Given a function f(x) = x+y, 0≤x+2y≤2 , otherwise = 0 (a) Show that f is a PDF. (b) Find the marginal of X and Y . (c) Find the Cov(X, Y ).

Answer:

Step-by-step explanation:

The assumptions include that the path of the ball can be modeled by a parabolic function, that data on the trajectory of the ball is needed, and that matrices can be used to solve for the constants a, b, and c. Finally, the inverse of the matrix can be computed using matrix algebra.

A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are organized in rows and columns. In addition to representing and transforming data in statistics, physics, and computer science, matrices are also used to represent and convert linear equations and transformations in linear algebra.

We need to make some assumptions and approximations in order to develop an equation for the flight of the golf ball because the actual path of the ball is influenced by a number of variables, including wind, temperature, humidity, and spin. The idea that a parabolic function may simulate the ball's trajectory is one that is frequently held.

We would need information on the ball's trajectory, such as height and distance at various points along the trip, in order to perform regression. Regression analysis cannot be used to derive an equation for the trajectory of the golf ball in the absence of this data.

To use matrices, we can set up a system of equations based on the parabolic function:

[tex]y = ax^2 + bx + c[/tex]

where x is the distance traveled by the ball, y is the height of the ball, and a, b, and c are constants to be determined.

We can set up three equations based on the following assumptions:

At the starting point (x=0), the height of the ball is zero.

At the point where the ball hit the tree (x = d), the height of the ball is the height of the tree (90 feet).

At the landing point on the green (x = D), the height of the ball is zero.

Using these assumptions, we can set up the following system of equations:

c = 0 (from assumption 1)

[tex]ad^2 + bd + c[/tex] = 90 (from assumption 2)

[tex]aD^2 + bD + c[/tex] = 0 (from assumption 3)

To solve for the constants a, b, and c, we can use matrix algebra to write the system in matrix form:

[tex][0 0 1] [c] [0][/tex]

c[tex][d^2 d 1] * [b][/tex] = [90]

[tex][D^2 D 1][/tex] [a] [0]

Multiplying the matrices, we get:

[0 0 1] [c] [0]

[tex][d^2 d 1][/tex] * [b] = [90]

[tex][D^2 D 1][/tex] [a] [0]

Simplifying, we get:

[c] [0]

[b] = [90] * [tex][d^2 d 1]^-1 * [d^2 d 1][/tex]

[a] [0]

where the inverse of the matrix [tex][d^2 d 1][/tex] can be computed using matrix algebra. Once we have the values of a, b, and c, we can plug them into the equation [tex]y = ax^2 + bx + c[/tex] to get the equation for the path of the golf ball.

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Answer: B= (5z+9) (5z-9)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Use the sum-product pattern

25z² - 81 =

25z² + 45z - 45z - 81 =

Step 2: Common factor from the two pairs

(25z² + 45z) + (−45z − 81) =

Step 3: Rewrite in Factored Form

5z (5z + 9) − 9 (5z + 9) =

(5 - 9) (5 + 9)

Solution:

B: (5 + 9) (5 - 9)

The 95% confidence interval for the mean is (1.6048, 1.6352).Hence, option (d) is the correct answer.

As given, a machine that is programmed to package 1.60 pounds of cereal is being tested for its accuracy in a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.62 pounds. The population standard deviation is known to be 0.06 pounds. We are required to find the 95% confidence interval for the mean. Here are the steps to solve this problem:

The formula to find the confidence interval is as follows;

Lower limit = x - zα/2 (σ/√n)

Upper limit = x + zα/2 (σ/√n)

Where,

x= sample mean

zα/2 = z-value of the level of significance

σ = population standard deviation

n = sample size

We are given;

x = 1.62 pounds

σ = 0.06 pounds

n = 40

We need to find the z-value of the level of significance, which can be found using the z-table or by using the calculator.Using the z-table, we get the z-value at 95% confidence interval as zα/2 = 1.96

Substituting the values, we get

Lower limit = 1.62 - 1.96(0.06/√40)

Upper limit = 1.62 + 1.96(0.06/√40)

Lower limit = 1.6048, Upper limit = 1.6352

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The surface area of a right circular cone can be found using the formula:

A = πr²+ πrl

where r is the radius of the base, l is the slant height, and π is approximately 3.14159.

In this case, the diameter of the base is 8 m, so the radius is 4 m. The slant height is 18.5 m. The height is not needed for this calculation.

Substituting the given values, we get:

A = π(4 m)² + π(4 m)(18.5 m)

A = π(16 m²) + π(74 m²)

A = π(90 m²)

Using the approximation π ≈ 3.14159, we get:

A ≈ 282.74 m²

Therefore, the surface area of the right circular cone is approximately 283 m² rounded to the nearest whole.

Answer: There are 8 campers for every 1 counselor.

Step-by-step explanation:

A ratio is relation in number between two things. 8:1 means that there are 8 ___s for every 1 ____.

The probability that Karen's second card will be a black card is 3/650.

After Sandra deals Karen a red seven, there are 51 cards remaining in the deck, of which 26 are black cards. So the probability of Karen drawing a black card on her second draw depends on whether or not the first card she drew was black or red:

If the first card Karen drew was black, then there are 25 black cards left in the deck out of 50 cards, since one card has already been drawn. So the probability of Karen drawing a black card on her second draw is 25/50 = 1/2.

If the first card Karen drew was red, then there are still 26 black cards left in the deck out of 50 cards, since one card has already been drawn. So the probability of Karen drawing a black card on her second draw is 26/50 = 13/25.

Since there are 26 red cards and 26 black cards in a standard deck of playing cards, the probability of Karen being dealt a red seven by Sandra is 2/52 = 1/26.

To find the overall probability of Karen being dealt a red seven and then drawing a black card on her second draw, multiply the probability of these two events occurring:

P(red seven and black card) = P(red seven) × P(black card on second draw | red seven)

P(red seven) = 1/26

P(black card on second draw | red seven) = 13/25

P(red seven and black card) = (1/26) × (13/25) = 13/650

Therefore, the probability of Karen's second card being a black card, given that Sandra dealt her a red seven, is 13/650.

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The complete question:

Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen’s second card will be a black card?

Using the median, which is not affected by outliers, would provide a better representation of the typical or central value of the data.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.

Based on the given information, the median is the best measure of center because there are outliers present. The reason for this is because the presence of outliers can greatly affect the mean and make it a less representative measure of central tendency.

In this case, the dots above 6, 7, and 3 may be considered as outliers since they are far from the other data points.

Therefore, using the median, which is not affected by outliers, would provide a better representation of the typical or central value of the data.

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The true statements are:

C) -5 is a solution to f(x).

E) f(x) = 2x^2 + 9x - 5

F) 0 is a solution to f(x).

I) 5 is a solution to f(x).

K) -3 is a solution to f(x).

L) (-5,0) is an x-intercept of f(x).

From the given factors of f(x), we know that:

f(x) = 3 * (2x-1) * (x+5)

Using the  information, we can calculate  the  statements are true:

A) 1 is a solution to f(x).

Not necessarily true. We need to substitute x=1 into the expression for f(x) to check if it equals zero.

B) f(x) = 6x^2 - 33x - 15

Not true. The correct expression for f(x) is given above.

C) -5 is a solution to f(x).

True. Substituting x=-5 into f(x) gives us: f(-5) = 3*(-11)*0 = 0.

D) 3 is a solution to f(x).

Not necessarily true. We need to substitute x=3 into the expression for f(x) to check if it equals zero.

E) f(x) = 2x^2 + 9x - 5

True. This is the expanded form of f(x) using the given factors.

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Answer:

the ruler showed 7 inch segment

Step-by-step explanation:

have an amazing weekend

Answer:

7÷2= 3.5

Step-by-step explanation:

The length of each part is 3.5

Answer:

The answer to your problem is, C. -2

Step-by-step explanation:

To solve : 4(y - 3) +19=8(2y + 3) + 7?

Open the bracket:

4y - 12 + 19 = 16y + 24 + 7 

Collect like terms

4y - 16y = 24 + 7 + 12 - 19

-12y = 24

Divide both sides by - 12 to isolate y

-12y / - 12 = 24 / - 12 

y = -2

Thus the answer to your problem is, C. -2

For first step you do not really need to “ open the bracket “ just solve it.

The dilated triangle has vertices

The coordinates of the vertex of the triangle before dillation is given as

P (-6, 4 )

Q (2, 8)

R (2, -4)

To dilate a figure by a scale factor of 1/2, we need to multiply the coordinates of each point by 1/2.

The coordinates of P are (-6, 4). Multiplying by 1/2, we get:

(-6 * 1/2, 4 * 1/2) = (-3, 2)

The coordinates of Q are (2, 8). Multiplying by 1/2, we get:

(2 * 1/2, 8 * 1/2) = (1, 4)

The coordinates of R are (2, -4). Multiplying by 1/2, we get:

(2 * 1/2, -4 * 1/2) = (1, -2)

Therefore, the dilated triangle has vertices P'(-3, 2), Q'(1, 4), and R'(1, -2).

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Given:

[tex]\angle\text{L}=90^\circ[/tex]

[tex]\text{KJ}=41[/tex]

 [tex]\text{JL}=40[/tex]

  [tex]\text{LK}=9[/tex]

To find the cosine of angle J

By using cosine ratio,

[tex]\text{cos J}=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]

       [tex]\text{cos J}=\dfrac{\text{JL}}{\text{JK}}[/tex]

         [tex]\text{cos J}=\dfrac{\text{40}}{\text{41}}[/tex]

The ratio of cosine of angle J is 40/41.

The events ranked from least likely to most likely are:

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

To rank the events from least likely to most likely, we need to consider the probability of each event occurring.

Event 3: Choosing a blue pen from Box A

This event is the least likely because there are no blue pens in Box A. The probability of choosing a blue pen is 0.

Event 2: Choosing a white pen from Box B

This event is more likely than Event 3 because there are white pens in Box B. The probability of choosing a white pen from Box B is 2/8 or 1/4.

Event 4: Choosing a green pen from Box A

This event is more likely than Event 2 because there are green pens in Box A. The probability of choosing a green pen from Box A is 3/15 or 1/5.

Event 1: Choosing a green or white pen from Box B

This event is the most likely because it includes both a green and a white pen in Box B. The probability of choosing a green or white pen from Box B is 6/8 or 3/4.

Therefore, the events ranked from least likely to most likely are:

Event 3: Choosing a blue pen from Box A

Event 2: Choosing a white pen from Box B

Event 4: Choosing a green pen from Box A

Event 1: Choosing a green or white pen from Box B

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Step-by-step explanation:

When x -5 is a positive

   x -5  = 2

    x = 7

when x -5 is a negative

    x-5 = -2

       x = 3

Part A: Sample space of randomly selecting 2 lollipops with replacement:

{GG, GC, GL, CG, CC, CL, LG, LC, LL}

Part B: Sample space of randomly selecting 2 lollipops without replacement:

{GC, GL, CG, CL, LG, LC}

The experiment of randomly selecting 2 lollipops without replacement shows dependent events because the probability of drawing the second lollipop depends on what the first lollipop was.

For example, if the first lollipop drawn is grape, then the probability of drawing another grape lollipop is decreased because there is only one left in the bag.

The experiment of randomly selecting 2 lollipops with replacement shows independent events because each lollipop can be chosen without affecting the probability of choosing the other lollipops.

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Based on the above, the width of the rectangle is 10.

Let's use "w" to represent the width and "l" to represent the length of the rectangle.

From the problem, we know that the area of the rectangle is 40, so we can write:

Area = length × width

40 = l × w

We also know that the width is 2 less than 3 times the length, so we can write:

width = 3l - 2

Now we can substitute this expression for "w" in the equation for the area: 40 = l × (3l - 2)

Expanding the right side gives: 40 = 3l² - 2l

Rearranging and dividing by 2 gives:

3l²- 2l - 40 = 0

(3l + 10)(l - 4) = 0

Therefore, l = 4 (because the length cannot be negative), and we can find the width using the expression we found earlier:

width = 3l - 2

width = 3(4) - 2

width = 10

So the width of the rectangle is 10. Therefore, the answer is  10.

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To write an absolute value Equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

To write an absolute value equation for a given solution set, we need to first understand what absolute value is. Absolute value is a mathematical function that returns the positive value of a given number, irrespective of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. Now, let's consider the given figures and their respective solution sets:

Figure 1: The solution set for this figure is {2, -2}. To write an absolute value equation for this solution set, we can use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 2.

Figure 2: The solution set for this figure is {5}. To write an absolute value equation for this solution set, we can use the formula |x - b| = a, where b is the midpoint of the solution set and a is the distance from the midpoint to one of the solutions. Therefore, the absolute value equation for this figure is |x - 5| = 0.

Figure 3: The solution set for this figure is {-3, 3}. To write an absolute value equation for this solution set, we can again use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 3.

In conclusion, to write an absolute value equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

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The bag contains $4.60 in coins.

What are coins?

Let's use P, N, D, and Q to represent the number of pennies, nickels, dimes, and quarters, respectively, in the bag.

We know that the total number of coins is 50, so:

P + N + D + Q = 50

We also know that 10% of the coins are pennies, so:

P = 0.1(50)

P = 5

There are 2 more nickels than pennies, so:

N = P + 2

N = 5 + 2

N = 7

Now we can use this information to find the number of dimes and quarters. Since there are 50 coins in total, we can substitute the values we have found for P and N into the first equation:

P + N + D + Q = 50

5 + 7 + D + Q = 50

12 + D + Q = 50

D + Q = 38

We also know the values of P and N, so we can find the total value of all the coins in the bag:

Total value = (value of pennies) + (value of nickels) + (value of dimes) + (value of quarters)

Total value = (5 cents x 5) + (7 cents x 5) + (10 cents x D) + (25 cents x Q)

Total value = 25 + 35 + 10D + 25Q

We can substitute D + Q = 38 into this equation to get:

Total value = 25 + 35 + 10(D + Q)

Total value = 60 + 10(38)

Total value = 460 cents, or $4.60

Therefore, the bag contains $4.60 in coins.

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Answer:

-4860

Step-by-step explanation:

The formula for finding the nth term (An) of a geometric sequence is;

An = a₁ * r^(n-1)

where a₁ is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have;

An = 20 * (-3)^(6-1)

An = 20 * (-3)^5

An = 20 * (-243)

An = -4860

Therefore, the answer is (Ob) -4860

Answer:

blank1: 9

blank2: 30°

blank3: 60°

blank4: 90°

blank5: half

Step-by-step explanation:

The 30°-60°-90° triangle has some great shortcuts associated with it (there are math reasons, trig reasons for these shortcuts)

One of these great shortcuts is that the short leg is half the hypotenuse (or the hypotenuse is double the short leg)

For your question, the kite string, 18ft, is the hypotenuse. The kite height is half that--9ft.

see image.

Answer:

let n be the number

6 less than the number

= (n-6)^5 = 32

(n-6)^5 = 2^5

since powers are equal we equate the bases

n-6 =2

n=8

The probability of choosing a password with no Y's and O's is 20/30 = 2/3, or approximately 0.667. The two probabilities are the same, so neither is greater than the other.

Probability is a measure of the likelihood or chance that an event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In mathematical terms, probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

To calculate the probability of choosing a password with no Y's or no O's, we need to first count the number of valid passwords without Y's or O's and then divide it by the total number of possible passwords.

Number of valid passwords without Y's:

There are 5 choices for the first character (B, R, O, G, P), since Y is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except Y), since we cannot repeat the first letter.

So the total number of valid passwords without Y's is 5 x 4 = 20.

Number of valid passwords without O's:

There are 5 choices for the first character (Y, B, R, G, P), since O is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except O), since we cannot repeat the first letter.

So the total number of valid passwords without O's is 5 x 4 = 20.

The total number of possible passwords is the number of ways to choose 2 characters out of 6, without repetition. This is given by the formula:

6P2 = 6! / (6 - 2)! = 6 x 5 = 30

Therefore, the probability of choosing a password with no Y's is 20/30 = 2/3, or approximately 0.667.

Similarly, the probability of choosing a password with no O's is also 20/30 = 2/3, or approximately 0.667.

The two probabilities are the same, so neither is greater than the other.

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The volume of cat food in the can is approximately 9.63 cubic inches.

What is the volume of a cylinder?

The volume of a cylinder can be found using the formula:

V = πr²h

where V is the volume, r is the radius of the circular base, h is the height of the cylinder, and π is the constant pi (approximately equal to 3.14).

To find the volume of the can of cat food, we can use the formula for the volume of a cylinder, which is V = πr²h, where r is the radius (half the diameter) and h is the height.

The radius of the can is 3.5/2 = 1.75 inches, and the height is 1 inch. So, the volume of the can is:

V = π(1.75)²(1)

= 9.62 cubic inches

≈ 9.63 cubic inches (rounded to the nearest hundredth)

Therefore, the volume of cat food in the can is approximately 9.63 cubic inches.

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The probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions = 0.24

Let us assume that X be the number of returns containing illegitimate deductions in the sample.

Here, X has a hypergeometric distribution.

We need to find the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deduc-tions.

Here, N = 15, r = 9, n = 5

So, P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

We know that the combination formula:

⁹C₂ = 9! / (2! × 7!)

     = 36

⁶C₃ = 6! / (3! × 3!)

     = 20

¹⁵C₅ = 15! / (5! 10!)

      = 3003

P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

              = (36 × 20) / (3003)

              = 0.24

Therefore, the required probability is: 0.24

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The estimated total number of moles in the local area is 4.

The farmer needs to use the capture-recapture method to estimate the total number of moles in the local area. This involves tagging a population sample, releasing them back into the population, and then capturing another sample to determine the proportion of tagged individuals in the second sample. Using this proportion, the total population can be estimated using the following formula:

total population = (number in first sample * number in the second sample) / number of tagged individuals in the second sample

In this case, the farmer tagged 30 moles in the first sample and found that half of the second sample had tags. We can use these values to estimate the total number of moles:

total population = (30 * 2) / 15

total population = 4

Note that the actual population size may be larger or smaller than this estimate due to factors such as migration, birth, and death rates.

To correctly estimate the number of moles in a substance, the farmer needs to use the grams to moles formula, which is:

n = m / M

where n is the number of moles, m is the mass of the substance in grams, and M is the molar mass in grams per mole . To calculate the molar mass of a substance, the farmer can sum the molar masses of its component atoms

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