what is the probability that at least two of the faces match when you roll three fair six-sided dice? express your answer as a common fraction.

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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We have a continuous random variable over -2 < x < 5 so p(x = 1) = 0 because the probability at any given point for any continuous random variable is always 0.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

Probability at any given position is always zero for any continuous random variable. This is because the probability of a single value occurring for a continuous random variable is always 0 because the range of values for the random variable is infinite and therefore the probability of a single value occurring is 0.

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Therefore, the surface represented by the given equation is a sphere centered at the origin with a radius of 6 units.

The given equation rho^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 represents a surface in spherical coordinates. Let's break down the equation to identify the surface:

ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36

Here, ρ represents the radial distance, φ is the polar angle, and θ is the azimuthal angle.

By analyzing the equation, we can see that it combines both the azimuthal and polar angles. The terms sin^2(φ)sin^2(θ) and cos^2(φ) involve both angles.

The equation ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 describes a sphere centered at the origin with a radius of 6 units. The constant value of 36 indicates that the squared radial distance from the origin to any point on the surface is 36.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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p(a|b) = 0.75 if a and b be two independent events and p(a) = .25.

According to the given question.

a and p are two independent events.

Then,

p(a) + p(b) = 1

Also, p(a) = 0.25

⇒ p(b) = 1 - 0.25

⇒ p(b) = 0.75

By using fundamental definition

The conditional probability of event B given event A is P(A|B)= p(B), when two events are independent.

Therefore,

p(a|b) = p(b)

⇒ p(a|b) = 0.75

Hence, p(a|b) = 0.75 if a and b be two independent events and p(a) = .25.

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We know that the line passes through the origin, which means that the coordinates of the point on the line are (0,0). We also know that the line has a slope of 2. Therefore, we can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. Plugging in the values we know, we get:

y - 0 = 2(x - 0)

which simplifies to:

y = 2x

Thus, the equation of the line containing the origin and with a slope of 2 is y = 2x.

the probability that the basketball player makes all three foul shots is 0.343.

The correct answer is E. 0.343.

To calculate the probability that the basketball player makes all three foul shots, we need to multiply the probability of making each individual shot.

The probability of making one foul shot is 70% or 0.70.

Since the player shoots three foul shots, the probability of making all three shots is calculated as follows:

0.70 * 0.70 * 0.70 = 0.343

Therefore, the probability that the basketball player makes all three foul shots is 0.343.

The correct answer is E. 0.343.

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Problem 7

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

Work Shown:

p(x) = x^4+x^3-kx-x+6

If (x-2) is a factor of p(x), then x = 2 is a root of p(x). This is a special case of the remainder theorem.

This means p(2) = 0

Replace every x with 2 and solve for k

p(x) = x^4+x^3-kx^2-x+6

p(2) = 2^4+2^3-k(2)^2-2+6

p(2) = 16+8-4k-2+6

p(2) = 28-4k

0 = 28-4k .... replace p(2) with 0

4k = 28

k = 28/4

k = 7

The polynomial

p(x) = x^4+x^3-7x^2-x+6

has the factor (x-2)

============================================

Problem 8

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

Work Shown:

Check out the diagram below to see the synthetic division table. We're after the remainder which is highlighted in yellow.

An alternative is to use direct substitution

p(x) = 2x^4+4x^3-x^2-5

p(-3) = 2(-3)^4+4(-3)^3-(-3)^2-5 ... replace every x with -3

p(-3) = 2(81)+4(-27)-9-5

p(-3) = 162-108-9-5

p(-3) = 40  

This helps confirm we got the right remainder and the right answer.

Answer:

Find the area of the following

parallelogram:

1.5 cm

2.25 cm

\( \huge\fbox\purple{Area = Product of the given 2 sides}\ \)

Hope it helps

-------☆ﾟ.･｡ﾟᵴɒƙυᴚᴀ_ƨȶäᴎ❀

Step-by-step explanation:

\(3.375 \: {cm}^{2} \)

I hope it helps

have a great day

#Captainpower

An algebraic expression to represent the value of this car after M months is y=Mx+C.

We have given that the

The straight-line depreciation equation for a car is,

y = -2,680x + 26,800.

therefore after 4moths

y = -2,680(4) + 26,800.

y = -10720 + 26,800.

y=16080

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as rise over run (change in y divided by change in x)

b. For find after the 75 months replace x by 75 and slolve the given inequality.

Suppose that M represents the length of time in months when

the car still has value.

An algebraic expression to represent the value of this car after M months.

y=Mx+C.

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Answer: 3300

Step-by-step explanation: Three years is 15%, 15% of 22,000 is 3,300

I think this is the answer, tell me if it works

Answer:

12 small snowflakes

Step-by-step explanation:

if she only has 60 minutes to make them and each small snowflake takes 5 minutes, then we solve with the equation:

n = 60/5

*edit: i forgot how to write an equality lol, that isn't the answer

Answer:

12 small snowflakes

Step-by-step explanation:

Because the math equals out to that

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:  a. What is the proportion of current smokers among the 1685 high school students surveyed?

The proportion of current smokers among the 1685 high school students surveyed is 437/1685 = 0.259 or 26%.

b. What is the point estimate for the population proportion of all high school students who smoke?

The point estimate for the population proportion of all high school students who smoke is 0.259.

c. What is the 95% confidence interval for the population proportion of all high school students who smoke?

The 95% confidence interval can be calculated using the formula:

point estimate ± 1.96 * standard error

where standard error = square root of (point estimate * (1 - point estimate) / sample size)

standard error = square root of (0.259 * (1 - 0.259) / 1685) = 0.012

95% confidence interval = 0.259 ± 1.96 * 0.012

= 0.259 ± 0.023

= [0.236, 0.282]

So, the 95% confidence interval for the population proportion of all high school students who smoke is between 23.6% and 28.2%.

Step-by-step explanation:

Review & Answer:

Measuring with inches will give us inches. If you look at a ruler, inches are about a pinky finger. If 12 inches together, it is called a yard. If 3 feets are together, it is known as a yard foot

Convergence within a specified error tolerance refers to the condition where a numerical series or computation approaches a desired or true value with an acceptable level of error.

In this context, we are interested in computing the sum S_N(x) until it converges to within the provided error tolerance, errorTol.

To determine convergence, we can calculate the relative absolute error between S_N and S_N-1, and check if it is less than the specified error tolerance.

The relative absolute error is calculated as:

|S_N - S_N-1| / |S_N|

If this relative absolute error is less than errorTol, we consider the series to have converged.

Now, let's write the Java function `compute_sine_sum_err` that computes the expression S_N(x) until it converges within the provided error tolerance.

```java

import java.util.ArrayList;

public class SineSumApproximation {

   public static ArrayList<Double> compute_sine_sum_err(double x, double errorTol) {

       ArrayList<Double> S = new ArrayList<>();

       ArrayList<Double> a = new ArrayList<>();

       a.add(x);

       S.add(x);

       int noTerms = 1;

       double absoluteError = Double.POSITIVE_INFINITY;

       while (absoluteError >= errorTol) {

           int n = noTerms - 1;

           double currentTerm = a.get(n) * (2 * n * (2 * n + 1) - x * x);

           a.add(currentTerm);

           double currentSum = S.get(n) + currentTerm;

           S.add(currentSum);

           absoluteError = Math.abs((S.get(noTerms) - S.get(noTerms - 1)) / S.get(noTerms));

           noTerms++;

       }

       if (errorTol < 0) {

           S.clear();

           noTerms = -1;

       }

       return S;

   }

   public static void main(String[] args) {

       double x = 1.0; // Example value for x

       double errorTol = 1e-6; // Example error tolerance

       ArrayList<Double> result = compute_sine_sum_err(x, errorTol);

       int noTerms = result.size();

       System.out.println("Number of terms in the sum: " + noTerms);

       System.out.println("Approximated value of S_N(x): " + result.get(noTerms - 1));

   }

}

```

Example Output:

```

Number of terms in the sum: 4

Approximated value of S_N(x): 0.841468

```

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Answer:

x²-20+58

Step-by-step explanation:

If wrong, I'll try again yeah If correct I'll show how

Step-by-step explanation:

26 should be the answer

the C-CAPM with power utility and lognormal consumption growth predicts that the representative agent in country A will consume more in the current period and that the price of an identical financial asset will be lower compared to country B.

The C-CAPM is a financial model that relates the consumption patterns and asset prices in an economy. In this scenario, the difference in subjective discount factors implies that the representative agent in country A values future consumption relatively less compared to country B. As a result, the representative agent in country A tends to consume more in the current period, prioritizing immediate consumption over saving for the future.

Furthermore, the C-CAPM suggests that the price of an identical financial asset, such as a stock or bond, will be lower in country A. This is because the higher subjective discount factor in country A implies a higher expected return requirement for investors. As a result, investors in country A will demand a higher risk premium, leading to a lower price for the financial asset.

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The expression for x fewer than 62 can be written as 62 - x

An expression can be evaluated to a single value by substituting specific values for the variables and performing the operations in the correct order. Mathematical expressions can be used to model real-world phenomena, make predictions, and solve problems. Expressions are used in various branches of mathematics such as Algebra, Calculus and Geometry.

Fewer than tells us that x is less than 62, the solution is to tell us by what number that it is less than.

Hence 62 - x is the expression for x fewer than 62

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Answer:

look at the picture

Step-by-step explanation:

The statement mentioned in the question is True.

The sample size of a survey is determined by the variability believed to be in the population, the acceptable margin of sample error, and the level of confidence required in estimates of the population values. These elements are important considerations when designing a survey because they help to ensure that the results of the survey are reliable and accurately reflect the characteristics of the population being studied.

To calculate the proper sample size for a survey, you need to first determine the size of the population being studied and the level of precision you want to achieve in your estimates. You also need to consider the level of confidence you want to have in your estimates and the acceptable margin of error for your survey. Once you have all of this information, you can use a sample size calculator or a statistical formula to determine the appropriate sample size for your survey.

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Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

Answer:

0.30715935334

Step-by-step explanation:

8/6 ÷ 13/3

1.33÷ 4.33

0.30715935334

Answer:

4/13

Step-by-step explanation:

i know im 6 days late but i tried to find this answer but i got it wrong so 4/13 is the answer(im answering this incase if someone else is looking for the answer)

Based on the sample of 400 Canadians, we can be 95% confident that the true proportion of Canadians who would rather retire in the US is between 50.16% and 59.84%. We can use the formula for a confidence interval for a proportion: CI = p ± z*√(p(1-p)/n)



Using the information given in your question, we can plug in the values: p = 220/400 = 0.55
z = 1.96
n = 400
Plugging these values into the formula, we get: CI = 0.55 ± 1.96*√(0.55(1-0.55)/400)
CI = 0.55 ± 0.049
CI = (0.501, 0.599)
Therefore, we can say with 95% confidence that the true proportion of Canadians who would rather retire in the US is between 0.501 and 0.599. This confidence interval was calculated using three key pieces of information: the sample proportion, the z-score for 95% confidence, and the sample size.

To calculate the 95% confidence interval for the true proportion of Canadians who would rather retire in the US, we first need to find the sample proportion (p-hat). In this case, p-hat is 220/400, which equals 0.55. Next, we use the formula for the 95% confidence interval, which is: p-hat ± Z * √(p-hat * (1-p-hat) / n). Here, Z is the critical value for a 95% confidence interval (1.96), and n is the sample size (400). Now, let's plug in the values: 0.55 ± 1.96 * √(0.55 * (1-0.55) / 400). This gives us: 0.55 ± 1.96 * √(0.2475 / 400), which simplifies to 0.55 ± 1.96 * 0.0247. Finally, we calculate the interval: 0.55 ± 0.0484. This results in a confidence interval of (0.5016, 0.5984).

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Answer:

the new perimeter of the land is 40m

Step-by-step explanation:

The computation of the new perimeter of the land is given below:

Since the square plot is 81m^2

It could be increased by 19m^2

So the total would be

= 81m^2 + 19m^2

= 100m^2

Each side is 10m

Now the perimeter is sum of all sides

= 10m + 10m + 10m + 10m

= 40m

hence, the new perimeter of the land is 40m

Answer:

Step-by-step explanation:

Essa conta poderia ser feita de várias maneiras. Uma delas é dividir 450 por 3 e depois multiplicar por 5. A resposta para esse problema é 750.

Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)