Probability 0.35 0.3 0.05 0.1 0.05 0.15 8 9 10 11 Find the expected value of the above random variable.

The system of linear equations has no solutions for any value of k except when k = 2, where it has infinitely many solutions.

(a) To reduce the augmented matrix for the system of linear equations to row-echelon form, we can write the system of equations as:

2 - y = kx

-y = k

To eliminate y in the first equation, we can multiply the second equation by (-1) and add it to the first equation:

(2 - y) - (-y) = kx - k

2 = kx - k

This gives us a new system of equations:

2 = kx - k

Now, we can represent this system in augmented matrix form:

[1 -k | 2]

(b) To find the values of k, we can examine the augmented matrix.

If the system has no solutions, it means that the rows of the augmented matrix result in an inconsistent equation, where the last row has a leading nonzero entry. In this case, for the system to have no solutions, the augmented matrix should have a row of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix [1 -k | 2] doesn't have this form, so there are no values of k that lead to no solutions.

If the system has exactly one solution, the augmented matrix should be in row-echelon form, with each row having at most one leading nonzero entry. In this case, the augmented matrix should not have any rows of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix can be reduced to row-echelon form as follows:

[1 -k | 2]

From this form, we can see that there are no restrictions on the value of k. For any value of k, the system will have exactly one solution.

If the system has infinitely many solutions, the augmented matrix should have at least one row of the form [0 0 | 0]. In our case, the augmented matrix can be reduced to:

[1 -k | 2]

From this form, we can see that if k = 2, the last row becomes [0 0 | 0]. Therefore, for k = 2, the system will have infinitely many solutions.

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Answer:

C-D = 6

A-B = 3.25

D = 118

Step-by-step explanation:

C-D = 6 because the line is the same as B-C

A-B = 3.25 because the line is the same as A-D

D = 118 because the angle of B is vertically opposite to D

Answer:

a= 126 degrees

b= 54 degrees

r= 54 degrees

s= 126 degrees

Step-by-step explanation:

Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).

To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.

Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.

However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.

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Answer:

The First Choice

Step-by-step explanation:

1/4 is equal to .25

.25 x 4= 1.00

25 x 4= 100

Answer:

a=[tex]\sqrt{28.32}[/tex]≈5.3217 cm

Step-by-step explanation:

Use the Pythagorean Theorem

a^2+4.7^2=7.1^2

a^2+22.09=50.41

a^2=28.32

a=[tex]\sqrt{28.32}[/tex]

≈5.3217

Answer:

5.3

Step-by-step explanation:

Check the attached image for explanation if you are interested, as I did not feel like spending 20 minutes re-formatting the equations to work on Brainly.

Also, I did not do this

Money needed to have accumulated if the RRSPs averaged a real return of four percent per year is $432,000

Amount of income stream = $25,000

Time = 30 years

According to the 4% rule, a retiree can risk not having enough money for at least 30 years by comfortably withdrawing 4% of their assets in their first year of retirement and adjusting that amount for inflation each year after that.

Calculating the present value -

[tex]PV = FV / (1 + r)^n[/tex]

Substituting the values -

[tex]PV = $25,000 / (1 + 0.04)^30[/tex]

[tex]PV = $25,000 / (1.04)^30[/tex]

= 432,309

Rounded the nearest thousand the return amount comes to $432,000

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Answer:

5x+2(3x+8)

5x+6x+16

11x+16

11x=-16

X=16/11

The probability density function of Y = exp(U) is given by:

                   f(y) = { 1/y, 2 ≤ y ≤ e³ ; 0, elsewhere }.

Given that: U follows the Uniform distribution U ~ U[2, 3]. We have to find the probability density function of Y = exp(U).

The formula used: The probability density function of a random variable X, is denoted by f(x), is the derivative of the cumulative distribution function (cdf), denoted by F(x). We have F(x) = P(X ≤ x).

The probability density function of the uniform distribution U(a,b), is given by

f(x)=1/(b-a), where a ≤ x ≤ b.

Here, U[2,3]So, a = 2, b = 3

Let's find the probability density function of Y = exp(U).

So, for finding the probability density function of Y = exp(U), first, we need to find the cumulative distribution function F(y) of Y. Let's do that.

So, F(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln y)

We have, Y = exp(U), which is a one-to-one function of U and increasing in U. Hence, we can use the one-to-one transformation formula. Hence, the probability density function of Y, f(y) = f(u) / |dy/du|.f(u) = 1/ (3-2) = 1

Here, dy/du = d/dy [exp(u)] = exp(u) = Y

Therefore, f(y) = 1/Y, for 2 ≤ u ≤ 3.

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Suppose that U follows the Uniform distribution U ~ U[2, 3].

Find the probability density function of Y = exp(U).

Let fU(u) be the pdf of U.Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:

fU(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.

Now we need to find the pdf of Y = exp(U).

Let FY(y) be the cdf of Y.

Then we can write:

FY(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.

Since U is continuous and its pdf is given by fU(u), we have:

[tex]FY(y) = ∫_{2}^{ln(y)} fU(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]

We can differentiate FY(y) to find the pdf of Y:

fy(y) = d/dy FY(y) = (1 / y) fY(ln(y)) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.

Therefore, the probability density function (pdf) of Y = exp(U) is given by:

fy(y) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.

In general, if U is a continuous random variable with pdf fU(u) and Y = g(U) is a monotonic transformation of U, then the pdf of Y can be found using the formula:

[tex]fy(y) = fU(g^{-1}(y)) / |dg^{-1}(y) / dy|,[/tex]

where g^{-1}(y) is the inverse function of g(y) and |dg^{-1}(y) / dy|

is the absolute value of the derivative of g^{-1}(y) with respect to y.

The probability density function (pdf) of the random variable

Y = exp(U)

where U is distributed uniformly over the interval [2, 3] can be found as follows:

Let f_U(u) be the pdf of U.

Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:

f_U(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.

Now we need to find the pdf of Y = exp(U).

Let F_Y(y) be the cdf of Y.

Then we can write:

[tex]F_Y(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.[/tex]

Since U is continuous and its pdf is given by f_U(u), we have:

[tex]F_Y(y) = ∫_{2}^{ln(y)} f_U(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]

We can differentiate F_Y(y) to find the pdf of Y:

[tex]fy(y) = d/dy F_Y(y) = (1 / y) f_Y(ln(y)) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.[/tex]

Therefore, the probability density function (pdf) of Y = exp(U) is given by:

fy(y) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.

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Answer:

Step-by-step explanation:

Rule for the dilation of a point about the origin is,

(x, y) → (kx, ky)

Here, k = scale factor

Dilating points D, E and F about the origin by a scale factor 'k' = [tex]\frac{1}{3}[/tex]

D(-9, -6) → D'(-3, -2)

E(-6, -3) → E'(-2, -1)

F(0, -9) → F'(0, -3)

Now we can plot these points on graph.

The sum of n consecutive integers, where n is an odd positive integer, is divisible by n.

To prove the statement, let's consider a set of n consecutive integers starting from a.

The sum of n consecutive integers can be expressed as:

S = a + (a+1) + (a+2) + ... + (a+n-1)

To find the sum, we can use the formula for the sum of an arithmetic series:

S = (n/2) × (2a + (n-1))

Since n is an odd positive integer, we can represent it as n = 2k + 1, where k is a non-negative integer.

Substituting this value of n into the sum formula, we get:

S = ((2k+1)/2) × (2a + ((2k+1)-1))

Simplifying further:

S = (k+1) × (2a + 2k)

S = 2(k+1)(a + k)

Since k is an integer, (k+1) is also an integer. Therefore, we can rewrite the sum as:

S = 2m(a + k)

Now, we can see that S is divisible by n = 2k + 1, where m = (k+1).

Thus, we have proven that the sum of n consecutive integers, where n is an odd positive integer, is divisible by n.

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Answer:

(21x-25)

Step-by-step explanation:

We need to find an equivalent expression for the following.

5x-3+4(4x-6)+2

We can solve it as follows:

5x-3+4(4x-6)+2 = 5x-3+16x-24+2

= 5x+16x-3-24+2

= 21x-25

So, the equivalent expression is equal to (21x-25).

Option (b) is the correct answer. Minimum usual value: 54.65

Maximum usual value: 79.92.

The given values are n = 267 and p = 0.239. The minimum usual value and the maximum usual value are to be calculated. We use the formula of the mean and the standard deviation for this purpose:

Mean = µ = np = 267 × 0.239 = 63.93Standard Deviation = σ = sqrt (npq) = sqrt [(267 × 0.239 × (1 - 0.239)] = 5.01The minimum usual value is obtained when the z-value is -2, and the maximum usual value is obtained when the z-value is +2. We use the z-score formula: z = (x - µ) / σwhere µ = 63.93 and σ = 5.01(a) When the z-value is -2, x = µ - 2σ = 63.93 - 2(5.01) = 53.91(b) When the z-value is +2, x = µ + 2σ = 63.93 + 2(5.01) = 73.95

Therefore, the minimum usual value is 53.91, and the maximum usual value is 73.95 (rounded to the nearest hundredth).

Thus, option (b) is the correct answer. Minimum usual value: 54.65Maximum usual value: 79.92.

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The given values are: n=267, p=0.239

We need to find the minimum usual value and the maximum usual value using these values of n and p.

Let X be a random variable with a binomial distribution with parameters n and p.

The mean of the binomial distribution is:μ = np

The standard deviation of the binomial distribution is:σ = sqrt(npq)where q = 1-p

Let X be a binomial distribution with parameters n = [tex]267 and p = 0.239μ = np = 267 × 0.239 = 63.813σ = sqrt(npq) = sqrt(267 × 0.239 × 0.761) = 6.788[/tex]

The minimum usual value is given by:[tex]μ - 2σ = 63.813 - 2 × 6.788 = 50.236[/tex]

The maximum usual value is given by:[tex]μ + 2σ = 63.813 + 2 × 6.788 = 77.39[/tex]

Thus, the minimum usual value is 50.24 and the maximum usual value is 77.39(rounded to the nearest hundredth).

Therefore, the answer is:Minimum usual value: 50.24, Maximum usual value: 77.39

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Answer:

4,684 km

Step-by-step explanation:

simply saying its circular measure

Answer:

x = 94

Step-by-step explanation:

(86 + x)/2 = 90

86 + x = 180

x = 94

The ordered pair (x, y) that is a solution to the equation -x + 5y = 2 is (0, 2/5).

To find the coordinates of the other endpoint D given that the midpoint of CD is M(2, -1) and one endpoint is C(-3, -3), we can use the midpoint formula:

Midpoint formula:

The coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

Using the given information, we can substitute the known values into the midpoint formula and solve for the coordinates of D:

M(2, -1) = ((-3 + x₂) / 2, (-3 + y₂) / 2)

Simplifying the equation:

2 = (-3 + x₂) / 2

-1 = (-3 + y₂) / 2

To solve for x₂:

4 = -3 + x₂

x₂ = -3 + 4

x₂ = 1

To solve for y₂:

-2 = -3 + y₂

y₂ = -3 - 2

y₂ = -5

Therefore, the coordinates of the other endpoint D are D(1, -5).

To find an ordered pair (x, y) that is a solution to the equation -x + 5y = 2, we can choose any value for either x or y and solve for the other variable. Let's choose x = 0:

-0 + 5y = 2

5y = 2

y = 2/5

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Answer:

what is this a different answer orrrr?

Answer:

No coz 2:3 is 2+3=5

1:2 is 1+2=3 so they are not equivalent.

Answer:

Step-by-step explanation:

10^7 = 1 and 7 zeros after it.

=> 10000000

Answer:

1.is 12

2. is 36

3. is 18

4. is 4.5

Step-by-step explanation:

sorry if im wrong

Answer:

x=4

Step-by-step explanation:

The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.

Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.

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The standard deviation of the fish Zagreus will catch is approximately 0.6833.

Given probability of catching fish by Zagreus in a single run of Hades is as follows: P(0 fish) = 0.10 P(1 fish) = 0.40 P(2 fish) = 0.35 P(3 fish) = 0.15

To calculate the standard deviation of the fish Zagreus will catch, we need to follow these steps:

Find the expected value, µ, of the fish he will catch.

Then, calculate the variance, σ², using the formula:σ² = Σ [(x - µ)² P(x)]

Finally, calculate the standard deviation, σ, which is the square root of the variance.μ = Σ [xP(x)]μ = (0 × 0.10) + (1 × 0.40) + (2 × 0.35) + (3 × 0.15)μ = 0.75

The expected value, µ, of the fish he will catch is 0.75.

To find the variance:σ² = [(0 - 0.75)² × 0.10] + [(1 - 0.75)² × 0.40] + [(2 - 0.75)² × 0.35] + [(3 - 0.75)² × 0.15]σ² = 0.4675

Finally, the standard deviation, σ, is the square root of the variance:σ = √σ²σ = √0.4675σ ≈ 0.6833

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Given: In a single run of hades, zagreus has a 10% chance of catching 0 fish, 40% chance of catching 1 fish, 35% chance of catching 2 fish, and a 15% chance of catching 3 fish. The standard deviation of the fish that Zagreus will catch is 0.49 fish.

The standard deviation of the fish that Zagreus will catch can be calculated using the following formula

σ = sqrt [∑(x-μ)²/N], where σ is the standard deviation, ∑ is the sum of, x is the fish, μ is the mean, and N is the total number of chances.

The mean value of the fish Zagreus is expected to catch is given by:

μ = (0 x 10/100) + (1 x 40/100) + (2 x 35/100) + (3 x 15/100)

μ = 0 + 0.4 + 0.7 + 0.45

μ = 1.55.

Therefore, the mean value of the fish Zagreus will catch is 1.55 fish.

To calculate the standard deviation, we first calculate the deviation of each value from the mean as shown below: Deviation = x - μ

The deviations for each value of fish that Zagreus could catch are: -1.55, -0.55, 0.45, and 1.45.

Now, we can plug in these values into the formula above to calculate the standard deviation as shown below:

σ = sqrt [(-1.55² x 10/100) + (-0.55² x 40/100) + (0.45² x 35/100) + (1.45² x 15/100)]

σ = sqrt [0.24025]

σ = 0.49

Therefore, the standard deviation of the fish that Zagreus will catch is 0.49 fish.

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Answer: x=3/5

Step-by-step explanation:

Answer:

A.) 0.25

B.) 0.125 (maybe don't trust me)

Step-by-step explanation:

Answer:

k=62

Step-by-step explanation:

K divided by 5 = 12.4

Multiply both sides by 5

5k/5=12.4×5

Simplify;

k=62

Hope this helped!!

Answer:

k = 62

Step-by-step explanation:

To solve we need to get k on one side alone.

To do this we can multiply buth sides by 5

[tex]\frac{k}{5} =12.4[/tex] --->  =12.4*5

This gives us x=62

You can check this by putting 62 in for k and solving the problem.

The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.

To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.

Starting with the given equation, we can simplify it step by step:

2 = -x√(x + 2) - x

Adding x to both sides:

2 + x = -x√(x + 2)

Squaring both sides to eliminate the square root:

(2 + x)^2 = (-x√(x + 2))^2

Expanding and simplifying:

4 + 4x + x^2 = x^2(x + 2)

Simplifying further:

4 + 4x = x^3 + 2x^2

Rearranging terms:

x^3 + 2x^2 - 4x - 4 = 0

Factoring the equation:

(x + 1)(x^2 + x - 4) = 0

Setting each factor to zero:

x + 1 = 0 or x^2 + x - 4 = 0

Solving the first equation, we find x = -1.

For the second equation, we can use the quadratic formula:

x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.

Hence, the set of all solutions to the equation is {x = -1}.

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