W = 35.28 J (joules).

Answer:

Step-by-step explanation:

Hello!

In descriptive statistics, the median is a measurement of center position. It separates the sample in halves. (bottom 50% from upper 50%)

The manager took a sample of 11 cashiers and recorded the worked hours in a week

To identify the median you have to calculate it's position:

The position is calculated as

PosMe= (n+1)/2= (11+1)/2= 6 cashier

This means that the Median of hours worked is a week observed corresponds to the 6th cashier (after ordering the data from lowest to highest)

If you observe the histogram, the x-axis corresponds to worked hours and the y-axis shows the number of workers.

The workers were already arranged from least hours worked to most hours worked.

The first interval corresponds to 0-10 worked hours and two workers recorded these working times.

The second interval corresponds to 10-20 worked hours and three workers recorded these working times.

In the third interval of 20-30 hours, no workers recorded these working times.

The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.

The fifth interval corresponds to 40 - 50 worked hours and only one worker recorded these working hours.

The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"

I hope this helps!

The interval that contains the median number of hours worked is "30 - 40 hours"

The manager took a sample of 11 cashiers and recorded the worked hours in a week

To identify the median you have to calculate it's position:

The position is calculated as

PosMe= (n+1)/2= (11+1)/2= 6 cashier

The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.

The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"

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The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.

The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.

To find the probability, we divide the number of successful outcomes (rolling a 6) by the total number of possible outcomes (numbers 1 to 6), which is 6.

So the probability is 1/6 or 0.1667.

Since a standard number cube has equal chances of landing on any number from 1 to 6, each outcome has the same probability of occurring, which is 1/6.

Thus, the theoretical probability of the event when rolling a standard number cube is found to be  1/6 or approximately 0.1667.

Final answer:

The theoretical probability of rolling a six on a standard six-sided die is 1 in 6, or P(6) = 1/6.

Explanation:

The student has asked about finding the theoretical probability of rolling a six, P(6), with a standard six-sided die. In a fair six-sided die, the outcomes are equally likely, meaning the probabilities for each number 1 through 6 are the same. Given that there are six possible outcomes, the probability of rolling any one specific number, for example 6, is 1 out of the 6 total possible outcomes. Therefore, P(6) = 1/6. This probability reflects that, theoretically, if we were to roll the die many times, we'd expect to roll a 6 in approximately one-sixth of all the rolls.

Answer:

c

Step-by-step explanation:

just did it on the assignment

Answer:

Probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.

Step-by-step explanation:

We are given that the the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour.

Let X = speed of car

The z-score probability distribution for normal distribution is given by;

           Z = [tex]\frac{ X-\mu}{\sigma}} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean speed = 61 miles per hour

            [tex]\sigma[/tex] = standard deviation = 4 miles per hour

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the next car passing will be travelling more than 66 miles per hour is given by = P(X > 66 miles per hour)

        P(X > 66) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] > [tex]\frac{ 66-61}{4}} }[/tex] ) = P(Z > 1.25) = 1 - P(Z [tex]\leq[/tex] 1.25)

                                                     = 1 - 0.89435 = 0.10565                       

So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 in the z table which has an area of 0.89435.

Hence, the probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.

Final answer:

The probability that the next car passing will be traveling more than 66 miles per hour, given a mean speed of 61 mph and standard deviation of 4 mph, is approximately 10.56%.

Explanation:

To calculate the probability that the next car passing will be traveling more than 66 miles per hour, given the speeds are normally distributed with a mean of 61 miles per hour and a standard deviation of 4 miles per hour, we use the Z-score formula.

The Z-score formula is: Z = (X - μ) / σ, where μ is the mean, σ is the standard deviation, and X is the value we're interested in.

Substitute the given values into the formula to find the Z-score for 66 miles per hour.

Z = (66 - 61) / 4 = 5 / 4 = 1.25.

Next, we look up the Z-score of 1.25 on the standard normal distribution table or use a calculator to find the area to the left of Z. The area to the left of Z=1.25 is approximately 0.8944. To find the probability of a car traveling more than 66 miles per hour, we subtract this value from 1.

Probability = 1 - 0.8944 = 0.1056.

Therefore, the probability that the next car passing will be traveling more than 66 miles per hour is approximately 10.56%.

Answer:

I like it when im high marks a lil by and he say he fly but he dono ha ta fly OoOoooOoOoOOoO

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]x^{2}[/tex]+[tex]y^{2}[/tex]= [tex]\sqrt{x^{2}+y^{2} }[/tex]+2y

Answer:

The equation of equivalent is,[tex]x^{4}+ y^{4} +3 y^{2} +2x^{2} y^{2} -4y^{3} -4 x^{2} y-x^{2} =0[/tex]

Step-by-step explanation:

If two systems of equations have the same solution, they are equivalent (s). This article explains how to determine whether two systems are equal. Equivalent systems are sets of equations that have the same solution.

Given, r = 1+2sinФ

[tex]r^{2} =r+2rsin[/tex]θ

[tex]x^{2}+ y^{2} =r+2y\\x^{2} + y^{2} -2y=r\\[/tex]

Squaring, both side:

[tex](x^{4} +y^{4} -2 y^{2}) = r^{2} \\x^{4}+ y^{4} + 4y^{2}+2 x^{2} y^{2} - 4y^{3} -4x^{2} y =x^{2} +y^{2} \\x^{4} + y^{4} +3 y^{2} +2 x^{2} y^{2} -4y^{3} -4x^{2} y^}-x^{2} =0[/tex]

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Answer:

Event is not unusual(p>0.05).

Step-by-step explanation:

Given that :

[tex]p=0.10\\\\n=1100\\\\x=121[/tex]

#The sample proportion is calculated as:

[tex]\hat p=\frac{x}{n}\\\\=\frac{121}{1100}\\\\=0.1100[/tex]

#Mathematically, the z-value is the value decreased by the mean then divided  the standard deviation :

[tex]z=\frac{\hat p- p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\\\=\frac{0.11-0.10}{\sqrt{\frac{0.10(1-0.10)}{1100}}}\\\\\\=1.1055[/tex]

#We use the normal probability table to determine the corresponding probability;

[tex]P(X\geq 121)=P(Z>1.1055)\\\\=0.1314[/tex]

Hence, the probaility is more than 0.05, thus the event not unusual  and thus  this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.