A and B are complementary angles measures 32 What is the measure of b

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:

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]

Answer:

$6,376.92

Step-by-step explanation:

-Let d be the rate of depreciation per year.

-Therefore, the value after n years can be expressed as:

[tex]A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years[/tex]

#We substitute for the years 2009-2013 to solve for d:

[tex]A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698[/tex]

#We then use the calculated depreciation rate above to solve for A after 10 yrs:

[tex]A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\$6,376.92[/tex]

Hence, the value of the car after 10 yrs is $6,376.92

To find the future value of a car in 2019, we calculate the percentage decrease in value from 2009 to 2013 and apply it for 6 years.

To find the future value of the car in 2019, we need to determine the percentage decrease in value each year. From 2009 to 2013, the car depreciated from $41,000 to $19,000.

This is a decrease of $22,000. To find the percentage decrease, divide this by the initial value: 22,000 / 41,000 = 0.5366 (approximately).

To find the future value in 2019, we need to apply this percentage decrease continuously for 6 years. Multiply the current value by the percentage decrease repeatedly.

= 19,000 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366

= $5,862.54 (approximately).

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Step-by-step explanation:

[tex]2 {y}^{2} (35 - 4y) \\ = 2 {y}^{2} \times 35 - 2 {y}^{2} \times 4y \\ = 70 {y}^{2} - 8 {y}^{3} \\ = \red { \bold{ - 8 {y}^{3} + 70 {y}^{2} }} \\ is \: in \: the \: standard \: form.[/tex]

(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.

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.

Answer:

if you divide 80 and 5 would give you 16

Step-by-step explanation:

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.

Answer: j=-5 as long as you follow my steps you will also be able to show your work.

Combine multiplied terms into a single fraction

Distribute it then

Multiply all terms by the same value to eliminate fraction denominators.

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:

Im not 100% sure but i think its first row second

Answer: all the triangle are similar

Step-by-step explanation: ;)

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:

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:

6000000 mm squared

Step-by-step explanation:

We first convert the meters to millimeters. We got 4000 and 3000. The area of a triangle is base times height divided by 2. So we get 12000000 divided by 2 or 6000000 mm squared

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! :)

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.

I believe the answer is 21

21 × 6 = 126

and both numbers are divisible by 3

Answer:

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

Step-by-step explanation:

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:

8.2*10^-3

Step-by-step explanation:

Answer:

0.0082

(scientific notation)-step explanation:

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:

0.8 gallons

Step-by-step explanation:

4 gallons of juice divided into 5 pitchers equally, 4/5=0.8 per pitcher.

Answer:

the dimensions xyz of a box with volume 10 cubic feet that has minimum cost is;

x = 1.68 ft

y = 1.68 ft

z = 3.54 ft

Step-by-step explanation:

See attachment for the full explanation.

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:

a.  [tex]\int\limits^5_0 {f(x)} \, dx[/tex]

Step-by-step explanation:

Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:

[tex]\int\limits^5_0 {f(x)} \, dx[/tex]

Therefore, the answer is alternative a.

Answer: -3 1/4 or -13/4

Step-by-step explanation:

Answer:

[tex]\frac{-7}{4}[/tex]

Step-by-step explanation:

-3*3/4-1/2

-9/4+1/2

-9/4+2/4

(-9+2)/4

-7/4

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:

The calculated p-value is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

Step-by-step explanation:

For hypothesis testing, we first clearly state our null and alternative hypothesis.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the direction of the test.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the direction of the test.

For this question, we are to investigate that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

The null hypothesis would be that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate. That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

The alternative hypothesis is that there is significant evidence to suggest that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

This is evidently a one tail hypothesis test (we're investigating only in one direction; less than the claim

Mathematically, the null hypothesis is

H₀: μ ≥ 15

The alternative hypothesis is

Hₐ: μ < 15 minutes

To do this test, we will use the z-distribution because the population standard deviation is known.

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 13 minutes

μ₀ = the advocate's claim = 15 minutes

σₓ = standard error of the poll proportion = (σ/√n)

where n = Sample size = 50

σ = population standard deviation = 11 minutes.

σₓ = (σ/√n) = (11/√50) = 1.556

z = (13 - 15) ÷ 1.556 = -1.29

checking the tables for the p-value of this z-statistic

p-value (for z = -1.29, at 0.05 significance level, with a one tailed condition) = 0.098525

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 5% = 0.05

p-value = 0.098525

0.098525 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

Hope this Helps!!!

Answer:

A: (m + p, n + r)

Step-by-step explanation:

[tex]Midpoint \: of \: AC \\ = \bigg( \frac{2m + 2p}{2} \: \: \frac{2n + 2r}{2} \bigg) \\ \\ = \bigg( m + p, \: \: n + r \bigg)[/tex]