find and sketch the domain of the function. f(x, y) = ln(9 − x2 − 9y2)

If the true population distribution is close to the population distribution assumed in the null hypothesis, the power tends to be lower.

Explanation:
1. True population distribution refers to the actual distribution of the population.
2. Null hypothesis is the assumption that there is no significant difference between the observed and expected data.
3. Power is the probability of correctly rejecting the null hypothesis when it is false.

So if the true population distribution is close to the null hypothesis distribution, it is less likely that significant differences will be found in the sample.

When the true population distribution is close to the null hypothesis, it becomes more difficult to detect a significant difference, leading to a lower power in the statistical test.

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Based on the given inverse variation between x and y, y = 1 when x = 2.

x = k/y

Where,

k = constant of proportionality

When x = 1 and y = 2

x = k/y

1 = k/2

cross product

1 × 2 = k

2 = k

So,

x = 2/y

find y when x = 2.

x = 2/y

2 = 2/y

cross product

2y = 2

divide both sides by 2

y = 2/2

y = 1

Ultimately, the value of y when x = 2 is 1.

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The company that has a lower minimum and find the minimum value will be B- f(x) at (16, 536)

The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:

f(16) = 0.25(16)^2 - 8(16) + 600 = 536

So, the minimum value of f(x) is 536, and it occurs at x = 16.

In conclusion, the correct option is B.

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Tt is requried to check their answers for extraneous solutions if there is a radical involved in the equation.

Yes, it is recommended to check for extraneous solutions when solving equations involving radicals. In this case, we would need to solve the equation and then substitute the solution back into the original equation to see if it results in a true statement. If it does not, then it is an extraneous solution and should be discarded.

Thus, it is requried to check their answers for extraneous solutions if there is a radical involved in the equation.

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The value of the equation gives mILR = 52°.

Since TL is a diameter, we know that mICR + m/RCL = 90°. Substituting the given values, we get:  (3x + 5)° + (x - 1)° = 90°

Simplifying the equation, we get:

4x + 4 = 90

Solving for x, we get:

x = 22

Therefore, x = 22.

2. Since TL is a diameter, we know that mICR = 90°. Substituting the value of x, we get:

mICR = (3x + 5)° = (3 × 22 + 5)° = 71°

Therefore, mICR = 71°.

3. Since TL is a diameter, we know that mILR = 180° - mICR - m/RCL. Substituting the values of x, we get:

mILR = 180° - (3x + 5)° - (x - 1)° = 180° - 4x - 4°

Substituting the value of x, we get:

mILR = 180° - (4 × 22 + 4)° = 52°

Therefore, mILR = 52°.

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The expression |62| is equal to 62.

We have,

The absolute value of 62 is 62, because the absolute value is a measure of distance from zero, and 62 is 62 units away from zero in the positive direction on the number line.

The absolute value of a number is defined as the distance of that number from zero on the number line, regardless of the direction.

It is always a non-negative value.

In this case, the number is 62.

If we locate 62 on the number line, we can see that it is 62 units away from zero in the positive direction, because we count 62 units to the right of zero to reach 62.

Since the absolute value of a number is always non-negative, we take the positive value of 62 and conclude that the absolute value of 62 is 62, written as |62| = 62.

Therefore,

|62| is equal to 62.

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The volume of the rectangular pyramid is 130.7 cubic units.

The volume of a rectangular pyramid can be calculated as:

V = 1/3 × l × w × h

where l, w, and h are the length, width, and height of the rectangular pyramid, respectively.

Given that a rectangular pyramid with a length of 7 units, a width of 7 units, and a height of 8 units.

To find the volume of a given pyramid,  substitute the values into the formula:

V = 1/3 × l × w × h

V = 1/3 × 7 × 7 × 8

V = 130.7 units³

Therefore, the volume of the rectangular pyramid is 130.7 cubic units.

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The missing figure has been attached below.

The expression 2p + 4 = 6 solved with the defined steps is p = 1

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

2p + 4 = 6

Subtract 4 from both sides

2p = 2

Divide both sides from 2

p = 1

Hence, the solution is p = 1

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The iPad bought by Mr. Lee has the original price of $294 if he paid $250 with 15% off the iPad

Discount refers to the reduction in the original price to allure customers to buy the product.

Original price = discounted price + discount

Let the original price be x

Given, discounted price (or price after discount) = $250

Discount % = 15%

Discount % = (original price - discounted price) / original price * 100

15 = [tex]\frac{x-250}{x}*100[/tex]

15x = (x - 250) 100

3x = 20x - 5000

5000 = 17x

x = 294.1

Therefore, the original price is around $294

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Answer:

triangle

Step-by-step explanation:

The cross section must be a vertical cross section that includes the vertex of the pyramid.

Answer: triangle

The speed baba Yaga flies in calm weather is 8.88889 km/hr.

Given the speed of tailwind is 2 km/hr

Total distance = 2 * distance to mountain

Total distance= 2 * 40

Total distance = 80 km

total time taken for the journey = the time it took Baba Yaga to fly to the mountain (6 hours)  +  time it took her to fly back home (3 hours)

The total can be calculated using the above equation which gives us a total time of 9 hours.

So, total time for the journey = 9 hours

speed in calm weather = the total distance by the total time

speed in calm weather = 80 / 9 = 8.88889 km/hr

So, Total distance =  80 km

total time = 9 hours

speed in calm weather = the total distance by the total time

speed in calm weather = 80 / 9 = 8.88889 km/hr

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The largest integer that can be in the data-set is given as follows:

13.

The data-set in this problem has five integers, hence the median of 5 is the third element, given as follows:

x, y, 5, w, z.

The mean is also of 5, meaning that the sum of the other elements is 20, that is:

x + y + w + z = 20.

z will be maximized when x = 1,  y = 1 and w = 5, hence:

1 + 1 + 5 + z = 20

z = 13.

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The amount of money you will get if you invest $1000 in an account with 4.5% annual interest, compounded annually, in 5 years is: $1221.

If we assume that the interest is compounded annually, the formula we would apply to calculate the future value of an investment is given as:

[tex]FV = PV x (1 + r)^n[/tex] where we have:

PV = present value (the initial investment)

r = annual interest rate (as a decimal)

n = number of compounding periods

In this case, we are given the following:

PV = $1000

r = 0.045 (4.5% expressed as a decimal)

n = 5 (5 years)

Substituting these values into the formula, we would get the following:

FV = $1000 x (1 + 0.045)^5

FV = $1000 x 1.221

FV = $1221

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Option c.  A = 1/2 bcSin A is the area of a traingle

The sine rule is a mathematical equation that links the side lengths of a triangle to the sines of its respective angles. The formula for determining the area in such a triangle is represented as follows:

A = (1/2) ab sin C

= (1/2) bc sin A

= (1/2) ac sin B

where a, b, and c symbolize the lengths of the triangle's sides while A, B, and C stand for the measures of their opposite angles.

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J = 2G + 5.96/2 will give you the distance Joe ran last week.

Three friends were training to run a race. Joe ran 8.5 miles. If Gavin ran 2.98 miles less than Joe, then;

G = J - 2.98 ...... 1

If Nate ran twice as far as Joe, then Nate distance will be:

N = 2J ....... 2

From equation 1

J = G + 2.98 .........  3

Substitute equation 3 into 2 to have;

N = 2(G + 2.98)

N = 2G + 5.96

J = N/2
J = 2G + 5.96/2

Hence the equation to find the distance that Joe ran last week is J = 2G + 5.96/2

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Independent variable (x) is time in minute, dependent variable (y) is amount of fuel in the tank in liters and the rate of change for this linear relationship is 270 L/min.

The variable that is independent in time because no matter what, it will flow. The dependent variable is amount of fuel. The rate of change of this linear relationship is the slope of the line, which is equal to the amount of fuel added per unit time, in this case, 1620 L added every 6 minutes, or 270 L/min. This indicates that the amount of gasoline in the tank rises at a constant pace of 270 liters per minute.

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The tips as well as tricks that can help you know about right angle trig are::

Know the trig ratios such as: sine, cosine, and digression. One can be able to make use of them to know  the length of a side or the measure of an point in a right-angled triangle.

By Learning the SOH-CAH-TOA acronym, it will help assist you tp keep in mind the ratio to use .

Lastly, make sure that your calculator is set to the proper mode such as (degrees or radians) which you are using the right buttons to solve for the trig capacities.

Hone with parts of illustrations.

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If 8 men and 8 women collaborate, the task can be finished in 36 days for the former and 45 days for the latter.

Using the following formula, we can determine the total quantity of work that needs to be done.

Total work equals (people) ×(time spent).

The first scenario is as follows:

Total work is equal to (288 man-days)= (12 men x 24 days)

Total work is calculated as (15 women) x (24 days) = (360 woman-days).

Using the same approach, we can now determine how many days it would take eight people—either eight men or eight women—to do the same amount of work:

Eight men:

Total labor: (8 men)× (time required)

288 man-days = (8 men) × (time taken)

time taken = 36 days

Eight women:

total work = (8 women) × (time taken)

360 woman-days = (8 women) × (time taken)

time taken = 45 days

Thus, if 8 males collaborate, they can finish the job in 36 days, and if 8 women collaborate, they can finish the job in 45 days.

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One of the factors of the quadratic polynomial -200x² + 2,800x - 4,800 = 0 is x - 2.

Given information:

The owner of a hotdog stand wants to make the price of her hotdogs reasonable but also maximize her profits.

First, we can simplify the equation by factoring out -200:

-200x² + 2,800x - 4,800 = 0

Next, we can simplify further by dividing each term by -200:

x² - 14x + 24 = 0

To factor this trinomial expression, we need to find two numbers that multiply to 24 and add to -14. These numbers are -2 and -12:

(x - 2)(x - 12) = 0

Therefore, the factor is x - 2, which corresponds to option A.

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The best estimate for the worms population in the region is 600 worms.

Given that, Sherry catches 750 worms, marks them, and releases them. Then later, she catches 400 worms, 12 of which are marked.

Estimated Population Size = (Number of worms captured) x (Number of worms recaptured) / (Number of marked worms recaptured)

In this case, the equation would be:

Estimated Population Size = (750 × 400)/12

This equation simplifies to:

Estimated Population Size = 300000/12

= 25000

Therefore, the best estimate for the worms population in the region is 600 worms.

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True. In a 5 by 5 matrix, if A has two pivots, then the dimension of the nullspace (Nul A) is 3, which can be found using the rank-nullity theorem:

rank(A) + dim(Nul A) = 5

Since A has two pivots, its rank is 2.

Suppose we have an m x n matrix A. The rank-nullity theorem states that the sum of the rank of A and the dimension of the nullspace of A is equal to the number of columns in A, that is:

rank(A) + dim(Nul A) = n

where rank(A) is the number of linearly independent rows or columns in A, and dim(Nul A) is the dimension of the nullspace of A.

Now, suppose we have a 5 x 5 matrix A that has two pivots. Since A has two pivots, it means that there are two linearly independent rows or columns in A. Therefore, the rank of A is 2. Applying the rank-nullity theorem, we get:

rank(A) + dim(Nul A) = 5

Substituting rank(A) = 2, we get:

2 + dim(Nul A) = 5

which implies that dim(Nul A) = 3. This means that the nullspace of A has dimension 3, which means that there are 3 linearly independent solutions to the equation Ax = 0.

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a. The probability that a train arrives in 35 minutes or more is 0. This is because, according to the uniform probability distribution, there should be a 100% chance (probability of 1.00) that a train will arrive within the 0 to30-minutes time frame.
b. It may be possible that there were additional factors affecting the train schedule that your friend was not aware of, such as delays or schedule changes.

a. Given your friend's information, the probability of a train arriving in 35 minutes or more would be 0 because according to your friend, a train stops at the station every 30 minutes. Therefore, the maximum waiting time should have been 30 minutes.

b. Based on your actual experience of waiting for 35 minutes, you can conclude that your friend's information about the train schedule was not accurate or up-to-date. It is possible that the train schedule has changed or that there was a delay or some other unforeseen circumstance that caused the train to arrive later than expected. It is important to verify the information and not rely solely on assumptions or generalizations.

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It will take x/n hours to complete the painting at this rate

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

1/x of the fence in 1/n of the hour

This means that

Time = 1/n hour

Length = 1/x fence

So, we have

Unit rate = Hour/Length

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (1/n)/(1/x)

Evaluate the expression

Unit rate = x/n

Hence, the time taken is x/n hour

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There are 95 chairs in row 9.

b. Consider a_n to signify the number of chairs in the nth row with the purpose of making a recursive rule for this sequence. In terms of a_n-1, we can thus write a_n as a_n = a_n-1 + 5.

The default setting is a_1 = 15.

c. Utilizing the formula for an arithmetic series' nth term, we can devise a clear-cut rule to define this sequence: a_n = a_1 + (n - 1)d. Here, 'd' is a common difference, 'a_1' represents the initial term, and 'n' denotes the sequential number of said term.

As such, applying these variables to our scenario with 'a_1=15' and 'd=5', we conclude that:

a_n = 15 + (n - 1)5

a_n = 10n + 5

d. To find the number of chairs in row 9 using the explicit rule, we plug in n = 9

a_9 = 10(9) + 5

a_9 = 90 + 5

a_9 = 95

Therefore, there are 95 chairs in row 9.

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A trigonometric equation to express d in terms of t is d = A sin(Bt - C) + D, the weight is approximately 16 centimeters above the floor at 4 seconds.

The distance, d, of the weight above the floor at time t can be expressed as a sinusoidal function of the form:

d = A sin(Bt - C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

We are given that the weight reaches its first high point (maximum) at 0.5 seconds, which means that the phase shift is 0.5 seconds. At this point, d = 42 centimeters, which means that the amplitude is 42/1 = 42 centimeters.

We are also given that the next low point (minimum) occurs at 1.2 seconds, which means that the function has completed one full period between 0.5 and 1.2 seconds. Therefore, the period of the function is:

T = 1.2 - 0.5 = 0.7 seconds

The frequency, B, is the reciprocal of the period:

B = 1/T = 1/0.7 ≈ 1.43

Finally, we need to find the vertical shift, D. At time t = 0, the weight is at its equilibrium position, which is the midpoint between the maximum and minimum heights:

D = (42 + 11)/2 = 26.5

Putting all of this together, we get:

d = 42 sin(1.43(t - 0.5)) + 26.5

To find the weight's distance from the floor at 4 seconds, we simply need to plug in t = 4 into the equation and round to the nearest centimeter:

d = 42 sin(1.43(4 - 0.5)) + 26.5 ≈ 16 centimeters

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The 90% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is (approximately) 1.6 ± 2.3. This means that we can be 90% confident that the true difference in testing averages lies between -0.7 and 3.9.

To construct the 90% confidence interval for the true difference between testing averages for students using method 1 and students using method 2, we can use the following formula:

CI = (x1 - x2) ± t(alpha/2, df) * sqrt(s1^2/n1 + s2^2/n2)

where:
x1 = 54.8 (sample mean for method 1)
x2 = 53.2 (sample mean for method 2)
s1 = 5.1 (standard deviation for method 1)
s2 = 12.47 (standard deviation for method 2)
n1 = 149 (sample size for method 1)
n2 = 180 (sample size for method 2)
alpha = 0.1 (1 - 0.9 for a 90% confidence interval)
df = n1 + n2 - 2 (degrees of freedom)

Plugging in the values, we get:

CI = (54.8 - 53.2) ± t(0.05, 327) * sqrt((5.1^2/149) + (12.47^2/180))
  = 1.6 ± 1.65 * 1.423
  = 1.6 ± 2.344

Therefore, the 90% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is (approximately) 1.6 ± 2.3. This means that we can be 90% confident that the true difference in testing averages lies between -0.7 and 3.9.

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In both cases, for a line of k+1 people, there exists a woman directly in front of a man. Thus, by mathematical induction, the statement holds true for all positive integers n where the first person is a woman and the last person is a man.

To prove this statement using mathematical induction, we will first establish a base case. When n = 2, there are only two people in the line, and the statement is true. The first person is a woman and the last person is a man, and therefore the woman is directly in front of the man.

Next, we assume that the statement is true for n = k, where k is a positive integer. That is, if k people stand in a line with a woman first and a man last, then there is a woman directly in front of a man somewhere in the line.

Now, we need to show that the statement is also true for n = k + 1. Suppose k + 1 people stand in a line, with a woman first and a man last. We can remove the first person (the woman) and consider the remaining k people. By our induction hypothesis, there is a woman directly in front of a man somewhere in this line of k people.

Now, we have two cases for the position of the woman and man in the line of k people:

Case 1: The woman directly in front of the man is in the first k positions. In this case, we can add the first person back into the line, and the statement is true for n = k + 1.

Case 2: The woman directly in front of the man is in the last k positions. In this case, we can remove the first person and consider the line of k people from the second person to the last person. By our induction hypothesis, there is a woman directly in front of a man somewhere in this line of k people. When we add the first person back into the line, this woman will be directly in front of the man, and the statement is again true for n = k + 1.

Therefore, by mathematical induction, we have shown that if n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line there is a woman directly in front of a man.

Mathematical induction to prove the given statement. We'll use the terms base case, induction hypothesis, and induction step.

Base case (n=2): When there are two people in the line (a woman followed by a man), it's clear that there's a woman directly in front of a man. This establishes our base case.

Induction hypothesis: Assume that for some positive integer k, if there are k people in a line with a woman at the beginning and a man at the end, there exists a woman directly in front of a man.

Induction step: Let's prove this for k+1 people. We have two cases:

1. If the second-to-last person is a woman, we can remove the last man and have a line of k people. By the induction hypothesis, there exists a woman directly in front of a man in this line, and this also holds for the k+1 people line.

2. If the second-to-last person is a man, we can remove the first woman and have a line of k people. By the induction hypothesis, there exists a woman directly in front of a man in this line. When we add back the first woman, she is now directly in front of the second-to-last man, which also satisfies the condition.

In both cases, for a line of k+1 people, there exists a woman directly in front of a man. Thus, by mathematical induction, the statement holds true for all positive integers n where the first person is a woman and the last person is a man.

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It is not likely that NASA repeatedly made the same data entry errors in recording temperatures in Los Angeles. The use of the value 999.9 in the data file that was downloaded is more likely a placeholder value used to indicate missing data.

This is a common practice in data collection and analysis, as it allows for the inclusion of all available data points in the analysis without compromising the accuracy of the results. It is important to note that missing data can occur for a variety of reasons, including instrument malfunctions, power outages, or human error.

In order to ensure the accuracy and reliability of the data, it is important to identify and account for missing data in the analysis. This can be done through various methods, such as imputation or exclusion of incomplete data points.

In conclusion, while data entry errors can occur, it is not likely that NASA repeatedly made the same errors in recording temperatures in Los Angeles. The use of the value 999.9 in the data file is more likely a placeholder value used to indicate missing data, and it is important to properly account for missing data in the analysis to ensure the accuracy and reliability of the results.

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To solve (2b) to the 4th power, we need to raise the entire quantity of 2b to the power of 4.

This can be done by multiplying the quantity (2b) by itself 4 times using the power rule of exponents, which states that (a^m)^n = a^(m*n).

So we have:

(2b)^4 = (2b) x (2b) x (2b) x (2b)

Expanding this expression, we get:

(2b)^4 = 2 x 2 x 2 x 2 x b x b x b x b

Simplifying further, we can multiply the 2's together to get:

(2b)^4 = 16b^4

Therefore, the expression (2b) to the 4th power simplifies to 16b^4.

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