A small post office has two open windows. Customers arrive according to a Poisson distribution at the rate of 1 every 3 minutes. However, only 80% of them seek service at the windows. The service time per customer is exponential, with a mean of 5 minutes. All arriving customers form one line and access available windows on a FIFO basis.

(a) What is the probability that an arriving customer will wait in line?
(b) What is the probability that both windows are idle?
(c) What is the average length of the waiting line?
(d) Would it be possible to offer reasonable service with only one window? Explain.

Answer:

standard deviation = ±0.4667

Step-by-step explanation:

In Normal distribution, approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

Therefore, for a confidence interval of 99.7% the standard deviation of the x¯ must be 3 standard deviations from the mean,

3σ = ±1.4

σ = ±1.4/3

σ = ±0.4667

Therefore, 0.4667 is the standard deviation that x¯ must have so that 99.7% of all samples give an x¯ within 1.4 point of μ.

The solution of the quadratic equation is x = ±3/7

Quadratic equations are equations that have a leading degree of 2

Given the quadratic function

49x^2 = 9

Divide both sides by 49
49x^2/49 = 9/49
x^2 = 9/49
x = √9/49
x = ±3/7

Hence the solution of the quadratic equation is x = ±3/7

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Final answer:

The mortgage amount for the home is $192,000 after a 20% down payment on a $240,000 purchase price. The cost for two points at closing is $3,840, which is 2% of the mortgage amount.

Explanation:

The amount of the mortgage can be found by subtracting the 20% down payment from the purchase price of the home. For a home priced at $240,000, a 20% down payment is $48,000 ($240,000 × 0.20), leaving a mortgage amount of $192,000 ($240,000 - $48,000).

Next, the cost of the two points at closing is calculated based on the mortgage amount. Each point costs 1% of the mortgage amount, so two points would be 2% of $192,000, which comes to $3,840

Answer:

x^3-x^2-17x+12

Step-by-step explanation:

Multiply

Answer:

E: None of the above

Step-by-step explanation:

Hello!

The objective is to find out how much time it takes people to commute to work.

Two samples where taken and two hypothesis tests where made:

One:

Sample mean 71 min; p-value: 0.03

Two:

Sample mean 72 min; p-value: 0.06

You have to choose from the options, a possible pair of hypotheses used for these two tests.

The parameter of the study is the population mean μ.

In the statistic hypotheses, the parameters are given either a known population value or a suspected value. So all options including sample values are wrong.

As said before the objective of the survey is to "determine how much time people spend commuting to work" in other words, whether or not the population mean is equal to a certain value.

H₀: μ = μ₀

H₁: μ = μ₀

Where μ₀ represents the theoretical value of the population mean. As you can say the hypotheses pair is two-tailed, not one-tailed.

Then the correct answer is E: None of the above

I hope this helps!

Answer:

4

Step-by-step explanation:

because 4x4 is 16 and 16 x four is 64

Answer:

4³

I think this is right. the problem isnt explained very well.

Answer:

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:  

Null hypothesis:[tex]p=0.146[/tex]  

Alternative hypothesis:[tex]p \neq 0.146[/tex]  

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Step-by-step explanation:

Data given and notation

n=865 represent the random sample taken

X=159 represent the housing units that are vacant

[tex]\hat p=\frac{159}{865}=0.184[/tex] estimated proportion of vacant units

[tex]p_o=0.146[/tex] is the value that we want to test

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

z would represent the statistic (variable of interest)

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

Solution to the problem

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:  

Null hypothesis:[tex]p=0.146[/tex]  

Alternative hypothesis:[tex]p \neq 0.146[/tex]  

A. One-proportion z-test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And the conditions required are:

1) The data comes from a random sampling

2) Independence condition between observations

3) np>10 and n(1-p)>10

4) The sample size is 10 times lower than the population size.

Answer:

The probability that Jones is lying is 6/7

Step-by-step explanation:

First we will list out 2 different cases when the outcome is a lie

1.probability that Jones tells lies is = 0.6 and probability that dalgiliesh analyses it correctly is 0.8

So the probability that dagliesh correctly analyses that he is telling lies is 0.8*0.6=0.48

2.Probability that Jones tells truth is 0.4 and if dagliesh analyses it incorrectly (which has a probability of 0.2) the outcome(as analysed by dagiliesh) is a lie

So probability that dagliesh analyses Jones truth as a lie is 0.2*.0.4=0.08

Total probability of outcome being a lie is 0.48+0.08=0.56

But we need the probability of Jones actually saying a lie which is nothing but 0.48/0.56= 6/7

The probability of that Jones is lying is [tex]\frac{6}{7}[/tex] .

Probability is defined as, divide favourable outcomes by total outcomes.

First case:

Probability that Jones tells lies is = 0.6

Probability that Dalgliesh analyses it correctly is, =  0.8

Therefore,  the probability that Dalgliesh correctly analyses that Jones is telling lies is,

                       [tex]P=0.8*0.6=0.48[/tex]

Second case :

Probability that Jones tells truth is, =  0.4

Probability of Dalgliesh  analyses it incorrectly that Jones tells truth is,

                                                = 0.2

So, Probability that Dalgliesh analyses Jones truth as a lie is,

                          [tex]0.2*.0.4=0.08[/tex]

Total probability of outcome being a lie is,

                               [tex]0.48+0.08=0.56[/tex]

Thus, Probability of Jones telling lie is,  [tex]=\frac{0.48}{0.56} =\frac{6}{7}[/tex]

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Here,

py+qy=-4y+8

or, py+qy+4y=8

or,y(p+q+4)=8

therefore,

y=8/(p+q+4)

Salt flows in at a rate of

(2 g/L) * (4 L/min) = 8 g/min

and out at a rate of

(B/(200 + t) g/L) * (3 L/min) = 3B/(200 + t) g/min

where B is the amount of salt in the tank at time t.

Then the net rate at which B changes is governed by the ODE,

[tex]B'=8-\dfrac{3B}{200+t}[/tex]

[tex]B'+\dfrac{3B}{200+t}=8[/tex]

Multipy both sides by [tex](200+t)^3[/tex]:

[tex](200+t)^3B'+3B(200+t)^2=8(200+t)^3[/tex]

[tex]\left(B(200+t)^3\right)'=8(200+t)^3[/tex]

Integrate both sides:

[tex]B(200+t)^3=2(200+t)^4+C[/tex]

[tex]B=2(200+t)+C(200+t)^{-3}=\dfrac{2(200+t)^4+C}{(200+t)^3}[/tex]

The tank starts with 30 g of salt, so B(0) = 30, which gives

[tex]30=2(200) + C(200)^{-3}\implies C=-2,960,000,000[/tex]

Answer with Step-by-step explanation:

We are given that

[tex]f(x)=-sin x[/tex]

[tex][0,\infty][/tex]]

Average value of the function is given gy

[tex]f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx[/tex]

[tex]f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}[/tex]

Using the formula

[tex]\int sin xdx=-cos x[/tex]

[tex]f_{avg}=\frac{1}{\pi}(cos\pi-cos0)[/tex]

[tex]f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}[/tex]

[tex]f(x)=f_{avg}[/tex]

[tex]-sinx=-\frac{2}{\pi}[/tex]

[tex]sinx=\frac{2}{\pi}[/tex]

[tex]x=sin^{-1}(\frac{2}{\pi})=0.69radian[/tex]

The average value of the function is [tex]-\frac{2}{\pi}[/tex].

The average value of the function is given as,

                    [tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {f(x)} \, dx[/tex]

Given function is, [tex]f(x)=-sinx[/tex]

Substitute values in above relation.

                [tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {-sinx} \, dx\\\\Average=\frac{1}{\pi} (cosx)^{\pi} _{0}\\\\Average=\frac{1}{\pi}(cos\pi - cos 0)\\\\Average=\frac{1}{\pi}(-1-1)\\\\Average=-\frac{2}{\pi}[/tex]

The values of x in the interval for which the function equals its average value is,

              [tex]-sinx=-\frac{2}{\pi}\\ \\x=sin^{-1} (\frac{2}{\pi} )=39.56[/tex]

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The recursive formula for the arithmetic sequence 12, 10, 8, 6, ... is a sequence where a(1) = 12, and a(n) = a(n - 1) - 2.

The recursive formula of an arithmetic sequence is a rule that uses each term to find the next. In this case, we start with the first term of the sequence, which is 12, and each following term decreases by 2. So, to find any term in the sequence, we take the previous term and subtract 2.

The recursive formula for the arithmetic sequence 12, 10, 8, 6, ... is:

a(1) = 12

a(n) = a(n - 1) - 2

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Answer:

x = 25

Step-by-step explanation:

[tex] \frac{5}{7} = \frac{x}{35} \\ \\ x = \frac{5 \times 35}{7} \\ \\ x = 5 \times 5 \\ \\ \huge \red{ \boxed{ x = 25}}[/tex]

Answer: Skewed left. (If there is an answer choice for it)

Step-by-step explanation: The data on the Y-Axis is higher on the left side of the graph than the right side of the graph. If it was higher on the right side of the graph, then it would be skewed right. Hope this helps!

Answer:

$2000

Step-by-step explanation:

biweekly is defined as every 2 weeks

assume each month has 4 weeks

there are 12 months in a year and she is paid 2x per month so there are 24 weeks she is paid

48000/24 can be used to find the biweekly pay which is 2000

Pam's gross pay per biweekly paycheck is calculated by dividing her annual salary ($48,000) by the number of pay periods in a year (26). This results in an approximate gross pay of $1,846.15 per biweekly paycheck.

The student's question pertains to calculating her gross pay per paycheck given her annual salary. To carry out this process, you need to understand that there are typically 52 weeks in a year and that being paid biweekly results in 26 pay periods (52 weeks divided by 2). Hence, you divide Pam’s annual gross pay amount of $48,000 by the 26 pay periods to get her gross pay, per paycheck.

Steps:

So, $48,000 / 26 = $1,846.15
This means Pam's biweekly paycheck would be roughly $1,846.15, before taxes and other deductions.

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Answer:

C) ⅙

Step-by-step explanation:

Starting with A:

April, August

2/12

1/6

Answer:

Step-by-step explanation:

kupa

645665465

Answer:

y=x(x-2)

Step-by-step explanation:

Answer:

a) π = np

π represents the number of heads that turn up in 1000 tosses of the coin.

b) The null hypothesis is represented as

H₀: p ≤ 0.50

The alternative hypothesis is given as

Hₐ: p > 0.50

c) The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.

The validity conditions are met because we have 1000 tosses with 520 heads and 480 tails, indicating that we have more than 20 sample size in this sample.

The sample proportion (0.52) and the standard error of the sample proportion (0.0158) show that the distribution approximates a normal distribution and isn't skewed. So, the theory based test for this study is valid.

d) Check Explanation

e) The p-value obtained is greater than the significance level at which the test might have been performed, hence, we fail to reject the null hypothesis and conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.

The researchers' claim then has to be wrong.

Step-by-step explanation:

a) If p corresponds to the proportion of 1000 tosses that turn up heads,

π = np

where n = number of tosses.

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

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 directions of the test.

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

For this question where we want to verify that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head. That is, the proportion of heads in multiple tosses is more than 0.5 given that the first toss was a head.

The null hypothesis would be that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.

That is, the coin is likely to turn up heads less than or equal to 50% of the time, when it is tossed multiple times, starting with a first toss that gives a head.

The alternative hypothesis is that there is significant evidence to conclude that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.

Mathematically,

The null hypothesis is given as

The null hypothesis is represented as

H₀: p ≤ 0.50

The alternative hypothesis is given as

Hₐ: p > 0.50

c) The conditions that need to be satisfied before a theory based test is used include:

The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.

d) The standardized statistic shows how far away from the standard proportion (the proportion that the population proportion is being compared with) the sample proportion is in terms of the standard error of the sample proportion.

It is given mathematically as,

t or z = (x - μ)/σₓ

x = p = sample proportion of the number of heads obtained in the multiple tosses starting with a first result of a head turning up = 0.52

μ = p₀ = 0.50 (the standard being tested against.

σₓ = standard error of the sample proportion, given as σₓ = √[p(1-p)/n]

n = sample size = 100

σₓ = 0.0158

The standardized statistic is also used to obtain the p-value that indicates how significant the results of the theory based test is.

e) 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, like all other hypothesis testing, the significance level is usually at 0.05. On rare occasions, 0.01 and 0.10 are often used.

Whichever of the 3 is used,

p-value = 0.1030

0.1030 > 0.05, 0.01 or 0.10

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.

Hope this Helps!!!

The expected value of this marble-drawing game is approximately -$0.032, meaning that you would expect to lose about 3.2 cents per play on average.

In order to calculate the expected value of this marble-drawing game, you need to consider the probability of drawing each color of marble and the payoff associated with each one. The probabilities are as follows: P(gold) = 3/31, P(silver) = 6/31, and P(black) = 22/31, based on the quantities provided in the bag. The payoffs are $3 for a gold marble, $2 for a silver marble, and -$1 for a black marble.

The formula for expected value, E(X), is given by:

E(X) = (P(gold) * payoff gold) + (P(silver) * payoff silver) + (P(black) * payoff black)

Substituting the given values leads to:

E(X) = (3/31 * $3) + (6/31 * $2) + (22/31 * -$1)

After calculations, we get:

The expected value in playing this game would be -$0.032 approximately. This means that on average, you would expect to lose about 3.2 cents per play.

Answer:

Check attachment for solution

Step-by-step explanation:

Given that,

6 out of 30 times would be written as

6/30 which reduces to 1/5 which would mean the spinner is divided into 5 different colors.

There could be more than one solution. The spinner could be divided into 10 spaces and red could be 2 of the spaces, or any other multiple of 5s

Answer:

The spinner has 5 equal sections, with one section red.

It can have 5N equal sections, with N sections Red

Step-by-step explanation:

p(red) = 6/30 = 1/5

1/5 = 2/10

Out of 10 sections, 2 are Red

In general,

It can have 5N equal sections, with N sections Red

Answer:

a, b. c, e

Step-by-step explanation:

Hence, Justin will have to ask for 1480 from family and friends  to cover cost.

What is cost?

Amount at which any product prices , that is it can be sold or bought.

How to calculate?

I Tuition = -$2,900

Other educational expenses = -$280

Housing and living expenses =- $4,100

estimates of grants= $3,500

work-study program =$2,800

savings = $500

hence cost = 3500-2900-280-4100+2800-500=-1480

∴ Justin will have to ask for 1480 from family and friends  to cover cost.

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No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year and this can be determined by using the formula of z-score.

Given :

The following steps can be used in order to determine whether you have to buy a vehicle or not:

Step 1 - The formula of z-score can be used in order to determine whether you have to buy a vehicle or not.

Step 2 - The z-score formula is given below:

[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]

Step 3 - Substitute the known terms in the above expression.

[tex]\rm z = \dfrac{6000-12494}{1290}=-5.0341[/tex]

Step 4 - Now, the p-value is given below:

[tex]\rm P(x < 6000)=P(z<-5.0341)[/tex]

Step 5 - Now, using the z table the value of P is:

P(x < 6000) = 0

No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year.

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The volume of a cube is found using the formula v = s^3, where s is the length of a side.

The volume of a cube with a side of 1/2cm is

V = 1/2^3 = 1/8 cubic cm.

Now multiply the volume of one cube by total cubes:

1/8 x 96 = 12 cubic cm

The prism has a volume of 12 cubic cm.

Answer:

it is 12 if u still need it

Step-by-step explanation:

Answer:

4711

Step-by-step explanation:

Answer by rothauserc(4711)   (Show Source):  

You can put this solution on YOUR website!

the probability that the first student picked has a lunch is 6/9 or 2/3

the probability that the second student picked has a lunch is 5/8

Answer:

4

Step-by-step explanation:

It works with the second one

Answer:

Check the explanation

Step-by-step explanation:

1

a) A is an Equivalence Relation

Reflexive : x is parallel to itself => x R x

Symmetric : x is parallel to y => y is parallel to x.

Therefore x R y => y R x

Transitive :  x is parallel to y and y is parallel to z then x, y, z are parallel to each other.

=> x R y and y R z => x R z

Therefore A is equivalent.

1. b)

x r y if and only if |x-y| less than or equal to 7

Reflexive : |x-x| = 0 <= 7 => x R x Satisfied.

Symmetric : let x R y => |x-y| <= 7

Consider |y-x| = |(-1)*(x-y)| = |x-y| <= 7

=> y R x => Satisfied

Transitive : let x R y and y R x

=> |x-y| <= 7 and |y-z| <= 7

but this doesn't imply x R z

Counter-Example : x = 1, y = 7, z = 10

Therefore this relation is neither Equivalent nor Partial Order Relation.

The relation x r y if and only if x is parallel to y for lines in the plane is an equivalence relation as it is reflexive, symmetric, and transitive. For the set of real numbers with the relation x r y if and only if |x - y| ≤ 7, the relation is neither an equivalence relation nor a partial ordering because it lacks antisymmetry.

When determining if a relation is an equivalence relation or a partial ordering, we must assess whether it satisfies specific properties. For a relation to be an equivalence relation, it must be reflexive, symmetric, and transitive. In the case of A = { lines in the plane } and relation r defined by x r y if and only if x is parallel to y, we can say:

Therefore, this relation is an equivalence relation.

For the set A = R and the relation r defined by x r y if and only if | x − y | ≤ 7, the relation is not a partial ordering because it is not antisymmetric (if x r y and y r x, then x must equal y, which isn't necessarily true for all real numbers within 7 units of each other). However, it is reflexive and symmetric.

Answer:

The answer would be, 79.8%.

-Hope this helps! :D

Answer:

[tex]0.798\%[/tex]

Step-by-step explanation:

[tex]0.798 \times 100\% \\ 0.798 \times \frac{100}{100} \\ = \frac{0.798 \times 100}{100} \\ = 0.798\%[/tex]