Given m||n, find the value of x

Given M||n, Find The Value Of X

Answers

Answer 1

Since alternative angles are equal

[tex](7x - 15) = 97[/tex]

[tex]7x = 97 + 15[/tex]

[tex]7x = 112[/tex]

[tex]x = \frac{112}{7} [/tex]

[tex]x = 16[/tex]

Answer 2

Answer:

x = 16

Step-by-step explanation:

The angle (7x - 15) is vertical to the 97° angle, meaning they will be equal.

Find the value of x.

7x - 15 = 97°

7x = 112

x = 16


Related Questions

Which is a prime number? 10, 12, 17

Answers

Answer: 17 is a prime number.

Explanation:

17 is a prime number because it is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, 17 can only be divided evenly by 1 and 17. It is not possible to find any other whole number that can divide into 17 without a remainder. This property is what makes 17 a prime number.

Answer:

17

Step-by-step explanation:

17 is the only # in the set that is only divisible by 1 and itself, make it prime.

On the other hand,

10 is divisible by:

1, 10

2, 5.


12 is divisible by:

1, 12

2, 6

3, 4


So only 17 is prime.

At maturity, the U.S. Rule, the interest calculated from the last partial payment
if the answers are 1. Subtracted from adjusted balance 2. Added to beginning balance 3. Subtracted from beginning balance 4. Added to adjusted balance 5. None of these. What would it be?

Answers

At maturity, using the U.S. rule, the interest calculated from the last partial payment is subtracted from beginning balance added to adjusted balance.

Here, we have,

The payment of money above the principal amount (the amount borrowed) at a predetermined rate to a lender or depositor by a borrower or deposit-taking financial institution is referred to as paying interest in the fields of finance and economics.

It is different from a fee that the borrower may pay to the lender or another entity.

It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve, but not at a set rate predetermined beforehand, but rather on a pro rata basis as a portion of the rewards received by risk-taking businesspeople when revenue is earned that exceeds all costs.

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if no digit may be used more than once, how many 5-digit numbers can be formed using only the digits 3, 8, 1, 2, 5, and 7? (1 point)

Answers

To solve this problem, we need to use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are choosing. In this case, we are choosing 5 digits from a set of 6 digits (since we can't repeat any digit), so we have:

6P5 = 6! / (6 - 5)! = 6 x 5 x 4 x 3 x 2 = 720

Therefore, there are 720 5-digit numbers that can be formed using only the digits 3, 8, 1, 2, 5, and 7, where no digit is used more than once.
To form a 5-digit number using the digits 3, 8, 1, 2, 5, and 7 without repetition, follow these steps:

1. Choose a digit for the first position: You have 6 options (3, 8, 1, 2, 5, or 7).
2. Choose a digit for the second position: You now have 5 remaining options (since you cannot repeat the digit chosen in step 1).
3. Choose a digit for the third position: You have 4 remaining options (excluding the digits chosen in steps 1 and 2).
4. Choose a digit for the fourth position: You have 3 remaining options (excluding the digits chosen in steps 1, 2, and 3).
5. Choose a digit for the fifth position: You have 2 remaining options (excluding the digits chosen in steps 1, 2, 3, and 4).

Now, multiply the number of options for each position: 6 × 5 × 4 × 3 × 2 = 720

So, there are 720 different 5-digit numbers that can be formed using the digits 3, 8, 1, 2, 5, and 7 without repetition.

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the manager of a city recreation center wants to estimate the percent of city residents who favor a proposal to build a new dog park. to gather data, the manager will select a random sample of city residents.

Answers

The manager of the city recreation center aims to estimate the percentage of city residents who support the proposal to build a new dog park. To achieve this, the manager will gather data by selecting a random sample of city residents, which helps ensure an unbiased representation of the population's opinion on the matter.

The manager of the city recreation center can use statistical methods to estimate the percentage of city residents who support the proposal for a new dog park. By selecting a random sample of city residents, the manager can get an idea of what the overall population thinks about the proposal. However, it's important to note that the accuracy of the estimate will depend on the size of the sample and how representative it is of the overall population. Therefore, the manager should make sure to choose a large enough and diverse enough sample to ensure that the estimate is as accurate as possible.

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A rat is placed in a box with three push buttons (electronic buttons), one red, one blue, and one white. If he presses the buttons at random twice, determine the following:What is the probability that he presses the red key exactly 2 times?A) ⅓B) 4/9C) 1/9D) 5/9

Answers

The probability that the rat presses the red button exactly 2 times is 1/9, which corresponds to option C in the multiple-choice list.

To calculate the probability of the rat pressing the red button exactly 2 times, we need to consider the sample space of possible outcomes. Since there are 3 buttons and the rat presses them twice, there are 3 x 3 = 9 possible outcomes.
Now, let's identify the favorable outcomes: The only outcome that satisfies the condition of pressing the red button exactly 2 times is when the rat presses the red button first and then presses the red button again (RR).
There is only 1 favorable outcome, so the probability of pressing the red button exactly 2 times is:
P(RR) = Number of favorable outcomes / Total number of possible outcomes
P(RR) = 1/9

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Please help me with this homework only the answer

Answers

Answer: 11/9 is the slope

11/9

I suggest just googling "slope calculator" if possible because that's a fast way to do these without doing the math

a machine used to fill beverage cans is supposed to put exactly ounces of beverage in each can, but the actual amount varies randomly from can to can. in a sample of cans, the standard deviation of the amount was ounce. a simple random sample of filled cans will have their volumes measured, and a confidence interval for the mean fill volume will be constructed. estimate the number of cans that must be sampled for the margin of error to be equal to ounce.

Answers

Approximately 97 cans must be sampled to achieve a margin of error of 0.01 ounce.

To estimate the number of cans that must be sampled for the margin of error to be equal to 0.01 ounce, we'll use the formula for the sample size in a confidence interval:

[tex]n = \left(\frac{Z \cdot \sigma}{E}\right)^2[/tex]

where n is the sample size, Z is the Z-score for the desired confidence level (95% in this case), σ is the standard deviation (0.05 ounce), and E is the margin of error (0.01 ounce).

For a 95% confidence interval, the Z-score is approximately 1.96. Plugging the values into the formula, we get:

n = [tex]\(\left(\frac{{1.96 \cdot 0.05}}{{0.01}}\right)^2\)[/tex]
n ≈ (9.8)²
n ≈ 96.04

Since we can't have a fraction of a can, we'll round up to the nearest whole number. Therefore, a sample size of approximately 97 cans is needed for the margin of error to be equal to 0.01 ounce with a 95% confidence interval.

This question should be provided as:

A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies randomly from can to can. in a sample of cans, the standard deviation of the amount was σ= 0.05 ounce. A simple random sample of filled cans will have their volumes measured, and a 95% confidence interval for the mean fill volume will be constructed. Estimate the number of cans that must be sampled for the margin of error to be equal to 0.01 ounce.

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A hospital wants to expand its main facility. It can do so using one of two plans (Plan A or Plan B), but must eventually get approval from the State for Plan B. The approval process will take several months, so the hospital must decide whether to seek approval now and await the response, proceed with Plan A, or proceed with Plan B and seek approval later.
1. How many decision nodes are in the tree?
2. Based on the tree, what is the best course of action for the hospital?
A) Seek approval first, and proceed with Plan A whether approved or denied for Plan B
B) Seek approval first, and proceed with Plan B if approved, and Plan A if denied
C) Proceed with Plan A from the start
D) Proceed with Plan B from the start, and switch to Plan A only if denied for Plan B
E) None of these
3. Examine the decision tree carefully. What can you conclude?
A) The tree does not contain conditional probabilities
B) In "rolling back" the decision tree, TreePlan is maximizing the EMV to determine the best course of action
C) The probability of approval for Plan B does not depend on when approval is sought
D) All of these
E) B & C only
4. What is the EMV for choosing Plan B from the start?
A) -96
B) -137.5
C) -88
D) -184.8
E) None of above

Answers

1. There are 3 decision nodes in the tree.
2. The best course of action for the hospital is option B - seek approval first, and proceed with Plan B if approved, and Plan A if denied.
3. The answer is E) B & C only. The decision tree shows conditional probabilities, but TreePlan is not maximizing the EMV. The probability of approval for Plan B does not depend on when approval is sought.
4. The EMV for choosing Plan B from the start is -137.5.


1. Decision nodes are points in a decision tree where a decision must be made. To determine the number of decision nodes in the tree, count the number of places where a choice must be made between different options.

2. To determine the best course of action, you would analyze the decision tree by considering the expected monetary value (EMV) of each path. Choose the path with the highest EMV.

3. Examine your decision tree and determine which conclusions apply. Some things to consider are:
  A) Conditional probabilities: Are there probabilities given based on the outcomes of previous decisions?
  B) "Rolling back" the decision tree: Is the tree being analyzed by working backward from the final outcomes to determine the best course of action?
  C) Probability of approval: Does the chance of getting approval for Plan B change based on when approval is sought?

4. To find the EMV for choosing Plan B from the start, calculate the probability-weighted average of the possible monetary outcomes for that path. Multiply the probability of each outcome by its monetary value, then sum those products.

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Biologists stocked a lake with 400 fish and estimated the carrying capacity ( the maximal population of the species that the lake can support) to be 5400. The number of fish tripled in the first year.
a. Assuming that the size of the fish population satisfies the logistic equation dP/dt=kP(1−Pk), determine the constant k and then solve the equation to find an expression for the size of the population after t years.
b. How long will it take the population to reach 2700?

Answers

It will take approximately 6.96 years for the fish population to reach 2700. The initial fish population (P0) is 400, and after the first year, the population triples, making it 1200. The carrying capacity (K) is 5400. We can use these values to find the constant k.

a. To determine the constant k, we can use the initial conditions given in the problem. In the first year, the number of fish tripled, which means the population increased by a factor of 3. Therefore, we can set P(1) = 3(400) = 1200. We also know that the carrying capacity is 5400, so we can set K = r(1-Pmax/P0) where r is the intrinsic growth rate and P0 is the initial population. Substituting in the values we get K = 0.372.

Now we can solve the logistic equation:

dP/dt = kP(1-P/5400)

Separating variables and integrating, we get:

ln|P/ (5400-P)| = 0.372t + C

where C is the constant of integration. To find C, we can use the initial condition that P(0) = 400:

ln|400/5000| = C

C = -4.605

Substituting C back into the equation, we get:

ln|P/ (5400-P)| = 0.372t - 4.605

Taking the exponential of both sides:

|P/ (5400-P)| = e^(0.372t-4.605)

Multiplying both sides by the denominator and simplifying:

P = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))

b. We want to find the time t when the population reaches 2700. So we can set P = 2700 and solve for t:

2700 = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))

Multiplying both sides by the denominator and simplifying:

2700 + 2700e^(0.372t-4.605) = 5400e^(0.372t-4.605)

Dividing both sides by 2700 and simplifying:

1 + e^(0.372t-4.605) = 2

Taking the natural logarithm of both sides:

0.372t - 4.605 = ln(1)

0.372t = 4.605

t = 12.4 years

Therefore, it will take approximately 12.4 years for the population to reach 2700.

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A circle has a diameter of 12.5 mm. What is the approximate circumference for the circle? Use 3.14 for TT.
39.25 mm
O 490.63 mm²
O 122.66 mm²
O 19.63 mm

Answers

Answer:

39.25 mm

Step-by-step explanation:

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Answers

the probability that a randomly chosen point is in the black region is: 17/36 ≈ 0.472 or about 47.2%

To find the probability that a randomly chosen point is in the black region, we need to divide the number of black squares by the total number of squares in the grid.

Counting the number of black squares, we see that there are 17.

Counting the total number of squares in the grid, we see that there are 36.

Therefore, the probability that a randomly chosen point is in the black region is: 17/36 ≈ 0.472 or about 47.2%

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a committee of four people is formed by selecting members from a list of 12 people. how many different committees can be formed?

Answers

495 different committees can be formed by selecting 4 members from a list of 12 people.

In this case, we have 12 people to choose from and we want to form a committee of 4 people. The number of different committees that can be formed is represented by the combination formula:

C(n, r) = n! / [r! * (n - r)!]

Where n = total number of people (12), r = number of people in the committee (4), and ! represents the factorial function.

Applying the formula:
C(12, 4) = 12! / (4! * (12 - 4)!)

C(12, 4) = 12! / (4! * 8!)

C(12, 4) = (12 * 11 * 10 * 9 * 8!)/(4 * 3 * 2 * 1 * 8!)

The 8! in the numerator and denominator cancels out:

C(12, 4) = (12 * 11 * 10 * 9)/(4 * 3 * 2 * 1)

C(12, 4) = 11880/24

C(12, 4) = 495

So, 495 different committees can be formed by selecting 4 members from a list of 12 people.

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Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3√28

Answers

Using a linear approximation (or differentials) we estimate 3√28 is 3.11111.

To estimate the cube root of 28 using linear approximation, we first need to find a nearby perfect cube. In this case, the closest perfect cube is 27, since [tex]3^3[/tex] = 27.
Let's use the function f(x) = [tex]x^{(1/3)}[/tex]. We want to approximate f(28) using linear approximation. To do this, we will find the tangent line to f(x) at x=27, which will give us a good approximation for f(28).
First, find the derivative of f(x):
f'(x) = [tex](1/3)x^{(-2/3)}[/tex]
Now, evaluate the derivative at x=27:
f'(27) = [tex](1/3)(27)^{(-2/3)}[/tex] = [tex](1/3)(3^{(-2)})[/tex] = 1/9
Next, find the value of f(27):
f(27) = [tex]27^{(1/3)}[/tex] = 3
Now, we can find the equation of the tangent line at x=27:
y = f(27) + f'(27)(x - 27)
y = 3 + (1/9)(x - 27)
Finally, approximate f(28) by plugging x=28 into the tangent line equation:
y ≈ 3 + (1/9)(28 - 27)
y ≈ 3 + (1/9)(1)
y ≈ 3 + 1/9
y ≈ 3.11111
So, using linear approximation, we estimate that the cube root of 28 is approximately 3.11111, rounded to five decimal places.

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T/F : The absolute value of the determinant of A equals the volume of the parallelepiped determined by the columns of A

Answers

True.

The determinant  of a matrix A is defined as the scaling factor of the linear transformation determined by A.



The determinant  of a matrix A is defined as the scaling factor of the linear transformation determined by A. Geometrically, the absolute value of the determinant of a matrix A can be interpreted as the factor by which the linear transformation determined by A changes the volume of a unit cube.

Consider the columns of A as vectors in n-dimensional space. The parallelepiped determined by the columns of A is the n-dimensional generalization of a parallelogram in two dimensions or a parallelepiped in three dimensions. The volume of this parallelepiped can be computed as the absolute value of the determinant of A.

To see why this is true, consider the special case of a 2x2 matrix A:

```
A = [[a, c],
[b, d]]
```

The columns of A are the vectors `[a, b]` and `[c, d]`. The parallelogram determined by these vectors has area equal to the absolute value of the determinant of t of

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one key assumption of correlation analysis is that the variables have an essentially relationship. select one: a. linear b. non-linear c. curvilinear d. circular

Answers

One key assumption of correlation analysis is that the variables have a linear relationship. This means that the relationship between the two variables can be described by a straight line. In other words, as one variable increases, the other variable increases or decreases in a consistent manner.

When conducting correlation analysis, it is important to ensure that the relationship between the variables is indeed linear. This can be done by examining a scatterplot of the data, which allows you to visualize the relationship between the two variables. If the relationship appears to be curvilinear, non-linear, or circular, then a different type of analysis may be more appropriate.

Overall, the assumption of a linear relationship is important for ensuring the accuracy and validity of the correlation analysis. It allows for a clear and interpretable understanding of the relationship between the two variables and can inform further statistical analysis or decision-making.

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How many gallons are equivalent to 24 cup? show your work. 1 gallon = 4 quart = cups

Answers

1.5 gallons are equivalent to 24 cups because 1 gallon = 4 quarts or 16 cups.

What are equivalent values?

Equivalent values are values that are equal or equivalent, notwithstanding the unit of expression or measurement.

For instance, we know that 1 gallon equals 4 quarts, and 4 quarts are equivalent to 16 cups.

The total number of cups = 24

1 gallon = 4 quart

1 quart = 4 cups

1 gallon = 16 cups

24 cups = 1.5 gallons (24 ÷ 16).

Thus, since we can state categorically that 1 gallon is equivalent to 16 cups, 24 cups will be equivalent to 1.5 gallons.

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the salary for workers at a company are normally distributed with a mean of $60,000 and a standard deviation of $9,000. a random sample of 36 employees was taken. the top 10% salaries of workers at that company is or more. round to the nearest dollar.

Answers

To find the top 10% salaries of workers at the company, we need to use the standard normal distribution table. First, we need to find the z-score that corresponds to the top 10% of the distribution, which is 1.28 (found using the table).

Next, we can use the formula:

z = (x - mean) / (standard deviation / sqrt(sample size))

We know the mean is $60,000, the standard deviation is $9,000, and the sample size is 36. We can solve for x:

1.28 = (x - 60,000) / (9,000 / sqrt(36))

1.28 = (x - 60,000) / 1,500

1.28 * 1,500 = x - 60,000

1,920 + 60,000 = x

x = $61,920

Therefore, the top 10% salaries of workers at the company is $61,920 or more.
To find the top 10% salary for workers at this company, we need to first determine the z-score that corresponds to the 90th percentile. This is because 100% - 10% = 90%.

Step 1: Look up the z-score for the 90th percentile in a standard normal distribution table. You will find a z-score of approximately 1.28.

Step 2: Use the z-score formula to find the salary corresponding to this z-score:
X = μ + Z * σ / √n
where X is the salary, μ is the mean, Z is the z-score, σ is the standard deviation, and n is the sample size.

Step 3: Plug in the given values:
X = $60,000 + 1.28 * $9,000 / √36

Step 4: Simplify the equation:
X = $60,000 + 1.28 * $9,000 / 6

Step 5: Calculate the result:
X = $60,000 + $1,920 = $61,920

The top 10% of salaries for workers at this company is $61,920 or more, rounded to the nearest dollar.

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Find the coordinates of point W. A. (0.25, 3.75) B. (2.75, 0.25) C. (3.5, 0.25) D. (3.75, 0.25)

Answers

The coordinate of point w is (3.75, 0.25).

Option D is the correct answer.

We have,

From the graph, we can see that,

The coordinate on the x-coordinate at point w is 3.75.

The coordinate on the y-coordinate at point w is 0.25.

Thus,

The coordinate of point w is (3.75, 0.25).

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What does it mean when eigenvalues are equal?

Answers

When the eigenvalues of a matrix are equal, it means that the matrix has repeated eigenvalues. This can occur for matrices of any size, but is most commonly encountered for 2x2 or 3x3 matrices.

When a matrix has repeated eigenvalues, it can exhibit some special behaviors that are not observed for matrices with distinct eigenvalues. In particular, the matrix may not be diagonalizable, meaning that it cannot be transformed into a diagonal matrix using a change of basis. Instead, it may have only one eigenvector associated with the repeated eigenvalue, or it may have a full set of linearly independent generalized eigenvectors.

In the case of a 2x2 matrix A with repeated eigenvalues λ, the matrix may be expressed in Jordan canonical form as:

A = P * J * P^-1

where J is a matrix with λ on the diagonal and 1 on the super-diagonal, and P is the matrix whose columns are the eigenvectors and generalized eigenvectors of A. In this case, the solutions of the system x' = Ax may have a non-trivial component along the generalized eigenvector, which can lead to more complicated behavior than for matrices with distinct eigenvalues.

Overall, the presence of repeated eigenvalues in a matrix can indicate that the matrix has some special structure or symmetry, and may require additional techniques beyond diagonalization to fully understand its behavior.

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how many grams of CaC2 are needed to react completely with 490 moles of H2O

Answers

It takes 15,699.5 grams of CaC2 to thoroughly react with 490 moles of water.

The balanced chemical equation for the reaction of calcium carbide (CaC₂) with water (H₂O) is:

CaC₂ + 2H₂O → Ca(OH)₂ + C₂H₂

From the equation, we can see that 1 mole of CaC₂ reacts with 2 moles of H₂O. Therefore, to find the number of moles of CaC₂ needed to react completely with 490 moles of H₂O, we divide 490 by 2:

Number of moles of CaC₂ = 490 moles of H₂O / 2 = 245 moles of CaC₂

Now, we need to use the molar mass of CaC₂ to convert the number of moles to grams:

Molar mass of CaC2 = 64.10 g/mol

Mass of CaC₂ = Number of moles of CaC₂ x Molar mass of CaC₂

= 245 moles x 64.10 g/mol

= 15,699.5 g

Therefore, 15,699.5 grams of CaC₂ are needed to react completely with 490 moles of H₂O.

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Annette cut a piece of wood in the shape of a triangular pyramid. The diagram shows the dimensions of the wood piece.

The volume of the wood is 18 cubic inches. What is h, the height of the wood in inches?

_________________​

Answers

Answer:

the height of the triangular pyramid is 2.25 inches.

Step-by-step explanation:

To find the height of the triangular pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × base area × height

where the base area is the area of the triangle and the height is the height of the pyramid.

We know that the volume of the wood is 18 cubic inches, so we can substitute the given values into the formula:

18 = (1/3) × (4 × 6) × h

Multiplying both sides by 3, we get:

54 = 24 × h

Dividing both sides by 24, we get:

h = 2.25

Therefore, the height of the triangular pyramid is 2.25 inches.

How much will 2 pencils cost if 7 pencils cost $1.82

Answers

Answer:

$0.52

Step-by-step explanation:

1. Find the cost of 1 pencil by dividing the cost of 7 pencils by 7 pencils:

1.82 / 7 = 0.26

This means 1 pencil cost $0.26.

2. To find the cost of 2 pencils multiply the cost of 1 pencil by 2:

0.26 x 2 = 0.52

Hence, 2 pencils cost $0.52 of 7 pencils cost $1.82.

the average house has 15 paintings on its walls. is the mean larger for houses owned by teachers? the data show the results of a survey of 12 teachers who were asked how many paintings they have in their houses. assume that the distribution of the population is normal. round your mean and standard deviation to three decimal places when doing these calculations.

Answers

Since the calculated t-value of 4.38 is greater than the critical value of -1.796, we reject the null hypothesis and conclude that there is evidence to suggest that the mean number of paintings on the walls of houses owned by teachers is larger than the mean number of paintings on the walls of all houses.

Let μ be the population mean number of paintings on the walls of all houses, and let μt be the population mean number of paintings on the walls of houses owned by teachers. The null hypothesis is that there is no difference between the mean number of paintings on the walls of all houses and the mean number of paintings on the walls of houses owned by teachers:

H0: μ = μt

The alternative hypothesis is that the mean number of paintings on the walls of houses owned by teachers is larger than the mean number of paintings on the walls of all houses:

Ha: μ < μt

We can use a one-sample t-test to compare the sample mean number of paintings on the walls of houses owned by teachers to the population mean of 15 paintings. Let X be the sample mean number of paintings on the walls of houses owned by teachers and s be the sample standard deviation. We are given the following data from the survey:

n = 12

X = 20

s = 5.48

The test statistic is:

t = (X - μ) / (s / √(n))

Using the null hypothesis μ = 15, we get:

t = (20 - 15) / (5.48 / √(12))

= 4.38

The degrees of freedom for this test are n - 1 = 11. Using a t-distribution table with 11 degrees of freedom and a significance level of 0.05, we find a critical value of -1.796.

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WILL MARK BRAINLIEST!!!
What is the boat’s velocity vector? PLEASE SHOW YOUR WORK AND INCLUDE ALL CORRECT UNITS!

Answers

Answer:

Magnitude: 23.4 kph

Direction: 50.2° below horizontal.

Step-by-step explanation:

15² + 18² = s²

s² = 549

s = 23.4

Θ = tan^-1 18/15

Θ = 50.2°

The velocity vector is the sum of the two vectors which is a vector that starts at the boat and goes until the lower tip of the vertical arrow.

Its magnitude is 23.4 kph, and its direction is 50.2° below horizontal.

Answer:  boats vector is 23.45 kph, 50.2° south of east

Step-by-step explanation:

A  vector has both direction and magnitude.

The vector for the boat is the shortest route from the boat to that end point which is a diagonal.

In order to find magnitude you use pythagorean

c²=a²+b²

m=15²+18²

m=√549

magnitude=23.45 kph

direction you would use tan∅

tan∅=opp/adj=18/15

∅= [tex]tan^{-1} \frac{18}{15}[/tex]

∅=50.2

So the boats vector is 23.45 kph, 50.2° south of east

please help i need a good explanation!! thanks!! :)

Answers

The sides of the quadrilateral are

FG = 11

GH = 22

HJ = 33

FJ = 44

How to find sides of the quadrilateral

When the quadrilateral are similar according to the ratio 7 : 11 and the similar sides are:

FG : AB

GH : BC

HJ : CD

FJ : AD

Since FJ : AD the ratio is 11 : 7, therefore where FJ = 11 then AD = 7 = x

FG : AB

AB = 2x = 2 * 7 = 14

For FG

11 ⇔ 7

FG ⇔ 14

cross multiplying

7 * FG = 14 * 11

FG = 22

For GH

11 ⇔ 7

GH ⇔ BC = 3 * 7 = 21

cross multiplying

7 * GH = 21 * 11

GH = 33

For HJ

11 ⇔ 7

HJ ⇔ CD = 4 * 7 = 28

cross multiplying

7 * GH = 28 * 11

GH = 44

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The hits to a Web site occur at the rate of 10 per minute between 7:00 P.M. and 10:00 P.M. The random variable X is the number of hits to the Web site between 7:56 P.M. and 8:22 P.M. State the values of land for this poisson process.

Answers

Given that the hits to a web site occur at a rate of 10 per minute between 7:00 P.M. and 10:00 P.M., we can say that the web site experiences a Poisson process. The value of land for this Poisson process is 260.

The random variable X represents the number of hits to the web site between 7:56 P.M. and 8:22 P.M.

To find the values of λ, we need to use the formula for the Poisson distribution:

P(X = k) = (λ^k * e^-λ) / k!

where λ is the average number of hits per unit time.

Since we are interested in the hits between 7:56 P.M. and 8:22 P.M., which is a duration of 26 minutes, we need to adjust the rate of hits accordingly. Therefore, λ for this duration would be:

λ = 10 hits/min * 26 min = 260 hits

So, the values of λ for this Poisson process would be λ = 260.

To determine the values of λ (lambda) for this Poisson process, we need to first calculate the time interval between 7:56 P.M. and 8:22 P.M. and then find the expected number of hits to the website during that time.

Step 1: Calculate the time interval
The time interval between 7:56 P.M. and 8:22 P.M. is 26 minutes.

Step 2: Determine the expected number of hits
The website receives hits at a rate of 10 per minute. To find the expected number of hits during the 26-minute interval, multiply the rate by the length of the interval:
10 hits/minute * 26 minutes = 260 hits

Step 3: State the value of λ for the Poisson process
The random variable X represents the number of hits to the website during this interval. Since the expected number of hits is 260, the value of λ for this Poisson process is 260.

Your answer: The value of λ for this Poisson process is 260.

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An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?

40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches

Answers

The dimensions of the actual painting are 32 inches by 40 inches

What are the dimensions of the actual painting?

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

Scale = 4:1.

The dimensions of the scaled painting are 8 inches by 10 inches.

So, we have

Actual = 4 * 8 inches by 4 * 10 inches

Evaluate

Actual = 32 inches by 40 inches

Hence, the dimension is 32 inches by 40 inches

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kate started solving the problem by finding 200% of of $25,000 how might she have finished solving the problem??​

Answers

The value of the expression 200% of of $25,000 is $50,000

Calculating the percentage expression

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

200% of $25,000

The above expression is a percentage expression and mathematically, can be expressed as

Value = 200% of $25,000

Express "of" as products

So, we have

Value = 200% of $25,000

Evaluate the products in the expression

So, we have the following

Value = $50,000

Hence, the solution of the expression 200% of of $25,000 is $50,000

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A solid wooden post in the shape of a right rectangular prism measuring 5 cm by 9 cm by 24 cm is drilled with a cylindrical hole of radius 2 cm. Find the volume of the post after the hole has been drilled. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.)

Answers

The final volume of the wooden post after the hole has been drilled is 778.41 cm³.

The volume of a right rectangular prism is given by the formula V = l × w × h, where l, w, and h represent the length, width, and height of the prism, respectively. In this case, the wooden post has dimensions of 5 cm by 9 cm by 24 cm, so its original volume is:

V1 = 5 cm × 9 cm × 24 cm = 1080 cm³

Now, we need to find the volume of the cylindrical hole. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the cylinder and h is its height. In this case, the hole has a radius of 2 cm and goes through the entire length of the wooden post, so its volume is:

V2 = π × 2 cm² × 24 cm ≈ 301.59 cm³

To find the final volume of the wooden post, we need to subtract the volume of the hole from the original volume:

Vfinal = V1 - V2 = 1080 cm³ - 301.59 cm³ = 778.41 cm³

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A large chocolate bar has a base area of 63.80 square feet and its length is 0.6 foot shorter than twice its width. Find the length and the width of the bar.

Answers

The length and the width of the bar are 11.06 feet and 5.83 feet respectively

Solving for the dimensions of a bar

Let the width of the chocolate bar be x

From the question, the length of the chocolate bar is 0.6 feet shorter than twice its width. Therefore, the length (l) can be expressed as:

l = 2x - 0.6

The base area of the chocolate bar is given as 63.80 square feet. We can use this information to write an equation for the area of the chocolate bar in terms of its length and width:

area = length * width

63.80 = (2x - 0.6) * x

Expanding the right-hand side, we get:

63.80 = 2x² - 0.6x

Subtracting 63.80 from both sides, we get:

2x² - 0.6x - 63.80 = 0

Dividing both sides by 2, we get:

x² - 0.3x - 31.90 = 0

We can now solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = -0.3, and c = -31.90

Substituting in the values, we get:

x = (-(-0.3) ± sqrt((-0.3)^2 - 4(1)(-31.90))) / 2(1)

x = (0.3 ± sqrt(0.09 + 127.60)) / 2

x = (0.3 ± 11.36) / 2

We can now solve for the two possible values of x:

x = (0.3 + 11.36) / 2 = 5.83 or x = (0.3 - 11.36) / 2 = -5.53

Since the width of the chocolate bar cannot be negative, therefore, the width of the chocolate bar is 5.83 feet.

We can now use the equation for the length of the chocolate bar to find its length:

l = 2x - 0.6

l = 2(5.83) - 0.6

l = 11.06

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