Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between successive arrivals. The length of a phone call is distributed exponentially with mean 3 minutes. The probability that an arrival does not have to wait before service is A0.3B0.7C0.5D0.9

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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The corrected exact values are cosine (5π/6) = -1/2, cosine (π/12) cannot be simplified further, sine (5π/6) = 1/2, sine (π/12) cannot be simplified further.

Let's correct the calculation of the exact values of the given trigonometric expressions:

1. Cosine (5π/6):

  The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. Since the cosine function is negative in the second quadrant, the exact value is -cos(π/6) = -1/2.

2. Cosine (π/12):

  The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.

3. Sine (5π/6):

  The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. The sine function is positive in the second quadrant, so the exact value is sin(π/6) = 1/2.

4. Sine (π/12):

  The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.

Therefore, the corrected exact values are:

cosine (5π/6) = -1/2,

cosine (π/12) cannot be simplified further,

sine (5π/6) = 1/2,

sine (π/12) cannot be simplified further.

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The probability of getting the fewer than four twos is 0.5665.

       P(X = x) = C(n,x). p ˣ .(1 - p)ⁿ⁻ˣ

        C(n,x) = n!/x!(n-x)!

For the given question-

p is the likelihood that X will occur.

20 times of a die are rolled;

This indicates that; n = 20.

Six sides, one of which is two:

This indicates that; p = 1/6 = 0.1667.

Probability of having three or fewer twos:

Such is:

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

So,

P(X < 4) = C(n,x).  p ˣ .(1 - p)ⁿ⁻ˣ

P(X = 0) = C(20,0).  0.1667⁰ .(0.8333)²⁰

P(X = 0) = 0.0261

P(X = 1) = C(20,1).  0.1667¹ .(0.8333)¹⁹

P(X = 1) = 0.1043

P(X = 2) = C(20,2).  0.1667 ² .(0.8333)¹⁸

P(X = 2) = 0.1982

P(X = 3) = C(20,3).  0.1667³ .(0.8333)¹⁷

P(X = 3) = 0.2379

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

P(X < 4) = 0.0261 +  0.1043 + 0.1982 + 0.2379

P(X < 4) = 0.5665

Thus, the probability of getting the fewer than four twos is 0.5665.

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Answer:

y-intercept: 11

which means the baby weighs 11 lb when it is born (t=0).

Step-by-step explanation:

The line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

A graph is a mathematical representation of a set of objects, called vertices or nodes, and the connections between them, called edges or arcs. Graphs are commonly used to model relationships between entities in various fields such as computer science, mathematics, physics, social sciences, and many others.

To determine the line that the angle has been reflected across, we need to find the line of reflection, which is the perpendicular bisector of the segment joining each point and its corresponding image.

We can start by finding the midpoint of the segment joining A and A', which is the point that is equidistant from these two points and lies on the line of reflection. The midpoint of AA' is:

Midpoint of AA' = ((x-coordinate of A + x-coordinate of A')/2, (y-coordinate of A + y-coordinate of A')/2)

Midpoint of AA' = ((4 + (-5))/2, (5 + (-4))/2)

Midpoint of AA' = (-1/2, 1/2)

Next, we can find the midpoint of the segment joining B and B':

Midpoint of BB' = ((x-coordinate of B + x-coordinate of B')/2, (y-coordinate of B + y-coordinate of B')/2)

Midpoint of BB' = ((1 + (-2))/2, (2 + (-1))/2)

Midpoint of BB' = (-1/2, 1/2)

We can see that the midpoint of AA' and the midpoint of BB' are the same point, which means that the line joining these midpoints is the perpendicular bisector of both segments, and therefore the line of reflection.

So, the line of reflection is the line passing through the points (-1/2, 1/2) and (-2, -1), which can be found using the slope formula:

slope of line of reflection = (y2 - y1) / (x2 - x1)

slope of line of reflection = (-1 - 1/2) / (-2 - (-1/2))

slope of line of reflection = (-3/2) / (-3/2)

slope of line of reflection = 1

We now have the slope of the line of reflection, and we can find its equation by using the point-slope form:

y - y1 = m(x - x1)

Using the point (-1/2, 1/2) and the slope 1, we get:

y - 1/2 = 1(x + 1/2)

Simplifying, we get:

y = x + 1

Therefore, the line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

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Answer:

$600

Step-by-step explanation:

1,200 · 0.05 = 60

60 · 10 = 600

Answer:

Discrete set

Step-by-step explanation:

A discrete consists of a fixed number of elements, such that each element or point in the set is a standalone point or isolated. This differs from a continous set which still consists of points in between each set of values. Therefore the property of isolated point is a characteristic of a discrete set. The can be written as a list. The values are isolated on a discrete set as opposed to that of a continuous set whereby values can take up any value within any two intervals in the set.

Answer:

66/100 (or simplify to 33/50), 0.89

Step-by-step explanation:

The vibrational partition function of HCN at 900 K is 3.319.

To calculate the vibrational partition function (Qvib) of HCN at 900 K, we first need to calculate the vibrational energies of each mode:

The vibrational energy of each mode is given by:

E(v) = (v + 1/2) × h × nu

where v is the vibrational quantum number, h is Planck's constant (6.626 x 10^-34 J s), and nu is the frequency in cm^-1.

For the symmetric stretch mode, nu = 3311 cm^-1:

E(v) = (v + 1/2) × h × nu = (0 + 1/2) × 6.626 x 10^-34 J s × 3311 cm^-1 = 1.096 x 10^-20 J

For the two bend modes, nu = 937 cm^-1:

E(v) = (v + 1/2) × h × nu = (0 + 1/2) × 6.626 x 10^-34 J s × 937 cm^-1 = 3.108 x 10^-21 J

Therefore, the total energy of both bend modes is 2 * E(v) = 6.216 x 10^-21 J

For the asymmetric stretch mode, nu = 2097 cm^-1:

E(v) = (v + 1/2) × h × nu = (0 + 1/2) × 6.626 x 10^-34 J s × 2097 cm^-1 = 6.933 x 10^-21 J

Now we can calculate the vibrational partition function as the sum of the individual contributions:

Qvib = exp(-E(0)/(kT)) + exp(-E(1)/(kT)) + exp(-E(2)/(kT)) + ...

where k is the Boltzmann constant (1.38 x 10^-23 J/K) and T is the temperature in Kelvin.

At 900 K, we have:

Qvib = exp(-E(0)/(kT)) + exp(-E(1)/(kT)) + exp(-E(2)/(kT))

= exp(-(1.096 x 10^-20 J)/(1.38 x 10^-23 J/K × 900 K)) + exp(-(3.108 x 10^-21 J)/(1.38 x 10^-23 J/K × 900 K)) + exp(-(6.933 x 10^-21 J)/(1.38 x 10^-23 J/K × 900 K))

= 1.249 + 1.060 + 1.010

= 3.319

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Answer:

-5x - 4

Hope this helps!!! :)

Answer:

-8x-4. I hope that this helps kid

Answer:

I think it's $15 I hope this helps

Answer:

$15

Step-by-step explanation:

If 14 cards cost $6, then 7 cards will cost $3

So 35 cards will cost: $3 x 5 = $15

Answer:

30

Step-by-step explanation:

Step-by-step explanation:

im sorry but im not sure about this question

Answer:

334.488 miles

Step-by-step explanation:

You don't have a specific request on what I should answer, if it was distance then here's your answer

Answer:

Step-by-step explanation:

Pls give brainlest if right.

10/20-3/6 ?

Answer:

8x + x^2

Step-by-step explanation:

See attached image

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37

hope its helps

Step-by-step explanation:

total area = 99m² + 39.4m²

= 138.4m²

Answer:

What numbers?

Step-by-step explanation:

.

Answer:

what numbers should i list

Step-by-step explanation:

Answer:

m∠3 = 57.5 , Angle No.1 = 82, Angle No.2 = 98

Step-by-step explanation:

4.

m∠3 = 90 - 32.5

m∠3 = 57.5°

5.

Linear pair means a pair of adjacent angles formed when two lines intersect, and their sum is 180°

In the question it want one of the angles to be 16° more then the other, so the measures of the angles will be

180 - 16 = 164

164/2 = 82

Angle 1 = 82°    Angle 2 = 82°+16 = 98°

Draw a straight angle (straight line), intersect it with another line such that the two angles that will be formed one of them will be of measure 98° and the other 82°

The company was supposed to finish the order in 9 days.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

The company must have produced 60 items daily if it produced 20 more than the daily average of 40 items.

The company had 120 products to make, which should have taken three days (120 items, 40 items/day), but it finished in just two days (120 items, 60 items/day). They completed this order one day earlier than expected.

However, the issue is that they completed 3 days ahead of schedule. Thus, our estimate is 360 items or three times 120 items.

According to this, they should have completed their order in 9 days (360 things, at a rate of 40 items per day), but they did so in 6, at a rate of 60 items per day. Since 6 is three fewer than 9, our assumption of 360 items was accurate.

We've demonstrated that the business should have completed the order in 9 days.

Let the desired number of days be x.

Then, the company finished its order in x - 3 days.

Since the number of items produced is the number of days times items per day, and it doesn't change:

number of items = 40 items/day * x days

= 60 items/day * (x - 3) days

40x = 60(x - 3) = 60x - 180

180 = 20x

x = 9

Hence, the company was supposed to finish the order in 9 days.

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The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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If one of the female student is chosen, and she is in to be in a research scientist. The probability of the female student will be 4.6417%.

Total female students = 2219 (refer the picture below)

total female in research science department = 103 (refer the picture below)

calculating the probability that the chosen student is a future research scientist

= female research scientist ÷ female total

= 103/ 2219

= 0.046417

now, to calculate the probability that the chosen student is a future research scientist as percentage, multiply 0.046417 by 100.

By multiplying it with 100, we get the percentage as

= 0.046417 × 100

= 4.6417%.

Therefore, The probability of the female student will be 4.6417%.

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The question is -

the two-way table shows the attendant careers among the incoming class of first-year college students, divided by gender. If a female student is chosen at random, what is the probability that she intends to be a research scientist? (also, refer the picture) .

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Answer:

i think its the second one

Step-by-step explanation:

Answer:

1) 8 cups

2)2/3 of a yard

3)1 5/8 miles

4) 3/4 cups

Step-by-step explanation:

I hope this helps :)

Let me know if you need an explanation for any of them

Answer:

Yes

Step-by-step explanation:

8/10 can be simplified to become 3/4

Answer:

I can't answer your question but get an idea of this

Step-by-step explanation:

If ΔABC is dilated by a scale factor of 1/2

with a dilation center of A, what will be the coordinates of point C'?

Point C is at (2,0)

Cut each coordinate in half to get (1,0)

2*(1/2) = 1

0*(1/2) = 0

So point C will move to (1,0)

Not the answer but an example on how to do it