A chord is 16 units from the center of a circle. The radius of the circle is 20 units. What is the length of the chord?

How is the measure of a central angle and the corresponding chord related to the measure of the arc intercepted by the chord?

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)

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: 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.

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:

68/99

Step-by-step explanation:

.68686868686 repeating

Let x= .68686868668repeating

Multiply by 100

100x = 68.686868686repeating

Subtract x = .68686868repeating from this equation

100x = 68.686868686repeating

-x = .68686868repeating

------------------------------------------

99x = 68

Divide each side by 99

99x / 99 = 68/99

x = 68/99

Answer:

68/99 I agree with the other person

Step-by-step explanation:

Answer:

The probability that he makes one of the two free throws is 0.38

Step-by-step explanation:

Hello!

Considering the situation:

A pro basketball player shoots two free throws.

The following events are determined:

A: "He makes the first free throw"

Ac: "He doesn't make the first free throw"

B: "He makes the second free throw"

Bc: "He doesn't make the second free throw"

It is known that

P(A)= 0.48

P(B/A)= 0.62

P(B/Ac)= 0.38

You need to calculate the probability that he makes one of the two free throws.

There are two possibilities, that "he makes the first throw but fails the second" or that "he fails the first throw and makes the second"

Symbolically:

P(A∩Bc) + P(Ac∩B)

Step 1.

P(A)= 0.48

P(Ac)= 1 - P(A)= 1 - 0.48= 0.52

P(Ac∩B) = P(Ac) * P(B/Ac)= 0.52*0.38= 0.1976≅ 0.20

Step 2.

P(A∩B)= P(A)*P(B/A)= 0.48*0.62= 0.2976≅ 0.30

P(A)= P(A∩B) + P(A∩Bc)

P(A∩Bc)= P(A) - P(A∩B)= 0.48 - 0.30= 0.18

Step 3

P(Ac∩B) + P(A∩Bc) = 0.20 + 0.18= 0.38

I hope this helps!

The probability that the player makes one of the two free throws using the multiplicative rule is 0.4952 or 49.52%.

To find the probability that the player makes one of the two free throws using the multiplicative rule, we need to consider the two possible ways he can do this:

We can calculate the probability for each case and sum them up to find the total probability:

p(make 1st and miss 2nd) = (0.48) * (0.62) = 0.2976

p(miss 1st and make 2nd) = (0.52) * (0.38) = 0.1976

Total probability = p(make 1st and miss 2nd) + p(miss 1st and make 2nd) = 0.2976 + 0.1976 = 0.4952

Therefore, the probability that the player makes one of the two free throws is 0.4952, or 49.52%.

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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:

0.8 gallons

Step-by-step explanation:

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

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: -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:

1.  3/4 + 3/4 + 3/4 +3/4

2. 0.75 * 4

Step-by-step explanation:

1. add 3/4 four times

3/4 + 3/4 + 3/4 +3/4

2. You can turn 3/4 into a decimal.  3/4 =0.75

0.75 * 4

Final answer:

3/4 × 4 can be solved through repeated addition by adding 3/4 to itself four times to get 9/4 or 2 1/4. Alternatively, by simplifying before multiplying, recognizing that 4 is the reciprocal of 1/4, we easily find that the product is 3.

Explanation:

When solving 3/4 × 4 using repeated addition, we use the concept that multiplying a number by a whole number is the same as adding that number to itself that many times. In this case, 3/4 is added to itself 4 times:

We have four 3/4's, and when we add them up, we get:

When we add 3/2 (1 1/2) and 3/4, we can convert 1 1/2 into 6/4 to make it easier to add the fractions, obtaining:

Therefore, 3/4 × 4 equals 9/4 or 2 1/4 through repeated addition.

Another way to approach the problem is by simplifying before multiplying. Since we are multiplying by 4, which is the reciprocal of 1/4, we can simplify by understanding that:

Thus, by canceling out the common factors (4 in the numerator and 4 in the denominator), the multiplication becomes 3 × 1, which equals 3. This satisfies the condition that as long as we perform the same operation on both sides of the equals sign, the expression remains an equality.

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]

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:

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:

$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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(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.

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:

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:

160 plus 35 = 185

Step-by-step explanation:

8×20

hopefully this helps you

Answer:

if you divide 80 and 5 would give you 16

Step-by-step explanation:

I believe the answer is 21

21 × 6 = 126

and both numbers are divisible by 3

Answer:

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

Answer: all the triangle are similar

Step-by-step explanation: ;)

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!!!

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]

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

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:

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

Step-by-step explanation:

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.