how to solve this 7/8 n=63

The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

Learn more about probability https://brainly.com/question/31828911

#SPJ11

Answer:

mateo has more cards

Step-by-step explanation:

1/2 is greater than 1/4 because 1/4 is 1/2 of a 1/2

An expression evaluate to 3.5 is (double) (2 / 4) 3.

or the question given, we are to determine which of the following expressions evaluates to 3.5.

We have:

(double) 2 / 4= 1 (double) (2 / 4) 3= 1.5 (double) (2 / 4 3)= 0.3333333333333333

The only expression that evaluates to 3.5 is (double) (2 / 4) 3. Therefore, the correct answer is (B) (double) (2 / 4) 3.

Learn more about decimal number at

https://brainly.com/question/4708407

#SPJ11

Answer:

\((x-5)^2=4(y+2)\)

Please note that alternative forms of this equation (vertex and standard) are in the explanation.

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

Given:

Therefore:

Calculate p:

\(\implies -2+p=-1\)

\(\implies p=-1+2\)

\(\implies p=1\)

Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:

\(\implies (x-5)^2=4(1)(y-(-2))\)

\(\implies (x-5)^2=4(y+2)\)

In vertex form:

\(\implies y=\dfrac{1}{4}(x-5)^2-2\)

In ax² + bx + c form:

\(\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}\)

Answer:

\(y = x + 2\)

Step-by-step explanation:

y=x+2

Answer:

I think its 10 donuts for $11.50

Step-by-step explanation:

Because...

1 dozen donuts for $15 = 1.25 each

10 donuts for $11.50 = 1.15 each

Answer:

10 donuts for $11.50 i think

Step-by-step explanation:

You only get 2 less donuts and it is much cheaper than $15

Answer:

3(x-10)(x-6)

Step-by-step explanation:

3(x²-16x+60)

60 16

-10 × -6 -10 + -6

3(x-10)(x-6)

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

Answer:

Step-by-step explanation:

A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

To know more about centimeters visit:

https://brainly.com/question/9133571

#SPJ11

we must rely on estimates instead

The population is larger than the sample, and the entire group of cases we want information on.

In statistics, a population refers to the whole set of people, items, or events under consideration.

The sample is a smaller subset of the population that is taken into account.

The sample should be an accurate representation of the population from which it was chosen in order for it to be useful in making predictions or generalizations about the population. Let's look at the options and select the correct ones.

(a) Larger than the sample:

The population is the entire collection of individuals, items, or events that a researcher is interested in studying, and it is always larger than the sample. It is vital to select a sample that represents the population well to make inferences about it.

(b) The entire group of cases we want information on:

The population is the entire collection of people, items, or events that a researcher is interested in studying. It is the group of individuals from which a sample is taken. A sample is a representative of the population.

(c) Impractical or too expensive to collect information from:

When the population size is too big, it is impractical or too expensive to collect information from it.

In such cases, we have to select a representative sample.

For example, it would be impossible to count all the people who have ever lived on the planet, so we must rely on estimates instead.

To know more about subset visit:

https://brainly.com/question/31739353

#SPJ11

The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

The general solution to the differential equation d(r)/dt = 5tln(t) can be found using the method of integrating factors.

First, we find the integrating factor:

I = e^∫5ln(t)dt = e^(5t - 5)

Next, we multiply both sides of the equation by the integrating factor:

I * d(r)/dt = I * 5tln(t)

Now, we can integrate both sides of the equation:

∫I * d(r)/dt = ∫I * 5tln(t)dt

Using the substitution u = r and du/dt = d(r)/dt, we can simplify the left side of the equation:

du/dt = I * d(r)/dt

And on the right side, we use integration by parts:

∫I * 5tln(t)dt = (5/2)t^2ln(t) - 5te^5 + C

Finally, we can solve for r:

r = (5/2)t^2ln(t) - 5te^5 + C

The general solution to the differential equation d(r)/dt = 5tln(t) is:

r = (5/2)t^2ln(t) - 5te^5 + C.

Note that C is an arbitrary constant and represents the freedom in choosing the initial conditions for the solution.

Therefore, The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

To learn more about differential equation,

Visit; brainly.com/question/14620493

#SPJ4

The risk of developing heart disease is increased by option C: 25–30% for nonsmokers who breathe secondhand smoke at home or at work.

According to the Centers for Disease Control and Prevention (CDC), Nonsmokers who breathe secondhand smoke at home or at work have a 25–30% higher chance of getting heart disease. Additionally, secondhand smoke 20–30% increases the risk of stroke. Secondhand smoking exposure can result in coronary heart disease, heart attacks, and strokes.

Only completely smoke-free environments can totally protect you and your loved ones from the dangers of secondhand smoke. Making sure your home and automobile are properly ventilated is another strategy to safeguard yourself from secondhand smoke. This can assist in lowering the amount of smoke in the air and lowering your exposure.

To know more about smoking, refer:

https://brainly.com/question/26187004

#SPJ4

Correct question:

How much do nonsmokers increase their risk of developing heart disease by exposing themselves to secondhand smoke at home or work? responses

15 to 20 percent

20 to 25 percent

25 to 30 percent

30 to 35 percent

The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.

Bursting of Water Pipes During a Very Cold Winter

The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.

As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.

The pressure that the ice builds up inside the pipes could rupture the pipe walls.

Learn more about pressure here:

https://brainly.com/question/356585

#SPJ4

Answer:

  yes

Step-by-step explanation:

The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.

The attachment shows a graph of the circle. Its equation is ...

  (x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r

We have (h, k) = (2, 13) and r = 5, so the equation is ...

  (x -2)² +(y -13)² = 25 . . . . graphed equation

The point in question is also graphed, and is shown to lie on the circle.

If the given point satisfies the circle's equation, it lies on the circle.

For (x, y) = (-2, 10), we find ...

  (-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied

Answer:

5(x-4)

Step-by-step explanation:

Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

To learn more about Binomial probability distribution, refer:

https://brainly.com/question/24239758

#SPJ4

Interpreting the situation, we have that:

a) The system of equations is:

\(y = 2x - 7\)

\(y = 6 + x\)

b) Solving the above system, it is found that Jacob scored 13 and Paul scored 19.

Item a:

In our system, we have that:

Jacob said that Paul's score would be twice his own score if he earned 7 more points, which means that:

\(y + 7 = 2x\)

\(y = 2x - 7\)

Paul responded to Jacob by telling him his score was only 6 points higher then Jacob's, which means that:

\(y = 6 + x\)

Item b:

Equaling both equations:

\(2x - 7 = 6 + x\)

\(x = 13\)

\(y = 6 + x = 6 + 13 = 19\)

Jacob scored 13 and Paul scored 19.

A similar problem is given at https://brainly.com/question/24104709

Brent can lift a total of 9600 ounces without resting.

To find the total number of ounces Brent can lift without resting, we need to convert the weight from pounds to ounces and then multiply it by the number of lifts.

Given:

Weight Brent can lift: 200 pounds

Number of lifts: 3

To convert pounds to ounces, we know that 1 pound is equal to 16 ounces.

Calculating the total number of ounces Brent can lift:

Total weight in ounces = (200 pounds) * (16 ounces/pound)

Total weight in ounces = 3200 ounces

Since Brent can lift this weight three times without resting, we multiply the total weight in ounces by the number of lifts:

Total weight in ounces without resting = (3200 ounces) * (3 lifts)

Total weight in ounces without resting = 9600 ounces

Therefore, Brent can lift a total of 9600 ounces without resting.

To know more about ounces, refer here:

https://brainly.com/question/26950819

#SPJ4

The difference between the prices of both books is: $4,266.67.

Let's call the price of the cheapest book "x". According to the statement, the other book costs twice the price of the cheapest one, that is, "2x". Furthermore, we are told that this second book is worth $200 more than the other.

Therefore, we can establish the following equation:

x + 2x + $200 = $13,000

Add like terms:

3x + $200 = $13,000

We subtract $200 from both sides of the equation:

3x = $12,800

We divide both sides by 3 to solve for "x":

x = $4,266.67

The price of the most expensive book is 2 times the price of the cheapest, that is, 2 * $4,266.67 = $8,533.33.

The difference between the prices of both books is:

$8,533.33 - $4,266.67 = $4,266.67.

To learn more about difference :

https://brainly.com/question/17695139

#SPJ11

The elevation after three seconds is 108 feet.

It should be noted that elevation simply has to do with the height above sea level.

From the information, the elevation h (in feet) of the balloon is modeled by the function h(x) = 6x + 90, where x is the time (in seconds).

After three seconds, the elevation will be:

h(x) = 6x + 90,

h(3) = 6(3) + 90

h(3) = 18 + 90

h(3) = 108 feet

The elevation is 108 feet.

Learn more about elevation on:

brainly.com/question/88158

#SPJ1

Complete question

You notice a hot air balloon ascending. The elevation h (in feet) of the balloon is modeled by the function h(x)=6x+90, where x is the time (in seconds) since you first noticed the hot air balloon. What is the elevation after three seconds?

Answer:

\(Total = 20v + 40x + 80y\)

\(Total = 20(v + 2x + 4y)\)

Step-by-step explanation:

The options were not given,en but the question can still be solved.

Given

\(Daises = \$ x\)

\(Magnolias = \$ y\)

\(Vase = \$ v\)

Required

Determine the cost of 20 vases, 40 daises and 80 magnolias

If 1 vase costs $v, then

\(20\ vases = 20 * v\)

\(20\ vases = 20v\)

If 1 daises costs $x, then

\(40\ daises = 40 * x\)

\(40\ daises = 40x\)

If 1 magnolias costs $y, then

\(80\ magnolias = 80 * y\)

\(80\ magnolias = 80y\)

\(Total = 20v + 40x + 80y\)

Another expression that represents the total is to factorize the expression.

\(Total = 20(v + 2x + 4y)\)

Hi there!

\(\large\boxed{4x - 2}\)

7x - (3x + 2)

Simplify by distributing the negative sign:

7x - (3x) - (2)

Combine like terms:

4x - 2

Answer:

2(2x - 1)

Step-by-step explanation:

opening the parenthesis and distributing the - sign to both 3x and 2

= 7x - 3x - 2

= 4x - 2

taking 2 common

= 2 (2x - 1)

Answer:

131

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 38 and a₈₅ = 257 , then

a₁ +11d = 38 → (1)

a₁ + 84d = 257 → (2)

Subtract (1) from (2) term by term

73d = 219 ( divide both sides by 73 )

d = 3

Substitute d = 3 into (1)

a₁ + 11(3) = 38

a₁ + 33 = 38 ( subtract 33 from both sides )

a₁ = 5

Thus

5 + 3(n - 1) = 395 ( subtract 5 from both sides )

3(n - 1) = 390 ( divide both sides by 3 )

n - 1 = 130 ( add 1 to both sides )

n = 131

Thus there are 131 terms in the sequence

Answer:

-38

Step-by-step explanation:

4-(3^4-6^2)+2(3)÷2

=>     4 - (81-36) + 2(3) ÷ 2      

=>     4 -  45 + 2(3)÷2

=>     4 -  45 + 6÷2

=>     4 -   45 + 3

=>     -41 + 3

=>     - 38

hope this helps :)

Answer:

x=-6/b

x=-2

Step-by-step explanation:

-2(bx - 5) = 16

-2bx+10=16

bx=-6

x=-6/b

------

x==-6/3

x=-2

Answer:

The value of x in terms of b is -6/b

The value of x when b is 3 is​ -1

Two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

Given measure: 3, 5, 4, 6, 10, 5, 6, 9, 2, 13.(D) To calculate \(x_2\), first we need to sort the data in ascending order: 2, 3, 4, 5, 5, 6, 6, 9, 10, 13

Now, we need to find the median, which is the middle value of the data. Since the data has even number of values, we will calculate the mean of middle two values, that is:(5+6)/2 = 5.5 Therefore, \(x_2 = 5.5\).\( \frac{2}{x}= \) To find the value of x, we will first cross-multiply and then take the reciprocal of both sides:\[\frac{2}{x} = y \Rightarrow 2 = xy \Rightarrow x = \frac{2}{y}\] Therefore, \( \frac{2}{x}= \frac{2}{y}\).

(b) To calculate Fried m, we will use the formula: \[f_m = L + \frac{(n/2 - F)}{f} \times c\]where L is the lower limit of the modal class, F is the cumulative frequency of the class preceding the modal class, f is the frequency of the modal class, c is the class interval, and n is the total number of values.

First, we will calculate the class interval:c = (upper limit of class - lower limit of class) = (7-6) = 1 Next, we will construct a frequency table to find the modal class:| Class Interval | Frequency ||-------------------|------------|| 2-3 | 1 || 3-4 | 1 || 4-5 | 1 || 5-6 | 2 || 6-7 | 2 || 7-8 | 1 || 9-10 | 1 || 10-11 | 1 || 13-14 | 1 |The modal class is the class with highest frequency.

Here, two classes have frequency 2, so both are modes. They are 5-6 and 6-7.

Therefore, L = 5, F = 2, f = 2, n = 10, and c = 1. Substituting the values, we get:\[f_m = L + \frac{(n/2 - F)}{f} \times c = 5 + \frac{(10/2 - 2)}{2} \times 1 = 7\] Therefore, Fried m = 7.

(c) To find the mode, we look for the value(s) with highest frequency. Here, two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

To know more about modes visit:

brainly.com/question/33298559

#SPJ11

Answer:

9.9

Step-by-step explanation: