Consider the function g(x)=^3√x+2

Which ordered pair lies on the inverse of the function?
(−1,−3)
(−4,−1)
(3, 1)
(0,−1)

The correct description for the given data representing the distances covered by a particle (micro-millimeters) is Symmetric-bell.  A normal distribution is characterized by a symmetrical, bell-shaped graph.

Here's the solution to the question provided:

Given data:

2, 2, 2, 2, 2, 1.5, 1.5, 1.5, 3, 3, 4, 5.

The given data does not have any specific structure; thus, it cannot be a boxplot, and there are no meaningful conclusions that can be drawn from it.

On the other hand, when we create a histogram of the given data, it is a symmetric bell shape. Hence, the correct description for the given data representing the distances covered by a particle (micro-millimeters) is Symmetric-bell. A symmetric bell-shaped histogram is used to describe data with a normal distribution. A normal distribution is characterized by a symmetrical, bell-shaped graph.

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According to the information provided by the graph, it can be inferred that in town A there is a lower percentage (20%) than the national percentage of bicycles with off-road wheels, while in town B the percentage is higher (45%).

To calculate the percentage of bicycles with off-road wheels in each town, we must perform the following mathematical operation.

First we must add the number of bicycles of each type to know the total number of bicycles in the town:

Now we must calculate what percentage is equivalent to 3 bicycles with off-road wheels from town A and what percentage is equivalent to 9 bicycles with off-road wheels from town B.

15 ÷ 100 = 0.15

0.15 × 20 = 3

So, 3 bicycles with off-road wheels from town A are equivalent to 20% of the total number of bicycles.

Then the 9 bicycles with off-road wheels in town B are equivalent to 45% of the total number of bicycles.

According to the above, 20% of the bicycles in town A have off-road wheels, while 45% of the bicycles in town B have off-road wheels.

Note: This question is incomplete because there are some missing information. Here is the missing information.

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Answer:

One solution

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

4x + 3 = -5x + 21

4x + 5x = 21 - 3

9x = 18

Divide both sides by 9

9x / 9 = 18 / 9

x = 2

Hope it helps.

Answer: cookbook $40 and science $15

Step-by-step explanation:

Answer:

Cookbook: 40$ and Science: 15$

Step-by-step explanation:

Guess!

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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The variable associated with the interior and exterior angles in the triangle is equal to 56.

The value of the exterior angle is equal to 116°.

This question presents the case of a geometric system formed by a triangle and a semirray that includes two interior angles and a exterior angle. Please notice that the sum of the measures of interior angles in a triangle equals 180° and the sum of two supplementary angles equals 180°.

First, derive the equation of the missing interior angles in triangle PQR:

m ∠ R = 180° - 60° - x

m ∠ R = 120° - x

Second, obtain the equation for the two supplementary angles:

(120° - x) + (2 · x + 4°) = 180°

124° + x = 180°

x = 56

Third, determine the value of the exterior angle:

θ = 2 · x + 4

θ = 2 · 56 + 4

θ = 116°

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Given: A continuous uniform distribution over the interval [1.8, 5.4].To find:(a) Mean of X.(b) Variance of X.(c) P(X < 3.4)

The following formula is used to determine the mean of X when its continuous uniform distribution falls within the range [a, b]. And X's variance is given by 2 = (b - a)2/12.

Part (a): Mean of X The given interval is [1.8, 5.4].So, a = 1.8 and b = 5.4By using the above formula of mean,μ = (a + b)/2μ = (1.8 + 5.4)/2μ = 3.6Hence, the mean of X is 3.6.

Part (b): Variance of X By using the formula of variance,σ² = (b - a)²/12σ² = (5.4 - 1.8)²/12σ² = (3.6)²/12σ² = 12.96/12σ² = 1.08Hence, the variance of X is 1.08.

Part (c): P(X < 3.4)We have to find P(X < 3.4)The given distribution is a continuous uniform distribution over the interval [1.8, 5.4].The probability density function for this is,f(x) = 1/(5.4 - 1.8)f(x) = 1/3.6We have to find P(X < 3.4) = P(1.8 ≤ X ≤ 3.4)

From the probability density function,f(x) = 1/3.6And we know that, P(a ≤ X ≤ b) = ∫[a,b] f(x) dxBy using this, we get,P(1.8 ≤ X ≤ 3.4) = ∫[1.8, 3.4] 1/3.6 dxP(1.8 ≤ X ≤ 3.4) = [x/3.6]1.8³.⁶ - 1.8P(1.8 ≤ X ≤ 3.4) = [3.4/3.6] - [1.8/3.6]P(1.8 ≤ X ≤ 3.4) = 0.56 - 0.50P(1.8 ≤ X ≤ 3.4) = 0.06. Hence, P(X < 3.4) = 0.06.  

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Answer:

Step-by-step explanation:

2/5r=2/3 : multiply both sides by the reciprocal of 2/5 (5/2)

(5/2)(2/5)r=(2/3)(5/2) : 5/2 and 2/5 cancel out, leaving r

r=(2/3)(5/2) : cancel 2

r= 5/3

The Fourier transform of the periodic signal is (1/2j) * [(1/(j(2π - ω))) * \(e^{j(2\pi -w)t+j\pi /4}\) - (1/(j(2π + ω))) * \(e^{j(2\pi+w)t-j\pi /4}\)] + C.

To determine the Fourier transform of the periodic signal sin(2πt - π/4), we can use the properties and formulas of Fourier transforms.

The Fourier transform of a periodic signal is represented by a series of discrete frequency components. In this case, the signal is periodic with a fundamental period of T = 1/f, where f is the frequency. Since the signal is in the form of sin(2πt - π/4), the frequency can be identified as f = 1/2π.

The Fourier transform of sin(2πt - π/4) can be calculated using the formula:

F(ω) = ∫[f(t) * \(e^{-jwt}\)] dt,

where F(ω) is the Fourier transform of the signal, ω is the angular frequency, f(t) is the periodic signal, and j is the imaginary unit.

Substituting the given signal sin(2πt - π/4) into the formula, we have:

F(ω) = ∫[sin(2πt - π/4) * \(e^{-jwt}\)] dt.

To solve this integral, we can apply Euler's formula to rewrite the sine function in terms of complex exponentials:

sin(2πt - π/4) = (1/2j) * [\(e^{j(2\pi t-\pi /4)}\) - \(e^{-j(2\pi t-\pi /4)}\)].

Now, we can substitute this expression into the integral:

F(ω) = ∫[(1/2j) * [\(e^{j(2\pi t-\pi /4)}\) - \(e^{-j(2\pi t-\pi /4)}\)] * \(e^{-jwt}\)] dt.

Simplifying the expression inside the integral, we have:

F(ω) = (1/2j) * ∫[\(e^{j(2\pi t-\pi /4)-jwt}\) - \(e^{-j(2\pi t-\pi /4)+jwt}\)] dt.

Expanding the exponentials and combining terms, we get:

F(ω) = (1/2j) * ∫[\(e^{j(2\pi-w)t+j\pi /4}\) - \(e^{j(2\pi+w)t-j\pi /4}\)] dt.

Now, we can integrate each term separately:

F(ω) = (1/2j) * [(1/(j(2π - ω))) * \(e^{j(2\pi -w)t+j\pi /4}\) - (1/(j(2π + ω))) * \(e^{j(2\pi+w)t-j\pi /4}\)] + C,

where C is the constant of integration.

This expression represents the Fourier transform of the periodic signal sin(2πt - π/4).

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Answer:

30.4%

Step-by-step explanation:

Given data

originally price $457

new price= $318

Required

The percent mark down

Percent markdown= original- new/original*100

substitute

Percent markdown= 457- 318/457*100

Percent markdown= 139/457*100

Percent markdown=0.304*100

Percent markdown=30.4%

Hence the price was reduced by 30.4%

Answer:

This is a function. Use y=mx+b equation

Step-by-step explanation:

To find the x and y values, simply plug in 0.98 to m. For every pound of peaches, you pay $0.98. The equation would be y=0.98x, where x is the number of pounds of peaches and y is the total cost.

Step-by-step explanation:

If we use both hoses, we fill the pool at 40 + 60 = 100 gallons per hour.

The volume of the pool is 60 * 300 = 45 * 400 = 18,000 gallons.

Hence, we need 18,000 / 100 = 180 hours.

The sequence {S_n^2 - T_n^2 : n = 1, 2, ...} satisfies the adaptedness, bounded increments, and martingale property, making it a martingale.

To show that the sequence {S_n^2 - T_n^2 : n = 1, 2, ...} is a martingale, we need to demonstrate three properties: the sequence is adapted, it has bounded increments, and it satisfies the martingale property.

1. Adaptedness:

For a sequence to be adapted, each term in the sequence should be measurable with respect to the information available at that time. In this case, since the random variables X_1, X_2, ..., X_n are independent, their sum S_n = X_1 + X_2 + ... + X_n is measurable with respect to X_1, X_2, ..., X_n. Therefore, S_n^2 is also measurable with respect to X_1, X_2, ..., X_n. Similarly, T_n^2 = σ_1^2 + σ_2^2 + ... + σ_n^2 is a constant and hence measurable. Therefore, S_n^2 - T_n^2 is measurable with respect to X_1, X_2, ..., X_n, making the sequence adapted.

2. Bounded Increments:

To show that the increments of the sequence are bounded, we need to demonstrate that the absolute difference between consecutive terms is bounded. Let's consider two consecutive terms, (S_n+1^2 - T_n+1^2) - (S_n^2 - T_n^2). Simplifying this expression, we get (S_n+1^2 - S_n^2) - (T_n+1^2 - T_n^2).

The difference in the sum of squares is (S_n+1^2 - S_n^2) = (X_n+1 + S_n)^2 - S_n^2 = X_n+1^2 + 2X_n+1S_n. Since the sequence X_1, X_2, ... is a sequence of independent random variables, the terms X_n+1 and S_n are independent. As a result, the expected value of their product is zero, E(X_n+1S_n) = 0. Therefore, the difference (S_n+1^2 - S_n^2) has a zero mean.

The difference in the variances is (T_n+1^2 - T_n^2) = σ_n+1^2 - σ_n^2. The variances σ_n+1^2 and σ_n^2 are constants, and their difference is also a constant. Therefore, the difference (T_n+1^2 - T_n^2) has a zero mean.

Since both differences have zero means, the absolute difference between consecutive terms is bounded, satisfying the bounded increments property.

3. Martingale Property:

To show that the sequence satisfies the martingale property, we need to demonstrate that for any n, the conditional expectation of the next term given the information up to time n is equal to the current term. In other words, E[S_n+1^2 - T_n+1^2 | X_1, X_2, ..., X_n] = S_n^2 - T_n^2.

Expanding the left-hand side of the equation, we have:

E[S_n+1^2 - T_n+1^2 | X_1, X_2, ..., X_n] = E[(S_n + X_n+1)^2 - (T_n + σ_n+1)^2 | X_1, X_2, ..., X_n].

Simplifying further, we get:

E[(S_n^2 + 2X_n+1S_n + X_n+1^2

) - (T_n^2 + 2σ_n+1T_n + σ_n+1^2) | X_1, X_2, ..., X_n].

= (S_n^2 - T_n^2) + 2S_nE[X_n+1 | X_1, X_2, ..., X_n] - 2T_nE[σ_n+1 | X_1, X_2, ..., X_n] + E[X_n+1^2] - E[σ_n+1^2].

Since the random variables X_1, X_2, ..., X_n have zero mean, E[X_n+1 | X_1, X_2, ..., X_n] = 0. Similarly, E[σ_n+1 | X_1, X_2, ..., X_n] = 0, as the variances σ_1^2, σ_2^2, ..., σ_n^2 are constants. Therefore, the above expression simplifies to:

(S_n^2 - T_n^2) + E[X_n+1^2] - E[σ_n+1^2].

Since the random variables X_n+1 and σ_n+1^2 are independent of X_1, X_2, ..., X_n, their expectations do not depend on X_1, X_2, ..., X_n. Hence, E[X_n+1^2] - E[σ_n+1^2] = 0.

Therefore, we have shown that E[S_n+1^2 - T_n+1^2 | X_1, X_2, ..., X_n] = S_n^2 - T_n^2, satisfying the martingale property.

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The required probability that the hand is a full house is; 0.00144 or 0.144%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Consider the provided information we have Five cards are drawn from an ordinary deck of 52 playing cards.

Thus full house is a hand that consists of two of one kind and three of another kind.

The total number of ways to draw 5 cards are 78 was.

Now we want two of one kind and three of another.

Therefore, the hand has the pattern AAABB, where A and B are from distinct kinds. The number of such hands are:

3744/25989611

= 0.00144

Hence, the required probability is 0.00144 or 0.144%.

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If x = M/10^t, where M is an integer not divisible by 10, then x has a terminating decimal representation.

To prove this, let's consider the fraction x = M/10^t, where M is an integer not divisible by 10 and t is a positive integer.

The decimal representation of x is obtained by dividing M by 10^t. Since M is not divisible by 10, it means that the prime factorization of M does not contain any factors of 2 or 5.

We can express 10^t as 2^t * 5^t. Since the prime factorization of M does not include any factors of 2 or 5, when we divide M by 10^t, all the factors of 2 and 5 will cancel out in the denominator.

For example, let's consider x = 37/10^3:

x = 37/(2^3 * 5^3)

x = 37/(8 * 125)

x = 37/1000

Here, we can see that all the factors of 2 and 5 have canceled out in the denominator. Therefore, the decimal representation of x will terminate, as there are no recurring digits.

If x = M/10^t, where M is an integer not divisible by 10, then x will have a terminating decimal representation. This is because the prime factorization of M does not contain any factors of 2 or 5, resulting in the cancellation of these factors in the denominator when dividing by 10^t. As a result, there are no recurring digits, and the decimal representation of x will terminate.

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Answer:

2 balloons.

Step-by-step explanation:

6x = 430

x = 71.6

He has to buy 72 packs, there will be:

72 * 6 = 432 - 430 = 2 balloons left.

Answer:

45/10, 4 3/5, 19/4

Step-by-step explanation:

19/4 = 4.75

45/10 = 4.5

4 3/5 = 23/5 = 4.6

4.75 > 4.6 > 4.5

Best of Luck!

Answer:

19/4, 4 3/5, 45/10

Step-by-step explanation:

first you have to divide the fractions TIBO (top in bottom out)

then once you divide them you should get

4 1/2 or 4 5/10 (45/10)

4 3/5 and

4 3/4 (19/4)

since 3/4 is more than half and 3/5 is more than half (2.5 is half of five) but is less than 3/4 is should be 19/4, 4 3/5, 45/10

PLEASE tell me if this is any shape or form helpful to you :)

if not i'm sorry :(

Answer:

2

Step-by-step explanation:

next two the = there are 2 ys

Answer:

Only 1

Step-by-step explanation:

It does not have the same slope thus meaning its not it does not have infinite or no solution, which leaves out 1 solution

Tripling the linear size of an object multiplies its area by a factor of nine.

When the linear size of an object is tripled, the area of the object is multiplied by 9.

This can be understood by considering the relationship between the linear size and the area of an object. If we assume that the object has a regular shape and the linear size refers to the length of its sides, then the area is directly proportional to the square of the linear size.

Let's denote the initial linear size of the object as L and the initial area as A. When the linear size is tripled, it becomes 3L. According to the square proportionality, the new area (A') can be expressed as:

A' = (3L)^2

A' = 9L^2

Comparing A' with the initial area A, we can see that A' is 9 times larger than A. Therefore, tripling the linear size of an object multiplies its area by 9.

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The formula to calculate the standard deviation (σ) of a binomial distribution is σ = √[n * p * (1 - p)] where n is the number of trials and p is the probability of success in each trial.

Substituting the given values, we get:

σ = √[10 * 0.70 * (1 - 0.70)]

σ = √[10 * 0.70 * 0.30]

σ = √2.1

σ ≈ 1.45

Therefore, the standard deviation of the binomial distribution with n = 10 and p = 0.70 is approximately 1.45.

Hence, the answer is 1.45.

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Answer:

  A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

  A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

  A.3: ∠2 ≅ ∠3

  B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

  B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

  see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

__

Left

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

  ∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

  ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

Center

  ∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

  ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

Right

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

  ∠2 ≅ ∠3

__

Left

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

  ∠ACD ≅ ∠CAB (30°)

  ∠CDA ≅ ∠ABC (90°)

  ∠DAC ≅ ∠BCA (60°)

Right

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

  ∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

  ∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

Additional comment

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

  a ≅ b ≅ c   ⇒   (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

  a ≅ b ≅ c ≅ d   ⇒   (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

The required solution of the given numeral are,
(A) 10⁴ bottles contain 4500 ounces of eye drops. Opion A is correct.
(B) Decimal point moves 4 places to the right. Option D is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
(a)
A bottle of eye drops has 0.45 fluid ounces of liquid.
Now, 10⁴ bottles of eye drops have,
= 10⁴ × 0.45 = 4500 ounces of eye drops.

(b)
When 10⁴ multiplied by 0.45, the decimal located former of 4 will shift itself after 4 digits right so the answer will be 4500.

Thus, Solutions of the given numeral has been given above.

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Thus, the object travels a distance of 10π units along the given trajectory.

To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for arc length is given by:

L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt

where L is the arc length, a and b are the start and end points of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.

In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:

dx/dt = -20 sin 2t
dy/dt = 20 cos 2t

Substituting these values into the formula for arc length, we get:

L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt
 = ∫_0^(π/2) √400 dt
 = ∫_0^(π/2) 20 dt
 = 20t |_0^(π/2)
 = 10π

Therefore, the object travels a distance of 10π units along the given trajectory.

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a) f(x) is a probability mass function.

b) P(X < 0.5 or X > 2) = P(X = 0) + P(X = 3) = 2/8 + 1/8 = 3/8

c) The cumulative distribution function of X is CDF(x) = [1/4, 5/8, 7/8, 1]

d) The mean of X is 5/4 and the variance of X is 11/16.

(a) To verify that f(x) is a probability mass function (PMF), we need to ensure that the probabilities sum up to 1 and that each probability is non-negative.

Let's check:

f(x) = [2/8, 3/8, 2/8, 1/8]

Sum of probabilities = 2/8 + 3/8 + 2/8 + 1/8 = 8/8 = 1

The sum of probabilities is equal to 1, which satisfies the requirement for a valid PMF.

Each probability is also non-negative, as all the values in f(x) are fractions and none of them are negative.

Therefore, f(x) is a probability mass function.

(b) To calculate the probabilities:

P(X < 1) = P(X = 0) = 2/8 = 1/4

P(X = 1) = 3/8

P(X < 0.5 or X > 2) = P(X = 0) + P(X = 3) = 2/8 + 1/8 = 3/8

(c) The cumulative distribution function (CDF) gives the probability that X takes on a value less than or equal to a given value. Let's calculate the CDF for X:

CDF(X ≤ 0) = P(X = 0) = 2/8 = 1/4

CDF(X ≤ 1) = P(X ≤ 0) + P(X = 1) = 1/4 + 3/8 = 5/8

CDF(X ≤ 2) = P(X ≤ 1) + P(X = 2) = 5/8 + 2/8 = 7/8

CDF(X ≤ 3) = P(X ≤ 2) + P(X = 3) = 7/8 + 1/8 = 1

The cumulative distribution function of X is:

CDF(x) = [1/4, 5/8, 7/8, 1]

(d) To compute the mean and variance of X, we'll use the following formulas:

Mean (μ) = Σ(x * P(x))

Variance (σ^2) = Σ((x - μ)^2 * P(x))

Calculating the mean:

Mean (μ) = 0 * 2/8 + 1 * 3/8 + 2 * 2/8 + 3 * 1/8 = 0 + 3/8 + 4/8 + 3/8 = 10/8 = 5/4

Calculating the variance:

Variance (σ^2) = (0 - 5/4)^2 * 2/8 + (1 - 5/4)^2 * 3/8 + (2 - 5/4)^2 * 2/8 + (3 - 5/4)^2 * 1/8

Simplifying the calculation:

Variance (σ^2) = (25/16) * 2/8 + (9/16) * 3/8 + (1/16) * 2/8 + (9/16) * 1/8

= 50/128 + 27/128 + 2/128 + 9/128

= 88/128

= 11/16

Therefore, the mean of X is 5/4 and the variance of X is 11/16.

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Answer:

0.7890176%

Step-by-step explanation:

First, there is a 64% chance of failing a test.

Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces. You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.

Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%

Now we need to multiply each chance of something happening by one another

64% × 7.4% = 0.04736%

4.736% × 16.66% = 0.7890176%

So there is a 0.7890176% of all of these happening

The probability that you will fail a test, draw a red ace, and then roll a 6 is  0.7890176%

We have given that,

First, there is a 64% chance of failing a test.

We have to determine the probability

Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces.

You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.

Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%

Now we need to multiply each chance of something happening by one another

64% × 7.4% = 0.04736%

4.736% × 16.66% = 0.7890176%

So there is a 0.7890176% of all of these happening

Therefore the probability that you will fail a test, draw a red ace, and then roll a 6 is  0.7890176%.

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Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.

Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.

As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and  it is given by the formula

\(\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\)

where the value of the α is expressed as,

\(\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}\)

Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,

\(\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42\)

Further, the critical probability, assuming a confidence level of 58% is,

\(\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79\)

Hence, the critical probability is 0.79.

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Answer:

y = 12 + 0.5m

Step-by-step explanation:

y represents the total weight

We know an object weighs 12 pounds in original

And increase by 0.5 pounds per month m.

So, the equation is y = 12 + 0.5m

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The average effect size of each gene on the trait would be 17.6 / 100 = 0.176 grams, and the minimum number of genes affecting this trait would be estimated as 2.47.

To estimate the minimum number of genes affecting this trait, we can use Falconer's formula:

Vg = (n/2) * (1/n) * (π * a)^2,

where:

Vg is the genotypic variance

n is the number of genes affecting the trait

a is the average effect size of a single gene on the trait

We can rearrange this formula to solve for n:

n = 2 * Vg / (π * a)^2

Given that Vg = 0.88, and the difference in mean phenotype between the two strains is 17.6 grams, we can estimate a as follows:

a = 17.6 / (number of genes affecting the trait)

Substituting a in the formula for n, we get:

n = 2 * Vg / (π * (17.6/n))^2

Simplifying this expression, we get:

n = 2 * 0.88 / (π * (17.6/n))^2

n = 0.5 / (π^2 * (17.6/n)^2)

We can now use trial and error or iterative methods to solve for n. For example, we can plug in different values of n until we find a value that satisfies the equation.

Let's try n = 100:

n = 0.5 / (π^2 * (17.6/100)^2)

n = 0.5 / (3.1416^2 * 0.176^2)

n = 2.47

This means that if 100 genes were involved, the average effect size of each gene on the trait would be 17.6 / 100 = 0.176 grams, and the minimum number of genes affecting this trait would be estimated as 2.47. However, this is just an estimate and the actual number of genes affecting the trait may be different.

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