What is the solution to the system of equations graphed below?


A. (2, 4)
B. (4, 2)
C. (0, 6)
D. (6, 0)

Using the formula for a 95% confidence interval and a Z score of 1.96, Joseph's 95% confidence interval for the percentage of students reporting bullying at their school is roughly 10.1% to 11.9%.

The subject of this problem is statistics, specifically the creation of a 95% confidence interval based on collected data. A confidence interval is a type of estimate computed from the statistics of observed data. This gives a range of values for an unknown parameter (in this case, the number of students experiencing bullying).

In this case, the mean (or average) is 0.15 or 15%. The standard deviation is 0.045 or 4.5%. The sample size, often denoted as 'n', is 186.

Based on the 95% confidence interval, we will use a Z score of 1.96. We can start to calculate our interval using the formula for the confidence interval: sample mean ± (Z * (standard deviation/sqrt(n))).

Using these numbers:

The lower end of the confidence interval is 0.11 - (1.96 * (0.045 / sqrt(186))) = about 0.101 or 10.1%.

The upper end of the confidence interval is 0.11 + (1.96 * (0.045 / sqrt(186))) = about 0.119 or 11.9%.

So, the 95% confidence interval for the percentage of students who reported experiencing bullying one to three times within the most recent month is approximately 10.1% to 11.9%.

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Answer:

A) Slope - 1.1889. The Predicted distance the drivers were able to drive increases by 1.1889

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

split the triangle in to 5 different shapes

3 of them are rectangles, and 2 are triangles

all of the rectangles are the same size being:

12 by 5  so 12 times 5. then do this 3 times for each rectangle.

Now take the triangles and find the area for those.

which is 1/2 or base times height . so half of 5 multiplied by height (4.3)

being 2.5 times 4.3 giving you 10.75

now take the area of the rectangles and triangles and add them together

60+60+60+10.75+10.75= 201.5 ft2

Answer:

[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]

[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(13.776,3,TRUE)"

If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

[tex]n=4[/tex] represent the sample size

We can calculate the sample deviation with this formula:

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

[tex]\alpha[/tex] represent the confidence level  

[tex]s =1.5 [/tex] represent the sample variance obtained

[tex]\sigma^2 =0.7[/tex] represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population deviation is higher than 0.7, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma \leq 0.7[/tex]

Alternative hypothesis: [tex]\sigma >0.7[/tex]

Calculate the statistic  

For this test we can use the following statistic:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 3. And since is a right tailed test the p value would be given by:

[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(13.776,3,TRUE)"

Conclusion

If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7

Answer:

18.15% probability of producing a bad product

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 3.01, \sigma = 0.02[/tex]

What is the probability of producing a bad product?

Less than 2.97 or more than 3.03.

Less than 2.97

pvalue of Z when X = 2.97. So

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

[tex]Z = \frac{2.97 - 3.01}{0.02}[/tex]

[tex]Z = -2[/tex]

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

More than 3.03

1 subtracted by the pvalue of Z when X = 3.03. So

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

[tex]Z = \frac{3.03 - 3.01}{0.02}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

1 - 0.8413 = 0.1587

Then

0.0228 + 0.1587 = 0.1815

18.15% probability of producing a bad product

Answer: b

Step-by-step explanation:

The solutions to the quadratic equation x^2 = -5x - 3 are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2, calculated using the quadratic formula -b ± √(b² - 4ac) / (2a).

The subject of this question is Mathematics, specifically, the solution of quadratic equations. A quadratic equation is in the form ax²+bx+c = 0. You can find the solutions or roots of any quadratic equation using the formula: -b ± √(b² - 4ac) / (2a).

Let's apply this formula to the quadratic equation, x^2 = -5x - 3. Here, a = 1, b = 5, and c = 3. Substituting these values into the formula, the solutions to this quadratic equation are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2. However, in the question, there seems to be multiple options. It's essential to note that the correct solutions match the ones derived from our calculations.

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Answer:

The standard deviation of the number of runs required is 2447.26

Step-by-step explanation:

For each run, there are only two possible outcomes. Either the program fails, or it does not. The probability of the computer failing during a run is independent of other runs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

The standard deviation for the expected number of trials for r sucesses is:

[tex]\sqrt{V(X)} = \sqrt{\frac{r(1-p)}{p^{2}}}[/tex]

A computer program has a bug that causes it to fail once in every thousand runs, on average.

This means that [tex]p = \frac{1}{1000} = 0.001[/tex]

In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?

This means that r = 6. So

[tex]\sqrt{V(X)} = \sqrt{\frac{6*0.999}{(0.001)^{2}}} = 2447.26[/tex]

The standard deviation of the number of runs required is 2447.26

Answer:

40 and 1/2

Step-by-step explanation:

Multiply 4 1/2 by 1 1/2. Then multiply the product of 4 1/2 and 1 1/2 by 6.

Answer:

y = 18x

72 cupcakes = 18 cups of flour

Step-by-step explanation:

y= cupcakes

x=flour

4/1

72/18

18x4=72

Answer:

72 cupcakes

Step-by-step explanation:

Take 4 and multiply it by 18! Simple! :)

Final answer:

To calculate the labourer's pay for 22 days, divide the total pay for 5 days by 5 to get the daily wage, and then multiply this by 22. The labourer would earn #4400 for 22 days of work.

Explanation:

The question posed is regarding the calculation of a laborer's pay for a certain number of days based on a known daily wage rate.

If a labourer is paid #1000 for 5 days work, to find out his pay for 22 days work we follow these steps:

In conclusion, the labourer's pay for 22 days of work would be #4400.

I believe the answer is 21

21 × 6 = 126

and both numbers are divisible by 3

Answer:

4

Step-by-step explanation:

use the order of operations- (parentheses, exponets, multiply, divide, add, subtract...)

54-200/4

-200/4=-50

54-50=4

Answer:

(D)

x (x + 2) × (x + 4) = 75

Answer:

D.)x (x + 2) · (x + 4) = 75

Step-by-step explanation:

Well, the easiest way to look at this is by first placing both the 2nd odd integer and the 3rd odd integer into parenthesis finally you simply add the 1st integer to the beginning of the equation. You simply just use the information given and piece it all together into an equation usually written in the same order that the information was given.

Also, to find out the operations in the equations you simply use the keywords given in the problem itself. In this problem, they used the phrase "The product of three consecutive odd integers is 75." since we know that product means to multiply then we also know that we are multiplying all of the integers together to give us our final answer of 75.

Answer:

[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]  

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]

Since is a one side test the p value would be:

[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]

And the best option for this case would be:

None of the above (it should be t(38) = 5.07, p < .01)

Step-by-step explanation:

Data given and notation

[tex]\bar X_{1}=7[/tex] represent the mean for the sample 1

[tex]\bar X_{2}=10[/tex] represent the mean for the sample 2

[tex]s_{1}=\sqrt{2.5}= 1.581[/tex] represent the sample standard deviation for the sample 1

[tex]s_{2}=\sqrt{4.5}= 2.121[/tex] represent the sample standard deviation for the sample 2

[tex]n_{1}=20[/tex] sample size selected for 1

[tex]n_{2}=20[/tex] sample size selected for 2

[tex]\alpha[/tex] represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the group 1 is higher than the mean for group 2, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{2} \leq \mu_{1}[/tex]

Alternative hypothesis:[tex]\mu_{2} > \mu_{1}[/tex]

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{2}-\bar X_{1}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]  

P-value

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]

Since is a one side test the p value would be:

[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]

And the best option for this case would be:

None of the above (it should be t(38) = 5.07, p < .01)

Answer:

large of a sample size  n = 2645

Step-by-step explanation:

Explanation:-

The population standard deviation 'σ' = 39.9

Given data the estimate is within 2 of the true population mean so given the margin of error = 2

we know that margin of error is determined by

Margin of error = [tex]\frac{z_{\alpha }S.D }{\sqrt{n} }[/tex]

cross multiplication , we get

                    [tex]\sqrt{n} = \frac{2.578 X S.D}{M.E}[/tex]

                    [tex]\sqrt{n} = \frac{2.578 X 39.9}{2}= 51.4311[/tex]

squaring on both sides , we get

                    n = 2645.15

                    n = 2645

Conclusion:-

large of a sample size  n = 2645

Answer:

4

Step-by-step explanation:

4 data points are between 13 and 18 they are 13, 14, 15, and 18.

Answer:

4

Step-by-step explanation:

i took test

Answer:

i) the margin of error for a​ 95% confidence interval for estimating the population mean is

M.E = 8.909

ii)  the margin of error for a​ 95% confidence interval for estimating the population mean is

M.E = 5.025

Step-by-step explanation:

Step:-(i)

i )   Given sample size n = 484

Given sample standard deviation 'S' = 100

Margin of error for 95% confidence interval for estimating the population mean is determined by

              [tex]M.E = \frac{1.96 X 100}{\sqrt{484} } = 8.909[/tex]

ii) Given sample size n =1521

Given sample standard deviation 'S' = 100

Margin of error for 95% confidence interval for estimating the population mean is determined by

              [tex]M.E = \frac{1.96 X 100}{\sqrt{1521} } = 5.025[/tex]

The question revolves around calculating queueing system performance measures for a software company's call center and adjusting the service rate to maintain consistent service levels during an operational change. Calculations would apply queue theory but specifics require further details about the model type, such as M/M/1 or M/M/2. Algebraic methods would be needed to adjust the service rate to keep waiting times consistent.

The question deals with determining key performance measures (L, Lq, W, Wq) for a queueing system at People's Software Company call center, under two different operational scenarios, and solving for the service rate (μ) that equates waiting times between these scenarios. The system initially with two representatives and an arrival rate of 10 calls per hour, transitioning to one representative and a decreased arrival rate of 5 calls per hour, is examined assuming exponential service times with a mean of 5 minutes.

For the current system with two technical representatives and ten calls arriving per hour, assuming the call arrival rate follows a Poisson process and service times are exponentially distributed, key performance measures could be calculated utilizing formulas from queueing theory. However, these formulas depend highly on the specifics of the queueing model used, such as M/M/1, M/M/2, etc., and are not directly provided here.

For next year's system with a reduction in technical representatives and a halved arrival rate, similar analytical methods could be applied to predict performance based on the adjusted arrival rate and the assumption of unchanged service time distributions.

Regarding the adjustment of μ to maintain the same waiting time (W), algebraic solutions involving the exponential service time distribution and Poisson arrival processes must be derived, factoring in the reduction of workers and the change in arrival rate, to find the new service rate (μ) that would ensure continuity in service level expectations.

Answer:

Step-by-step explanation:

Labor: 40.55 x 4 = $162.20 for total Labor.

Total Charges: 25.75 + 38.75 + 162.20 = $226.70 Total charges.

Answer:

if you divide 80 and 5 would give you 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Vowels are defined as sound repeated as a, e, i, o, u and the rest 21 letters are classified as consonants.

The given words are generated from English alphabet as a combination of Vowels and alphabets. Thus the combination of vowels and consonant help in the formation of words. There are n number of unique letters are formed.

1) Speed is fast = SPEEFAS

2) Minimum number of participants = MINIPART

3) Sum of excess = SUMCESS

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To find the number of unique words that can be generated with a given word length and maximum number of consecutive vowels, multiply the number of possible vowel arrangements by the number of possible consonant arrangements.

To determine the number of unique words that can be generated given the length of a word (wordLen) and the maximum number of consecutive vowels (maxVowels), we need to consider the different possibilities for the arrangement of vowels and consonants in the word. Since vowels can be repeated consecutively up to maxVowels times, we can have up to maxVowels + 1 vowels in a row in any word. Similarly, we can have up to wordLen - maxVowels + 1 consonants in a row in any word. Therefore, the total number of unique words that can be generated is (maxVowels + 1) * (wordLen - maxVowels + 1).

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Answer:

8 ( x + 3 ) , Need more details , hope this was answer

Step-by-step explanation:

Final answer:

The expression 8x + 24 can be factored to 8(x + 3) by taking out the common factor of 8, which is a usual step in simplifying algebraic expressions.

Explanation:

The expression 8x + 24 is a linear algebraic expression with two terms. Typically in algebra, when simplifying expressions or solving equations, we might look for ways to factor or combine like terms. However, in this expression, there's no immediate algebraic simplification other than factoring out a common factor if we wanted to rewrite the expression in a different form.

If we observe that 24 is divisible by 8, we might factor out the number 8 to express the original expression in the form of 8(x + 3). This shows that the expression can be seen as the product of 8 and the quantity (x + 3), which is particularly useful when solving equations or simplifying further expressions that include 8x + 24.

Final answer:

The interest earned on $9.02 at an 8% interest rate for three years is $2.16.

Explanation:

To calculate the amount of interest earned on a principal of $9.02 at an interest rate of 8% for three years, we would use the formula for simple interest: Interest = Principal  imes Rate  imes Time. Plugging in the values we get:

Interest = $9.02  imes 0.08  imes 3

Interest = $2.166. Therefore, the interest earned on the principal amount of $9.02 invested at an 8% interest rate for three years would be $2.16, after rounding to the nearest cent.

Answer: 12

Step-by-step explanation: To find the radius you have to do the opposite of 2r(pi). So you divide 75 by 2 and then by 3.14, getting 11.9, which rounds to 12

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

(1) Given:

Given that Corrin has twin boys. She buys a box of 10 toy cars to share evenly between them.

We need to determine the unit rate of toy cars for one boy.

Unit rate:

The unit rate for toy cars for one boy can be determined by dividing the total number of cars by the total number of boys.

Thus, we have;

[tex]Unit \ rate=\frac{10}{2}[/tex]

[tex]Unit \ rate=5[/tex]

Thus, the unit rate is 5 cars per boy.

Hence, Option b is the correct answer.

(2) Given:

Given that the Belle works at a donut shop. They sell a box of donut holes for $1.80. There are 20 donut holes in the box.

We need to determine the unit rate.

Unit rate:

We need to determine the cost of one donut hole in the box.

The cost of one donut hole can be determined by dividing the cost of box of donut holes by the total number of donut holes in the box.

Thus, we have;

[tex]Unit \ rate=\frac{1.80}{20}[/tex]

[tex]Unit \ rate=0.09[/tex]

Thus, the unit rate is $0.09 per donut hole.

Hence, Option a is the correct answer.

Since PQ = SR, hence the length of PQ is 4 units

From the given figure, w are told that triangle PTQ is similar to that of RTS, this means that;

PQ = SR

Given the following

Length of SR = 4 units

Since PQ = SR, hence the length of PQ is 4 units

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Answer:

it would be a distance of 7 units

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

the absolute value of -5 - 2 = 7

Answer:

The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.

Step-by-step explanation:

A confidence interval of proportions has two bounds, a lower bound and an upper bound.

These bounds depend on the sample proportion and the margin of error.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this problem, we have that:

Sample proportion 59%

Margin of error 4%

59 - 4 = 55%

59 + 4 = 63%

The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.

Final answer:

The Republican candidate can neither be certain of victory nor of defeat based on the poll with a margin of error of 3 percentage points. The poll suggests a favorable leaning towards the Republican, but the actual support could range from 53% to 59%, implying the election could be close. Historical examples illustrate that polls are not foolproof predictors of election outcomes.

Explanation:

Whether the Republican candidate should expect to win based on a poll showing 56​% favoritism with a margin of error of 3 percentage points cannot be said with certainty. The margin of error indicates that the true support could theoretically range from 53% to 59%.

To understand the implication, consider that if the candidate's actual support is at the lower end of the margin of error (53%), then it is possible that the race is very close, depending on the percentage of voters favoring the Democratic candidate. If the Democratic candidate has close to 47% support, the election could go either way. Conversely, if the Republican candidate's support is at the higher end (59%), then it is more likely, though not guaranteed, that the Republican would win. Polls provide a snapshot of voter preferences at a particular time and have limitations, including potential sampling errors, nonresponse bias, and inability to predict who will actually turn out to vote.

Historical polls and election outcomes show that while polls can be predictive, they are not always accurate reflections of election results. An example is the 2000 election between George W. Bush and Al Gore, which was a toss-up based on polls but ended with a narrow victory. Similarly, in a hypothetical situation where a state's population is largely liberal, a conservative might still win if the liberal vote is split between two candidates.

Answer:

We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.

Step-by-step explanation:

Jenna claims that the average time of texting at her larger high school is greater than 94 minutes per day.

From here we can see that we have to perform a hypothesis test about a sample mean. The null and alternate hypothesis will be:

Null Hypothesis: [tex]\mu \leq 94[/tex]

Alternate Hypothesis: [tex]\mu > 94[/tex]

Jenna collected data from a sample of 32 students. So, sample size will be:

Sample Size = n = 32

Sample Mean = x = 96.5

Sample Standard Deviation = s = 6.3

We have to perform a hypothesis test, to test Jenna's claim. Since, the value of Population Standard Deviation is unknown and the value of Sample Standard Deviation is known, we will use One Sample t-test in this case.

The formula to calculate the test statistic is:

[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

Using the values, we get:

[tex]t=\frac{96.5-94}{\frac{6.3}{\sqrt{32} } }=2.245[/tex]

The degrees of freedom will be:

df = n - 1 = 32 - 1 = 31

We have to convert the t-score 2.245 with 31 degrees of freedom to its equivalent p-value. From t-table this value comes out to be:

p-value = 0.0160

The significance level is:

[tex]\alpha =0.05[/tex]

Since, the p-value is lesser than the level of significance, we reject the Null Hypothesis.

Conclusion:

We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.

This p value the significant level  0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.

Given-

Jenna claims that the average for the students at her large high school is greater than 94 minutes. The null hypothesis is  [tex]\mu\leq 94[/tex]  and alternate hypothesis  [tex]\mu >94[/tex].

Now given that,

The value of sample size [tex]n[/tex] is 32, sample means [tex]x[/tex] is 96.5 and the sample standard deviation [tex]s[/tex] is 6.3.

Here one-sample t-test will be used for the as sample standard deviation is given. The formula for the test statics is,

[tex]t=\dfrac{x-\mu}{\dfrac{s}{\sqrt{n}} }[/tex]

[tex]t=\dfrac{96.5-94}{\dfrac{6.3}{\sqrt{32}} }[/tex]

[tex]t=2.245[/tex]

Now the degrees of freedom is n-1. thus,

[tex]D_f=n-1[/tex]

[tex]D_f=32-1=31[/tex]

Now from the t table the value of t score 2.245 having degree 31 is,

p value[tex]=0.0160[/tex]

For this p value the significant level  0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.

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