A bag contains 24 green marbles, 22 blue marbles, 14 yellow marbles, and 12 red marbles. Suppose you pick one marble at random. What is each probability? P( not blue )

The sum of the radical expression [tex]\sqrt{x^2y^3} + 2\sqrt{x^3y^4} +xy\sqrt y[/tex] is [tex]2xy\sqrt{y} + 2x^2y^2\sqrt{x}[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\sqrt{x^2y^3} + 2\sqrt{x^3y^4} +xy\sqrt y[/tex]

Evaluate the exponents

So, we have

[tex]xy\sqrt{y} + 2x^2y^2\sqrt{x} +xy\sqrt y[/tex]

Add the like terms

[tex]2xy\sqrt{y} + 2x^2y^2\sqrt{x}[/tex]

Hence, the sum of the radical expressions is [tex]2xy\sqrt{y} + 2x^2y^2\sqrt{x}[/tex]

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To guarantee that at least 20 rolls result in the same number on the top face of a six-sided die, one would need to roll the die at least 25 times. to solve the problem we need to consider the worst-case scenario. In this case, we want to find the fewest number of rolls necessary to ensure that at least 20 rolls result in the same number.

Let's consider the scenario where we roll the die and get a different number on each roll. In the worst-case scenario, each new roll will result in a different number until we have rolled all six possible numbers.
To guarantee that we have at least 20 rolls of the same number, we need to exhaust all possibilities for the other five numbers before repeating any number. This means we need to roll the die 6 times to ensure that we have covered all six numbers.
After these 6 rolls, we have exhausted all possibilities for one number. Now, we can start repeating that number. Since we want to have at least 20 rolls of the same number, we need to roll the die 19 more times to reach a total of 20 rolls of the same number.
Therefore, the fewest number of rolls necessary to guarantee that at least 20 rolls result in the same number on the top face of the die is 6 (to cover all possible numbers) + 19 (to reach 20 rolls of the same number) = 25 rolls.
In summary, to guarantee at least 20 rolls of the same number on the top face of a six-sided die, you would need to roll the die at least 25 times.

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Step-by-step explanation:

[tex]18^{10}\approx3.57*10^{12}[/tex]

Answer:

3.57

Step-by-step explanation:

3.570467 a bit longer if needed

The solution to the inequality [tex]6x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1[/tex] ≥ 0 is satisfied for all real numbers.

The transitive property of inequality states that for any real numbers a, b, c, If a ≤ b and b ≤ c, then a ≤ c.

If either of the premises is a strict inequality, then the conclusion is a strict inequality.

If a ≤ b and b < c, then a < c.

To determine the solution to the inequality [tex]x^6 - 6x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1[/tex]≥ 0,

we can analyze the factors and their signs.

The expression  [tex]x^6 - 6x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1[/tex] can be factored as follows:

Now, we can examine the sign of each factor to determine when the expression is greater than or equal to zero:

1. [tex](x - 1)^6[/tex]: This factor is always non-negative or zero for all real values of x.

Since the entire expression is the power of (x - 1), the inequality [tex]6x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1[/tex] ≥ 0 is satisfied for all real numbers.

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The result of the recurrence: an=9a n−1 for n≥2 with the initial condition a1=−6. an=  -6 × (-9)n-1

There is the recurrence relation: an = 9an - 1 with the initial condition a1 = -6. The task is to find the solution to the recurrence relation. Let's use the backward substitution method to solve the recurrence relation. In the backward substitution method, we start from the value of an and use the relation an = 9an - 1 to calculate an - 1, then use an - 1 = 9an - 2 to calculate an - 2, and so on until we reach the given initial value.

Here, a1 = -6, so we can start with a2. Using the relation an = 9an - 1, we get:

a2 = 9a1 = 9(-6) = -54

Using the relation an = 9 an - 1, we get:

a3 = 9a2 = 9(-54) = -486

Using the relation an = 9an - 1, we get:

a4 = 9a3 = 9(-486) = -4374

Similarly, we can calculate a5:

a5 = 9a4 = 9(-4374 ) = -39366

So, the result of the recurrence relation with the initial condition a1 = -6 is:

an = -6 × (-9)n-1

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(a) If Leo builds five standard and three deluxe models, he has 56 different choices in positioning the eight houses.
(b) If Leo builds two deluxe and six standard models, he has 28 different positionings.

To determine the number of different choices Leo has in positioning the eight houses, let's consider the two scenarios separately:

(a) If Leo decides to build five standard and three deluxe models, we can calculate the number of different choices using combinations.

For the standard models, Leo has to choose 5 out of the 8 positions for them. This can be calculated using the combination formula: C(8, 5) = 8! / (5! * (8-5)!) = 56.

Similarly, for the deluxe models, Leo has to choose 3 out of the remaining 3 positions. This can be calculated using the combination formula: C(3, 3) = 1.

To find the total number of choices, we multiply the number of choices for the standard models and the deluxe models: 56 * 1 = 56.

Therefore, Leo has 56 different choices in positioning the eight houses if he decides to build five standard and three deluxe models.

(b) If Leo builds two deluxe and six standard models, we can use a similar approach to calculate the number of different positionings.

For the deluxe models, Leo has to choose 2 out of the 8 positions. This can be calculated using the combination formula: C(8, 2) = 8! / (2! * (8-2)!) = 28.

For the standard models, Leo has to choose 6 out of the remaining 6 positions. This can be calculated using the combination formula: C(6, 6) = 1.

To find the total number of choices, we multiply the number of choices for the deluxe models and the standard models: 28 * 1 = 28.

Therefore, Leo has 28 different positionings if he builds two deluxe and six standard models.

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(a) fog: (fog)(x) = f(g(x)) = f(x - 3) = (x - 3) + 8 = x + 5

(b) gof: (gof)(x) = g(f(x)) = g(x + 8) = (x + 8) - 3 = x + 5

(c) gog: (gog)(x) = g(g(x)) = g(x - 3) = (x - 3) - 3 = x - 6

(a) The composition fog refers to the function obtained by performing the function g(x) first and then applying the function f(x).

fog(x) = f(g(x)) = f(x - 3) = (x - 3) + 8 = x + 5

In other words, fog(x) is equal to x plus 5.

(b) The composition g of f refers to the function obtained by performing the function f(x) first and then applying the function g(x).

gof(x) = g(f(x)) = g(x + 8) = (x + 8) - 3 = x + 5

Therefore, gof(x) is also equal to x plus 5.

(c) Finally, the composition go g refers to the function obtained by performing the function g(x) twice.

gog(x) = g(g(x)) = g(x - 3) = (x - 3) - 3 = x - 6

Thus, gog(x) simplifies to x minus 6.

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The equation of the parabola with vertex at the origin and the given directrix y = -1/3 is:
[tex]x^2 = 4/3y[/tex].

To write the equation of a parabola with vertex at the origin and the given directrix, we can use the standard form of the equation for a parabola with vertical axis of symmetry:

[tex](x - h)^2 = 4p(y - k)[/tex]

where (h, k) represents the vertex coordinates and p represents the distance from the vertex to the directrix.
In this case, the vertex is at the origin (0, 0), and the directrix is y = -1/3.
1: Determine the value of p.
Since the directrix is below the vertex, the value of p is positive and represents the distance from the vertex to the directrix. In this case, p = 1/3.
2: Substitute the vertex and the value of p into the equation.
[tex](x - 0)^2 = 4(1/3)(y - 0)[/tex]
Simplifying this equation, we get:
[tex]x^2 = 4/3y[/tex]

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b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

[tex]Future Value = Principal * (1 + rate/n)^(n*time)[/tex]

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

[tex]$3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)[/tex]

Taking the natural logarithm (ln) of both sides:

[tex]ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)[/tex]

Solving for time:

[tex]time = ln(30) / (12 * ln(1.0025))[/tex]

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

[tex]Effective Interest Rate = (1 + (0.05 / 2))^2 - 1[/tex]

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

[tex]Effective Interest Rate = (1 + (0.05 / 4))^4 - 1[/tex]

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

[tex]Effective Interest Rate = (1 + (0.05 / 365))^365 - 1[/tex]

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

[tex]Effective Interest Rate = e^(nominal rate) - 1[/tex]

For a nominal rate of 5%:

[tex]Effective Interest Rate = e^(0.05) - 1[/tex]

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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Answer:

Without knowing the specific diagram, it is difficult to give a step-by-step proof. However, if lines k and m intersect at point P, we can use the following reasoning:

- The angles formed by intersecting lines are either congruent or supplementary.

- Angles 1 and 3 are opposite each other, meaning they are vertical angles. By definition, vertical angles are congruent.

- Angles 2 and 3 are alternate interior angles, meaning they are on opposite sides of the transversal line and between the two intersected lines. When two lines are cut by a transversal and alternate interior angles are congruent.

- Therefore, angles 1 and 3 are congruent because they are vertical angles, and angles 2 and 4 are congruent because they are alternate interior angles.

Alternatively, we could use the following proof:

- Draw a line n that passes through point P and is parallel to line k.

- Since line n is parallel to line k, angle 1 and angle 2 are corresponding angles and are therefore congruent.

- Draw a line l that passes through point P and is parallel to line m.

- Since line l is parallel to line m, angle 3 and angle 4 are corresponding angles and are therefore congruent.

- Therefore, angle 1 is congruent to angle 2, and angle 3 is congruent to angle 4.

The LU-decomposition of the matrix A is L = [1 0; 5 1] and U = [19 0; -3 1].

The given problem involves finding the LU-decomposition of a matrix A and solving the equation Ax = b.

In the LU-decomposition process, the matrix A is decomposed into the product of two matrices, L and U, where L is a lower triangular matrix and U is an upper triangular matrix.

This decomposition allows for easier solving of linear systems of equations. Once the LU-decomposition of A is obtained, the equation Ax = b can be solved by first solving the system Ly = b for y using forward substitution, and then solving the system Ux = y for x using back substitution.

By performing these steps, the solution to the equation Ax = b can be determined.

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The company make per day is  941.5 feet.

To find the average number of feet of licorice made per day, we can divide the total amount of licorice made by the number of days:

Average = Total amount / Number of days

In this case, the total amount of licorice made is 6,590.7 feet, and the number of days is 7. Plugging in these values into the formula, we get:

Average = 6,590.7 feet / 7 days

Calculating this division gives us:

Average ≈ 941.5286 feet

Rounding this value to the nearest tenth of a foot, the average number of feet of licorice made per day by Max's Licorice Company is approximately 941.5 feet.

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To raise the free chlorine level from 3.0 ppm to 5.0 ppm in a 75,000-gallon pool, we need 15,000 gallons of sodium hypochlorite. None of the given answer choices match this value.

To calculate the amount of sodium hypochlorite needed to raise the free chlorine level in a pool, we can use the following formula:

Amount of chlorine needed = (desired chlorine level - current chlorine level) x pool volume / 10

In this case, the desired chlorine level is 5.0 ppm, the current chlorine level is 3.0 ppm, and the pool volume is 75,000 gallons. Substituting these values into the formula, we get:

Amount of chlorine needed = (5.0 - 3.0) x 75,000 / 10 = 15,000 gallons

Therefore, we need 15,000 gallons of sodium hypochlorite to raise the free chlorine level from 3.0 ppm to 5.0 ppm in a 75,000-gallon pool. None of the given answer choices match this value.

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Answer: I believe you can find the answer! Therefore, I will include how to solve it and not the answer.

Step-by-step explanation:

First step: Make prediction

Second step: solve

The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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The resulted inequality is y > (9 + x) / 7.

To make y the subject of the inequality x < -9/y - 7, we need to isolate y on one side of the inequality.

Let's start by subtracting x from both sides of the inequality:

x + 9/y < 7

Next, let's multiply both sides of the inequality by y to get rid of the fraction:

y(x + 9/y) < 7y

This simplifies to:

x + 9 < 7y

Finally, let's isolate y by subtracting x from both sides:

x + 9 - x < 7y - x

9 < 7y - x

Now, we can rearrange the inequality to make y the subject:

7y > 9 + x

Divide both sides by 7:

y > (9 + x) / 7

So, the inequality x < -9/y - 7 can be rewritten as y > (9 + x) / 7.


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(i) False. The sequence (1 + 1/n)^(n) is convergent.

(ii) True. The subsequences ((-1)^(2n-1)) and ((-1)^(2n)) of the divergent sequence ((-1)^n) are convergent.

(i) The sequence (1 + 1/n)^(n) is actually convergent. This can be proven by using the concept of the limit of a sequence. As n approaches infinity, the term 1/n tends to 0, and thus the sequence becomes (1 + 0)^(n), which simplifies to 1^n. Since any number raised to the power of infinity is 1, the sequence converges to 1.

(ii) The given statement is true. The original sequence ((-1)^n) is divergent since it alternates between -1 and 1 as n increases. However, its subsequences ((-1)^(2n-1)) and ((-1)^(2n)) are both convergent. The subsequence ((-1)^(2n-1)) consists of terms that are always -1, while the subsequence ((-1)^(2n)) consists of terms that are always 1. In both cases, the subsequences do not alternate and approach a constant value, indicating convergence.

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The probability that either event A or event B occurs is 1/4.

Two events A and B overlap each other partially, and the probability of A and B are P(A) and P(B) respectively.The events A and B overlapping each other.The probability that either event A or event B occurs is given by:

[tex]$$P(A \ \text{or} \ B)=P(A)+P(B)-P(A \ \text{and} \ B)$$[/tex]

Given that the probability of event A is 3/12, and the probability of event B is 1/6.

The overlapping area of A and B is given as 2/12.

Using the above formula, we can find the probability of either event A or event B occurs as follows:

[tex]$$\begin{aligned} P(A \ \text{or} \ B)&=P(A)+P(B)-P(A \ \text{and} \ B) \\ &=\frac{3}{12}+\frac{1}{6}-\frac{2}{12} \\ &=\frac{1}{4} \end{aligned}$$[/tex]

Hence, the probability that either event A or event B occurs is 1/4.

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Susan needs to pay back approximately $516.37 at the end of the 60-day loan period, and the total interest she needs to pay is approximately $16.37.

To calculate the total amount Susan needs to pay back at the end of the 60-day loan period, we can use the formula for simple interest: Interest = Principal * Rate * Time. Given that Susan takes a cash advance of $500 and the interest rate is 19.99%, we can calculate the interest she needs to pay as follows: Interest = $500 * 0.1999 * (60/365);  Interest ≈ $16.37. Therefore, Susan needs to pay back the principal amount ($500) plus the interest ($16.37) at the end of the loan period.  

Total amount to pay back = Principal + Interest = $500 + $16.37 = $516.37. Hence, Susan needs to pay back approximately $516.37 at the end of the 60-day loan period, and the total interest she needs to pay is approximately $16.37.

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To determine the forces in members CD, Cl, and Hl in the given truss, we need additional information such as the lengths of the truss members and the angles between them.

However,  the general approach to solving such problems.

1. Force in member CD: To find the force in member CD, we need to perform a force analysis of the joints connected by this member. This involves applying the equations of equilibrium to the forces acting on the joint. By considering the forces in the other members and the applied load, we can determine the force in member CD.

2. Force in member Cl: Similar to finding the force in member CD, we need to analyze the forces acting on the joints connected by member Cl. By applying equilibrium equations, we can solve for the force in this member.

3. Force in member Hl: Again, we perform a force analysis on the joints connected by member Hl. Equilibrium equations are applied to determine the force in this member.

To obtain specific values for the forces, it is necessary to know the lengths of the truss members, the angles between the members, and any additional information such as support conditions or external loads. With these details, the truss can be analyzed using methods like the method of joints or the method of sections to determine the forces in each member.

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Answer: CD

Step-by-step explanation:

Step-by-step explanation:

Without a visual aid or more information about the diagram, it is difficult to determine the value of m/7. Please provide more details or information about the diagram.

Step-by-step explanation:

250%  is 2.5 in decimal form

   2.5 x 22 = 55 specials the next month

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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a) A is diagonalizable (True)

b) A² = 0 (False)

c) The eigenvalues of A² are all different (False)

d) A is not invertible (False)

To determine the properties of the matrix A based on its characteristic polynomial, let's analyze each statement:

a) A is diagonalizable.

For a matrix to be diagonalizable, it needs to have distinct eigenvalues that span its entire vector space. In this case, the eigenvalues of A are the roots of its characteristic polynomial, p(x) = −(x − 1)(x + 1)(x + 2022).

The eigenvalues are: λ₁ = 1, λ₂ = -1, and λ₃ = -2022. Since these eigenvalues are distinct, A has three distinct eigenvalues, which means A is diagonalizable.

b) A² = 0.

To determine whether A² is zero, we need to examine the eigenvalues of A. Since the eigenvalues of A are 1, -1, and -2022, the eigenvalues of A² would be the squares of these eigenvalues.

(λ₁)² = 1, (λ₂)² = 1, and (λ₃)² = 4088484.

Since none of the eigenvalues of A² are zero, we cannot conclude that A² is zero.

c) The eigenvalues of A² are all different.

As mentioned earlier, the eigenvalues of A² are 1, 1, and 4088484. We can see that the eigenvalue 1 is repeated, so the statement is false. The eigenvalues of A² are not all different.

d) A is not invertible.

A matrix A is not invertible if and only if it has a zero eigenvalue. From the characteristic polynomial, we can see that A does not have a zero eigenvalue since none of the roots of p(x) = −(x − 1)(x + 1)(x + 2022) are zero. Therefore, A is invertible.

In summary:

a) A is diagonalizable (True)

b) A² = 0 (False)

c) The eigenvalues of A² are all different (False)

d) A is not invertible (False)

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(a) There are 16 treatment combinations possible in the experiment with four factors, each at two levels.

(b) The chosen design is a 2⁴⁻¹ fractional factorial design with generating relations ACD and BCD. The generalized interaction is CD. The resolution III design allows for estimating main effects and two-factor interactions. The alias structure reveals confounding relationships among factors. The ANOVA table includes main effects, two-factor interactions, and error sources of variation with corresponding degrees of freedom.

(a) The number of treatment combinations in this experiment can be calculated by multiplying the number of levels for each factor. Since each factor has two levels (2²), the total number of treatment combinations is 2⁴ = 16.

(b) One-quarter replication is chosen, the generating relations selected are ACD and BCD.

(i) The generalized interaction of these generating relations can be determined by taking the intersection of the factors present in both relations. In this case, the intersection of ACD and BCD is CD. Therefore, the generalized interaction is CD.

(ii) The design can be denoted using a suitable notation for resolution, which in this case is a 2⁴⁻¹ fractional factorial design. The notation for this resolution is 2⁴⁻¹.

The resolution is chosen to balance the trade-off between the number of runs required and the ability to estimate the main effects and interactions. A resolution III design, such as this one, allows for the estimation of main effects and two-factor interactions, which are often of primary interest.

(iii) The alias structure of this design can be constructed by finding the confounding relationships between the factors. In this case, the alias structure can be represented as follows:

AC = BD

AD = BC

CD = ABD

(iv) The ANOVA table for this design would consist of the following sources of variation and degrees of freedom:

Source of Variation       Degrees of Freedom

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

Main Effects (A, B, C, D)      3

Two-Factor Interactions      3

Error                                      4

Note: The degrees of freedom for main effects and two-factor interactions are determined based on the resolution of the design.

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The graph of the function lies below or touches the x-axis but does not rise above it.

The axis of symmetry is a vertical line passing. For the function y = -1.5(x + 20)², the vertex is (-20, 0), the axis of symmetry is the vertical line x = -20, the function has a maximum value of 0, the domain is all real numbers (-∞, ∞), and the range is y ≤ 0.

The vertex of the function is obtained by taking the opposite sign of the values inside the parentheses of the quadratic term. In this case, the vertex is (-20, 0), indicating that the vertex is located at x = -20 and y = 0.

The axis of symmetry is a vertical line passing through the vertex. In this case, the axis of symmetry is x = -20.

Since the coefficient of the quadratic term is negative (-1.5), the parabola opens downward, and the vertex represents the maximum point of the function. The maximum value is 0, which occurs at the vertex (-20, 0).

The domain of the function is all real numbers since there are no restrictions on the x-values.

The range of the function is y ≤ 0, indicating that the function has values less than or equal to 0. The graph of the function lies below or touches the x-axis but does not rise above it.

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Given that 90% of the voters favor Ms Stein. If 2 voters are chosen at random, we need to find the probability that all 2 voters support Ms Stein.

Let's say that there are 'n' total voters and that 'p' proportion of voters support Ms. Stein. Since there are only two possible outcomes in this scenario: the voter will vote for Ms. Stein, or the voter will not vote for Ms. Stein. This suggests that the Binomial probability model is suitable. P(x=2) represents the probability of two voters out of the total population voting for Ms. Stein. P(x=2) can be determined by using the following formula:

P(x = 2) = nC2 p2 q^(n-2)Where q is the probability of the voter not voting for Ms. Stein. Since there are only two possible outcomes, q is equal to 1-p. Hence we can write this as:P(x = 2) = nC2 p2 (1-p)^(n-2)

Here, p = 0.9, q = 0.1, and n = 2. Therefore, P(x = 2) is:P(x = 2) = nC2 p2 q^(n-2) = 2C2 × 0.9² × 0.1⁰= 0.81. Therefore, the probability that all 2 voters support Ms. Stein is 0.81. Hence, this is the required solution.

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