Which of the following is false (a) A chi-square distribution with k degrees of freedom is more right-skewed than a chi-square distribution with k + 1 degrees of freedom. (b) A chi-square distribution never takes negative vales (e) The degrees of freedom for a chisquare test are deter- (d) P(X'>10) İs greater when clf k + 1 than whet te) The area under a chi-square density curve is alk mined by the sample size df alwrv equal to

Answer:

[tex]m = \frac{2 - ( - 4)}{1 - ( - 1)} = \frac{6}{2} = \frac{3}{1} = 3[/tex]

Answer:no it doesn’t it makes a trapezoid which doesn’t have 90 degree angles or right angles

Step-by-step explanation:

The Intermediate Value Theorem states that for any value c between the function's values at the endpoints (f(a) and f(b)), there exists a value x in the interval [a, b] such that f(x) = c.

The assumptions (or conditions) required for the Intermediate Value Theorem are:

1. The function is continuous: The function must be continuous on the closed interval [a, b]. This means that there are no breaks, jumps, or holes in the graph of the function within the given interval.

2. The interval is closed and bounded: The interval [a, b] must be a closed interval, meaning it includes both endpoints a and b. Additionally, the interval must be bounded, meaning the function has a maximum and a minimum value within the interval.

By satisfying these two assumptions, the Intermediate Value Theorem states that for any value c between the function's values at the endpoints (f(a) and f(b)), there exists a value x in the interval [a, b] such that f(x) = c.

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To find the future value of this investment, we can use the formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value
- P is the principal (or starting amount)
- r is the nominal annual interest rate (as a decimal)
- n is the frequency of conversion per year
- t is the time (in years)

Plugging in the given values, we get:
FV = 9400(1 + 0.031/2)^(2*9)
FV = 9400(1.0155)^18
FV = 9400(1.367576)
FV = 12848.92
Therefore, the future value of the investment is $12,848.92 (rounded to the nearest cent).

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The probability assigned to each experimental outcome must be: b. between zero and one

The probability assigned to each experimental outcome must be between zero and one. This is because probability is a measure of how likely an event is to occur, and it cannot be negative or greater than 100%. A probability of zero means that the event will not occur, while a probability of one means that the event is certain to occur. Probabilities between zero and one indicate the likelihood of an event occurring, with higher probabilities indicating greater likelihood. It is important for probabilities to add up to one across all possible outcomes, as this ensures that all possible events are accounted for and that the total probability is normalized. Probability theory is used in many fields, including statistics, finance, and engineering, and is essential for making informed decisions based on uncertain events. By assigning probabilities to different outcomes, we can calculate expected values and make predictions about future events, helping us to better understand the world around us.

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The factors to the given expression are -1(x+3)(x-8)

The x-intercepts of the quadratic relationship are -3, 8. When we write an expression in its factors and multiplying those factors gives us the original expression, then this process is known as factorization.

How do we factorize the given expression?

We equate the given expression to f(x)

   (-[tex]x^{2}[/tex] + 5x + 24) = f(x)

⇒ -1([tex]x^{2}[/tex] - 5x - 24) = f(x)

⇒ -1([tex]x^{2}[/tex] - (8-3)x - 24) = f(x)

⇒ -1([tex]x^{2}[/tex] + 3x - 8x -24) = f(x)

⇒ -1(x(x+3) -8(x+3)) = f(x)

⇒ -1(x+3)(x-8) = f(x)

∴The factor to the given expression is -1(x+3)(x-8)

How do we find the x-intercepts?

We equate f(x) = 0 to find the x-intercepts.

⇒ -1(x+3)(x-8) = 0

⇒ (x+3)(x-8) = 0

The roots of the above equation are x-intercepts.

Therefore, the x-intercepts occur where x = -3 and x = 8

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The complete question is "Factor the expression (-x^2 + 5x + 24.) and use the factors to find the x-intercepts of the quadratic relationship it represents.

Type the correct answer in each box, starting with the intercept with the lower value.

The x-intercepts occur where x =

and x = "

The variance of X is 3/80.

Given the probability density function of X,

f(x) = {3x² for 0 < x < 1

{0 otherwise

We can use this to answer the following:

(a) Find P(X < 0.5)

To find P(X < 0.5), we need to integrate the density function from 0 to 0.5:

P(X < 0.5) = ∫[0,0.5] f(x) dx

= ∫[0,0.5] 3x² dx

= [x³]₀.₃

= 0.125

(b) Find the cumulative distribution function of X, F(x)

The cumulative distribution function (CDF) of X is given by:

F(x) = P(X ≤ x) = ∫[0,x] f(t) dt

If x ≤ 0, then F(x) = 0. If 0 < x ≤ 1, then

F(x) = ∫[0,x] f(t) dt

= ∫[0,x] 3t² dt

= [t³]₀.ₓ

= x³

If x > 1, then F(x) = 1. So, the CDF of X is:

F(x) = {0 if x ≤ 0

{x³ if 0 < x ≤ 1

{1 if x > 1

(c) Find the expected value of X, E(X)

The expected value of X is given by:

E(X) = ∫[−∞,∞] x f(x) dx

Since the density function f(x) is zero outside the interval [0,1], we can restrict the integration to this interval:

E(X) = ∫[0,1] x f(x) dx

= ∫[0,1] 3x³ dx

= [3/4 x⁴]₀.₁

= 3/4 * 1⁴ - 0

= 3/4

Therefore, the expected value of X is 3/4.

(d) Find the variance of X, Var(X)

The variance of X is given by:

Var(X) = E(X²) - [E(X)]²

We have already found E(X) in part (c). To find E(X²), we integrate x² times the density function:

E(X²) = ∫[0,1] x² f(x) dx

= ∫[0,1] 3x⁴ dx

= [3/5 x⁵]₀.₁

= 3/5 * 1⁵ - 0

= 3/5

Substituting into the formula for variance:

Var(X) = E(X²) - [E(X)]²

= 3/5 - (3/4)²

= 3/5 - 9/16

= 3/80

Therefore, the variance of X is 3/80.

Complete question: Let X be a random variable defined by the density function

[tex]$$f(x)=\left\{\begin{array}{cl}3 x^2 & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array}\right.$$[/tex]

Find

(a)[tex]$E(X)$[/tex]

(b) [tex]$E(3 X-2)$[/tex]

(c) [tex]$E\left(X^2\right)$[/tex]

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The width of the river (AB) is approximately 265.85 meters.

We have to solve this using the tangent formula

Tan(angle) = opposite side / adjacent side

In this case:

tan(28°) = AB / BC

We know that BC = 500 m.

So, we can write the equation as:

tan(28°) = AB / 500

To get AB we would have to cross multiply the equation

Now, we can solve for AB:

AB = 500 * tan(28°)

Using a calculator we will have

AB = 500 * 0.5317

AB = 265.85

So, the width of the river (AB) is approximately 265.85 meters.

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In the right triangle JKL, the statement cosL = 24/25 is not true considering the right use of trigonometric ratios.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tanL = 24/7 {opposite/adjacent is a correct statement}

cosL = 24/25 {not a correct statement because cosL = 7/25, adjacent/hypotenuse}

tanJ = 7/24 {opposite/adjacent is a correct statement}

sinJ = 7/25 {opposite/hypotenuse is a correct statement}

Therefore, the statement cosL = 24/25 is not true considering the right use of trigonometric ratios.

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The length of a 45° arc include the following: 3.925 or 5π/4 inches.

In Mathematics and Geometry, if you want to calculate the arc length formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

Where:

By substituting the given parameters into the arc length formula, we have the following;

Arc length = 2 × 3.14 × 5 × 45/360

Arc length = 3.925 or 5π/4 inches.

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To solve for I and Q in this electric circuit, we can use the equations for the charge and current in a series RL circuit with a capacitor:

Q = CV(1 - e^(-t/RC))
I = (E/R)e^(-t/tau) + (Q/R) where tau = L/R

Plugging in the given values, we have:

Q = (100 micro farads)(100 volts)(1 - e^(-t/(20 ohms)(0.05 henry)))
I = (100 volts/20 ohms)e^(-t/(0.05 henry/20 ohms)) + Q/20 ohms

Using the initial conditions Q = 0 and I = 0 at t = 0, we can simplify the equations to:

Q = 100 micro farads * 100 volts * (1 - e^(-t/1 millisecond))
I = (100 volts/20 ohms)e^(-t/1 millisecond)

So at t = 1 millisecond, we have:

Q = 100 micro farads * 100 volts * (1 - e^(-1))
 ≈ 42.36 microcoulombs
I = (100 volts/20 ohms)e^(-1)
 ≈ 1.831 amperes

Therefore, at t = 1 millisecond, the charge on the capacitor is about 42.36 microcoulombs and the current in the circuit is about 1.831 amperes.

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Answer: yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

13. B

14. A

15. D

To determine whether a data set is approximately periodic, we need to look for patterns that repeat over time. If we see a consistent pattern in the data that repeats with some regularity, then we can say that the data set is approximately periodic.

If the data set is approximately periodic, we also need to determine its period and amplitude. The period is the time it takes for the pattern to repeat, while the amplitude is the distance between the highest and lowest points of the pattern.

Without more information about the data set, it's difficult to say for certain whether it's approximately periodic. However, if we assume that it is, we can make some educated guesses about its period and amplitude.

Based on the information given, it's possible that the data set has a period of either 3 or 4, and an amplitude of about 5 or 7.5. It's difficult to be more precise without seeing the data itself.

In summary, the data set may be approximately periodic with a period of either 3 or 4, and an amplitude of about 5 or 7.5. However, without more information, we can't say for certain whether it's truly periodic.
To determine if the data set is approximately periodic, you need to look for repeating patterns in the data. A periodic data set will have a constant period and amplitude throughout.

Period refers to the interval between repetitions, while amplitude is the maximum value of the fluctuation from the average value.

Unfortunately, you didn't provide a specific data set for me to analyze. However, I can provide you with a general explanation of how to identify periodicity and determine the period and amplitude.

1. Observe the data set to see if there are any repeating patterns.
2. If a pattern is present, find the interval between repetitions - this is the period.
3. Determine the difference between the maximum and minimum values in the pattern.
4. Divide this difference by 2 to find the amplitude.

Once you have applied these steps to your data set, you can compare your results to the provided options to find the best match.

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The Fourier series for the original function f(x) is:

f(x) = (1/2) + ∑[n=1,∞] [(4/nπ²) * (1 - (-1)^n) cos(nπx/2) + (4/nπ) * sin(nπ/2) sin(nπx/2)] for x € (-1,1)

To find the Fourier series coefficients for the given function, we need to first determine the period of the function.

Since the function is defined differently for x in the interval (-1,0) and (0,1), we can break down the function into two separate periodic functions, each with its own period.

For the interval (-1,0), the function is a constant function equal to 1. Hence, the period is simply 2.

For the interval (0,1), the function is a linear function given by f(x) = 2 - x. The period of a linear function is always infinite, but we can restrict the domain to a smaller interval to get a periodic function. We can choose the interval (0,2) as the period for this function, since f(x + 2) = 2 - (x + 2) = 2 - x = f(x) for all x in the interval (0,1).

Now, we can write the Fourier series for each of the two periodic functions:

For the function defined on (-1,0), the Fourier series coefficients are given by:

an = (1/2) * ∫[-1,1] f(x) cos(nπx/2) dx

= (1/2) * ∫[-1,0] cos(nπx/2) dx (since f(x) = 1 for x in (-1,0))

= (1/2) * [(2/π) * sin(nπ/2)]

bn = (1/2) * ∫[-1,1] f(x) sin(nπx/2) dx

= (1/2) * ∫[-1,0] sin(nπx/2) dx (since f(x) = 1 for x in (-1,0))

= (1/2) * [(2/π) * (1 - cos(nπ/2))]

For the function defined on (0,1), the Fourier series coefficients are given by:

an = (1/2) * ∫[0,2] f(x) cos(nπx/2) dx

= (1/2) * ∫[0,1] (2 - x) cos(nπx/2) dx

= (1/2) * [(4/nπ²) * (1 - (-1)^n)]

bn = (1/2) * ∫[0,2] f(x) sin(nπx/2) dx

= (1/2) * ∫[0,1] (2 - x) sin(nπx/2) dx

= (1/2) * [(4/nπ) * sin(nπ/2)]

Hence, the Fourier series for the original function f(x) is:

f(x) = (1/2) + ∑[n=1,∞] [(4/nπ²) * (1 - (-1)^n) cos(nπx/2) + (4/nπ) * sin(nπ/2) sin(nπx/2)] for x € (-1,1)

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25. The area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.

29. The area of the region that lies inside both curves is approximately 1.648 square units.

A 3D solid shape called a cylinder is formed by connecting two parallel and identical bases with a curving surface. The shape of the bases is similar to a disc, and the axis of the cylinder runs through the middle or connects the two circular bases.

25. To find the area of the region that lies inside the first curve and outside the second curve, we need to find the points where the two curves intersect, and then integrate the difference in the areas between the two curves from one intersection point to the other.

The two curves are given by:

r² = 8 cos θ   (first curve)

r = 2           (second curve)

To find the intersection points, we substitute r = 2 into the first equation and solve for θ:

2² = 8 cos θ

cos θ = 1/2

θ = ±π/3

So the two curves intersect at θ = π/3 and θ = -π/3. To find the area between the curves, we integrate the difference in the areas between the two curves from θ = -π/3 to θ = π/3:

A = ∫[-π/3,π/3] [(1/2)r² - 2²] dθ

Using the equation r² = 8 cos θ, we can simplify this to:

A = ∫[-π/3,π/3] [(1/2)(8 cos θ) - 4] dθ

A = ∫[-π/3,π/3] (4 cos θ - 4) dθ

A = 4 ∫[-π/3,π/3] (cos θ - 1) dθ

[tex]A = 4 [sin \theta - \theta]_{(-\pi/3)^{(\pi/3)[/tex]

A = 4 [sin(π/3) - π/3 - (sin(-π/3) + π/3)]

A = 4 [√3/2 - 2π/3]

Therefore, the area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.

29. To find the area of the region that lies inside both curves, we need to determine the points where the two curves intersect and then integrate the area enclosed between the curves over the appropriate range of polar angles.

The two curves are given by:

r = 3 cos(θ)  (first curve)

r = sin(θ)    (second curve)

To find the intersection points, we substitute r = 3 cos(θ) into the equation r = sin(θ) and solve for θ:

3 cos(θ) = sin(θ)

tan(θ) = 3

θ = tan⁻¹(3)

The intersection point lies on the first curve when θ = tan⁻¹(3), so we need to integrate the area enclosed between the curves from θ = 0 to θ = tan⁻¹(3).

The area enclosed between the curves at any angle θ is given by the difference in the areas of the circles with radii r = sin(θ) and r = 3 cos(θ). Thus, the area enclosed between the curves is:

A = ∫[0,tan⁻¹(3)] [(1/2)(3 cos(θ))² - (1/2)(sin(θ))²] dθ

Simplifying, we get:

A = ∫[0,tan⁻¹(3)] [9/2 cos²(θ) - 1/2 sin²(θ)] dθ

Using the identity cos(2θ) = cos²(θ) - sin²(θ), we can simplify this to:

A = ∫[0,tan⁻¹(3)] [(9/2)(cos²(θ) - (1/2)) + (1/2)cos²(2θ)] dθ

We can evaluate the first term of the integrand using the identity cos²(θ) = (1 + cos(2θ))/2, and the second term using the identity cos²(2θ) = (1 + cos(4θ))/2:

A = ∫[0,tan⁻¹(3)] [(9/4)(1 + cos(2θ)) - (1/4)(1 + cos(4θ))] dθ

Integrating each term separately, we get:

[tex]A = [(9/4)\theta + (9/8)sin(2\theta) - (1/16)sin(4\theta)]_{0^{(tan^-1(3))[/tex]

Simplifying and evaluating, we get:

A = (9/4)tan⁻¹(3) + (9/8)sin(2tan⁻¹(3)) - (1/16)sin(4tan⁻¹(3))

Using the identity sin(2tan⁻¹(3)) = 6/10 and simplifying, we get:

A = (9/4)tan⁻¹(3) + (27/40) - (3/40)tan⁻¹(3)

Therefore, the area of the region that lies inside both curves is approximately 1.648 square units.

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Answer: answer is 3

Step-by-step explanation:

The number 6.34 repeating is an irrational number because it can be expressed as a fraction of two integers.

The number 6.34 repeating is irrational.

An irrational number cannot be expressed as the ratio of two integers, and it has an infinite number of non-repeating decimal places.

In this case, 6.34 repeating can be expressed as 6.34343434..., where the digits "34" repeat infinitely.

This cannot be expressed as a ratio of two integers because there is no repeating pattern that can be represented by a fraction.

Therefore, 6.34 repeating is irrational.

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The correct SOR formula for the boundary condition Y'(0) = 1 is:

OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)

To derive the correct SOR formula for the boundary condition Y'(0) = 1, we start with the standard SOR formula:

OYᵢ = (1 - ω)Yᵢ + (ω/4)(Yᵢ₊₁ + Yᵢ₋₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²fᵢ)

where i and j are indices corresponding to the discrete coordinates in the x and y directions, ω is the relaxation parameter, and ∆ is the grid spacing in both directions.

To incorporate the boundary condition Y'(0) = 1, we use a forward difference approximation for the derivative:

Y'(0) ≈ (Y₁ - Y₀) / ∆

Substituting this into the original equation gives:

(Y₁ - Y₀) / ∆ = 1

Solving for Y₀ gives:

Y₀ = Y₁ - ∆

Now we can use this expression for Y₀ to modify the SOR formula at i = 1:

OY₁ = (1 - ω)Y₁ + (ω/4)(Y₂ + Y₀ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²f₁)

Substituting the expression for Y₀, we get:

OY₁ = (1 - ω)Y₁ + (ω/4)(Y₂ + Y₁ - ∆ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²f₁)

Simplifying:

OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)

So the correct SOR formula for the boundary condition Y'(0) = 1 is:

OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)

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The value of component form and the magnitude of the vector v is,

v = √52

We have to given that;

Two points on the graph are, (3, 5) and (- 1, - 1)

Hence, We can formulate value of component form and the magnitude of the vector v is,

v = √ (x₂ - x₁)² + (y₂ - y₁)²

v = √(- 1 - 3)² + (- 1 - 5)²

v = √16 + 36

v = √52

Thus, The value of component form and the magnitude of the vector v is,

v = √52

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All of the above are statistics

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

4)

We have,

James Lyne mentions that there are:

- 30,000 new infected websites every day

- 8 new internet users join every second

- 250,000 new pieces of malware appear every day.

All the above are statistics.

2)
E-commerce is generally more specialized and requires a more integrated approach to supply chain management. Additionally, traditional SCM is based on manufacturing, whereas e-commerce is mostly retail distribution.

Finally, traditional SCM usually doesn't include e-procurement functions, which are essential for e-commerce supply chain management.

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

Thus,

All of the above are statistics

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

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Answer:

b = 12 Km

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

b² + 16² = 20²

b² + 256 = 400 ( subtract 256 from both sides )

b² = 144 ( take square root of both sides )

b = [tex]\sqrt{144}[/tex] = 12

For part (c)(ii), we need to explain why the theorem in (b) does not apply to g(z).

The theorem in (b) states that for any polynomial with real coefficients, if zo € C is a root, then zo is also a root. However, g(z) = z^2 - 2z does not have real coefficients, as the coefficient of the z term is -2, which is not a real number.

Therefore, we cannot apply the theorem in (b) to g(z) since it does not satisfy the condition of having real coefficients. However, we can still find the roots of g(z) and show that they satisfy the conclusion of the theorem in (b) if we consider g(z) as a polynomial with complex coefficients.

To find the roots of g(z), we set g(z) equal to zero and solve for z:

z^2 - 2z = 0

z(z - 2) = 0

So the roots of g(z) are z = 0 and z = 2.

If we consider g(z) as a polynomial with complex coefficients, then we can apply the theorem in (b) and conclude that if z = 0 or z = 2 is a root of g(z), then it is also a root of g(z) with real coefficients. However, we cannot apply the theorem in (b) to g(z) directly since it does not have real coefficients.

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Answer:

The answer would be D. [tex]\frac{5\sqrt{11} }{11}[/tex]

If we follow Kaizen's principle and improve by 1% each day, we can get approximately 37.78 times better in a year.

If we follow Kaizen's principle of improving by 1% each day, we can calculate how much better we will get in a year by using the formula:

Final Value = Initial Value x (1 + Daily Improvement Percentage)^Number of Days

Since we are trying to calculate how much better we can get in a year, we can plug in the following values:

Initial Value = 1 (assuming we are starting from our current level of performance)

Daily Improvement Percentage = 0.01 (since we are trying to improve by 1% each day)

Number of Days = 365 (since there are 365 days in a year)

Using these values, we get:

Final Value = 1 x (1 + 0.01)³⁶⁵

Final Value ≈ 1 x 37.78

Final Value ≈ 37.78

This shows the power of continuous improvement and the importance of consistent effort towards our goals.

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William is currently 15 years old.

Let's start by using algebra to solve for the ages of Jade and Kevin now. Let J be Jade's current age and K be Kevin's current age. We have:

J = 2K - 6 (Jade is 6 years less than twice Kevin's age)

J - 2 = 3(K - 2) (two years ago, Jade was three times as old as Kevin)

We can use the first equation to substitute for J in the second equation:

(2K - 6) - 2 = 3(K - 2)

Simplifying this, we get:

2K - 8 = 3K - 6

K = 2

So Kevin is currently 2 years old, and Jade is:

J = 2K - 6 = 2(2) - 6 = -2

This doesn't make sense as an age, so there may be an error in the problem statement or in our solution method.

Let's use algebra to solve for Amanda's current age, which we can call A. Then we can use that to find her age 3 years from now. We have:

L = 3A - 2 (Len is 2 less than 3 times Amanda's age)

L + 3 = 2(A + 3) + 7 (three years from now, Len will be 7 more than twice Amanda's age)

Substituting the first equation into the second, we get:

(3A - 2) + 3 = 2(A + 3) + 7

Simplifying this, we get:

A = 5

So Amanda is currently 5 years old, and her age 3 years from now will be:

A + 3 = 5 + 3 = 8

Let's use algebra to solve for Faith's current age, which we can call F. Then we can use that to find Janna's and William's ages. We have:

J = 2F (Janna is twice as old as Faith)

W = F + 9 (William is 9 years older than Faith)

J - 3 = 3(F - 3) - 9 (three years ago, Janna was 9 less than 3 times Faith's age)

Substituting the first two equations into the third, we get:

(2F) - 3 = 3(F - 3) - 9

Simplifying this, we get:

F = 6

So Faith is currently 6 years old, Janna is:

J = 2F = 2(6) = 12

and William is:

W = F + 9 = 6 + 9 = 15

Therefore, William is currently 15 years old.

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Answer:

z = -95

Step-by-step explanation:

You simplify both sides of the equation, then isolate the variable.

The joint probability mass function of X and Y, E[X|Y=1] = 2, E[X|Y=2] = 5/2, and E[X|Y=3] = 8/3.If it is true for all values of x and y, then X and Y are independent. Otherwise, they are dependent.

To compute E[X|Y=i], we need to use the formula:

[tex]E[X|Y=i] = ∑ x*xp(x|Y=i) / P(Y=i)[/tex]

where xp(x|Y=i) is the conditional probability of X given Y=i, and P(Y=i) is the marginal probability of Y=i.

Using Bayes' theorem, we can compute the conditional probabilities xp(x|Y=i) as follows: xp(1|Y=1) = P(X=1,Y=1) / P(Y=1) = (1/9) / (1/9 + 1/3 + 1/9) = 1/3. xp(2|Y=1) = P(X=2,Y=1) / P(Y=1) = (1/3) / (1/9 + 1/3 + 1/9) = 1/3. xp(3|Y=1) = P(X=3,Y=1) / P(Y=1) = (1/9) / (1/9 + 1/3 + 1/9) = 1/3. xp(1|Y=2) = P(X=1,Y=2) / P(Y=2) = (1/9) / (1/9 + 0 + 1/18) = 2/3. xp(2|Y=2) = P(X=2,Y=2) / P(Y=2) = 0 / (1/9 + 0 + 1/18) = 0

xp(3|Y=2) = P(X=3,Y=2) / P(Y=2) = (1/18) / (1/9 + 0 + 1/18) = 1/2. xp(1|Y=3) = P(X=1,Y=3) / P(Y=3) = 0 / (1/9 + 1/6 + 1/9) = 0. xp(2|Y=3) = P(X=2,Y=3) / P(Y=3) = (1/18) / (1/9 + 1/6 + 1/9) = 1/3. xp(3|Y=3) = P(X=3,Y=3) / P(Y=3) = (1/9) / (1/9 + 1/6 +1/9) = 2/3

Using these conditional probabilities, we can compute the conditional expectations E[X|Y=i] as follows: E[X|Y=1] =

[tex]1*(1/3) + 2*(1/3) + 3*(1/3)[/tex]

= 2

E[X|Y=2] =

[tex]1*(2/3) + 20 + 3(1/2) = 5/2 E[X|Y=3][/tex]

=

[tex]10 + 2(1/3) + 3*(2/3) = 8/3[/tex]

To determine if X and Y are independent, we need to check if the joint probability mass function can be factored into the product of the marginal probability mass functions: p(x,y) = p(x) * p(y)

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The data provide convincing evidence that the pediatrician's claim is true

To test the pediatrician's claim that the mean weight of one-year-old boys is greater than 22 pounds, we can use a one-sample t-test.

Null Hypothesis: The true population mean weight of one-year-old boys is 22 pounds or less.

Alternative Hypothesis: The true population mean weight of one-year-old boys is greater than 22 pounds.

We can use a level of significance of 0.05, which corresponds to a 95% confidence level.

The test statistic for this one-sample t-test is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Substituting the given values:

t = (23.5 - 22) / (2.8 / sqrt(315)) = 10.15

Using a t-distribution table with 314 degrees of freedom (n-1), we find that the critical value for a one-tailed test at the 0.05 level of significance is 1.646.

Since the calculated t-value (10.15) is greater than the critical value (1.646), we reject the null hypothesis.

Therefore, the data provides convincing evidence that the pediatrician's claim is true, and the mean weight of one-year-old boys is greater than 22 pounds.

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