Suppose jobs arrive at a processor according to a Poisson distribution, and let . be the average arrival rate (per minute). The expression (201) (1 + 20+ (202)2 (204)3 + + 2! 3! (204) 9! equals the pr

The intervals on which the function is decreasing and increasing and the local minima and maxima are

a. f(x) = (x-2)(x+3),  increasing on the interval (-∞, -1/2) and (1/2, ∞) and decreasing on the interval (-1/2, 1/2). f(x) has a local minimum at x = -1/2 and a local maximum at x = 1/2.

b.  f(x) = (x+1)(x-2)(x+3),increasing on the interval (-∞, -1) and (2, ∞) and decreasing on the interval (-1, 2). f(x) has a local maximum at  x = -1 and a local minimum at x = 2

c. f(x) = x e⁻ˣ, increasing on the interval (1, ∞) and decreasing on the interval (0, 1). f(x) has a local minimum at  x = 1 and doesn't have local maximum or infinite

d.  f(x) = xˣ, decreasing on the interval (0, 1/e) and increasing on the interval (1/e, ∞). f(x) has a local maximum at x = 1/e. Note that there is no local minimum for this function.

a) f(x) = (x-2)(x+3)

To determine where the function is increasing or decreasing, we can take the derivative of f(x):

f'(x) = 2x + 1

This derivative is positive for x > -1/2, which means that f(x) is increasing on the interval (-∞, -1/2) and (1/2, ∞). The derivative is negative for x < -1/2, which means that f(x) is decreasing on the interval (-1/2, 1/2). The critical points occur at x = -1/2 and x = 1/2. f(x) has a local minimum at x = -1/2 and a local maximum at x = 1/2.

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

To determine where the function is increasing or decreasing, we can take the derivative of f(x):

f'(x) = 3x² - 6x - 3

This derivative can be factored as f'(x) = 3(x+1)(x-2). The derivative is positive for x > 2 and negative for x < -1, which means that f(x) is increasing on the intervals (-∞, -1) and (2, ∞), and decreasing on the interval (-1, 2). The critical points occur at x = -1 and x = 2. f(x) has a local maximum at x = -1 and a local minimum at x = 2.

c) f(x) = x e⁻ˣ

To determine where the function is increasing or decreasing, we can take the derivative of f(x):

f'(x) = e⁻ˣ - xe⁻ˣ

Setting this derivative equal to zero and solving for x, we get x = 1. Therefore, the function has a critical point at x = 1. We can evaluate the derivative for values of x less than and greater than 1 to determine the intervals on which f(x) is increasing and decreasing.

f'(x) is negative for x < 1 and positive for x > 1, which means that f(x) is decreasing on the interval (0, 1) and increasing on the interval (1, ∞). f(x) has a local minimum at x = 1.

d) f(x) = xˣ

To determine where the function is increasing or decreasing, we can take the derivative of f(x):

f'(x) = xˣ (ln(x) + 1)

Setting this derivative equal to zero and solving for x, we get x = 1/e.

Therefore, the function has a critical point at x = 1/e. We can evaluate the derivative for values of x less than and greater than 1/e to determine the intervals on which f(x) is increasing and decreasing. f'(x) is negative for 0 < x < 1/e and positive for x > 1/e, which means that f(x) is decreasing on the interval (0, 1/e) and increasing on the interval (1/e, ∞).

f(x) has a local maximum at x = 1/e. Note that there is no local minimum for this function.

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The null hypothesis and alternative hypothesis for the given data is equal to  H0: μ = 436 and Ha: μ ≠ 436.

Weight of the bag filled with machine works = 436 grams

The null hypotheses for the bag filled with machine work will be the statement of no effect

And it'll be the mean weight of the bag which is equal to 436grams.

Null hypothesis is equal to ,

H0: μ = 436

The alternative hypotheses for the above scenario representing that the bag isn't filled with 436grams.

They are either less filled or that is below 436grams or overfilled that is above 436grams.

Alternative hypothesis is equal to,

Ha: μ ≠ 436

Statistics is the study of surveys and research on numerical data.

Two different kinds of hypotheses.

A null hypothesis is one that holds true.

And an alternate hypothesis is another.

The null hypothesis is a default condition which represents there is nothing happening.

If there is no relationship between two given measured between groups.

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Answer:

it is 27

Step-by-step explanation:

because we need to add 27 and the 7m

Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.

Given:

an unbiased coin is tossed 20 times.

The probability that the coin lands heads exactly 11 times:

P = n(E)/n(S)

n(S) = 2^tosses

= 2^20

= 1048576

n(E) = C(20,11)

= 20!/11!(20-11)!

= 20!/11!*9!

= 167960

Probability P = 167960/1048576

= 0.16017 ≈ 0.1602

Therefore Probability that the coin lands heads exactly 11 times is 0.1602 so Option a is correct.

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The given sample's confidence interval is 4.73 ± 0.1199, or from 4.61 to 4.85

The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.

Given data;

Mean  = 4.73

Standard deviation  = 0.865

Sample size  = 200

interval  = 95%

Confidence interval=?

95% of samples contain the population mean (μ) within the confidence interval of 4.73 ± 0.1199.

Hence, the sample's confidence interval is 4.73 ± 0.1199, from 4.61 to 4.85

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Answer:

The correct option is;

We cannot infer a cause and effect relationship because the multiple variables were included

Step-by-step explanation:

The criteria required in order to establish a cause and effect relationship includes the following;

1) There must be a temporal precedence between the cause and the effect such that the cause must take place before the effect

In the question, it is not clearly stated weather there was a divorce (the likely cause) takes place before the event

2) In the vent that the cause occurs, the effect must occur

Therefore, all those who are not married are expected to be deceased for there to be a cause and effect relationship

3) The cause and effect relationship must not be explicable by other factors

In the question, it is stated that those who were married were more likely to be active physically, maintain an healthy weight and were nonsmokers, which are factors that contribute to longevity.

Answer:

Median is 5.

Step-by-step explanation:

Step 1: Arrange the data;

2, 2, 5, 7, 14

Formula:

\(\frac{n+1}{2}\)

\(\frac{5+1}{2} \\\frac{6}{2} \\3rd value\)

Median=5

The statement as a division problem is Sharing 21 apples among 5 friends

From the question, we have the following parameters that can be used in our computation:

21/5

The above expression is a quotient expression

A quotient expression is represented as

Quotient expression = dividend/divisor

Using the above as a guide, we have the following:

Dividend = 21

Divisor = 5

A division problem that represents this statement is

Sharing 21 apples among 5 friends

There are several other division problems that can be generated from the expression

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Using the equation, it is found that it will take 2.4 hours for the airplane to travel 1200 miles.

An airliner moves at a consistent pace from New York to London.

The equation that relates the time in hours needed to travel d miles is given by:

\(t = \frac{1}{500} d\)

In this problem, we want the time needed to travel 1200 miles, thus, and:

\(t = \frac{1}{500} * 1200 = 2.4\)

Hence, it will take 2.4 hours to travel 1200 miles.

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The rank of object according to acceleration from greatest to least is:

C = B > A

In the given question, we have to rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.

The acceleration is given by:

a = \(\frac{dv}{dt}\)

where, dv represents change in velocity and dt represents change in time.

Also, Acceleration = slope of velocity - time graph

For object A acceleration is 0 because velocity is constant.

Now for object B:

\(a_{B}=\frac{5-0}{10-0}\)

\(a_{B}=\frac{5}{10}\)

\(a_{B}=\frac{1}{2}\)

\(a_{B}\) = 0.5 m/s square

Now for the object C:

\(a_{C}=\frac{-5-0}{10-0}\)

\(a_{C}=-\frac{5}{10}\)

\(a_{C}=-\frac{1}{2}\)

\(a_{C}\) = -0.5 m/s square

As we know that magnitude cannot be negative, so

\(a_{C}\) = 0.5 m/s square

As we can see that acceleration of object B and C is same although the acceleration of object A is 0 which is smaller than the acceleration of B and C.

So the rank of object according to acceleration from greatest to least is:

C = B > A

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The complete question is:

The figure below shows velocity versus time graphs for objects. Rank the magnitude of each object's acceleration from greatest to least: Disregard the direction of the accelerations.

Answer:

Step-by-step explanation:

The slope for the given situation will be $2.96. 5.92/2 = $2.96 per meal

Hint

If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.

To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.

I hope this helps :)

Answer:

Nyana and Nelmaire ate 2/4, or 1/2 of the apple in all.

Step-by-step explanation:

1/4 + 1/4 equals 2/4
2/4 is equivalent to 1/2

Answer:

7/3

Step-by-step explanation:

17/12+11/12

28/12

=>7/3

Option C

Corresponding angles along parrellel lines are conguerent.

Answered by Gauthmath must click thanks and mark brainliest

Rita's old lawn mower will start after exactly three pulls 12.8% of the time,

The binomial probability formula states that the probability of success occurring precisely x times in n trials is equal to the product of the probability of success (p) and the probability of failure (1-p) raised to the power of n-x. This can be used to calculate this. The probability of success occurring exactly three times is equal to 0.2 x 0.8 x 0.8, or 12.8%, given that the number of trials (n) and the probability of success (p) is both 20 percent.

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Step-by-step explanation:

1) solution

Hypotenous(h)=?

perpendicular(p)=16

base(b)=12

By using formula

h^2 = p^2 + b^2

h^2 = 16^2 + 12^2

h^2 = 256 + 144

h^2 = 400

h^2 = 20^2

h = 20

therefore hypotenous (h) is 20

2) solution

hypotenous = (?)

perpendicular=(77)

base=(36)

by using formula

h^2 =p^2 + b^2

h^2=77^2+ 36^2

h^2=5929+1296

h^2=7225

h^2=85^2

h=85

therefore hypotenous (h) is 85

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing with an alpha value of 0.01.

If you are testing the null hypothesis with an alpha value of 0.05, the critical value will be smaller than if you were testing the alpha value of 0.01. This is because a smaller alpha value means a more stringent test of significance, which requires stronger evidence to reject the null hypothesis.

Therefore, the critical value is larger for a smaller alpha value to reflect the higher level of evidence required for rejection. Conversely, a larger alpha value allows for a less stringent test of significance, requiring weaker evidence to reject the null hypothesis, which results in a smaller critical value.

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Answer:

2x²-2x-24

Step-by-step explanation:

Something has roots of 4 and -3 we can write

(x-4)(x+3)

We then attach a constant, a that will ensure that it passes through the correct point

a(x-4)(x+3)

now plug in the numbers and solve for a

a(3-4)(3+3)= -12

a(-1)(6)= -12

-6a= -12

a=2

So we have

2(x-4)(x+3)

and now it's just a matter of mulitplying/simplifying things

(x-4)(x+3)= x²-x-12

2(x²-x-12)= 2x²-2x-24

Answer:

y = 2x² - 2x - 24

Step-by-step explanation:

Given a root x = a then the factor is (x - a )

Given roots are x = 4 and x = - 3 , the corresponding factors are

(x - 4) and (x - (- 3)) , that is (x - 4) and (x + 3)

The quadratic is then the product of the factors

y = a(x - 4)(x + 3) ← a is a multiplier

To find a substitute (3, - 12) into the equation

- 12 = a(- 1)(6) = - 6a ( divide both sides by - 6 )

2 = a

y = 2(x - 4)(x + 3) ← expand factors using FOIL

   = 2(x² - x - 12) ← distribute

y = 2x² - 2x - 24

The multiplication using Tape Diagram is $44.8

A tape diagram is a pictorial model resembling a tape, that is used to assist with the calculation of addition, subtraction, multiplication, etc.

Given: 7 × $6.4

7 × $6.4 means $6.4 in 7 places. Thus, we can write that:

7 × $6.4 = $6.4 + $6.4 + $6.4 + $6.4 + $6.4 + $6.4 + $6.4 = $44.8

Check the attached picture for the Tape Diagram

Therefore, the multiplication 7×$6.4 gives $44.8

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Answer:

last option,  1.65 x 10^-3

Step-by-step explanation:

Answer:

Step-by-step explanation: just / the $7.04 by 8 since there is 8 bars then boom

On the interval [0, 2π], the minimum values of f(x) = 12cos^2(x) - 1 are -1, and the maximum values are 11.

To find the minimum and maximum values of the function f(x) = 12cos^2(x) - 1 on the interval [0, 2π], we need to determine the critical points and endpoints within that interval.

First, let's differentiate the function f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -24cos(x)sin(x).

Next, we set f'(x) equal to zero and solve for x:

-24cos(x)sin(x) = 0

This equation is satisfied when cos(x) = 0 or sin(x) = 0.

For cos(x) = 0, we have x = π/2 and x = 3π/2 as critical points.

For sin(x) = 0, we have x = 0 and x = π as critical points.

Now, we evaluate the function f(x) at these critical points and the endpoints of the interval [0, 2π]:

f(0) = 12cos^2(0) - 1 = 11

f(π/2) = 12cos^2(π/2) - 1 = -1

f(π) = 12cos^2(π) - 1 = 11

f(3π/2) = 12cos^2(3π/2) - 1 = -1

f(2π) = 12cos^2(2π) - 1 = 11

From the evaluations, we see that the minimum values of f(x) are -1, occurring at x = π/2 and x = 3π/2, while the maximum values are 11, occurring at x = 0, x = π, and x = 2π.

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Based on the information you provided, R(t) is a differentiable function that represents the rate at which people leave a restaurant in people per hour after 6 hours since opening. In other words, R(t) describes the speed at which customers are leaving the restaurant as time goes by.

It's important to note that R(t) is only a function of time t, and not a function of the number of people currently in the restaurant or any other variables. This means that if the restaurant is empty at 6 hours since opening, R(t) will give you the rate at which people leave the restaurant from that point forward, regardless of whether there are any customers in the restaurant or not.

In terms of the restaurant's function, R(t) is a key component in understanding how many customers the restaurant is likely to have at any given time. By subtracting R(t) from the restaurant's initial capacity (i.e. the number of seats or tables available), you can estimate how many customers are likely to be in the restaurant at any given time.

Overall, R(t) is a powerful tool for understanding the behavior of customers in a restaurant and can help the restaurant make informed decisions about staffing, marketing, and other aspects of their business.

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The volume of the rectangular solids that is similar to the volume of a right circular cylinder is rectangular solid E.

Cuboid A:

Volume of rectangular solid = length × width × height

= 3 × 3 × 3

= 27 cubic units

Cuboid B:

Volume of rectangular solid = length × width × height

= 3 × 3 × 4

= 36 cubic inches

Cuboid C:

Volume of rectangular solid = length × width × height

= 5 × 4 × 3

= 60 cubic inches

Cuboid D:

Volume of rectangular solid = length × width × height

= 4 × 4 × 4

= 64 cubic inches

Cuboid E:

Volume of rectangular solid = length × width × height

= 4 × 4 × 3

= 48 cubic inches

Right circular cylinder:

Radius, r = 2

Height, h = 4

Volume of right circular cylinder = πr²h

= 3.14 × 2² × 4

= 3.14 × 4 × 4

= 50.24 cubic units

Hence, rectangular solid E is similar to right circular cylinder.

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Answer:The total cost is $41.04

Step-by-step explanation:

We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:

Z = (x - )/ ( / sqrt(n)

where,

Standard deviation equals 2

sample size, n With n = 5, calculating the z and p values:

The tables show that p(5) = 0.8686.

For n = 6, calculate the z and p values as follows:

The tables show that p(6) = 0.8888.

If both days to occur, the probability that each day will last no more than 11 minutes is as follows:

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The equivalent ratios to 8 to 3 following are :

16 to 6

24 to 9

To write equivalent ratios to 8 to 3, you can use multiplication.

For example, you can multiply both terms in the ratio by 2 to get 16 to 6, or by 3 to get 24 to 9.

In general, to write equivalent ratios, you can multiply or divide both terms in the ratio by the same number. For example, if the ratio is a:b, you can write equivalent ratios by multiplying or dividing both a and b by the same number.

For example, the following ratios are all equivalent to 8 to 3:

16 to 6 (obtained by multiplying both terms by 2)

24 to 9 (obtained by multiplying both terms by 3)

4 to 1.5 (obtained by dividing both terms by 2)

8 to 3 (the original ratio)

2 to 0.75 (obtained by dividing both terms by 4)

These ratios all represent the same relationship between the two quantities, but the numbers are different.

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Answer:

the equations they're equal

Step-by-step explanation:

3.75 divided by 5 = 0.75

7.50 divided by 10 = 0.75

12.00 divided by 16 = 0.75