Suppose that the random variables X, Y, and Z have the joint probability density function f(x, y, z)= 8xyz for 0 i) P(X < 0.5) ii) P(X < 0.5, Y < 0.5) iii) P(Z < 2)
iv) P(X < 0.5 or Z < 2) v) E(X)

Answer:

18 r2

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

for the first answere

The cyclist traveled an average of 62.4 miles per day over the course of 36 days. To find the average number of miles the cyclist traveled, we divide the total distance traveled by the number of days.

In this case, the cyclist traveled 2,248 miles in 36 days. So, to calculate the average, we divide 2,248 by 36, which equals approximately 62.4 miles per day.

To arrive at this calculation, we use the formula for average: Average = Total sum / Number of items. In this context, the total sum represents the total distance traveled, which is 2,248 miles, and the number of items corresponds to the number of days, which is 36. Dividing the total distance by the number of days gives us the average number of miles per day.

Therefore, the average number of miles the cyclist traveled over the 36-day period is approximately 62.4 miles per day. It is important to note that this value is an approximation, rounded to one decimal place.

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Answer:

The first two blanks are 12 and 22 and the last two blanks are 12 and 22

Step-by-step explanation:

Answer:

4/15 is the answer my guy

Step-by-step explanation:

5/3 x 4/25= 20/75 simplified is 4/15

The correct answer is "spines." Spines are the pointed edges of a droplet that radiate out from the spatter.

They can be useful in determining the direction of force applied to the droplet. When a droplet impacts a surface, it spreads out and creates elongated extensions or projections along its periphery, known as spines. By examining the shape and orientation of these spines, forensic analysts can infer the direction from which the force that caused the spatter originated.

The spines provide us with  valuable information about the trajectory and angle of impact, aiding in the investigation and analysis of the event.

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To find the nonpermissible replacement for y in the expression;

The nonpermissible replacement for y is the replacement for y at which the denominator of the expression is zero. (when the denomenator is zero, the final value can not be determined).

For the given expression, the denomenator is;

For y to be nonpermissible, the denometor must be equal to zero.

To get y, add 1 to both sides.

At y =1, the expression becomes;

Therefore, the nonpermissible replacement for y in the given expression is;

A psychological test with a reliability of zero means that the results obtained from the test cannot be trusted or relied upon.

Reliability refers to the consistency or stability of a test over time. If a test has a reliability of zero, it means that the results obtained from the test are completely random and do not provide any meaningful information. This could be due to a variety of factors, such as poor test design, inconsistent scoring methods, or unreliable measures of the construct being assessed.

It is important for psychological tests to have high reliability in order to ensure that they are accurately measuring what they are intended to measure. Without reliability, the results obtained from the test cannot be trusted and may even be misleading. For example, if a test is designed to measure anxiety levels, but has a reliability of zero, it is impossible to know whether the results obtained from the test reflect actual anxiety levels or are simply random. To improve the reliability of a test, it is important to carefully design the test and scoring methods, ensure that the measures used are consistent and reliable, and conduct multiple test administrations to assess consistency over time. By improving reliability, researchers and clinicians can be more confident in the results obtained from the test and use them to make more informed decisions about diagnosis and treatment.

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The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer:

-6 is the same as Subtracting 6, C.

Hope this helps!

Step-by-step explanation:

For example,

5 - 6

5 is positive, +5

and 6 is negative, -6

Answer:

easy subtracting 6 :))

Step-by-step explanation:

can i get brainliest uwu^_^

Answer:

447 cm³

Step-by-step explanation:

Finding volume of cuboid :-

Finding volume of triangle :-

Net Volume :-

Answer:

Your answer is  x \(\geq\) 77

Step-by-step explanation:

\(\frac{x}{7} \geq 8+3\)

\(\frac{x}{7} \geq 11\)

\(\frac{x}{7 } * 7 \geq 11*7\)

\(x \geq 77\)

Hope this helps!

The volume of the resulting solid is approximately 904.78 cubic units.

To find the volume of the resulting solid, we can subtract the volume of the smaller ball (the hole) from the volume of the larger ball. The volume of a sphere is given by the formula:

where V is the volume, r is the radius of the sphere, and π is approximately equal to 3.14.

Using this formula, we can find the volume of the larger ball:

We can then find the volume of the smaller ball (the hole):

Subtracting the volume of the smaller ball from the volume of the larger ball gives us the volume of the resulting solid: 4188.79 cubic units - 113.04 cubic units = approximately 904.78 cubic units. This is the volume of the resulting solid.

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Answer:

11.6404467268 ——> 11.64

Step-by-step explanation:

Since ur only in hs, there are no steps for this. Simply press the square root button on ur calculator and voila! Thx for the brainliest :)

The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

------------------------------------------

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

------------------------------------------

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

------------------------------------------------------

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

------------------------------------------------------

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

There are two ways you can find the slope(atleast thats what I know)

Step-by-step explanation:

Hello, i have two ways.

We can find the slope in y = mx+b form or the slope in y=mx+b itself

We can also find the slope with the graph drawn.

The probability that a student will have a raw score that is more than 45 is approximately 0.6915 or 69.15%.

To answer this question, we need to use the normal distribution formula:

\(z = (x - mu) /\)sigma

Where:

\(z =\) the z-score

\(x =\)the raw score we want to convert to a z-score (in this case, \(x = 45)\)

\(mu =\)the population mean (given as 50 in the problem)

sigma = the population standard deviation (given as 10 in the problem)

So, plugging in these values:

\(z = (45 - 50) / 10\)

\(z = -0.5\)

Next, we need to find the probability that a z-score is less than \(-0.5.\) We can use a standard normal distribution table or calculator to find this probability. The area to the left of a z-score of -0.5 is 0.3085 (or approximately 0.31).

However, we are interested in the probability that a student will have a raw score that is more than 45, not less than 45. To find this probability, we need to subtract the area to the left of -0.5 from 1 (which represents the total area under the curve):

\(P(x > 45) = 1 - P(x < 45)\)

\(P(x > 45) = 1 - 0.3085\)

\(P(x > 45) = 0.6915\)

Therefore, the probability that a student will have a raw score that is more than 45 is approximately 0.6915 or 69.15%.

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the volume of the cone is 94.2 cubic feet

The volume generated when the plane figure bounded by the curve y = x² + 5, the x-axis, and the ordinates x = 1 and x = 3 rotates about the y-axis through a complete revolution can be found using the method of cylindrical shells.

The volume can be calculated by integrating the formula V = 2π ∫[a,b] x f(x) dx, where a and b are the x-values of the bounds of the region, and f(x) represents the distance from the axis of rotation to the curve at each x-value.

In this case, the curve y = x² + 5 intersects the x-axis at y = 0 when x = ±√5i. We are given the bounds of x = 1 and x = 3, which lie entirely above the x-axis. Therefore, the volume can be obtained by integrating the formula V = 2π ∫[1,3] x (x² + 5) dx.

Evaluating this integral, we get V = 2π ∫[1,3] (x³ + 5x) dx = 2π [(1/4)x⁴ + (5/2)x²] evaluated from 1 to 3. Simplifying further, we have V = 2π [(81/4 + 45/2) - (1/4 + 5/2)] = 2π (99/4 - 3/4) = 96π/4 = 24π.

Therefore, the volume generated when the given figure rotates about the y-axis through a complete revolution is 24π cubic units.

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Answer:

510.1

Step-by-step explanation:

convert m to km by dividing by 1000 and add all of the numbers together

To find the first term can be calculated an = a1 + d(n - 1).

The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). It is possible to obtain a formula for the nth term of the AP using this kind of development. A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term. The nth term in this series equals 4n-2. You may get the terms of the series by changing the nth term to n=1,2,3,... i.e.,

first term = 4n-2 = 4 when n = 1 (1)

-2 = 4-2=2

Second term for n = 2 is 4n-2 = 4. (2)

-2 = 8-2=6

When n is 3, the third term is 4n-2 (3)

-2 = 12-2=10

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Answer:

x=\(-\frac{13}{15}\)

or 15x=-13

Step-by-step explanation:

20x+17=35x+30

20x-35x=30-17

-15x=13

x=\(-\frac{13}{15}\)

Answer:

Step-by-step explanation:

-15 + (-2) = -17

Answer: -17

Answer:

lower graph

Step-by-step explanation:

• Odd degree , positive leading coefficient

Then end behaviour is

As x → - ∞ then y → - ∞

As x → + ∞ , then y → + ∞

The graph also has roots at x = - 4, x = - 1 and x = 5

These features are displayed in the lower graph

The graph of the function is shown in second graph.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

A polynomial function has a root of -4 with multiplicity 4, a root of -1 with multiplicity 3, and a root of 5 with multiplicity 6.

Hence, Condition is, Odd degree and positive leading coefficient

Then end behavior is,

As x → - ∞ then y → - ∞

As x → + ∞ , then y → + ∞

Here, The graph also has roots at x = - 4, x = - 1 and x = 5

Hence, All of the above is shown in second graph.

Thus, Second graph is correct.

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We can solve this problem by using exponential growth. The answer is: after 40 years, Mr. Bean's parents would have approximately 640 descendants.

Given that the number of descendants doubles every 15 years, we can use the formula: N = N₀ * (2^(t / 15)). Where N is the number of descendants after t years, N₀ is the initial number of descendants, t is the number of years, and 2 is the base representing the doubling effect. In this case, N₀ is 80, t is 40 years, and we need to find the number of descendants after 40 years. N = 80 * (2^(40 / 15)) ≈ 80 * (2^(8/3)) ≈ 80 * 8 ≈ 640. Therefore, after 40 years, Mr. Bean's parents would have approximately 640 descendants.

It's important to note that in this calculation, we assume continuous exponential growth, which may not accurately represent real-world scenarios. Additionally, we assume that there are no factors that would limit the growth or affect the doubling rate of the descendants.

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Answer:

Step-by-step explanation:

100(-5.31/112.69)=-4.71%

So the stock decreased by 4.71%

The proportion of cranberries required for the muffins is 4 pounds x 16 ounces/pound = 64 ounces of cranberries. Therefore, to make the muffins for the party, you will need 64 ounces of cranberries.

To calculate the amount of cranberries needed for the muffins at a party of 12 people, making 11/2-ounce muffins and assuming each person will have three muffins, we need to convert the measurements and quantities.

Given that each muffin weighs 11/2 ounces, and each person will have three muffins, we can calculate the total weight of muffins needed. 11/2 ounces is equivalent to 1.5 ounces, so each person will consume 1.5 ounces x 3 muffins = 4.5 ounces of muffins.

For a party of 12 people, the total amount of muffins required is 4.5 ounces/person x 12 people = 54 ounces of muffins.

Now, to determine the amount of cranberries needed for the muffins, we need to consider the recipe's proportion. The recipe makes 15 pounds of dough and calls for 4 pounds of cranberries. To convert pounds to ounces, we know that 1 pound is equal to 16 ounces.

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