On reversing the digits of a two digit number, the number obtained is 9 less than three times the original number. If the difference of these two numbers is 45, find the original number. A 35
B 27
C 28
D 30

The expected value of Y is: 1.8

The student made a mistake by using the formula for the variance of XY instead of the expectation of XY^2.

(a) E(Y) = (0.2)(2) + (0.5)(1) + (0.3)(4) = 1.8

(b) Since X and Y are independent, the distribution of X + Y is the convolution of their respective distributions. That is, if Z = X + Y, then for any real number z,

F(z) = P(Z ≤ z) = P(X + Y ≤ z) = ∑P(X = i, Y ≤ z − i) for i = 0, 1, 2, ...

Now, since X has a Poisson distribution with parameter 2 and Y takes values 2, 3, and 4 with probabilities 0.2, 0.5, and 0.3 respectively, we have

P(X = i, Y = j) = P(X = i)P(Y = j) = e^(-2) (2^i/i!)p_j for i = 0, 1, 2, ... and j = 2, 3, 4

where p_2 = 0.2, p_3 = 0.5, and p_4 = 0.3. Then, for z ≥ 2,

F(z) = P(Z ≤ z) = ∑_{i=0}^{z-2} P(X=i, Y≤z-i) = ∑_{i=0}^{z-2} e^(-2) (2^i/i!) ∑_{j=2}^{min(z-i, 4)} p_j

(c) P(X > Y) = ∑_{i=0}^∞ ∑_{j=0}^{i-1} P(X=i, Y=j) = ∑_{i=0}^∞ ∑_{j=0}^{i-1} e^(-2) (2^i/i!) p_j

(d) The calculation is incorrect. It should be E[XY^2] = E[X]E[Y^2] = 2(0.2)(2^2) + 2(0.5)(3^2) + 2(0.3)(4^2) = 11.6. The student made a mistake by using the formula for the variance of XY instead of the expectation of XY^2.

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Answer:

48.8 square inches

Step-by-step explanation:

To find the area of the triangle, we can use the formula:

Area = 1/2 * base * height

In this case, the base of the triangle is the longer side, which is 13 inches, and the height is the shorter side, which is 7.5 inches. However, we need to make sure that the angle provided is the angle between the base and the height, and not one of the other angles of the triangle.

Assuming that the angle provided is indeed the angle between the base and the height, we can proceed with the calculation:

Area = 1/2 * 13 inches * 7.5 inches

Area = 48.75 square inches

Rounded to the nearest tenth, the area of the triangle is 48.8 square inches.

The length of segment d is 8 when the value segment a is  4 cm, b is 12 cm , c is 6 cm

If two segments intersect inside or outside the circle then ab=cd

Given values of a is 4 cm, b is 12 cm , c is 6 cm and d is x

ab=cd

Plug in the values of a, b , c and d

4×12=6×d

48=6d

Divide both sides by 6

8=d

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The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).

To find the equation of the plane tangent to the surface z = x²y + xy^2 + ln x + R at the point (1, 0, R), we'll need to find the partial derivatives with respect to x and y, and then use the point-slope form of the tangent plane equation. Here are the steps:

1. Find the partial derivatives of the surface function with respect to x and y:
∂z/∂x = 2xy + y² + (1/x)
∂z/∂y = x² + 2xy

2. Evaluate the partial derivatives at the given point (1, 0, R):
∂z/∂x(1, 0) = 2(1)(0) + (0)² + (1/1) = 1
∂z/∂y(1, 0) = (1)² + 2(1)(0) = 1

3. Use the point-slope form of the tangent plane equation:
z - z₀ = a(x - x₀) + b(y - y₀)

4. Substitute the point (x₀, y₀, z₀) = (1, 0, R) and the partial derivative values a = ∂z/∂x = 1, b = ∂z/∂y = 1:
z - R = 1(x - 1) + 1(y - 0)

5. Simplify the equation:
z - R = x - 1 + y

6. Rearrange the equation to the standard form:
z = x + y + (R - 1)

The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).

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The probability that you are not one of the first four students chosen is 0.75 or 75%.

For the first selection, the probability that you are not chosen is:

(16 - 1) / 16 = 15 / 16

For the second selection, the probability that you are not chosen is:

(16 - 1 - 1) / (16 - 1) = 14 / 15

For the third selection, the probability that you are not chosen is:

(16 - 1 - 1 - 1) / (16 - 1 - 1) = 13 / 14

For the fourth selection, the probability that you are not chosen is:

(16 - 1 - 1 - 1 - 1) / (16 - 1 - 1 - 1) = 12 / 13

To find the probability that you are not one of the first four students chosen, we multiply these probabilities together:

(15/16) x (14/15) x (13/14) x (12/13) = 0.75

Therefore, the probability that you are not one of the first four students chosen is 0.75 or 75%.

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a)

The events X and Y are not independent.

b)

(1)The value of P(B) is 1/124.

(ii) The value of P(A ∩ B') is 9/16.

We have,

a)

We have:

P(X) = 0.6

P(Y) = 0.2

P[(X Y) ∪ (X Y')] = 0.45 (using the distributive property of set operations)

We want to find P(X ∩ Y), which we can do using the formula:

P(X ∩ Y) = P(X) + P(Y) - P(X ∪ Y)

To find P(X ∪ Y), we can use the formula:

P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)

Using the values given, we have:

P(X ∪ Y) = 0.6 + 0.2 - P(X ∩ Y) (substituting in P(X) and P(Y))

P[(X Y) ∪ (X Y')] = 0.45 (given)

We can rewrite the left-hand side as:

P[(X Y) ∪ (X Y')] = P(X Y) + P(X Y') (using the distributive property of set operations)

Since X and Y are disjoint events, we have:

P(X Y') = P(X) - P(X ∩ Y) (using the formula for the probability of the complement of an event)

Substituting these values into the expression for P[(X Y) ∪ (X Y')], we get:

P(X Y) + (P(X) - P(X ∩ Y)) = 0.45

Simplifying, we get:

P(X Y) = 0.45 + P(X ∩ Y) - P(X)

Substituting in the values of P(X) and P(Y) given, we get:

P(X Y) = 0.45 + P(X ∩ Y) - 0.6

P(X Y) = -0.15 + P(X ∩ Y)

Since probabilities cannot be negative, we know that P(X Y) ≤ P(X ∩ Y). Therefore, we can conclude that X and Y are not independent.

b)

i. We have:

P(A) = 7/8

P(B) = 1/12

P(A ∩ B) = 5/16

We want to find P(B). We can use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Since A and B are disjoint events, we have:

P(A ∪ B) = P(A) + P(B)

Substituting in the values given, we get:

P(A) + P(B) = 7/8 + P(B) = 1 - P(B') = 11/12

Solving for P(B), we get:

P(B) = 11/12 - 7/8 = 1/24

ii.

We want to find P(A ∩ B'). We can use the formula:

P(A ∩ B') = P(A) - P(A ∩ B)

Substituting in the values given, we get:

P(A ∩ B') = 7/8 - 5/16 = 9/16

Thus,

a)

X and Y are not independent.

b)

(i) P(B) = 1/124

(ii) P(A ∩ B') = 9/16

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Answer:

Calcualate 40% (0.40) times 20 to get that there are 8 boys in the class. The rest must be girls, so 20 - 8 gives you 12 girls. 25% (0.25) times the 8 boys gives you that 2 of the boys wear glasses. 50% (0.5) times the 12 girls tives you that 6 girls wear glasses. Add together the 2 boys and the 6 girls that wear glasses to get that a total of 8 students wear glasses.

Step-by-step explanation:

Answer: 62

Step-by-step explanation:

top row has 12

the next row has 1 more =13

and it alternates

12+13+12+13+12=62

Answer: 0.3

Step-by-step explanation:

3/10 = 30/100 = 0.3

Answer:

0.3

Step-by-step explanation:

The 99% confidence interval for the mean score, μ, of all students taking the test is approximately (78.603, 87.397)

To construct a 99% confidence interval for the mean score, μ, of all students taking the calculus test, we need to follow these steps:

Step 1: Identify the sample mean, sample standard deviation, and sample size.
Sample mean (X) = 83
Sample standard deviation (σ) = 8.70
Sample size (n) = 26

Step 2: Determine the appropriate z-score for a 99% confidence interval.
For a 99% confidence interval, the z-score (z) is 2.576.

Step 3: Calculate the standard error of the mean (SEM).
[tex]SEM= \frac{σ }{\sqrt{n} } = \frac{8.70}{\sqrt{26} } = 1.706[/tex]

Step 4: Compute the margin of error (ME).
ME = z * SEM = 2.576 * 1.706 = 4.397

Step 5: Construct the 99% confidence interval.
Lower limit = X - ME = 83 - 4.397 = 78.603
Upper limit = X + ME = 83 + 4.397 =  87.397

Your answer: The 99% confidence interval for the mean score, μ, of all students taking the test is approximately (78.603, 87.397).

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Why don't you and Julián eat? Why not have something to eat?

How old am I? You have come nine years.

In the first sentence, Mario's answer is using the auxiliary verb "have" to suggest that they should eat something. The phrase "have something to eat" is a common way to express this idea.

In the second sentence, Mario's answer is using the verb "come" in the sense of "reach" or "attain". So, he is saying that his little sister has reached the age of nine years old. This is a colloquial way of answering the question about age, rather than saying "you are nine years old".

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Full Question: Mario's little sister is very curious and always wants to know why people do certain things. Complete Mario's answers with have and come. 1. Why don't you and Julián eat? Why not ______ hungry. 2. How old am I? You ____ nine years

Based on the newspaper report, it can be concluded that Candidate A is leading with 52% of the vote while Candidate B has 48% of the vote. However, it is important to note that the margin of error is +/- 4%. This means that there is a chance that the actual percentage of votes for each candidate could be 4% higher or lower than what the poll suggests.

For example, Candidate A's actual percentage of votes could be anywhere between 56% (52% + 4%) and 48% (52% - 4%), while Candidate B's actual percentage of votes could be anywhere between 52% (48% + 4%) and 44% (48% - 4%).

It is also important to note that opinion polls are not always accurate predictors of election results. They are simply a snapshot of public opinion at a particular moment in time and can be influenced by various factors such as the wording of the questions, the sample size, and the demographic makeup of the respondents.

In summary, based on the newspaper report, Candidate A has a slight lead over Candidate B with 52% of the vote, but there is a margin of error of +/- 4% which means that the actual percentage of votes for each candidate could be different. It is important to keep in mind that opinion polls are not always accurate predictors of election results.

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Answer:

The answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape

Step-by-step explanation:

We are given that, Julia had a bag filled with gumballs. There were 3 lemon-lime, 4 watermelon, and 6 grape gumballs.

There are 3 lemon-lime: Elements in sample space are lemon-lime, lemon-lime, lemon-lime

There are also 4 watermelon: Elements in sample space are watermelon, watermelon, watermelon, watermelon

Lastly there are 6 grape: Elements in sample space are grape, grape, grape, grape, grape, grape

Which can lead to the problem of:

3 + 4 + 6 = 13. Same as option B

Thus the answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape

To calculate the accuracy of the test, we need to create a 2x2 contingency table:

Actual Positive (Meningitis)Actual Negative (No Meningitis)Test PositiveTrue Positive (TP) = 6False Positive (FP) = 3Test NegativeFalse Negative (FN) = 2True Negative (TN) = 69

From the information given, we know that there are 8 actual positive cases (people with meningitis) and 72 actual negative cases (people without meningitis). We also know that there were 3 false positive results (people who tested positive for meningitis but did not have it) and 2 false negative results (people who tested negative for meningitis but actually had it).

Using this information, we can calculate the accuracy of the test as:

Accuracy = (TP + TN) / (TP + TN + FP + FN)

Accuracy = (6 + 69) / (6 + 69 + 3 + 2)

Accuracy = 75 / 80

Accuracy = 0.9375 or 93.75%

Therefore, the accuracy of the meningitis test is 93.75%.

The coordinates of the vertices after a reflection over the x-axis would be:

Reflecting a figure over the x-axis causes the y-coordinates of its vertices to change signs, while their respective x-coordinates remain unchanged.

To apply this principle to the given triangle, we flip the y-coordinate of point A from -3 to 3, that of point B from -1 to 1 and also for point C changing from -2 to 2 respectively. The outcome is as follows: A (0, 3), B (0, 1) and C (6, 2). It's noted that the x-coordinate remains constant across all points of the newly transformed shape.

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Answer:

The zeroes are x = -4 and x = 2.

The value of n is 5.

Given that, the Coordinate of P = (n,3)

R is on y-axis & the y-coordinate of P & R are equal.

So coordinate of R = (3,0)

Coordinate of Q = (n,-2)

Using distance formula,

Distance between P & Q =

[tex]=\sqrt{(n-n)^2+(-3-(-2)^2} \\\\=\sqrt{(3+2)^2} \\\\= \sqrt{25} = 5[/tex]

Distance between P & R =

[tex]\sqrt{(n-0)^2+(3-3)^2}[/tex]

= n

According to the question it is given that distance between P & Q is equal to the distance between P & R. So, n = 5.

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Therefore, the length of a side of the square is x/4 inches by the equation.

In this context, we have a wire that we need to bend into a square. A square has four equal sides, so if we let s be the length of one side of the square, then the total length of the wire must be 4s.

The equation 4s = x represents this relationship, where x is the total length of the wire.

To solve for s, we can isolate s on one side of the equation by dividing both sides by 4. This gives us:

4s / 4 = x / 4

Simplifying, we get:

s = x / 4

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Answer:

The answer to your problem is, D. If the data is categorical

Step-by-step explanation:

What a pictograph is:

Remember that a pictographs are less useful for comparing change over time or for presenting large sets of numerical data, as they can become cluttered and difficult to read.

Here is a little example, if you want to show how the population of a city has changed over the years, a line graph or a bar graph would be a better choice than a pictograph

Thus the answer to your problem is, D. If the data is categorical

Where c1 and c2 are arbitrary constants determined by initial conditions.

The differential equation given is:

y'' - 6y' + 25y = 0

To find the two linearly independent solutions of the differential equation, we assume a solution of the form:

y = e^(rt)

where r is a constant to be determined. We then substitute this into the differential equation and obtain:

r^2 e^(rt) - 6r e^(rt) + 25 e^(rt) = 0

Dividing both sides by e^(rt), we get:

r^2 - 6r + 25 = 0

This is the characteristic equation of the differential equation, and we can solve for r using the quadratic formula:

r = (6 ± sqrt(6^2 - 4*25)) / 2

r = 3 ± 4i

Therefore, the two linearly independent solutions of the differential equation are:

y1 = e^(3x) cos(4x)

y2 = e^(3x) sin(4x)

To verify that these solutions are linearly independent, we can take the Wronskian of the solutions:

W(y1, y2) = y1y2' - y1'y2

= e^(3x) cos(4x) (3e^(3x) sin(4x) + 4e^(3x) cos(4x)) - e^(3x) sin(4x) (3e^(3x) cos(4x) - 4e^(3x) sin(4x))

= 5e^(6x)

Since the Wronskian is nonzero, the two solutions are linearly independent.

The general solution to the differential equation is then a linear combination of the two linearly independent solutions:

y = c1 e^(3x) cos(4x) + c2 e^(3x) sin(4x)

where c1 and c2 are arbitrary constants determined by initial conditions.

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The solution to the given set of equations is Infinite solutions.

We have the equation

R: -3y = -3x -9

S: y = x + 3

Now, solving the equation R and S as

-3y = -3x - 9

3y =  3x + 9

_________

   0 = 0 + 0

   0 = 0

Also, -3/1 = 3/(-1) = 9/(-3)

-3/1 = -3/1 = -3/1

Thus, the equation have Infinite many solutions.

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Answer:5

explanation:

you are doing great finding the slopes:

Reverse logistics involves designing a customer-focused supply management system and understanding transportation options, but it does not necessarily require knowledge of e-procurement systems or triage.

Reverse logistics is the process of managing the flow of products, materials, and information from the end-user back to the point of origin. It involves activities such as returns, refurbishment, recycling, and disposal of products.

The options given are:

a. triage - This refers to the process of determining the priority of patients' treatments based on the severity of their condition. While triage is an important concept in healthcare, it is not directly related to reverse logistics.

b. designing a supply management system from the customer's perspective - This is a key aspect of reverse logistics. A successful reverse logistics system requires a customer-focused approach to ensure that products can be easily returned and that customers have a positive experience with the returns process.

c. understanding of e-procurement systems - While e-procurement systems can be helpful in managing the reverse logistics process, it is not a necessary component of reverse logistics. E-procurement systems are primarily used for purchasing and procurement activities.

d. understanding of transportation options - Transportation is a critical component of reverse logistics, as it is necessary to move returned products from the point of origin back to the manufacturer or retailer. Understanding transportation options and selecting the most cost-effective and efficient method of transportation is essential to managing the reverse logistics process.

In summary, reverse logistics involves designing a customer-focused supply management system and understanding transportation options, but it does not necessarily require knowledge of e-procurement systems or triage.

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Answer:

height = 9 in

Step-by-step explanation:

The formula for volume (V) of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height

In the question, we're given the volume and in the diagram, we're given the length (8.5 in.) and the width (2 in.).  We can solve for l by plugging in our volume, length, and width into the formula and solving for x (the length):

[tex]153=(8.5)(2)x\\153=17x\\9=x[/tex]

When you are given an equation for a function, it is important to know whether the function is increasing or decreasing. A function is said to be increasing if the value of the function increases as the input increases. Conversely, a function is said to be decreasing if the value of the function decreases as the input increases.

To determine whether a function is increasing or decreasing, you need to look at the sign of its first derivative. The first derivative of a function is the rate of change of the function with respect to its input. If the first derivative is positive, the function is increasing, and if it is negative, the function is decreasing. If the first derivative is zero, the function may have a local maximum or a local minimum.

To explain this in more detail, let's take the example of the function f(x) = x^2. To find the first derivative of this function, we need to differentiate it with respect to x. This gives us f'(x) = 2x. We can see that f'(x) is positive for x > 0, which means that the function f(x) = x^2 is increasing for x > 0. Similarly, f'(x) is negative for x < 0, which means that the function f(x) = x^2 is decreasing for x < 0.

In summary, to determine where a function is increasing or decreasing, you need to look at the sign of its first derivative. If the first derivative is positive, the function is increasing, and if it is negative, the function is decreasing. If the first derivative is zero, the function may have a local maximum or a local minimum.

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Answer:

303.375 or 303 3/8

Step-by-step explanation:

First, we can split the polygon into three smaller shapes: a triangle, a big rectangle, and a small rectangle. We will call them A, B, and C.

A:

Length: 28.25 - (3 + 13) = 28.25 - 16 = 12.25 (12 1/4)

Height: 10 + 9 = 19

Area: (12.25 * 19) / 2 = 232.75 / 2 = 116.375 ft

B:

Length: 3 + 13 = 16

Width: 10

Area: 16 * 10 = 160 ft

C:

Length: 3

Width: 9

Area: 3 * 9 = 27 ft

Now we have to add all three digits:

116.375 + 160 + 27 = 303.375 or 303 3/8

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Hope this helps :)

Sure, I can help with that. The problem is asking for the area of a polygon composed of two rectangles and a right triangle.

The area of a rectangle is given by the formula length * width, and the area of a right triangle is given by the formula 1/2 * base * height.

Let’s calculate the areas:

For the first rectangle with dimensions 9ft by 13ft, the area is 9 * 13 = 117 square feet.

For the second rectangle with dimensions 10ft by 8ft, the area is 10 * 8 = 80 square feet.

For the right triangle with dimensions 28ft by 4ft, the area is 1/2 * 28 * 4 = 56 square feet.

Adding these areas together gives the total area of the polygon:

117 + 80 + 56 = 253 square feet

So, the area of the polygon is 253 square feet.

Answer:

k<-10

Step-by-step explanation:

-3k+5>35

-3k+5-5>35-5

simplifica la expresión

k<-10

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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