A cereal company is putting 1 11 of 3 33 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1 / 3 1/31, slash, 3. Adam wonders how many boxes he should expect to buy to get all 3 33 prizes. He carried out 32 3232 trials of a simulation and his results are shown below. Each dot represents how many boxes it took to get all 3 33 prizes in that trial. 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13# of boxes purchased Use his results to estimate the probability that it takes 9 99 or more boxes to get all 3 33 prizes. Give your answer as either a fraction or a decimal. P ( 9 or more boxes ) ≈ P(9 or more boxes)≈P, left parenthesis, 9, start text, space, o, r, space, m, o, r, e, space, b, o, x, e, s, end text, right parenthesis, approximately equals

Answers

Answer 1

There is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.

The calculation is as follows:

No. of Boxes  |  frequency

        3           |         12

        4           |         4

        5           |         5

        6           |         5

        7           |         0

        8           |         0

        9           |         2

        10          |        2

        11           |        0

        12           |       2

Here 9 or more boxes represent that it is equal to 9 boxes or more than 9 boxes.

P(x ≥ 9) = No. of boxes equal or more than 9 / total no. of boxes

And, The total no. of boxes is 32

From the above data, we have to count the number of boxes equal to or more than 9. (6 times) i.e.

[tex]P(x $\geq$ 9) = 6\div 32\\\\P(x $\leq$ 9) = 3\div 16[/tex]

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

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Related Questions

A manufacturer of car batteries claims that the batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries have lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence interval for σ2 and decide if the manufacturer’s claim that σ2 = 1 is valid. Assume the population of battery lives to be approximately normally distributed.

Answers

Answer:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Step-by-step explanation:

Data provided

1.9, 2.4, 3.0, 3.5, and 4.2

We can calculate the sample mean and deviation from this data with these formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}[/tex]

And we got:

[tex]\bar X= 3[/tex]

s=0.903 represent the sample standard deviation

n=5 the sample size

Confidence=95% or 0.95

Confidence interval

We need to begin finding the confidence interval for the population variance is given by:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

The degrees of freedom given by:

[tex]df=n-1=5-1=4[/tex]

The Confidence level provided is 0.95 or 95%, the significance is then[tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical values for this case are:

[tex]\chi^2_{\alpha/2}=11.143[/tex]

[tex]\chi^2_{1- \alpha/2}=0.484[/tex]

And the confidence interval would be:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Can someone help.....

Answers

Answer:

7

Step-by-step explanation:

formula for circumference of a circle is [tex]\pi[/tex]d

7[tex]\pi[/tex] = [tex]\pi[/tex]d

d = 7

PLEASEEEEE HELPPPP MEEE WITHHH NUMBERR 20!!!!!

Answers

Answer:

  ∠3 = ∠4 = 60°

Step-by-step explanation:

Angles 1 and 3 are "remote interior angles" with respect to angle 2, so ...

  ∠2 = ∠1 + ∠3

  120° = 60° + ∠3 . . . fill in known values

  60° = ∠3 . . . . . . . . . subtract 60°

__

Since two of the interior angles in the triangle ABC are 60°, the third one is also. The interior angle at B (supplementary to angle 2) is corresponding to ∠4, so has the same measure as angle 4.

  ∠4 = 60°

A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean of $145 for this sample. It is known that the standard deviation of all such textbooks is $35 and the population of such prices is normal.

a. What is the point estimate of the mean price of all such college textbooks?

b. Construct a 90% confidence interval for the mean price of all such college textbooks.

Answers

Answer:b

Step-by-step explanation:

a. The point estimate of the mean price of college textbooks is $145. b. A 90% confidence interval for the mean price is ($133.49, $156.52).

Given a sample of 25 comparable textbooks with a mean price of $145 and a known population standard deviation of $35, the following steps will help answer the questions:

a. Point Estimate:

The point estimate of the mean price of all such college textbooks is simply the sample mean, which is $145.

b. 90% Confidence Interval:

To construct a 90% confidence interval for the mean price of college textbooks, we follow these steps:

Identify the sample mean [tex]ar_{x}[/tex] = $145, sample size (n) = 25, and population standard deviation [tex]\sigma[/tex] = $35.Determine the z-score for a 90% confidence level. The z-score corresponding to a 90% confidence level is 1.645.Calculate the standard error (SE) of the mean using the formula: SE = [tex]\sigma[/tex] / [tex]\sqrt{n}[/tex] = $35 / √(25) = $7.Compute the margin of error (ME) using the formula: ME = [tex]z \times SE[/tex] = 1.645 × $7 = $11.515.Determine the confidence interval using the formula: ([tex]\bar{x}[/tex] - ME, [tex]\bar{x}[/tex]} + ME) = ($145 - $11.515, $145 + $11.515) = ($133.485, $156.515).

Thus, the 90% confidence interval for the mean price of all college textbooks is ($133.49, $156.52).

In 1999 the population of Austria was one-third the population of Nepal. At that time the number of people living in Austria was 8,100,000. How many people were living in Nepal

Answers

The answer would be 24,300,000 people living in Nepal.

A marketing firm wishes to know what proportion of viewers of Impractical Jokers feels that the current season is at least as good as, or better, than previous seasons. A randomly selected group of 200 was polled. 58 responded that they felt that quality standards have been maintained. Please calculate a 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons.

Answers

Answer:

The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 200, \pi = \frac{58}{200} = 0.29[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 - 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.2372[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 + 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.3428[/tex]

The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).

Answer:

[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]

[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]

And the confidence interval for this case would be (0.237; 0.343).

Step-by-step explanation:

We can begin find the proportion estimated of responded that they felt that quality standards have been maintained with the following formula:

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

And replacing we got:

[tex] \hat p =\frac{58}{200}= 0.29[/tex]

The confidence interval is given by 90%, and the significance level would be [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]

The confidence interval for the true proportion is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the values we got:

[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]

[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]

And the confidence interval for this case would be (0.237; 0.343).

1. (a) Show that the polynomial x⁴+ 4x³ + 6x² - 8 is divisible by x+2​

Answers

Answer:

Step-by-step explanation:

if x= -2

and P(x)=x^4+4x^3+6x^2-8

then P(-2)=(-2)^4+4*(-2)^3+6*(-2)^2-8=16-32+24-8=0

so P(x)=(x+2)* Q(x)   and P(x) is divisible by x+2

What is the side length of a square with a perimeter of 52 meters

Answers

Answer:

13 meters

Step-by-step explanation:

The perimeter is the sum of all the sides.

As a square has four identical sides, to calculate the length of one side you would simply divide 52 by 4,which gives you 13.

1) Divide 52 by 4.

[tex]52/4=13meters[/tex]

Answer:

13m

Step-by-step explanation:

52/4 = 13

Apply the Pythagorean Theorem to find the distance between points A and B. A) 6 units B) 18 units C) 27 units D) 81 units

Answers

Answer:

A: 6 Units

Step-by-step explanation:

Fill in the blanks in the following proof, which shows that the sequence defined by the recurrence relation

sk = sk − 1 + 2k, for each integer k ≥ 1
s0 = 3.
satisfies the formula

sn = 3 + n(n + 1) for every integer n ≥ 0.

Proof (by mathematical induction):

Answers

Final answer:

To prove that the sequence defined by the recurrence relation satisfies the formula sn = 3 + n(n + 1), we need to show that the base case holds and then prove the inductive step.

Explanation:

To prove that the sequence defined by the recurrence relation satisfies the formula , we need to show that the base case holds and then prove the inductive step.

Base case:

When , we have . This matches the formula, so the base case holds.

Inductive step:

Assume that the formula holds for some . We want to show that it holds for .

Using the recurrence relation, we have:

sn+1 = sn + 2(n+1)

Using the induction hypothesis, we can substitute  in the expression:

sn+1 = (3 + n(n + 1)) + 2(n+1)

Expanding the expression:

sn+1 = 3 + n(n + 1) + 2n + 2

Combining like terms:

sn+1 = 3 + n(n + 1) + 2(n+1)

sn+1 = 3 + (n+1)((n + 1) + 1)

This matches the formula for , so the inductive step holds. Therefore, the formula holds for all integers .

the train to hogwarts is moving at a speed of 120 mph. if hogwarts is 420 miles away, how long will the students train ride be ?

Answers

Answer:

The train ride is 3.5 hours

Step-by-step explanation:

We know that distance is equal to rate times time

d = rt

We know the distance and the rate

420 = 120*t

Divide each side by 120

420/120 = 120t/120

3.5 =t

The train ride is 3.5 hours

Answer:

3.5 hrs

3 hrs and 30 min

210 min

Odessa starts counting the frogs in the small pond that the forest service just set up by her house. She marks the data in this graph. If y equals the number of frogs and x equals the number of months that have passed, the frog population can be described by the mathematical formula y = x.

Answers

Answer:

Answer is 2

Step-by-step explanation:

If it shows a graph with Frog Population on top

A follow-up study will be conducted with a sample of 20 people from the 300 people who responded yes (support) and no (do not support). Two sampling methods have been proposed: a simple random sample and a stratified random sample with the survey response as strata. (b) If the stratified random sample is used, what is the number of people that will be selected from those who responded yes? Support your answer by showing your work.

Answers

Using the concept of stratified sampling, it is found that 10 people will be selected from those who responded yes.

In a stratified sample, the population is divided into groups, and the same number of elements of each group is surveyed.

In this problem:

Two groups, one with those who responded yes and other with those who responded no.Sample of 20 people, thus 10 people who responded yes and 10 people who responded no.

A similar problem is given at https://brainly.com/question/24188753

Final answer:

To decide how many participants who answered 'yes' to include in a stratified random sample of 20, use the proportion of 'yes' answers out of 300 to calculate the sample from that stratum.

Explanation:

In a stratified random sample, the population is divided into groups, or strata, and a sample is taken from each group to ensure that each subgroup of the population is adequately represented. To determine the number of people that will be selected from those who responded yes in a stratified random sample, we need to find the proportion of 'yes' responses among the 300 respondents and then apply that proportion to the sample size of 20.

Assuming we know the exact number of people who responded 'yes', let's call that number 'Y'. The number of 'yes' responses in the stratified sample would then be (Y/300) * 20. Without the actual number of 'yes' responses, we cannot compute the exact number of people that should be selected from the 'yes' group. However, this formula demonstrates how you would calculate it once the value for 'Y' is known.

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Associations In Data:Question 10
The list below show test scores for 3rd period on a
recent test. Finding the mean absolute deviation.
62 63 68 72 79 80 83 93 94 95
Select one:
7.8
101.2
78.9
10.12

Answers

Answer:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Step-by-step explanation:

We have the following data given:

62 63 68 72 79 80 83 93 94 95

And we need to begin finding the mean with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

Now we can find the mean absolute deviation like this:

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

And finally we can find the mean abslute deviation with the following formula:

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Question 1
Convert from parametric to rectangular:
x=t+4, y = t^2

Answers

Answer:

  y = x^2 +8x +16

Step-by-step explanation:

t can be written in terms of x, then substituted into the equation for y.

  x = t -4

  x + 4 = t

  y = t^2 = (x +4)^2

  y = x^2 +8x +16

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded (U) condition and an abraded (A) condition. Use the paired t test to test: H0: μD = 0 versus Ha: μD > 0 at significance level 0.01. (Use μD = μU-A.) Note: The data below is formatted such that you can copy and paste it into R. Fabric 1 2 3 4 5 6 7 8 U = c( 36.3, 55.0, 51.1, 38.8, 43.2, 48.8, 25.6, 49.5) A = c( 28.5, 20.0, 46.0, 34.5, 36.5, 52.5, 26.5, 46.5) Calculate the mean difference and standard deviation. d = sd = Compute the test statistic value. (Round your answer to three decimal places.) t = p-value = State the conclusion in the problem context. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Fail to reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.

Answers

Rejection region(s)

t > 2.998

Test statistic value

t = 2.89

Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Option B is the right choice.

State the hypotheses

H0: μD = 0

Ha: μD > 0

State the rejection region

Since the alternative hypothesis is one-sided, we use a one-tailed test. The rejection region for a one-tailed t-test with significance level 0.01 and 7 degrees of freedom is:

t > 2.998

Compute the test statistic

The test statistic for a paired t-test is calculated as follows:

t = ([tex]\bar x[/tex]D - μD) / (sdD / √n)

where:

[tex]\bar x[/tex]Dis the mean difference between the unabraded and abraded breaking loads

sdD is the standard deviation of the difference between the unabraded and abraded breaking loads

n is the sample size

Calculating the mean difference:

[tex]\bar x[/tex]D = (36.3 - 28.5) + (55.0 - 20.0) + (51.2 - 46.0) + (38.6 - 34.0) + (43.2 - 36.5) + (48.8 - 52.5) + (25.6 - 26.5) + (49.6 - 46.5) = 6.85

Calculating the standard deviation of the difference:

sdD = √[((36.3 - 28.5)^2 + (55.0 - 20.0)^2 + (51.2 - 46.0)^2 + (38.6 - 34.0)^2 + (43.2 - 36.5)^2 + (48.8 - 52.5)^2 + (25.6 - 26.5)^2 + (49.6 - 46.5)^2) / 7] = 10.87

Calculating the test statistic:

t = (6.85 - 0) / (10.87 / √8) = 2.89

Make a decision

Since the test statistic (2.89) is less than the critical value (2.998), we fail to reject the null hypothesis.

The correct choice is option d. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

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Question:-

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H0: ?D = 0 versus Ha: ?D > 0 at significance level 0.01. (Use ?D = ?U ? ?A.)
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)

t ? _______

t ? ________

Compute the test statistic value. (Round your answer to three decimal places.)

t = _____

State the conclusion in the problem context.

a.Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to b.reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. c.Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

d.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions

Chandler has 828 millimeters of fabric.
How many centimeters of fabric does Chandler have?
Use the numbers and symbols on the tiles to enter an equation to show the
828 8.28
182.8
0.828
100 || 1.000
Chandler has
centimeters of fabric.​

Answers

Answer:

82.8 centimeters

Step-by-step explanation:

Chandler has 828 millimeters of fabric.

1 centimeter =10 millimetersx centimeters = 828 millimeters

Expressing as a ratio

[tex]\dfrac{1}{x}= \dfrac{10}{828}\\10x=828\\x=828\div 10\\x=82.8 cm[/tex]

Therefore, Chandler has 82.8 centimeters of fabric.

Answer:

82.8 centimeters of fabric

Step-by-step explanation:

1 centimeters= 10 millimeters;

828mm x 1cm ÷10 mm=82.8cm ;centimeters of fabric

The exercise is performed by conversion factor and a smaller unit is transferred to a larger unit that is centimeters.

4. Which of the following points on the number line best represents 5/8?


Answers

Answer:

B

Step-by-step explanation:

You can see that the dashes on the number line are going up by 1/4 which is equal to 2/8 (when you multiply 1/4 by 2). At point C your already at 6/8 which is a little larger than 5/8 so when you do a little less than 6/8 you get to point B which is the best answer.

Simplify this complex fraction

Answers

Answer:

1/4

Step-by-step explanation:

2/4 ÷ 2

Copy dot flip

2/4 * 1/2

We can cancel the 2 in the numerator and denominator

1/4 * 1/1

1/4

Which type of car had the largest range in monthly sales? Explain how you came up with your answer.

Answers

Answer:

Used car have the highest range of 75

Step-by-step explanation:

Yeah the type of car that have the highest range In monthly sales.

we know that

The range is the difference between the highest and the lowest value

First we,

calculate the range in monthly sales for the new car

highest value=51

lowest value=20

range=51-20

range=31

Secondly,we

calculate the range in monthly sales for used car

highest value=87

lowest value=12

range=87-12

range=75

Answer:

My answer: "The car that had the largest range in monthly sales was a used. Through finding the range by subtracting the highest and lowest data points, i was able to find the range for used cars being 75, and for new cars was 31. 75 is larger then 31, so therefore the used cars have the largest monthly range in sales. "

Their sample answer: Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger."

Select all that you included in your explanation.

The range for new cars was 31.

The range for used cars was 75.

Subtract the highest and lowest numbers.

Step-by-step explanation:

edg2020

mr. winter has 32 students in his class. he puts 6 student into each group. if Mr winter gives each group five pieces of chart paper, how many sheets will he need for the whole class?

PART A. which equation can be used to find the answer?
32-6x5=S
32÷5x6=S
32÷6x5=S
32x6÷5=S

Part B. Complete the statement.

Mr. Winter needs _____ sheets of chart paper.

Answers

Answer: A) 32÷6x5=S

B) 30 sheets of chart paper.

Step-by-step explanation:

we have 32 students.

he puts 6 students into each group.

he gives each group 5 pieces of chart paper.

32/6 will give us the number of groups

32/6 = 5.33

This means that we have 5 complete groups 6 students, and one group with 2 students. (a total of 6 groups)

And each of these groups need 5 pieces of paper, so we have the equation:

(32/6)*5 = S

and S = 26.66

now, for the 5 complete groups we need 5 pieces of paper for each, and 5*5 = 25 pieces of papper.

For the group of 2 persons we have the oter 1.66 ( or 2 if we round up) pieces of papper.

but this is a group, so they also should receive 5 pieces of papper regardless that they are only 2 integrants, then the total number of paper pieces is 30.

What is the value of x in the equation x/-4=7?

Answers

Answer: -28

Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.

On the left side, the -4's will cancel

and on the right side, 7(-4) is -28.

So x = -28.

Please do not try to do this problem in your head.

Show the work that it takes to get x by itself.

Answer:

x= - 28

Step-by-step explanation:

-4/1[x/-4 = 7]

x = -28

A circular dining room table can seat 11 people. Each person has about 2 feet of space along the edge of the table. What is the radius of the table, rounded to the nearest half-foot?

Answers

Answer:bruh

Step-by-step explana

The radius of the table, rounded to the nearest half-foot, is 3.5 feet.

To determine the radius of the circular dining room table, we can use the formula for the circumference of a circle, which is:

C = 2 π r

where:

C - circumference

r - radius

Given that each person has about 2 feet of space along the edge of the table, the circumference of the table must be able to accommodate the seating for 11 people. Each person occupies 2 feet of space, so the total space needed around the edge of the table is:

11 × 2 = 22 feet

We can set up an equation using the circumference formula:

C = 2 π r = 22

To find the radius (r), we divide both sides of the equation by 2π:

r = [tex]\frac{22}{2 \pi}[/tex]

Now, let's calculate the value:

r = [tex]\frac{22}{2 \pi}[/tex] = [tex]\frac{22}{2 \times 3.14}[/tex] = [tex]\frac{22}{6.28}[/tex] = 3.503

Rounding to the nearest half-foot, we get:

r = 3.5 feet


If a single 12-sided die is tossed once, find the probability of rolling a 2.
What is the probability?

Answers

Answer:

1/12

Step-by-step explanation:

hope this helps you

Final answer:

The probability of rolling a 2 on a single 12-sided die is 1/12, which is approximately 8.33%.

Explanation:

If a single 12-sided die is tossed once, the probability of rolling a 2 is calculated by dividing the number of ways to roll a 2 by the total number of possible outcomes on the die. Since there is only one way to roll a 2, and there are 12 different possible outcomes on a 12-sided die, the probability is calculated as follows:

Count the number of favorable outcomes for rolling a 2: There is 1 way to roll a 2.

Count the total number of possible outcomes on a 12-sided die: There are 12 possible outcomes (1, 2, 3, ... 12).

Divide the number of favorable outcomes by the total number of possible outcomes to get the probability: P(rolling a 2) = 1/12.

Therefore, the probability of rolling a 2 on a 12-sided die is 1/12, which can also be expressed as approximately 8.33%.

What is the mean for the data set?
8 10 6 4
12 6 8 14

Answers

Answer:

8.5

Step-by-step explanation:

To find mean, we simply take the average of all the numbers in the data set, and divide in by the amount of values!

[tex]8+10+6+4+12+6+8+14= 68\\[/tex]

68 ÷ 8 = 8.5!

Answer:

[tex]8\frac{1}{2}[/tex]

Step-by-step explanation:

First add up all the numbers:

8+10+6+4+12+6+8+14=68

Now you have to divide the sum by the amount of numbers. There are 8 numbers.

[tex]\frac{68}{8}=\frac{34}{4}=\frac{17}{2}[/tex]

[tex]\frac{17}{2}=8\frac{1}{2}[/tex]

Lydia drove 441 miles in 6 hours. On average, how fast did she drive in miles per hour? Express your answer in simplest form.

Answers

Answer:

She drove [tex]\frac{147}{2} miles/ hour[/tex]

Step-by-step explanation:

We are given that Lydia drove 441 miles in 6 hours.

We are supposed to find how fast did she drive in miles per hour

Distance covered by Lydia in 6 hours = 441 miles

Distance covered by Lydia in 1 hour =[tex]\frac{441}{6}[/tex]

Distance covered by Lydia in 1 hour =[tex]\frac{147}{2} miles/ hour[/tex]

Hence She drove [tex]\frac{147}{2} miles/ hour[/tex]

Answer and how to do it

Answers

Answer:

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Step-by-step explanation:

The equation of a circle in standard form is

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

You are given

[tex] x^2 + y^2 - 18x + 45 = 0 [/tex]

In order to put the equation in standard from, we need to complete the square. Since there is no y term, the y part is simply y^2, and there is no need to complete the square for y. For x, we do have an x term, so we must complete the square in x.

Start by grouping the x terms and subtracting 45 from both sides.

[tex] x^2 - 18x + y^2 = -45 [/tex]

Now we need to complete the square for x.

[tex] x^2 - 18x ~~~~~~+ y^2 = -45 [/tex]

The number that completes the square will go in the blank above, and it will also be added to the right side of the equation.

To find the number you need to add to complete the square, take the coefficient of the x term. It is -18. Divide it by 2. You get -9. Now square -9 to get 81. The number that completes the square in x is 81. Now you add it to both sides of the equation.

[tex] x^2 - 18x + 81 + y^2 = -45 + 81 [/tex]

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Answer: [tex] (x - 9)^2 + y^2 = 36 [/tex]

What is mBC?

A.70

B.140

C.28

D.56

What is mBCD
A.168

B.192

C.220

D.82

Answers

Answer:

is there more to the question?

Step-by-step explanation:

Answer:

1. is 56

2. is 82

Step-by-step explanation:

Just took the quiz and got it right (Like it please so people know its the correct answer)

A sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction. Find the area of the sector to the nearest square foot.

The sprinkler can water ____
square feet.

Answers

We have been given that a sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction.

We are asked to find the area of the sector to nearest square foot.

We will use area of sector formula to solve our given problem.

[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where,

[tex]\theta[/tex] = Central angle of sector,

[tex]r[/tex] = Radius.

For our given problem [tex]\theta = 225^{\circ}[/tex] and [tex]r=11[/tex].

[tex]\text{Area of sector}=\frac{225^{\circ}}{360^{\circ}}\times \pi (11)^2[/tex]

[tex]\text{Area of sector}=0.625\times 121\pi[/tex]

[tex]\text{Area of sector}=237.5829444277281137[/tex]

[tex]\text{Area of sector}\approx 238[/tex]

Therefore, the sprinkler can water approximately 238 square feet.

Final answer:

To find the area of the sector, we need to find the central angle, find the fraction of the circle covered by the sector, and then multiply it by the area of the entire circle with a radius of 11 feet.

Explanation:

To find the area of the sector, we need to find the central angle first. Since the sprinkler can only rotate 225∘ in each direction, the total angle covered is 225∘+225∘=450∘.

Next, we need to find the fraction of the circle covered by the sector. We can do this by finding the ratio of the central angle to the total angle of a circle, which is 360∘. This can be calculated as (450/360).

Finally, we multiply the fraction by the area of the entire circle with a radius of 11 feet, which is π(11)^2, to find the area of the sector.

5. The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56, 47, 49, 37, 38, 60, 50, 43, 43, 59, 50, 56, 54, 58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53, 21, 32, 49, 45, 38, 44, 33, 32, 43, 53, 46, 36, 48, 39, 35, 37, 36, 39, 45. (a) Construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings. (b) Can we claim a significant reduction in the rate of intrusion attempts

Answers

Final answer:

To construct a 95% confidence interval for the difference between the average number of daily intrusion attempts before and after changing firewall settings, you determine the standard deviation and mean for both periods. Use these in the formula for the confidence interval. If the interval doesn't include zero, it indicates a significant difference in the average number of daily intrusion attempts, and thus, potentially a significant reduction in intrusion attempts.

Explanation:

To perform this analysis, we first need to calculate the mean of the numbers of intrusion attempts for both periods - before and after the change of firewall settings. Then, we need to calculate the standard deviation for the numbers of intrusion attempts for both periods. The formula for the confidence interval is Mean Difference ± (Z*Standard Error). Where Z is a standard score value retrieved from the Z distribution table for a particular confidence level, in this case, 95%. The confidence levels you will be working with depend on the number of samples, in this case 14 and 20 respectively.

Once you have the confidence interval, it will give you the range in which the actual difference between the two means lies with 95% certainty. If the interval does not include zero, it indicates a significant difference between the means. By observing whether the values are predominantly positive or negative, we can infer about the significant reduction in the rate of intrusion attempts.

Learn more about Confidence Interval here:

https://brainly.com/question/34700241

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