Let X and Y be two jointly distributed RVs with the following joint distribution: x = 1 x = 2 x = 3 x = 4 y = 2 0.12 0.08 0.15 0.05 y = 4 0.07 0.06 0.12 0.05 y = 6 0.06 0.04 0.05 0.00 y = 8 0.05 0.02

Answer:

N>-6

Step-by-step explanation:

N/3+2>0

N/3>0-2

N/3>-2

N>-2*3

N>-6

Answer:

y = 2x - 4

Step-by-step explanation:

To solve this problem, we must first calculate the slope of the line AB using the formula:

\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

where:

m ⇒ slope of the line

(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line

Therefore, for line AB with points A = (2, 5) and B = (4, 4) :

\(m_{AB} = \frac{5 - 4}{2 - 4}\)

⇒ \(m_{AB} = \frac{1}{-2}\)

⇒ \(m_{AB} = -\frac{1}{2}\)

Next, we have to calculate the slope of the line BC.

We know that the product of the slopes of two perpendicular lines is -1.

Therefore:

\(m_{BC} \times m_{AB} = -1\)      [Since BC and AB are at right angles to each other]

⇒ \(m_{BC} \times -\frac{1}{2} = -1\)

⇒ \(m_{BC} = -1 \div -\frac{1}{2}\)      [Dividing both sides of the equation by -1/2]

⇒ \(m_{BC} = \bf 2\)

Next, we have to use the following formula to find the equation of line BC:

\(\boxed{y - y_1 = m(x - x_1)}\)

where (x₁, y₁) are the coordinates of a point on the line.

Point B = (4, 4) is on line BC, and its slope is 2. Therefore:

\(y - 4 =2 (x - 4)\)

⇒ \(y - 4 = 2x - 8\)         [Distributing 2 into the brackets]

⇒ \(y = 2x-4\)

Therefore, the equation of line BC is y = 2x - 4.

John only likes combinations where x2/x1 = 2, he would prefer (3, 7) over (10, 2) as it is the closest to the preferred ratio.

In a perfect complements preference model, the consumer only likes a particular combination of goods when they are consumed in fixed proportions to each other. The locus of kinks is the boundary where the consumer switches from one preferred combination to another as the price ratio changes.

In this case, the locus of kinks is given by 2x1 = x2, which means that John only likes combinations where the second good (x2) is twice as much as the first good (x1).

To determine which option John prefers between (3, 7) and (10, 2), we can calculate the ratios of x2/x1 for each option:

For (3, 7), x2/x1 = 7/3 = 2.33

For (10, 2), x2/x1 = 2/10 = 0.2

Since John only likes combinations where x2/x1 = 2, he would prefer (3, 7) over (10, 2) as it is the closest to the preferred ratio.

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Answer:

The four digit numbers are from 1000 to 9999

The number of four digits which are not divisible by 4 means 4 goes into them with a remainder

The number of four digit numbers 9999 inclusive which are not divisible by 4 are

Hope this helps you

Answer:

157.741

Step-by-step explanation:

3000=800 ( 1 + 0.05)^t

-800

2200=1.05^t

log(1.05)2200=t

log2200/log1.05

t=157.7...

Answer:

25

Step-by-step explanation:

d= √l²+w²= √24²+7²= √576+49= √625= 25

Answer:

25

Step-by-step explanation:

In Pythagoras' theorem a^(2) + b^(2) = C^(2)

If we input put values, 7^(2)+24^(2)= 625

The square root of 625 is 25  

Answer:

She get 84% right

Step-by-step explanation:

42 x 2 = 84

50 x 2 = 100

Answer:

84%

this is the picture of how I solved it.

hope you understand.

Answer:$1. 45

Step-by-step explanation:

The bill is $1

the quarter is .25

and the nickels together are .20

add everything together its 1.45

First, we need to know the value of each coin. The top coin is a quarter, and its value is $0.25. The four coins below are nickels, and they have a value of $0.05. The dollar bill at the bottom has a value of $1.00.

If we have one quarter, we start with a value of $0.25.

\($0.25\)

Now, we add on the nickels.

\(0.25 + 0.05+ 0.05+ 0.05+ 0.05 = 0.45\)

Now we have a total of $0.45.

Adding the dollar would look like this:

\(1.00 + 0.45 = 1.45\)

Therefore, the value of all the money in the picture is $1.45.

i think its 1.45in^2

The function f(x)=x^2 and g(x)=4(x+1)^2 have different shapes and properties when compared to each other.

While f(x) is a simple quadratic function with a parabolic shape, g(x) is a shifted and scaled version of the same quadratic function.

The factor of 4 in front of the function increases the steepness of the curve, while the addition of 1 inside the parentheses shifts the graph one unit to the left.

Additionally, the exponent of 2 in f(x) indicates that the function is an even function, meaning it is symmetric with respect to the y-axis. On the other hand, the function g(x) is not an even function as the shift to the left breaks the symmetry.

Overall, these functions differ in their shape, scale, and symmetry properties.

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Answer:

i dont know

Step-by-step explanation:

i dont know

The probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people in contest that no one win the prize is equals to 0.0000001269.

Total number of people present= 200

so, total possible outcomes= 200

We have to determine the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively.

The number of favourable outcomes for winning first prize = 1

So, probability that abby win the first prize = \(\frac{1}{200} \)

The number of favourable outcomes for winning second prize = 1

So, probability that barry win the second prize = \(\frac{1}{199} \)

The number of favourable outcomes for winning third prize = 1

So, probability that sylvia win the third prize = \(\frac{1}{198} \)

Now, total probability that no one can win more than one prize = \(\frac{1}{200} × \frac{1}{199} × \frac{1}{198} \)

= 0.0000001269

Hence, required probability value is 0.0000001269.

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Complete question :

what is the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people enter the contest no one can win more than one prize.

\(x_{v}\)Answer:

The vertex of an up - down facing parabola of the formy = ax" + bx + c is xy =

The parabola params are:

a = 8, b = -14, c =3

\(x_{v}=b/2a\)

\(x_{v}\)=-(-14)/2·8

simplify

\(x_{v}\)=-(-14)/2·8

\(x_{v} = 7/8\)

Plug in \(x_{v}\)=7/8to find the \(y_{v}\) value

\(y_{v}\)= -25/8

Therefore the parabola vertex is

(7/8 , -25/8)

If a < 0, then the vertex is a maximum value

If a > 0, then the vertex is a minimum value

a = 8

Minimum(7/8 , -25/8)

Answer: The correct answer for this question is $6.55

Step-by-step explanation:

Hope this helps

Answer:

28.75

Step-by-step explanation:

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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We have transformed the left side into the right side using trigonometric identities. We start with the left side of the equation:

(1 + cos 0) (1 – sin 0)

Expanding the product, we get:

1 - sin 0 + cos 0 - sin 0 cos 0

Using the identity sin² θ + cos² θ = 1, we can replace sin² θ with 1 - cos²θ:

1 - (1 - cos² θ) + cos θ - (1 - cos² θ) cos θ

Simplifying, we get:

2 cos² θ - cos θ - 1

Now we use the identity sin² θ + cos² θ = 1 again to replace cos² θ with 1 - sin²θ:

2(1 - sin² θ) - cos θ - 1

2 - 2 sin²θ - cos θ - 1

1 - 2 sin² θ - cos θ

Finally, using the identity sin 2θ = 2 sin θ cos θ, we can write:

1 - sin 2θ - cos θ

Which is the right side of the equation. Therefore, we have transformed the left side into the right side using trigonometric identities.

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Answer:

B) d=4t

Step-by-step explanation:

let's look at two points

1. t=0, d = 0

2. t = 1, d = 4

slope = change in vertical axis (d)/ change in horizontal axis (t)

change in d = 4 = d₂-d₁

change in t = 1 = t₂-t₁

slope = 4/1 = 4

vertical variable = slope * horizontal variable + horizontal axis intercept

d = 4 * t + horizontal axis intercept

horizontal axis intercept is the vertical axis variable (d) when the horizontal axis variable (t) is at 0. at t=0, d=0

thus, d = 4 * t + 0

d = 4t (B)

Answer:

answers found in pdf

Step-by-step explanation:

mathaway will help check your answers that what I did.

In a deck of playing cards has 52 cards of which 12 are face cards, The odds are 33 / 3315 or 0.01 that the top 3 are face cards.

The total number of cards was 52, and there were 12 face cards.

Probability equals the number of possible outcomes divided by the total number of possibilities.

The first attempt had a probability of 12/52,

the second attempt had a probability of 11/51,

and the third attempt had a probability of 10/50.

Therefore, the probability that each of the three cards are face cards is equal to 12 / 52 × 11 / 51 × 10 / 50 = 1320 / 132600 = 132 / 13260 = 33 / 3315

the probability that all three are face cards = 0.00995475113 ≈ 0.01

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The amplitude is 3

for a sine graph, the amplitude is the distance up or down from the midway point. The equation to find the amplitude is (max-min) / 2.

(3 - (-3)) / 2 = 3

The amount in the savings account in five years will be $88,619.51.

To compute the present value of the account, we need to use the formula for continuous compound interest:

A = Pe^(rt)

Where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this case, we know that the initial amount (P) is zero since Sam is continuously depositing money into the account. So we can simplify the formula to:

A = 10000/e^(0.06*5) * ∫(0 to 5) (3000t+10000)e^(0.06t) dt

The integral in this formula represents the accumulation of all the deposits made into the account over the five-year period. We can solve it using integration by parts:

∫(0 to 5) (3000t+10000)e^(0.06t) dt
= [(3000t+10000)/(0.06^2) - (3000/0.06) - 10000]e^(0.06t) from 0 to 5
= 54681.85

Plugging this value and the other known variables into the formula, we get:

A = 10000/e^(0.06*5) * 54681.85
= $51,119.51

So the present value of the account is $51,119.51.

To find out how much will be in the savings account in five years, we simply need to add up all the deposits made over the five-year period:

Total deposits = ∫(0 to 5) (3000t+10000) dt
= 37500

Adding this amount to the present value of the account, we get:

Final amount = $51,119.51 + $37,500
= $88,619.51

Therefore, the amount in the savings account in five years will be $88,619.51.

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Answer:

11.66 meters

Step-by-step explanation:

First draw a diagram. See attachment.

We notice that if we draw everything out, we get a right triangle.

The flag pole and its shadow are the two legs, with lengths 10 and 6 meters. We want to find the distance from the top of the pole to the end of the shadow, so we need to use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 10 and b = 6, and we want to find c:

a² + b² = c²

10² + 6² = c²

100 + 36 = c²

136 = c²

c = √136 = 2√34 ≈ 11.66 meters

~ an aesthetics lover

Answer:

11.7

Step-by-step explanation:

The conversion of the rates to unit rates is as follows:

The unit rate is the ratio of one quantity or value compared to another.

The unit rate is the average rate, which is the quotient of the numerator and the denominator.

The quotient is determined by division operation, one of the four basic mathematical operations.

1. Two liters of spring water costs $1.98. $0.99 per liter ($1.98/2)

2. A car goes 425 miles on 12.5 gallons of gas. 34 miles per gallon of gas (425/12.5)

3. A car travels 676 miles in 13 hours. 52 miles per hour (676/13)

4. Four pounds of chicken costs $7.96. $1.99 per pound ($7.96/4)

5. A plane travels 675 miles in 1.5 hours. 450 miles per hour (675/1.5)

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a)There are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements\(=A*B=m*n=mn\)

For each element, \(A*B\) we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

\(2*2*2......=2^m^n }\)

Then there are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

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The cost from company A and company B will be the same at 40 square feet of countertop

Given that:

Company A will sell Mikayla a countertop according to the given

graph, which includes a $1, 000 installation fee.

Company B will sell a countertop according to the values given in the

table, which includes an $800 installation fee and a constant rate of change

With this information, you can make cost function for both Company A and Company B

Company A

A linear function is of the form y = mx + c

where c is the y-intercept (starting point) and m is the slope (rate)

c = 1000  (from the graph)

m = 1150-1000 / 10-0  (By using the 2 points on the graph: m = y2-y1/x2-x1)

m = 15

y = mx + c

y = 15x+1000

Company B

c = 800  (given)

m = 1100-1000 / 15-10  (From table)

m = 100/5 = 20

y = mx + c

y = 20x+800

Equate the two cost functions and solve for x:

20x+800 = 15x+1000

20x-15x = 1000-800

5x = 200

x = 200/5

x = 40 square feet

Therefore, at 40 square feet of countertop, the cost from each company will be the same

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Conceptually, the arithmetic and geometric average returns are different measures used to describe the performance of an investment or an asset over a specific period.

The arithmetic average return, also known as the mean return, is calculated by adding up all the individual returns and dividing by the number of periods. It represents the average return for each period independently.

On the other hand, the geometric average return, also called the compound annual growth rate (CAGR), considers the compounding effect of returns over time. It is calculated by taking the nth root of the total cumulative return, where n is the number of periods.

When to use each measure depends on the context and purpose of the analysis:

1. Arithmetic Average Return: This measure is typically used when you want to evaluate the average return for each individual period in isolation. It is useful for analyzing short-term returns, such as monthly or quarterly returns. The arithmetic average return provides a simple and straightforward way to assess the periodic performance of an investment.

2. Geometric Average Return: This measure is more suitable when you want to understand the compounded growth of an investment over an extended period. It is commonly used for long-term investment horizons, such as annual returns over multiple years.

The geometric average return provides a more accurate representation of the overall growth rate, accounting for the compounding effect and reinvestment of returns.

In summary, the arithmetic average return is suitable for analyzing short-term performance, while the geometric average return is preferred  evaluating long-term growth and the compounding effect of returns.

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To calculate hte possible values of y you have to apply the Pythagoras theorem:

Where

c will be the distance between the given points, and the hypothenuse of a right triangle

a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)

b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)

So:

Replace the expression with the given measurements to calculate the y-coordinate of the first point:

The possible values for y, since its

Answer:

The answer is 3

Step-by-step explanation:

Answer:

\(3\)

Step-by-step explanation:

7-4=3

7+(-4) means 7-4

Hope it helps! :)

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Additional Comment

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Answer:

651/100

Step-by-step explanation:

Answer:6 51/100

Step-by-step explanation:I dont really feel like explaining lol