Let X be a Poisson random variablewith parameter λ. Show that i) E(X)=λ ii) Var(X)=λ

Answer:

We can calculate the difference between Lori's and Melissa's purse masses by subtracting Melissa's purse mass from Lori's purse mass:

Lori's purse mass = 16 ounces

Melissa's purse mass = 11 ounces

Difference = Lori's purse mass - Melissa's purse mass

Difference = 16 ounces - 11 ounces

Difference = 5 ounces

Therefore, the difference between Lori's and Melissa's purse masses is 5 ounces.

Answer:

a) x=-1.5

b) x=2

Step-by-step explanation:

The axis of symmetry is what straight line would divide the parabola directly in half.

Answer:

A. -1.5 B.2

Step-by-step explanation:

The Axis of symmetry is the line that goes through the center of the parabola. And resembles a symmetrical shape that makes the parabola look the same on both sides.

In this case for A, -1.5 would be the answer because it is in the center of the parabola on the x-axis. For B, 2 is the axis of symmetry because it lines up in the center of the parabola.

The principal that would need to be invested to have an accrued amount of 1 million dollars after 30 years is $90,717.95.

The formula compound interest where interest is compounded continuously is expressed as;

A = P × e^(rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for P.

A = P × e^(rt)

P = A / e^(rt)

P = $1,000,000 / e^( 0.08 × 30 )

P = $1,000,000 / e^( 2.4 )

P = $90,717.95

Therefore, the amount of principal is $90,717.95.

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Answer:

\(A = 118ft^2\)

Step-by-step explanation:

See attachment for complete question.

From the attachment, we have:

\(\theta = 80\)

\(r = 13ft\) -- Radius

Required

Determine the area of the sector

Area (A) of a sector is calculated as:

\(A = \frac{\theta}{360} * \pi r^2\)

Substitute values for r and \(\theta\)

\(A = \frac{80}{360} * \pi 13^2\)

\(A = \frac{80}{360} * \pi *169\)

\(A = \frac{80*169}{360} * \pi\)

\(A = \frac{13520}{360} * \pi\)

Take \(\pi\) as \(\frac{22}{7}\)

\(A = \frac{13520}{360} * \frac{22}{7}\)

\(A = \frac{13520 * 22}{360 * 7}\)

\(A = \frac{297440}{2520}\)

\(A = 118ft^2\)-- approximated

We have the next point: (-3, 5)

And we must find the equation of a vertical line that passes through the point.

To find the vertical line that passes through a point we must equal the equation for x to the x coordinate of the point and this will be the equation.

Now, in this case the equation of the vertical line is

Answer:

8 meters

Step-by-step explanation:

their formation creates a triangle

Shelby to Dillon =15

Shelby to Patty =17

Dillon to Patty =?

a^2 + 15^2 = 17^2

a^2 + 225 = 289

a^2 = 64

a = 8

Answer:

733

Step-by-step explanation:

18 - √81 + 9 × 3⁴ - ( 3 - 2 + 9 ) ÷ 2

18 - 9 + 9 × 81 - ( 10 ) ÷ 2

(18 - 9) + (9 × 81) (-10 ÷ 2)

9 + 729 - 5

738 - 5

733

I hope this helps!

Answer:

3 Months.

Step-by-step explanation:

1 Month: J = $160 P = $200

2 Months: J = $200 P = $220

3 Months: J = $240 P = $240

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

2,996 ÷ 11 = 272.36

Step-by-step explanation:

Answer:

10 sculptures.

Step-by-step explanation:

10x7=70 or painstakingly multiply 7 by each number until 10. It isn't that hard so go ahead. You can use a calculator as well. Put it into fraction form if you needed, but the answer is 10 sculptures for 70 paintings or 10/70.

Answer:

12

Step-by-step explanation:

First, let's calculate both of the medians.

Veronica's Median: 141

James' Median: 129

And now, the only thing left for us to do is complete some simple subtraction.

141 - 129 = 12

Your answer is 12.

Answer:

so first you have to find out the median of both of the people. then you have to subtract both of the medians to find out how much veronicas is higher than the other guy

Answer:

How many people like both drinks?

To find the overlap, we can do (104 + 74) - 140 = 38.

How many people like tea only?

To find this, we can do 74 - 38 = 36.

How many people like milk only?

To find this, we can do 104 - 38 = 66.

Answer:

Step-by-step explanation:

A = Number of people who likes tea

B = Number of people who likes milk

Total people = n(A U B) = 140

(i) n(AUB) = n(A) + n(B) - n(A ∩B)

n(A∩B) = n(A) + n(B) - n(A ∪B)

n(A∩B)  = 74 + 104 - 140

             = 178 - 140

n(A∩B)  = 38

Number of people who likes both tea and milk = 38

(ii)Number of people who likes tea only = n(A) - n(A∩B)

                                                                  = 74 - 38

                                                                 = 36

(iii) Number of people who likes milk only = n(B) -n(A∩B)

                                                                     = 104 - 38

                                                                     = 66

Answer:

Let's see what to do buddy..

Step-by-step explanation:

_________________________________

STEP (1)

We know that the quadratic functions form are like this :

\(y = a \: {x}^{2} + b \: x + c \)

The quadratic function opens upward so ;

\(a > 0\)

The axis of parabolic symmetry passes through the vertex of the parabolic.

So we know that x vertex is equal to -2.

The vertex's x is finding from this equation:

\(x = - \frac{b}{2a} \\ \)

So we have :

\( - 2 = - \frac{b}{2a} \\ \)

Multiply the sides of the equation by 2a :

\(b = 4a\)

_________________________________

STEP (2)

A quota passes through points (-3,2) and (0,11) , so points (-3,2) and (0,11) must be true in the quota equation.

\(y = f(x) = a{x}^{2} + bx + c \\ \\b = 4a \\ \\ y = f(x) = a {x}^{2} + 4ax + c \)

\(f( - 3) = 2 \\ \\ a ({ - 3})^{2} + 4a( - 3) + c = 2 \\ \\ 9a - 12a + c = 2 \\ \\ - 3a + c = 2 \\ \\ \\ \\ f(0) = 11 \\ \\ a ({0})^{2} + 4a(0) + c = 11 \\ \\ c = 11 \)

\( - 3a + c = 2 \\ \\ c = 11 \\ \\ - 3a + 11 = 2 \\ 11 \: goes \: to \: the \: other \: side \: \\ \\ - 3a = 2 - 11 \\ - 3a = - 9 \\ divided \: the \: sides \: of \: the \: equation \: by \: - 3 \\ a = 3\)

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

2,375,360

Step-by-step explanation:

a. Null hypothesis: The population means credit card charges for groceries and dining out are equal.

Alternative hypothesis: The population means credit card charges for groceries and dining out are not equal.
b. Using a level of significance of 0.05, we can conclude that the population means differ since the calculated p-value is less than 0.05.
c. The point estimate of the difference between the population means is also not provided in the question. Therefore, we cannot calculate the confidence interval estimate of the difference between the population means.

a. To formulate the null and alternative hypotheses, you can use the following notation:

H0 (null hypothesis): μ1 - μ2 = 0 (There is no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)

Ha (alternative hypothesis): μ1 - μ2 ≠ 0 (There is a difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)

b. To determine if the population means differ at a given level of significance (let's say α), you would need to perform a hypothesis test using the sample mean difference, sample standard deviation, and sample sizes for both populations. Unfortunately, you didn't provide these values, so I cannot perform the test or calculate the p-value.

c. To determine which category has a higher population mean annual credit card charge, you would need to compare the point estimate of the difference between the population means. Since you didn't provide the sample mean difference, I cannot determine which category has a higher population mean annual credit card charge.
We cannot determine which category, groceries or dining out, has a higher population mean annual credit card charge without additional information such as the sample mean credit card charges for each category. The point estimate of the difference between the population means is also not provided in the question.

Additionally, to calculate the confidence interval estimate of the difference between the population means, you would need the sample mean difference, sample standard deviation, and sample sizes. Without this information, I cannot provide the confidence interval estimate.

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Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

To find the perimeter (p) of a parallelogram, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.
Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in length. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by multiplying a by n/a, which is n.
So, the length of the other side is also n, and the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

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First, we will make a list of the bacteria growth during each hour.

Start: 15

1st hour: 30

2nd hour: 60

3rd hour: 120

4th hour: 240

5th hour: 480

6th hour: 960

7th hour: 1920

8th hour: 3840

9th hour: 7680

10th hour: 15360

11th hour: 30720

12th hour: 61440

As you can see, the number of bacteria present is doubled at the end of each hour, as the question states.

However the question refers to the number of bacteria that grow in the twelfth hour and not the total number of bacteria in the twelfth hour.

So the answer will be the subtraction between the bacteria in the twelfth hour minus the bacteria in the eleventh hour.

In conclusion, the answer is 30720

Answer:

Step-by-step explanation:

Answer:

by dividing it= 4/11

=0.363636363636

False. The Six Sigma DMAIC approach is a problem-solving methodology used to improve processes and reduce defects, but it is not the only tool available.

Sigma is a statistical measure of dispersion, which is used to measure the variability or spread of a given data set. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Sigma is commonly used in data analysis and is used to identify outliers and other patterns in data sets.

Depending on the nature of the problem, other problem-solving techniques may be more appropriate. For example, if the goal is to improve customer service, a method such as Lean Six Sigma, which focuses on customer value, may be more effective. Similarly, if the goal is to create new products or services, a design thinking approach could be used. In any case, it is important to assess the situation and choose the best course of action for the specific problem.

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(i) In the given context, A = [0, 3], and X = R with the metric d(x, y) = |x - y|.

(ii)  In the given context, A can be any subset, X can be any set, and the metric d(x, y) is the discrete metric.

(iii) In the given context, A = {f ∈ X: f(31​) ≤ 0}, X = C[0,1], and the metric d is the L-infinity metric.

(i) In this context, X = R represents the set of real numbers, and the metric d(x, y) = |x - y| represents the absolute difference between two real numbers. A = [0, 3] represents the closed interval from 0 to 3.

(ii) In this context, X can be any set, and the metric d(x, y) is the discrete metric. The discrete metric assigns a value of 1 if x and y are distinct elements, and 0 if x and y are the same element.

(iii) In this context, X = C[0,1] represents the set of continuous functions on the closed interval [0, 1], and the metric d is the L-infinity metric. The L-infinity metric measures the maximum absolute difference between two functions at any point in the interval.

The subset A in this context is defined as A = {f ∈ X: f(31​) ≤ 0}, which represents the set of continuous functions for which the value of f at the point 31​ is less than or equal to 0.

In summary, in context

(i), X is the set of real numbers, the metric is the absolute difference, and A is the closed interval [0, 3]. In context

(ii), X can be any set, the metric is the discrete metric, and A can be any subset. In context

(iii), X is the set of continuous functions on [0, 1], the metric is the L-infinity metric, and A represents the subset of functions satisfying f(31​) ≤ 0.

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Answer:

65.1 degrees north of east

Step-by-step explanation:

The boat sails 285 miles south, which means it moves in the direction of south (S) on the diagram. Then it sails 132 miles west, which means it moves in the direction of west (W) on the diagram. We draw a vector diagram to represent the boat's motion (I attached a picture of the diagram)

The boat's motion can be represented by a resultant vector R, which is the vector that connects the starting point to the ending point of the boat's motion. We want to find the direction of this vector.

R^2 = (285 miles)^2 + (132 miles)^2

R = √((285 miles)^2 + (132 miles)^2)

R ≈ 316.2 miles

Now we can use trigonometry to find the angle θ between the resultant vector and the east direction.

tan θ = opposite/adjacent

tan θ = 285 miles / 132 miles

θ = atan(285 miles / 132 miles)

θ ≈ 65.1 degrees

So, the direction of the boat's resultant vector is 65.1 degrees north of east (NE).

The average rate of speed of the wind is 18 mph and the average rate of speed of the plane is 36 mph.

To find the average rate of speed of the wind and the plane, we can set up a system of equations.

Let x be the average airspeed of the plane and y be the average wind speed.

From the initial trip, we have the equation: (x + y) * (1/3) = 18.
This is because the total distance traveled is the sum of the plane's speed and the wind's speed, multiplied by the time taken.

From the return trip, we have the equation: (x - y) * (3/5) = 18.
This is because the total distance traveled is the difference between the plane's speed and the wind's speed, multiplied by the time taken.

Now, we can solve these two equations to find the values of x and y.

Simplifying the equations, we get:
1/3 * (x + y) = 18
3/5 * (x - y) = 18

Cross-multiplying and simplifying further, we get:
x + y = 54
3x - 3y = 90

Next, we can solve this system of equations using any method (substitution, elimination, etc.).

Adding the two equations, we get:
4x = 144
x = 36

Substituting the value of x into one of the equations, we get:
36 + y = 54
y = 18

Therefore, the average rate of speed of the wind is 18 mph and the average rate of speed of the plane is 36 mph.

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Dalia had an average airspeed of

42

miles per hour.

The average wind speed was

12

miles per hour.

To find out how much the painter charged for the last job, we need to substitute h=15 and c=3 in the expression 35h 30c and simplify. The painter charged $615 for the last job which required 3 cans of paint and took 15 hours to complete.

The painter uses the expression 35h + 30c to determine the cost of a job, where h represents the hours spent and c represents the number of paint cans used. In the last job, it took the painter 15 hours and 3 cans of paint to complete the work. To find the cost, we will plug these values into the given expression.
Cost = 35h + 30c
Cost = 35(15) + 30(3)
Now, we will perform the calculations:
Cost = 525 + 90
By adding these values, we get the total cost:
Cost = 615

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