Suppose random variables X and Y are related Y=3X+5. Suppose the random variable X has mean zero, and variance 2. What is the variance X-Y?

Answer:

a) 6.10

Step-by-step explanation:

if you want to figure out the total number spent, then you simply add together the two amounts to get:

3.25+2.85=6.10

p.s. dont post such simple questions on brainly

Answer: a. $6.10

Step-by-step explanation:

2.85 + 3.25 = (2+3)+(.85+.25) = (5)+(1.10)=6.10
therefore, $6.10 is the right answer

The angle of intersection between the plane and the line is approximately 53.13 degrees.

To find the angle of intersection between the line and the plane, we need to determine the direction vector of the line and the normal vector of the plane.

The direction vector of the line is given as ~v(t) = t〈1,2,3〉+ 〈2,−11,9〉. The direction vector is 〈1,2,3〉.

The normal vector of the plane is the coefficient vector of x, y, and z in the equation 3x + 2y − 4z = 0. Therefore, the normal vector is 〈3, 2, -4〉.

To find the angle between the line and the plane, we can use the dot product formula: cos(theta) = (v · n) / (|v| |n|), where v is the direction vector of the line, n is the normal vector of the plane, and theta is the angle of intersection.

Taking the dot product of the direction vector and the normal vector, we have (1)(3) + (2)(2) + (3)(-4) = 3 + 4 - 12 = -5.

The magnitude of the direction vector is |v| = sqrt(1^2 + 2^2 + 3^2) = sqrt(14), and the magnitude of the normal vector is |n| = sqrt(3^2 + 2^2 + (-4)^2) = sqrt(29).

Substituting the values into the formula, cos(theta) = -5 / (sqrt(14) * sqrt(29)) ≈ -0.349.

Taking the inverse cosine of -0.349, we find theta ≈ 53.13 degrees.

The angle of intersection between the line and the plane is approximately 53.13 degrees.

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Answer:

the answer is 17/12 all u have to do is change it into a mix fraction

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{17}{12}}}}}} \)

Step-by-step explanation:

\( \sf{ \frac{7}{12} + \frac{5}{6} }\)

Take the L.C.M of 12 and 6

To find L.C.M , first of all find the prime factors of each numbers.

12 = 2 × 2 × 3

6 = 2 × 3

Take out the common prime factors i.e 2 and 3

Also take out the other remaining prime factors : 2

Multiply those all prime factors and obtain L.C.M

L.C.M = Common factors × Remaining factors

= 2 × 3 × 2

= 12

\( \dashrightarrow{ \sf{ \frac{7 \times 1 + 5 \times 2}{12}}} \)

\( \dashrightarrow{ \sf{ \frac{7 + 10}{12}}} \)

\( \dashrightarrow{ \sf{ \frac{17}{12}}} \)

Hope I helped!

Best regards! :D

Answer:

3 Dollars

Step-by-step explanation:

18/6 = 3

5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles

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Answer:

x=33

Step-by-step explanation:

x+13+4x+2=180

4x+x=5x

13 plus 2 =15

5x+15=180

subtract 15 from both sides

180-15=165

5x=165

divide 5 from both sides

x=33

The complete equation when the blanks are replaced is (a^2 + 3a + 1) - (-3a^2 + 5a - 6)=4a^2 - 2a + 7​

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

(a^2+blank+1)-(blank+5a+blank)=4a^2-2a+7​

By comparison, we have the following

a^2 - blank = 4a^2

blank - 5a = -2a

1 - blank = 7

When the above equations are solved, we have

blank = -3a^2

blank = 3a

blank = -6

So, we have

(a^2 + 3a + 1) - (-3a^2 + 5a - 6)=4a^2 - 2a + 7​

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Answer:

bruh i think EVERYBODY is at least failing one class rn

Step-by-step explanation:

The matrix a will have two distinct eigenvalues when a ≠ c or when b ≠ 0.

To find the conditions under which the matrix a has two distinct eigenvalues, we need to consider the eigenvalue equation a - λI = 0, where λ is an eigenvalue and I is the identity matrix. The determinant of this equation gives us the characteristic polynomial, which we can solve to find the eigenvalues.

The characteristic polynomial is given by det(a - λI) = (a - λ)(c - λ) - b² = λ² - (a + c)λ + ac - b². For the matrix to have two distinct eigenvalues, the discriminant of this quadratic equation, (a + c)^2 - 4(ac - b²), must be greater than zero.

Expanding the discriminant, we get (a²+ 2ac + c²) - 4ac + 4b² = a² - 2ac + c² + 4b². Simplifying further, we have (a - c)² + 4b² > 0.

Since a and c are nonzero constants, the expression (a - c)² will always be positive. Therefore, for the matrix a to have two distinct eigenvalues, we need the term 4b² to be greater than zero, which implies that b ≠ 0.

In summary, the matrix a will have two distinct eigenvalues when a ≠ c (or equivalently, a - c ≠ 0) and when b ≠ 0. These conditions ensure that the discriminant of the characteristic polynomial is positive, indicating the presence of two distinct eigenvalues.

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615 mph

Step-by-step explanation:

5 times 3 is 15

3,075 times 3 is 9,225

So 9,225 divided by 15 equals 615

Answer:

True .

Step-by-step explanation:

It's true because it sure is possible to calculate the approximate number of years by the rule of 82 .Thank you :)

The statement "the variance of a sum equals the sum of the variances" is true. This can be proven mathematically by using the formula for the variance of a sum of two random variables:
\(Variance of a sum = Var(X + Y) = Var(X) + Var(Y)\)

This formula states that the variance of a sum is equal to the sum of the variances of each individual random variable.

Addition is one of the mathematical operations.

Addition helps us to do mathematical calculations, its purpose is the combination of quantities in order to have a single result.

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The value of angle x is 34.992°

According to the question we have been given a right angled triangle with its two sides as 7 units which is the perpendicular and 10 units which is the base.

We need to find the value of x that we need to find the measure of angle x.

For that we will use trigonometry. We know that,

        tanΘ =P/B

where,   P = perpendicular

             B = base

Now we need to find first tan x which is

       tan x = 7/10

       tan x = 0.7

          x = tan⁻¹(0.7)

          x = 34.992°

Hence the value of x is 34.992°

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The probability that the selected person will be a freshman or a female is 34/43.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

So, we know that:

Male freshman = 21

Female Freshman = 7

Male Sophomores = 9

Female Sophomores = 6

So, the probability formula is:

P(E) = Favourable events/Total events

Now, insert the values as follows:

P(E) = Favourable events/Total events

P(E) = 21+7+6/43

P(E) = 34/43

Therefore, the probability that the selected person will be a freshman or a female is 34/43.

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Answer:

34 boys

Step-by-step explanation:

you divide 51 by 3 which gets yOU 17 and then you subtract 17 by 51 which gets you 34

Answer:

its

x = A/4y

Explanation:

when we send 4 and Y to the left hand side, their signs changes from multiplication to division and since they were in the numerator, they go to the denominator on the other side.

hope this helps.

Incomplete question. I inferred you want to know the properties of parallel and perpendicular lines. Which I provided below.

Explanation:

In geometry, parallel lines are two lines that are always drawn at the same distance apart and never touch each other. Parallel lines are usually denoted by the symbol ∥.

Here are some of their properties;

When a transversal intersects two parallel lines:

Perpendicular lines are two lines that meet at a right angle (90 degrees) to each other.

Properties: two lines that meet, implies all four angles are right angles.

Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Answer:

x=50

Step-by-step explanation:

This is a vertical angle, so the angle on top and the bottom are equal

[2(x+10)]=3x-30

2(x+10)=3x-30

2x+20=3x-30

50=x

$42 is the amount Zahra will save each year

How to find how much Zahra will save every year?

Given that:

Zahra does 1 load of wash per day

Hot wash & warm rinse = 71 cents per load

Warm wash & cold rinse = 25 cents per load

Right now three-fourths of all her laundry is done with the hotter water

Right now:

cost of hot wash in a year = 0.71 x 3/4 x 365 = $194.3625

cost of warm wash in a year = 0.25 x 1/4 x 365 = $22.8125

Total cost =  $194.3625 + $22.8125 = $217.175

After the cut:

cost of hot wash in a year = 0.71 x 1/2 x 365 = $129.575

cost of warm wash in a year = 0.25 x 1/2 x 365 = $45.625

Total cost =  $129.575 + $45.625 = $175.2

Savings = Total cost of right now - Total cost after the cut

Savings = $217.175 - $175.2 = $41.975 = $42

Note: we have 365 days in a year

Therefore, Zahra will save $42 every year. Option b. is the answer

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A resultant vector is given by the sum of the component vectors are c = 3·a, d = a + b and e = a - b.

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude.

The vector c comprises of three horizontal segments each of length a, therefore, we have;

c = 3·a

The vector d comprises of the vectors a followed by the vector b, therefore, we have;

d = a + b

The vector e comprises of the re verse of the vector b (which is -b) followed by the vector a to give;

e = a - b

Hence, a resultant vector is given by the sum of the component vectors are c = 3·a, d = a + b and e = a - b.

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Preparing for a negotiation process involves identifying the time limitations and devising a counter-strategy for potential unfavorable outcomes.

Identify the time constraints: It is essential to determine the time limits for the negotiation process as it helps in planning and allocating resources appropriately. This information will help in deciding the negotiation strategy and creating a timeline for the negotiation process.

Determine the best alternative to a negotiated agreement (BATNA): A BATNA is a strategy that outlines the best course of action in case the negotiation process does not yield the desired result. It is critical to identify the BATNA before starting the negotiation process to help create a fallback plan in case of unfavorable outcomes.

Research the other party: Before entering into negotiations, it is crucial to research and understand the other party's position, interests, and needs. This will help in crafting an effective negotiation strategy.

Develop a counter-strategy for the worst-case scenario: It is important to prepare a counter-strategy in case of the worst-case scenario. This strategy should outline how to respond if the other party makes unreasonable demands or if the negotiation process breaks down.

Set negotiation goals: It is essential to set clear and realistic negotiation goals. These goals should be specific, measurable, and achievable to help create a clear path to success.

Determine the negotiation strategy: Based on the research and information gathered, determine the negotiation strategy that will be most effective. There are several negotiation strategies, including distributive, integrative, and collaborative, that can be employed depending on the situation.

In conclusion, preparing for a negotiation process is crucial to achieving a successful outcome. It involves identifying the time constraints, researching the other party, developing a counter-strategy, setting negotiation goals, and determining the negotiation strategy. By following these steps, negotiators can increase their chances of achieving a positive result.

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The reflection over the x- axis are F" (-3/2 , -3/2), G" (-3/2 , 3) ,

H"  (-3 , -3).

Given,

Dilation: (x, y) -> (3/4 * x, 3/4 * y)

From the graph,

Angle FGH with vertices F(- 2, 2) , G(- 2, - 4) and H(- 4, - 4)

To find the reflection.

Now, According to the question:

Let's know the Reflection over x - axis:

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Come to the solution:

F(- 2, 2) , G(- 2, - 4) and H(- 4, - 4)

Dilation: (x, y) -> (3/4 * x, 3/4 * y)

F' (3/4 × -2 , 3/4 × 2) = (-3/2 , 3/2)

G'  (3/4 × -2 , 3/4 × -4) = (-3/2 , -3)

H'  (3/4 × -4 , 3/4 × -4) = (-3 , -3)

Reflection in the x -axis of FGH are:

F" (-3/2 , -3/2)

G" (-3/2 , 3)

H"  (-3 , -3)

Hence, The reflection over the x- axis are F" (-3/2 , -3/2), G" (-3/2 , 3) ,

H"  (-3 , -3).

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enlarging the capacity of the dock to handle two boats at a time can help in achieving the goal of minimizing customer waiting time and approaching an average time in the system close to 10 minutes.

Enlarging the capacity of the dock to handle two boats at a time can be a good way of achieving the goal of having the customer's average time in the system as close to 10 minutes as possible, but not exceeding 10 minutes. Let's analyze the statements provided:

Both channels will be empty approximately ______% of the time.
Enlarging the capacity to handle two boats at a time means that both channels can be utilized simultaneously.

If we assume that boat arrivals follow a random and evenly distributed pattern, the probability of both channels being empty at the same time is the product of the probabilities of each channel being empty.

If the arrival rate of boats is within the capacity of the dock, it is likely that both channels will be empty a significant portion of the time. The specific percentage will depend on the arrival rate and other factors.

When customers do show up, they ______ likely to have to wait for 10 minutes.
By enlarging the capacity and having two boats being served simultaneously, the waiting time for customers is expected to be reduced compared to when only one boat can be served at a time.

This means that customers are less likely to have to wait for the full 10 minutes.

On the whole, the expansion _______ be the best way of achieving their goal.
Based on the information provided, enlarging the capacity of the dock to handle two boats at a time seems like a reasonable approach to achieve the goal of having the customer's average time in the system as close to 10 minutes as possible.

However, without specific data on boat arrival rates, service times, and other factors, it is not possible to determine definitively if it is the best way.

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By the given condition we find that to calculate the cost of the notebooks and newspaper is impossible, from the given condition we get only no solutions.

Let the cost of the notebooks and newspaper in Liam's bookstore be x and y respectively.

According to the given question.

Liam's bookstore sold total 40notesbooks and 20 newspater for $130.

⇒ 40x + 20y = 130

⇒ 20(2x + y) = 130

⇒ 2x + y = 6.5 ...(i)

And the next day,

The bookstore sold 8 notebooks and 4 newspapers for $130.

⇒ 8x + 4y = 28

⇒ 4(2x + y ) = 28

⇒ 2x + y = 7 ...(ii)

Since, if we see the  two equations i and ii we find that the given conditions provide no solutions.

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According to the question the Alternating Series Test guarantees that the series \(\(\sum_{n=1}^{\infty} (-1)^n \frac{5}{n}\)\) converges. the correct answer is: The series converges.

To determine whether the alternating series \(\(\sum_{n=1}^{\infty} (-1)^n \frac{5}{n}\)\) converges or diverges, we can use the Alternating Series Test.

The Alternating Series Test states that if a series has the form \(\(\sum_{n=1}^{\infty} (-1)^n a_n\) or \(\sum_{n=1}^{\infty} (-1)^{n+1} a_n\),\) where \(\(a_n\)\) is a positive sequence that decreases as \(\(n\)\) increases, then the series converges if the limit of \(\(a_n\)\) as \(\(n\)\) approaches infinity is 0, and the terms \(\(a_n\)\) converge to 0.

In our case, the series is \(\(\sum_{n=1}^{\infty} (-1)^n \frac{5}{n}\),\) where \(\(a_n = \frac{5}{n}\)\). Let's check if the conditions of the Alternating Series Test are met:

1. \(\(a_n = \frac{5}{n}\)\) is a positive sequence.

2. \(\(a_n = \frac{5}{n}\)\) decreases as \(\(n\)\) increases.

3. \(\(\lim_{{n \to \infty}} \frac{5}{n} = 0\).\)

Since all the conditions are met, the Alternating Series Test guarantees that the series \(\(\sum_{n=1}^{\infty} (-1)^n \frac{5}{n}\)\) converges.

Therefore, the correct answer is: The series converges.

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Answer: 2 7/9

Step-by-step explanation:

Answer: 2 7/9

Step-by-step explanation:

First divide 25 by 9. You should get the answer of 2.7777777777778 which equals 2. Then to find the new numerator, you do 25-(9x2)=7. You keep the original denominator (9) and there it is. 2 7/9.

The surface area of the portion of the cone z = √(x² + y²) where z = 2 is approximately 12.57 square units.

To find the surface area of the portion of the cone z = √(x² + y²) where z = 2, we need to determine the boundaries of the cone in the x-y plane. Setting z = 2, we have:

2 = √(x² + y²)

Squaring both sides, we get:

4 = x² + y²

This equation represents a circle with a radius of 2 centered at the origin in the x-y plane. The surface area of the portion of the cone within this circle can be found by integrating the surface area element over the region of interest.

Using the formula for the surface area of a cone, which is given by A = πrℓ, where r is the radius of the base and ℓ is the slant height, we can find the surface area of each infinitesimally small triangular patch on the cone. Integrating over the region within the circle, we obtain the total surface area. Performing the calculations, the surface area is approximately 12.57 square units.

In conclusion, by determining the boundaries of the cone in the x-y plane and integrating the surface area element, we find that the surface area of the portion of the cone z = √(x² + y²) where z = 2 is approximately 12.57 square units.

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