When a biased coin is thrown 3 times, the probability of getting 3 tails is 27/125
Work out the probability of getting 3 heads when the coin is thrown 3 times

Answer:

-1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

The slope is referring to the gradient of the line.

To work out the gradient, you need to know this equation:

gradient = change in y / change in x = Δy / Δx

(the triangle Δ is the greek letter delta, and means "change in")

To work out the "change in" something, you subtract one from the other.

Let's say Point A = (-3, 4) and Point B = (2, -1)

To find the change in y, you take the two y values of the two points, and subtract one from the other. (Technically you could do it either way, but let's do A subtract B)

The y value of A is 4, and the y value of B is -1

4 - -1 = 4 + 1 = 5 = change in y

To work out the change in x, you do the same but with the x values.

The x value of A is -3, and the x value of B is 2

-3 - 2 = -5 = change in x

Now we substitute these numbers into the equation:

gradient = change in y / change in x = 5 / -5 = -1

So the answer is a gradient of -1

I hope this helps!

Having a small sample size compared to a large one may result in biased results due to sampling error.

Sampling is a crucial aspect of research because it allows researchers to generalize their findings to a larger population. In the case of the coal mine study, having a small sample size compared to a large one may result in what is known as a sampling error.

Sampling error is the difference between the sample's statistics and the true population's parameters. It occurs when the sample is not representative of the entire population, leading to biased results. In other words, the smaller the sample size, the greater the chance of sampling error occurring.

To understand this concept better, consider an example. Suppose we are trying to determine the average height of high school students in a particular city.

We randomly select ten students from one school and another ten from a different school, giving us a total of twenty students. If the average height of these students is 5'6", this may not be representative of the entire high school student population in the city. However, if we increase the sample size to 1000 students, the average height would likely be more accurate.

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Answer:

you do 8/2 which is 4, so that is ur radius

you do 3.14*4*4=50.24

there is ur answer!

Step-by-step explanation:

(a) A sound with an intensity of 1 watt per square meter has a decibel level of -120.

(b) A sound with an intensity of 10⁻² watt per square meter has a decibel level of -140.

(c) The number of decibels is not 100 times as great as the intensity, even though the intensity in part (a) is 100 times greater than the intensity in part (b).

Using the relationship of intensity of sound and number of decibels, we can calculated the required number of decibels as follows;

β =10 log(I x 10⁻¹²)

(a) Decibel level: plugging in I = 1 watt per square meter into the equation, we get:

β = 10 log(1 x 10⁻¹²) = 10 log(10⁻¹²) = -120 decibels

(b) Decibel level: plugging in I = 10⁻² watt per square meter into the equation, we get:

β = 10 log(10⁻² x 10⁻¹²) = 10 log(10⁻¹⁴) = -140 decibels

(c) Let's calculate the decibel level for the sound in part (a) using the given formula:

β₁ = 10 log(I₁ x 10⁻¹²) = 10 log(100 x I₂ x 10⁻¹²) = 10 log(I₂ x 10⁻¹⁴) + 20

where;

Using the result from part (b), we can substitute I₂ = 10⁻² watt per square meter and get:

β₁ = -140 + 20 = -120 decibels

Comparing this result to the decibel level for the sound in part (a) (which is also -120 decibels), we see that they are the same.

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Answer:

2.6 or 2.7

Step-by-step explanation:

Answer:

D. She showed that f(n) - f(n - 1) was a constant difference.

Step-by-step explanation:

The ages of people attending movie J and movie k are similar, as the median and range of ages in both groups are close.

The box plots show the ages of a random sample of 100 people who attended movie J and 100 people who attended movie k. The box plot for movie J shows that the median age is around 31 years old, and the range of ages is from around 18 to 45 years old. The box plot for movie K shows that the median age is slightly higher than movie J at 33 years old, and the range of ages is slightly wider at 15 to 48 years old. The median ages and range of ages for both movies are close, suggesting that the ages of people attending movie J and movie K are similar.

the complete question is :

Which of the following statements best compares the ages of the people attending movie J and movie K based on the box plots shown, representing a random sample of 100 people who attended each movie:

A. The median age of people who attended movie J is higher than the median age of people who attended movie K.

B. The range of ages for people who attended movie J is wider than the range of ages for people who attended movie K.

C. The interquartile range (IQR) of ages for people who attended movie J is smaller than the IQR of ages for people who attended movie K.

D. The ages of people who attended movie J and movie K have the same distribution.

E. It is not possible to make any conclusions about the ages of people who attended movie J and movie K based on the box plots shown.

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Answer:

I’m pretty sure the answer is 113.03

Answer:

the missing coordinate of "r" equals -14. (-5,-14)

The solution to the system of equations is (x,y) = (1.25, -2.5) and the solution to the system of equations is (x,y) = (0, -5/3).

Let's try these strategies on the given system of equations:

2x+3y=−5

2x−3y=10

A. Subtract the following formula from the above formula:

(2x + 3y) - (2x - 3y) = (-5) - 10

6 years = -15

y = -2.5

Substituting y = -2.5 into one of the equations gives:

2x + 3(-2.5) = -5

2x - 7.5 = -5

2x = 2.5

x = 1.25

So the solution to the system of equations is (x,y) = (1.25, -2.5).

This strategy eliminates the x variable, but not the y variable. B. Add equations.

(2x + 3y) + (2x - 3y) = (-5) + 10

4x = 5

x = 1.25

Substituting x = 1.25 into one of the equations gives:

2(1.25) + 3 years = -5

3 years = -7.5

y = -2.5

So the solution of the system of equations is (x,y) = (1.25, -2.5).

This strategy removes the variable y but not the variable x.

C. Multiply the above formula by 2, then sum these formulas. 2(2x + 3y) + (2x - 3y) = 2(-5) + 10

4x = 0

x = 0

Substituting x = 0 into one of the equations gives:

2(0) + 3 years = -5

y = -5/3

So the solution to the system of equations is (x,y) = (0, -5/3).

This strategy eliminates the x variable, but not the y variable.

Therefore, there is no way to completely eliminate variables in the system of equations. 

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Answer:

D. 6w + 5

Step-by-step explanation:

a² + 2ab + b² = (a + b)²

36w² + 60w + 25 = (6w + 5)²

Answer: D. 6w + 5

Divide any number by 9. Then then ur answer times 1 then times 8.

Example 9:9=1 1 and 8

36:9=4. 4 and 32

The teacher has to select four members out of a math club of twelve members. There are 495 possible ways for her to make the selection.

To determine the number of ways the teacher can select four members from a math club of twelve, we can use the concept of combinations. A combination is a selection of items without regard to the order in which they are chosen. In this case, the teacher needs to select four members, and the order in which they are chosen does not matter.

The formula for calculating combinations is given by "n choose k," which is denoted as C(n, k) or nCk. In this case, the teacher needs to choose four members out of twelve, so the calculation would be 12C4.

Using the formula for combinations, 12C4 = 12! / (4!(12-4)!), where "!" represents the factorial function. Simplifying the expression gives us 12! / (4!8!).

The factorial function represents the product of all positive integers up to a given number. So, 12! is equal to 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Simplifying further, we have 12! / (4!8!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1).

Calculating the expression gives us (11880) / (24) = 495.

Therefore, there are 495 possible ways for the teacher to make her selection of four members from the math club of twelve.

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Answer:

37

Step-by-step explanation:

Answer:8

Step-by-step explanation:

0.5*10=5

3+5=8

a. Montserrat runs 7.5 kilometers in her 10th training week.

b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:

\(a_n = a_1 + (n - 1) * d\)

where:

\(a_n\) is the nth term (the number of kilometers in the nth week),

\(a_1\) is the first term (the number of kilometers in the first week, which is 3 km),

n is the number of weeks (in this case, 10), and

d is the common difference (the amount by which the distance increases each week, which is 0.5 km).

\(a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km\)

So, Montserrat runs 7.5 kilometers in her 10th training week.

b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:

\(S_n = (n / 2) * (a_1 + a_n)\)

where:

\(S_n\) is the sum of the first n terms (the total number of kilometers run by the nth week),

\(a_1\) is the first term (3 km),

\(a_n\) is the nth term (which we found to be 7.5 km in her 10th week),

n is the number of weeks (15 in this case).

\(S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km\)

So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

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Answer:

x = x, y = −5 −3x

Step-by-step explanation:

hope this helps

A mean of a normal distribution's upper bound of a 95% confidence interval is 58.11.

For the given question,

The confidence bound's upper limit (UCB) is determined as follows:

UCB =  μ + z(α/2)×σ/√n

Now, α/2 = (1 - 0.95)/2

α/2 = 0.025

z(α/2) = 1.96  (obtain from t-distribution table for degree of freedom)

Put the values in the formula,

UCB =  μ + z(α/2)×σ/√n

UCB = 36.96 + 1.96×41.8/√15

UCB = 58.11

As a result, 58.11 is the upper bound of a 95% confidence interval for the mean of a normal distribution.

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Answer: Line BC and Line DE

Step-by-step explanation:

In geometry terms, we can say that for any set of two points, we always can find a line that passes through them.

For example, in the image, we can see two lines (but actually we could make more with those points)

We can see a line that connects points B and C, and we can call that line as:

Line BC

We also can see a line that connects the points D and E, we can call this line as:

Line DE

So the two lines are: Line BC and Line DE

The p-value for the test is found as 0.05 for the given hypothesis.

Given,Sample mean = 59.1 km

Sample standard deviation = 2.31 km

Population is normally distributed

P-value for the test is to be determined.

To find the p-value, we need to perform a hypothesis test. Here, we have to test whether the null hypothesis is true or not.

Hypothesis statements:

Null hypothesis (H0): µ = 60 km (The population mean is 60 km)

Alternative hypothesis (Ha): µ ≠ 60 km (The population mean is not equal to 60 km)

Level of significance, α = 0.05

Z-score formula is given as,Z = (x - µ) / (σ/√n)

Where,x = Sample mean = 59.1 km

µ = Population mean

σ = Standard deviation of the population = 2.31 km

n = Sample size

We have,σ/√n = 2.31/√n

For α = 0.05, the two-tailed critical values are ±1.96

Now, the calculated Z-score is given as,

Z = (59.1 - 60) / (2.31/√n)

Z = - (0.9) * ( √n / 2.31)

P(Z < -1.96) = 0.025 and P(Z > 1.96) = 0.025

P-value = P(Z < -1.96) + P(Z > 1.96)

P-value = 0.025 + 0.025

P-value = 0.05

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At the 0.05 significance level, for a p-value of 0.0005, you should find in favor of the alternative hypothesis and reject the null hypothesis, i.e., Option B is the correct answer.

The significance level, also known as alpha, is the threshold used to determine whether to reject or fail to reject the null hypothesis. In this case, the significance level is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is true.

The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. A small p-value indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against it.

In this scenario, the p-value of 0.0005 is smaller than the significance level of 0.05, indicating strong evidence against the null hypothesis. As such, you should find in favor of the alternative hypothesis and reject the null hypothesis. This means that there is significant evidence to support the alternative hypothesis and suggest that the observed results are not due to chance.

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The number of possible k-lists (x₁, x₂, ..., xₙ) where each xₙ is a positive integer and 1 ≤ x₁ ≤ x₂ ≤ · · · ≤ xₙ ≤ n is given by the formula n choose k, or (n choose k) = n!/(k!(n-k)!)

First, let's consider the case when k = 1. In this case, there is only one integer in the list, and it must be a positive integer between 1 and n inclusive. Therefore, there are n possible k-lists when k = 1.

We can continue this process for larger values of k.

In general, the number of possible k-lists is the number of ways we can choose k positive integers between 1 and n inclusive such that the first integer is less than or equal to the second integer, the second integer is less than or equal to the third integer, and so on up to the kth integer being less than or equal to n.

Using the formula for combinations, this is equal to n choose k, or (n choose k) = n!/(k!(n-k)!), where n! is the factorial of n.

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The volume of the region is 1024π cubic units.

To find the volume of the region, we need to integrate the function \(f(x,y) = x^2 + y^2\) over the region R,

which is defined by the cylinder \(x^2 + y^2 = 64\) and the xy-plane.

We can express R as follows:

\(R = {(x, y) | x^2 + y^2 ≤ 64, z ≥ 0}\)

To integrate over this region, we can use cylindrical coordinates.

In cylindrical coordinates, the equation of the cylinder is simply \(r^2 = 64\). The limits of integration for r are therefore 0 to 8.

The limits of integration for θ are 0 to 2π, since we want to integrate over the entire circle.

To express f(x,y) in terms of cylindrical coordinates, we first need to express \(x^2 + y^2\) in terms of r. This is simply \(r^2\). Therefore, we have:

\(f(x,y) = x^2 + y^2 = r^2\)

To set up the integral, we have:

\(V = \int\int R f(x,y) dA\)

where dA is the area element in cylindrical coordinates, which is given by r dr dθ. Therefore, we have:

\(V = \int0^{2\pi} \int0^8 r^3 dr d\theta\)

Evaluating the inner integral first, we get:

\(\int0^8 r^3 dr = [r^4/4]0^8 = 512\)

Substituting this result into the outer integral, we get:

\(V = \int0^{2\pi} 512 d\theta = 1024\pi\)

Therefore, the volume of the region is 1024π cubic units.

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Answer: The triangles are not congruent.

Step-by-step explanation:

We are given that the two triangles both contain a congruent angle and a congruent side. Additionally, the two triangles also share a side with each other, which is the center horizontal side (the one bisecting the two congruent angles). This "shared" side tells us that this side is congruent in both triangles, meaning that both triangles have two congruent sides with a non-included congruent angle among them.

However, because the two triangles only have two congruent sides, and the angle shared by each triangle is not included between the two sides, the triangle would be "congruent" by SSA, which is not a triangle congruency theorem or postulate.

Therefore, the two triangles are not congruent.

I hope this helps!

Answer:

Step-by-step explanation:

Step-by-step explanation:

If 3.25m is equal to 15kg then what about 1m?

3.25m = 15kg

1m =?

Then by cross multiplication we get 4.615 kg

Just substitue \(9\) for \(x\) in the expression.

\(= 9.5(9) - 2.5\)

\(= 85.5 - 2.5\)

\(= 83\)

Answer:

86

Step-by-step explanation:

The original equation is 9.5 times x - 2.5

9.5(9) - 2.5

9.5(9) = 88.5

88.5 - 2.5 = 86

9.5x - 2.5 = 86

The regression equation predicts the value of Rent based on the given independent variable. The equation suggests that as the independent variable (X) increases, the Rent is expected to increase.

The given output provides information about a regression analysis. The regression equation can be developed using the coefficients provided. The equation can be written as:

Rent = 1230.242 + 6.666983 * X

In this equation, "Rent" represents the dependent variable, and "X" represents the independent variable.

The coefficient of determination (R-squared) value is 0.892542, which indicates that approximately 89.25% of the variation in the dependent variable can be explained by the independent variable.

The coefficient of the independent variable (Rent) is 6.666983, indicating that for every unit increase in the independent variable, the dependent variable (Rent) is expected to increase by approximately 6.666983 units.

The intercept term is 1230.242, representing the estimated value of the dependent variable (Rent) when the independent variable (X) is zero.

The standard error of the estimate is 580.9854, which provides an estimate of the average distance between the observed dependent variable values and the values predicted by the regression equation.

Based on this information, we can conclude that the regression equation predicts the value of Rent based on the given independent variable. The equation suggests that as the independent variable (X) increases, the Rent is expected to increase.

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Answer:

Sightseeing

Step-by-step explanation:

The equivalent expression of 18 + 30 using distributive property is 6(3) + 6(5)

The distributive property states that for any numbers a, b, and c, a multiplied by (b+c) equals a multiplied by b plus a multiplied by c.

a(b + c) = a(b) + a(c)

The prime factor of 18 + 30 is written as;

18 + 30 = 2 x 3 x 3 + 2 x 3 x 5

18 + 30 = 2 x 3 x (3 + 5)

Simplifying the expression inside the parentheses gives:

2 x 3 x (3 + 5) = 6 (3 + 5)

applying distributive property we will have;

6 (3 + 5) = 6(3) + 6(5)

Thus, the final expression is; 18 + 30 = 6(3) + 6(5)

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