For two events E1 and E2, can we find the probability of E1 ∩ E2 by any way other than adding the two individual probabilities and subtracting the probability of the intersection?

Answer:

30 papers.

There is a sequence if you examine the minutes along with the papers he graded. And the sequence is 2 times. As the first one, he graded 2 papers in 4 minutes. Meaning one paper takes 2 minutes to mark. Same goes to the rest of them.

Extra explanation: 60÷2=30

Mr. Harris will grade 30 papers in 60 minutes. The answer is option A: 30 papers.

We can start by calculating Mr. Harris's rate of grading, which is the number of papers he can grade in one minute.

To do this, we can use the information in the table. For example, in 16 minutes, he graded 8 papers. So his rate of grading is:

8 papers / 16 minutes = 0.5 papers per minute

We can do the same calculation for the other time intervals:

4 minutes: 2 papers / 4 minutes = 0.5 papers per minute

20 minutes: 10 papers / 20 minutes = 0.5 papers per minute

24 minutes: 12 papers / 24 minutes = 0.5 papers per minute

We can see that Mr. Harris's rate of grading is consistent at 0.5 papers per minute.

So to find out how many papers he will grade in 60 minutes, we can simply multiply his rate by the number of minutes:

0.5 papers per minute × 60 minutes = 30 papers

Therefore, Mr. Harris will grade 30 papers in 60 minutes. The answer is option A: 30 papers.

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(A) The lower bound of the interval is 8378.3 lb and the upper bound is 8560.7 lb.

(B) The lower bound of the interval is 8366.9 lb and the upper bound is 8572.1 lb

(a) Using the given information, a 90% confidence interval for the true average yield point of the modified bar can be calculated. The sample mean is 8469 lb and the sample size is 64. The standard deviation of the population is known to be 100. Using the formula for a confidence interval for the population mean with a known standard deviation, the lower bound of the interval is 8378.3 lb and the upper bound is 8560.7 lb.

(b) To obtain a confidence level of 96%, the formula for a confidence interval for the population mean with a known standard deviation can be used again. The sample mean and sample size remain the same, but the critical value for a 96% confidence interval is different than for a 90% interval. The critical value for a 96% confidence interval is 1.75, compared to 1.645 for a 90% interval. Using this new critical value, the lower bound of the interval is 8366.9 lb and the upper bound is 8572.1 lb.

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Answer:

[tex]\frac{3}{26}[/tex] of pulling a queen or a black 3.

Step-by-step explanation:

Since there's 52 cards in an average deck and there's 4 queens, divide 52 with 4 and you'll get 13, so that means it's a [tex]\frac{1}{13}[/tex] chance of getting a queen.

Also because there's 4 "3"s and 50% of those cards are black (clubs and spades), divide 52 with 2 and you'll get a [tex]\frac{1}{26}[/tex] chance of getting a black 3.

Add both quotients to a common denominator of 52 and you will end up with 6/52. Then simplify the sum.

You should end up with [tex]\frac{3}{26}[/tex].

The appropriate measure of variability for this data set is the IQR, and its value is 350.

The range is one measure of variability, but it is heavily influenced by extreme values, which makes it less reliable. The IQR (interquartile range) is a better measure of variability because it is not affected by extreme values. Therefore, the appropriate measure of variability for this data set is the IQR.

To calculate the IQR, we first need to find the median, which is the middle value in the ordered list of data:

200, 450, 600, 650, 700, 800

The median is (600 + 650) / 2 = 625.

Next, we find the values that mark the 25th and 75th percentiles of the data set. The 25th percentile is the value that is greater than 25% of the values in the data set, and the 75th percentile is the value that is greater than 75% of the values in the data set. We can use the following formula to find these values:

25th percentile = (n + 1) × 0.25

75th percentile = (n + 1) × 0.75

where n is the number of values in the data set. In this case, n = 6, so:

25th percentile = (6 + 1) × 0.25 = 1.75

75th percentile = (6 + 1) × 0.75 = 5.25

We round these values up and down to get the indices of the corresponding values in the ordered list:

25th percentile index = 2

75th percentile index = 5

The values at these indices are 450 and 800, respectively. Therefore, the IQR is:

IQR = 800 - 450 = 350

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The value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function f(x) = 54 sec^2 x, over the interval [-4, 4] is zero.

The Mean Value Theorem for Integrals states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that the definite integral of f(x) from a to b is equal to f(c) times (b-a). In this case, the given function f(x) is continuous and differentiable over the interval [-4, 4]. Hence, by the Mean Value Theorem for Integrals, there exists a value c in (-4, 4) such that the integral of f(x) from -4 to 4 is equal to f(c) times (4-(-4)) = 8f(c).

As the function is periodic, its integral over the interval from 0 to π is equal to zero. Hence, the integral of the function over the interval [-4, 4] is also equal to zero. Therefore, the value(s) of c guaranteed by the Mean Value Theorem for Integrals is zero. Thus, the answer is 0.

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The two points at which the line intersects the curve are (2, -2) and (4/3, -4).

To find the coordinates of the point at which the line with a gradient of 3 intersects the curve y = 3x² - 7x after passing through the point (2, -2), we can set the equation of the line equal to the equation of the curve and solve for x and y.

The equation of the line passing through (2, -2) with a gradient of 3 can be written as:

y = 3x - 8

Substituting this equation into the curve equation, we get:

3x - 8 = 3x² - 7x

Simplifying the equation:

3x² - 10x + 8 = 0

We can solve this quadratic equation to find the values of x. Using factoring or the quadratic formula, we find:

(x - 2)(3x - 4) = 0.

Setting each factor equal to zero:

x - 2 = 0 --> x = 2

3x - 4 = 0 --> x = 4/3

So, there are two possible x-values where the line can intersect the curve: x = 2 and x = 4/3.

Now, we can substitute these x-values back into the equation of the line to find the corresponding y-values:

For x = 2:

y = 3(2) - 8 = 6 - 8 = -2

For x = 4/3:

y = 3(4/3) - 8 = 4 - 8 = -4

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(a) The set {(x1, x2)T | x1 + x2 = 0} forms a subspace of R2. This set contains the zero vector (0,0)T, is closed under vector addition, and is closed under scalar multiplication.

(b) The set {(x1, x2)T | x1x2 = 0} does not form a subspace of R2. Although it contains the zero vector (0,0)T and is closed under scalar multiplication, it is not closed under vector addition. For example, (1,0)T and (0,1)T are in the set, but their sum (1,1)T is not.

(c) The set {(x1, x2)T | |x1| = |x2|} does not form a subspace of R2. Although it contains the zero vector (0,0)T and is closed under vector addition, it is not closed under scalar multiplication.

For example, (1,1)T is in the set, but (2,2)T is not. Also, this set is not closed under vector addition since, for example, (1,0)T and (-1,0)T are in the set, but their sum (0,0)T is not.

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The given equation is simply cos(x), which represents the cosine function. The cosine function oscillates between -1 and 1 in the interval [0, 2π). Therefore, all the solutions to the equation cos(x) in the given interval are values of x for which cos(x) equals either 1 or -1. These solutions can be obtained by finding the values of x at which the cosine function reaches its maximum value of 1 or its minimum value of -1 in the given interval.

The solutions to cos(x) in the interval [0, 2π) are x = 0 and x = π. At x = 0, the cosine function reaches its maximum value of 1, and at x = π, it reaches its minimum value of -1. These are the only solutions to the equation cos(x) in the given interval.

To understand this better, it is useful to graph the cosine function over the interval [0, 2π). The graph shows that the cosine function oscillates between -1 and 1, with a period of 2π. The function crosses the x-axis at x = π/2 and 3π/2, which are not solutions to the equation cos(x) but are important points on the graph of the cosine function. The graph also shows that the function is symmetric about the vertical line x = π, which means that if x is a solution to the equation cos(x), then so is 2π - x.

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The formula that gives us the amount of the radioactive substance remaining at any time t since the start of the experiment, without using any approximations. is y = 19.2 * [tex](1/2)^{(t/15)[/tex]

The formula relating the amount of the radioactive substance at a given time t (in minutes) to the initial amount y₀ can be given as:

y = y₀ * [tex](1/2)^{(t/15)[/tex]

In this formula,  [tex](1/2)^{(t/15)[/tex] represents the fraction of the original amount that remains after t minutes. Since the half-life is 15 minutes, we know that after 15 minutes, half of the original amount remains. After 30 minutes, a quarter of the original amount remains, and so on.

To use this formula for the specific case given in the question, we know that the initial amount y₀ is 19.2 g. Therefore, we can write:

y = 19.2 * [tex](1/2)^{(t/15)[/tex]

This formula gives us the amount of the radioactive substance remaining at any time t since the start of the experiment, without using any approximations.

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Complete question is:

A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 15 minutes. At the start of the experiment, 19.2 g is present. Let t be the time (in minutes) since the start of the experiment, and let y be the amount of the substance at time t.

Write a formula relating y to t .Use exact expressions to fill in the missing parts of the formula.

The probability that Jack and Jill will end up in the same class is 19/59.

The principles of probability and counting are fundamental concepts in probability theory and combinatorics. They are used to solve problems that involve uncertain events and counting arrangements of objects, respectively.

The principles of probability include:

Sample space: The set of all possible outcomes of a random experiment.

Event: A subset of the sample space.

Probability: A measure of the likelihood of an event, expressed as a number between 0 and 1.

Here we have

A group of 60 students is randomly split into 3 classes of equal size.

All partitions are equally likely. jack and jill are two students belonging to that group

Let's assume that Jack is assigned to a class, say the first class.

There are 20 students in that class, and the remaining 40 students are split evenly between the second and third classes.

Since all partitions are equally likely, each of the 59 remaining students has an equal chance of being assigned to any of the two remaining classes.

Now, we want to know the probability that Jill is assigned to the same class as Jack. There are 19 other students in the first class besides Jack, so there are 19 possible students in that class that Jill can be assigned to.

Out of the remaining 59 students, there are 40 in the other two classes, so Jill has 40 possible students she can be assigned to if she is not in Jack's class.

Hence,

The probability that Jill is assigned to the same class as Jack

= 19/59

Therefore,

The probability that Jack and Jill will end up in the same class is 19/59.

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Step-by-step explanation:

log(5x) - log(2) = log(5x/2)

therefore,

log(4x - 1) = log(5x/2)

4x - 1 = 5x/2

8x - 2 = 5x

3x - 2 = 0

3x = 2

x = 2

since this is basically a linear equation in x, there is only one solution, and that is x = 2.

for x = 2 all arguments of the log functions are positive.

4x - 1 = 4×2 - 1 = 8 - 1 = 7

5x = 5×2 = 10

these are all valid arguments for the log function.

so, x = 2 is a valid and not extraneous solution.

The order of h can be any factor of 420 between 43 and 419, inclusive. This is because k is a proper subgroup of h, which means that |k| is a factor of |h|. Since |k| is greater than or equal to 5 and |g| is 420, the maximum possible order of h is 419 (since |h| cannot be equal to |g|). Similarly, the minimum possible order of h is 43 (since |h| cannot be equal to |k|). Therefore, the possible orders of h range from 43 to 419, inclusive, and can be any factor of 420 within this range.

Given that k is a proper subgroup of h and h is a proper subgroup of g, we know that |k| is a factor of |h| and |h| is a factor of |g|. Also, we are given that |k| is greater than or equal to 5 and |g| is 420. Therefore, the maximum possible order of h is 419 (since |h| cannot be equal to |g|), and the minimum possible order of h is 43 (since |h| cannot be equal to |k|).

Now, we need to find the possible orders of h between 43 and 419, inclusive. The factors of 420 within this range are: 43, 46, 69, 83, 138, 207, and 419. Hence, the possible orders of h can be any of these factors.

To sum up, the possible orders of h are any factors of 420 between 43 and 419, inclusive. The maximum possible order is 419, and the minimum possible order is 43. This is because k is a proper subgroup of h, which means that |k| is a factor of |h|, and |g| is 420. Therefore, h can have any factor of 420 within the given range.

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Answer: the answer is 32:12

Step-by-step explanation: add 12+6+14 yw

The percentage of data that falls within three standard deviations of the mean is 99.7%.

The percentage of data that falls within three standard deviations of the mean is determined as follows;

one standard deviation below the mean = 34%

one standard deviation above the mean = 34%

So one standard deviation of the mean = 34% + 34% = 68%

Based on this information, we can conclude the following for a  normal distribution:

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The complete question is below:

For a normal distribution (shown in the diagram), what percentage of data falls within three standard deviations of the mean?

a. The probability of exactly 13 calls is approximately 0.0765.

b. The probability of more than 10 but fewer than 19 calls is approximately 0.7472.

c. The probability of fewer than 10 calls is approximately 0.0952.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

This problem can be solved using the Poisson distribution, which models the number of events that occur in a fixed time interval, given the average rate of occurrence.

Let λ be the average number of calls received by the switchboard in a 30 minute period. Then we have:

λ = 17

(a) To find the probability of exactly 13 calls in a 30 minute period, we use the Poisson distribution with λ = 17 and x = 13:

P(x = 13) = [tex](e^{(-\lambda)} * \lambda^x)[/tex] / x!

P(x = 13) = [tex](e^{(-17)} * 17^{13})[/tex] / 13!

P(x = 13) ≈ 0.0765

So the probability of exactly 13 calls is approximately 0.0765.

(b) To find the probability of more than 10 but fewer than 19 calls in a 30 minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution. The probability of more than 10 calls is:

P(x > 10) = 1 - P(x ≤ 10)

To find P(x ≤ 10), we can sum the probabilities of 0 to 10 calls:

P(x ≤ 10) = Σ [tex](e^{(-\lambda)} * \lambda^x)[/tex] / x!

P(x ≤ 10) ≈ 0.2423

So:

P(x > 10) = 1 - P(x ≤ 10) ≈ 0.7577

Similarly, the probability of fewer than 19 calls is:

P(x < 19) = Σ [tex](e^{(-\lambda)} * \lambda^x)[/tex] / x!

P(x < 19) ≈ 0.9895

So:

P(10 < x < 19) = P(x < 19) - P(x ≤ 10) ≈ 0.7472

Therefore, the probability of more than 10 but fewer than 19 calls is approximately 0.7472.

(c) To find the probability of fewer than 10 calls in a 30 minute period, we can use the CDF of the Poisson distribution:

P(x < 10) = Σ [tex](e^{(-\lambda)} * \lambda^x)[/tex] / x!

P(x < 10) ≈ 0.0952

Therefore, the probability of fewer than 10 calls is approximately 0.0952.

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The recurrence relation is [tex]a n​ =3 n−1 +a n−2​ +2a n−2​ =3 n−1 +3a n−2​[/tex]with initial conditions $a_1=1$ and $a_2=4$.

Let $a_n$ be the number of n digit quaternary sequences with at least one 1 and the first 1 occurring before the first 0. We can split the sequences into two cases:

Case 1: The first digit is 1. There are $3^{n-1}$ possible sequences for this case, since the remaining $n-1$ digits can be any of the three quaternary digits 0, 2, or 3.

Case 2: The first digit is not 1. This means the first digit is 0, 2, or 3, and we must have a 1 before the first 0. There are two subcases:

Subcase 2a: The first digit is 0. In this case, we must have a 1 in the remaining $n-1$ digits. Moreover, the first 1 must occur before the first 0, which means the remaining $n-2$ digits can be any of the three quaternary digits 1, 2, or 3. Therefore, there are $a_{n-2}$ possible sequences for this subcase.

Subcase 2b: The first digit is 2 or 3. In this case, we can have any quaternary digit for the second digit (including 1), but once we have a 1, we must follow the same rules as in subcase 2a. Therefore, the number of possible sequences for this subcase is $2\cdot a_{n-2}$.

Putting everything together, we have the recurrence relation:

[tex]a n​ =3 n−1 +a n−2​ +2a n−2​ =3 n−1 +3a n−2​[/tex]

with initial conditions $a_1=1$ (since the only valid sequence is 1) and $a_2=4$ (since we can have 11, 12, 13, or 21).

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​

To find a basis for the subspace dimension w of R4, we need to find a set of linearly independent vectors that span w.

First, we can rewrite the given condition for w as follows:

w = {(s, 0, 0, 5s) + (0, 4t, 0, -t) + (0, 0, s, 0) + (0, 0, 0, -t) : s, t are real numbers}

Notice that each term in the above expression corresponds to one of the four standard basis vectors in R4. Therefore, the subspace w can be expressed as the span of the following four vectors:

v1 = (1, 0, 0, 5)
v2 = (0, 4, 0, -1)
v3 = (0, 0, 1, 0)
v4 = (0, 0, 0, -1)

To show that these vectors form a basis for w, we need to show that they are linearly independent and that they span w.

To show linear independence, suppose that a linear combination of these vectors is equal to the zero vector:

c1 v1 + c2 v2 + c3 v3 + c4 v4 = (0, 0, 0, 0)

Then we have the following system of equations:

c1 = 0
4c2 = 0
c3 = 0
5c1 - c2 = 0

Solving for the coefficients, we get c1 = c2 = c3 = c4 = 0, which shows that the vectors are linearly independent.

To show that they span w, we need to show that any vector in w can be expressed as a linear combination of these vectors. Let (s, 4t, s, 5s - t) be an arbitrary vector in w. Then we can write:

(s, 4t, s, 5s - t) = (s, 0, 0, 5s) + (0, 4t, 0, -t) + (0, 0, s, 0) + (0, 0, 0, -t)

which is a linear combination of the vectors v1, v2, v3, and v4. Therefore, these vectors span w.

Since we have found a set of four linearly independent vectors that span w, we can conclude that they form a basis for w. Thus, the dimension of the subspace w is 4.

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The value of x that satisfies the equation √3x + 4 = 6 is x = 4/3.

To solve the equation √3x + 4 = 6, we'll need to isolate the variable x. Let's go through the steps to find the solution:

Subtract 4 from both sides of the equation:

[tex]\sqrt{3x}[/tex] + 4 - 4 = 6 - 4

[tex]\sqrt{3x }[/tex]= 2

Square both sides of the equation to eliminate the square root:

[tex](\sqrt{3x)^2} = 2^{-2}[/tex]

3x = 4

Divide both sides of the equation by 3 to solve for x:

(3x)/3 = 4/3

x = 4/3

Therefore, the solution to the equation √3x + 4 = 6 is x = 4/3.

By substituting x = 4/3 back into the original equation, we can verify if it is indeed a solution:

√3(4/3) + 4 = 6

2 + 4 = 6

6 = 6

The equation holds true, confirming that x = 4/3 is the correct solution.

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Answer: Area of a trapezoid is 1/2 x (b1+b2) x height

Step-by-step explanation:

We can be 95% confident that the difference between the overall average waiting times of bank a's customers and bank b's customers is between -0.

to construct a 95% confidence interval for the difference between the overall average waiting times of the two banks' customers, we can use the two-sample t-test with pooled variance. here are the steps to calculate the confidence interval:

1. calculate the pooled variance:

sp² = ((na - 1) * sa² + (nb - 1) * sb²) / (na + nb - 2)     = ((64 - 1) * 1.10² + (100 - 1) * 1.21²) / (64 + 100 - 2)

    = 1.195

2. calculate the standard error of the difference:

se = sqrt(sp² * (1/na + 1/nb))   = sqrt(1.195 * (1/64 + 1/100))

  = 0.249

3. calculate the point estimate of the difference:

point estimate = xa - xb               = 4.87 - 4.50

              = 0.37

4. calculate the margin of error:

me = tα/2 * se   = 1.96 * 0.249

  = 0.488

5. calculate the confidence interval:

ci = point estimate ± margin of error   = 0.37 ± 0.488

  = (-0.118, 0.858) 118 and 0.858 minutes. since the interval contains zero, we cannot conclude that there is a significant difference in the waiting times between the two banks.

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The answer is (a) 0.8161.

In statistical analysis, the proportion of the variation in the response variable (selling price) explained by the predictor variables (square footage, age, number of bedrooms, number of bathrooms, and number of garages) is known as the coefficient of determination or R-squared value. The R-squared value ranges from 0 to 1, where a value closer to 1 indicates that the predictor variables explain a higher proportion of the variation in the response variable. In this case, an R-squared value of 0.8161 suggests that the predictor variables (square footage, age, number of bedrooms, number of bathrooms, and number of garages) explain about 81.61% of the variation in the selling price.

The R-squared value is an important statistic in regression analysis, as it indicates the goodness of fit of the regression model. A high R-squared value suggests that the model fits the data well and can be used to make accurate predictions. However, a high R-squared value does not necessarily mean that the regression model is the best model for the data. It is important to also consider other factors such as model complexity and statistical significance of the predictor variables.

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Answer: 5/4

Step-by-step explanation:

Ah yes terminal angles. I love these. Here's a formula to solve these.

With point P(x,y) and value r where r = square-root of x square + y square, we have:

Sin = y/r

Cos = x/r

Tan = y/x

Csc = r/y

Sec = r/x

Cot = x/y

so tan = y/x. here y = 5 and x = 4 so the answer is 5/4

Answer:

b. 5/4

Step-by-step explanation:

Without knowing the exact angle C, we cannot determine the value of tan θ.

However, we can use the coordinates of point P to determine the ratio of the opposite side to the adjacent side (which is equal to the value of tan θ).

Recall that in the coordinate plane, the x-coordinate represents the adjacent side and the y-coordinate represents the opposite side.

Therefore, in this case:

adjacent side = 4

opposite side = 5

tan θ = opposite/adjacent = 5/4

So, tan θ = 1.25.

1.25 = 5/4

Solving for the constant C using the given initial condition, we can obtain the specific function that satisfies the given conditions. In this case, we find that f(x) = (4/3)x^3 + (7/2)x^2 - 4x + 6.

To find the function f(x) that satisfies f'(x) = 4x^2 + 7x - 4 and f(0) = 6, we integrate the derivative function with respect to x. The result of the integration gives us the function f(x) in terms of x and an arbitrary constant C. Solving for the constant C using the given initial condition, we can obtain the specific function that satisfies the given conditions. In this case, we find that f(x) = (4/3)x^3 + (7/2)x^2 - 4x + 6.

The process of finding the function f(x) involves integrating the derivative function, which is a fundamental concept in calculus. This example illustrates how integration can be used to find the antiderivative of a function, allowing us to obtain the original function from its derivative. The arbitrary constant that appears in the antiderivative represents the family of functions that have the same derivative, and the constant is determined by a specific initial condition.

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Answer:

1/8

Step-by-step explanation:

2^2 / 2^5

2^2 = 2 x 2= 4

2^5 = 2 x 2 x 2 x 2 x 2 = 32

4/32 = 1/8

Note :

2 power 5 means you need to multiply 2, 5 times itself

(i.e) 2 x 2 x 2 x 2 x 2

The height of the trapezoid is 98 units

The space enclosed by the boundary of a plane figure is called its area.

A trapeziod is a closed shape or a polygon, that has four sides, four corners/vertices and four angles

The area of a trapezoid is expressed as;

A = 1/2( a+b)h

where a and b are the bases length of the trapezoid.

245= 1/2 ( 14+21)h

490 = 35h

divide both sides by 35

h = 490/35

h = 98 units

Therefore the height of the trapezoid is 98 units

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To find the distance between x and y, we need to know their coordinates. Let's assume x is located at point (x1, y1) and y is located at point (x2, y2). The distance between them can be calculated using the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

The distance formula is derived from the Pythagorean theorem and can be used to find the distance between any two points in a plane. The formula involves taking the square root of the sum of the squared differences in x and y coordinates between the two points.

In order to find the distance between x and y, we need to know their coordinates and then apply the distance formula. It is a useful formula to know when working with geometric figures and can be applied in various real-life situations such as calculating the distance between two cities on a map.

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The distance between x and y can be calculated using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2).

In order to find the distance between x and y, we need to know the coordinates or positions of x and y. Without this information, we cannot calculate the distance between them. Therefore, we cannot provide a specific answer to this question.

To use this formula, you need the coordinates of the points x and y (x1, y1) and (x2, y2). Plug the coordinates into the formula, then calculate the differences between the x and y values, square them, add them together, and finally, find the square root of the sum. This will give you the distance between x and y.

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The rule for the translated function is:

g(x) = log(x) + 2

We know that the function f(x) is the parent logarithmic function, it can be written as.

f(x) = log(x)

We know that g(x) is a translation of f(x), and we can see that the graph of g(x) is 2 units above the graph of f(x), then we can write:

g(x) = f(x) + 2

Now we can replace the function f(x) there to get:

g(x) = log(x) + 2

That is the translated function.

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Complete question:

"Which of the following functions describes g?

g(x) = log(x) + 2

g(x) = log(x + 2)

g(x) = log(x) - 2"

The exponential regression of the data is  y = 3.143 * 6.064ˣ

Exponential regression is a statistical technique used to model and analyze data that follows an exponential trend. It involves finding the equation of an exponential function that best fits a set of data points. The exponential regression equation has the general form:

y = abˣ

where y is the dependent variable, x is the independent variable, and a and b are the regression coefficients to be determined.

From the given data;

The regression equation is y = 3.143 * 6.064ˣ

The correlation of the data (r) = 0.9941

The r-squared of the data (r²) = 0.9883

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The dotplot depicts that Only 12% of the values of x were 64.7 or greater. Because this is such a small percentage it would be surprising to get a sample mean of 64.7 or larger in an SRS of size 20 from a Normal population with μ = 64 and σ = 2.5.

The dotplot shows that only 12% of the simulated sample means were 64.7 or greater. This means that it is unlikely to get a sample mean of 64.7 or greater if the population mean is actually 64. In other words, the evidence suggests that the population mean height is greater than 64 inches.

The dotplot shows the distribution of the sample means of 250 simulated samples of size 20. The population mean is 64 and the population standard deviation is 2.5.

The fact that only 12% of the simulated sample means were 64.7 or greater means that it is unlikely to get a sample mean of 64.7 or greater if the population mean is actually 64.

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