Multiply the following polynomials using distribution

We can use the ratio test to find the radius of convergence of the series. Therefore, the interval of convergence is i = (-∞, ∞).

lim |(x^2)^(n+1) * 2(n+1) ln(n+1) / ((x^2)^n * 2n ln(n))|

n->inf

= lim |x^2 * 2(n+1) ln(n+1) / (2n ln(n))|

n->inf

= |x^2| * lim [(n+1) ln(n+1) / n ln(n)]

n->inf

= |x^2| * lim [1 + 1/n * ln(1+1/n) / ln(n)]

n->inf

= |x^2|

So, the series converges absolutely for |x^2| < ∞, which means the radius of convergence is r = ∞.

To find the interval of convergence, we need to check the endpoints x = ±∞.

When x = ±∞, the terms of the series do not converge to zero, so the series diverges.

Therefore, the interval of convergence is i = (-∞, ∞).

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The probability for events A and B will be 5/18.

Two dice are tossed.

Event A: The first die is a 5 or 6

Event B: The second die is not a 1

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

The probability for event A is calculated as,

P(A) = 2/6

P(A) = 1/3

The probability for event B is calculated as,

P(B) = 5/6

The probability for events A and B is calculated as,

P(A and B) = P(A) x P(B)

P(A and B) = 1/3 x 5/6

P(A and B) = 5/18

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After choosing the level of significance in the computation of the F statistic, the next step is to compute the obtained value Option C

In statistics, hypothesis testing is a fundamental tool for making decisions about a population based on sample data. When performing a hypothesis test, we begin by stating our research hypotheses, which are statements about the population that we are interested in. We then collect data and use statistical methods to evaluate the evidence for or against these hypotheses.

One common type of hypothesis test involves comparing two population means using an F-test. The F-test involves calculating an F statistic, which is the ratio of two sample variances. We begin this process by setting the level of significance, which is the probability of making a Type I error rejecting the null hypothesis when it is actually true.

After choosing the level of significance, the next step is to compute the obtained value of the F statistic using the sample data. This involves calculating the sample variances and substituting them into the formula for the F statistic.

Once we have the obtained value of the F statistic, we can compare it to the critical value from an F-distribution table. This critical value depends on the degrees of freedom for the numerator and denominator of the F statistic, which in turn depend on the sample sizes and the number of groups being compared. If the obtained value of the F statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support our alternative hypothesis. Otherwise, we fail to reject the null hypothesis.

It's important to note that stating our research hypotheses is a critical first step in this process. The null hypothesis is the default position that we are trying to disprove with our data. The alternative hypothesis is the statement that we hope to support with our data. By stating these hypotheses upfront, we can make our statistical analysis more focused and avoid the pitfalls of data dredging or cherry-picking.

In summary, after choosing the level of significance in the computation of the F statistic, the next step is to compute the obtained value and compare it to the critical value.

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Complete Question

What is the next step after choosing the level of significance in the computation of the F statistic?

a. setting the level of risk

b. selecting the appropriate test

c. computing the obtained value

d. stating research hypotheses

The probability that both fruits are apples is 5/14.

We have,

There are 8 fruits in the basket, and 5 of them are apples.

When Sharon takes the first fruit, she has a 5/8 chance of getting an apple.

When Sharon takes the second fruit, there are only 4 fruits left in the basket, and 4 of them are apples.

So the probability of getting another apple is 4/7.

To find the probability of both events happening (i.e. getting two apples in a row), we multiply the probabilities:

P(getting two apples) = (5/8) x (4/7) = 20/56 = 5/14

Therefore,

The probability that both fruits are apples is 5/14.

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The required height of the lighthouse is 117.8 meters, as per the given condition

The angle of elevation in this case is given as 67°, and we know that the distance from the observer to the base of the lighthouse is 50 meters. Using these values, we can set up the following equation:

tan(67°) = k/50

This equation relates the height of the lighthouse, represented by "k", to the angle of elevation and the distance between the observer and the base of the lighthouse.

To solve for the height of the lighthouse, we can use algebra to isolate the variable "k". Multiplying both sides of the equation by 50, we get:

k = 50tan(67°)
k = 117.8 meters

Therefore, to the nearest meter, the height of the lighthouse is 117.8 meters.

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The probability that a randomly selected person is not a student or slept less than an average of 6 hours a night can be calculated as 2/10 or 20%, based on the given data.

To calculate the probability that a randomly selected person is not a student or slept less than an average of 6 hours a night, we need to consider the given data:

- Average number of hours slept per night:

 - Students who slept less than or equal to 6 hours: 0

 - Non-students who slept less than or equal to 6 hours: 2

- Average number of hours slept per night:

 - Students who slept greater than 6 hours: 5

 - Non-students who slept greater than 6 hours: 3

To find the probability, we need to determine the number of individuals who meet the given criteria and divide it by the total number of individuals.

A number of individuals who are not students and slept less than or equal to 6 hours: 2 (non-students: 2).

Total number of individuals who are either students or non-students: 5 (students: 5) + 5 (non-students: 5) = 10.

Therefore, the probability can be calculated as 2/10 or 1/5, which is equal to 0.2 or 20%. This means that there is a 20% chance that a randomly selected person is not a student or slept less than an average of 6 hours a night based on the given data.

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What is the probability that a randomly selected person is not a student or slept less than an average of 6 hours a night?

Answer:

288.4

Step-by-step explanation:

V=πr^2h=π·3^2·10.2≈288.39821

Answer:

A

Step-by-step explanation:

To determine the number of solutions for the system of equations y = x^3 + x + 3 and y = -2x - 5, we need to find the intersection points of the two equations.

Setting the expressions for y equal to each other:

x^3 + x + 3 = -2x - 5

Rearranging the equation:

x^3 + x + 2x + 8 = 0

x^3 + 3x + 8 = 0

Solving this cubic equation, we find that it does not have any rational solutions. Therefore, there are no real solutions for this system of equations.

The correct answer is:

A. no real solutions

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

There were 14 participants in each condition in the study, with a total sample size of 28. To determine the number of participants in each condition, we need to look at the degrees of freedom in the one-way ANOVA output.

In this case, the degrees of freedom for the numerator is 1 and the degrees of freedom for the denominator is 26. Since the ANOVA assumes equal sample sizes across conditions, we can calculate the total number of participants by multiplying the sample size by the number of conditions. Using the formula for degrees of freedom, we can calculate the sample size for each condition as follows:
df_between = k - 1
df_within = N - k
Where k is the number of conditions and N is the total number of participants.
In this case, df_between = 1 and df_within = 26. Thus,
1 = k - 1
k = 2
Substituting k = 2 into the df_within equation, we get:
26 = N - 2
N = 28
So, the total number of participants across both conditions is 28. Since we assume equal sample sizes, each condition has 14 participants. Therefore, the number of participants in each condition is 28 / 2 = 14.Therefore, we can conclude that there were 14 participants in each condition in the study, with a total sample size of 28. In summary, given the one-way ANOVA output and assuming equal sample sizes across conditions, we can use the formula for degrees of freedom to calculate the sample size for each condition and determine that there were 14 participants in each condition in the study.

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The unemployment rate for 2019 and 2020 is 4.76% and 16.67% respectively. The labor force participation rates for 2019 and 2020 is 70% and 58.06% respectively. Based on these changes the economy is in the contraction phase of the business cycle.

To calculate the unemployment rates and labor force participation rates for 2019 and 2020 for the country of Manga, we will use the following equations.

1. Calculate the labor force for each year: Labor force = Employment + Unemployment

2. Calculate the unemployment rate for each year: Unemployment rate = (Unemployment / Labor force) * 100

3. Calculate the labor force participation rate for each year: Labor force participation rate = (Labor force / Total adult population) * 100

2019:

1. Labor force = 100,000 (employment) + 5,000 (unemployment) = 105,000

2. Unemployment rate = (5,000 / 105,000) * 100 = 4.76%

3. Labor force participation rate = (105,000 / 150,000) * 100 = 70%

2020:

1. Labor force = 75,000 (employment) + 15,000 (unemployment) = 90,000

2. Unemployment rate = (15,000 / 90,000) * 100 = 16.67%

3. Labor force participation rate = (90,000 / 155,000) * 100 = 58.06%

Based on the changes in the unemployment rate and labor force participation rate between 2019 and 2020, it appears that the economy of Manga was in the contraction phase of the business cycle at the end of 2020. This is because the unemployment rate increased significantly and the labor force participation rate decreased, indicating a shrinking economy.

Note: The question is incomplete. The complete question probably is: Given the information below for the country of Manga, answer the following: Calculate the unemployment rates for both 2019 and 2020. Then calculate the labor force participation rates for both 2019 and 2020. Based on the changes in these rates, in which part of the business cycle would you say the economy of Manga was in at the end of 2020?

                 2019 2020

Real GDP $2,700,000 $2,200,000

Total Adult Population 150,000 155,000  

Employment 100,000 75,000

Unemployment 5,000 15,000

Discouraged  Workers 1,000 5,000

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After one year, Monica will have more money in Account Y than in Account X.

Monica has the option to choose between two savings accounts at her bank: Account X, which pays a simple annual interest rate of 2.1%, and Account Y, which pays a higher interest rate of 2.4% compounded annually. The difference between simple and compound interest is that simple interest is calculated based on the principal amount only, while compound interest is calculated based on both the principal and the interest earned in previous periods.

Assuming that Monica does not make any additional deposits or withdrawals after opening the account, she will earn more money with Account Y after one year than with Account X. This is because the interest earned with Account Y will compound annually, leading to a higher total amount of interest earned over time. On the other hand, with Account X, Monica will earn a simple interest rate of 2.1% on her initial deposit of $3,000, resulting in a lower total amount of interest earned. Therefore, choosing Account Y would be the more profitable option for Monica.

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The ancient Egyptians built dams to control the annual flooding of the Nile River, which was essential for their agriculture.

The ancient Egyptians built di-kes for several reasons, primarily to control the flooding of the Nile River.

The ancient Egyptians dug channels and canals to redirect water from the Nile River to areas where it was needed for irrigation.

Water wheels were used to lift water from the canals and channels to the fields.

The ancient Egyptians dug channels and canals to help distribute water from the Nile to other areas that were not directly affected by the river.

The ancient Egyptians built shadufs and water wheels to help lift and move water from the Nile to other areas. water wheels were more complex devices that used the power of the river's flow to lift and move water.

These machines were crucial for irrigation and helped to make the most of the limited water resources available to the ancient Egyptians.

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Answer:

The answers are...

to limit flooding

to store water

to bring water to their crops

to lift water from the river

Step-by-step explanation:

The solution of the quadratic equations are,

x = 1.75

x = 29.25

We have to given that;

The quadratic equation is,

0.04x² + 1.1x - 2 = 0

Now, We can solve by quadratic formula as;

0.04x² + 1.1x - 2 = 0

x = - (1.1) ± √(1.1)² - 4×0.04×- 2) / 2×0.04

x = (- 1.1 ± √1.21 + 0.32) / 0.08

x = (- 1.1 ± √1.53) / 0.08

x = (- 1.1 ± 1.24) / 0.08

x = (- 1.1 + 1.24) / 0.08

x = 1.75

x = (- 1.1 - 1.24) / 0.08

x = - 2.34 / 0.08

x = 29.25

Thus, The solution of the quadratic equations are,

x = 1.75

x = 29.25

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The probability that a student completely guesses on every question and makes a perfect score of a 100% is 1/64 or approximately 0.0156 or 1.56%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The number of possible answer responses for each question is 4, since there are 4 options.

The number of possible answer responses for all 3 questions can be found by multiplying the number of possible answer responses for each question. Therefore, the total number of possible answer responses for the quiz is 4 x 4 x 4 = 64.

If the student completely guesses on every question, there is a 1 in 4 chance (or a 25% chance) of getting each question correct. Since there are 3 questions, the probability of getting all 3 questions correct is (1/4) x (1/4) x (1/4) = 1/64.

Therefore, the probability that a student completely guesses on every question and makes a perfect score of a 100% is 1/64 or approximately 0.0156 or 1.56%.

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Answer:

156cm area of rhombus and 144cm for its diagonal

Step-by-step explanation:

Hope this helps

The first iterated integral integrates over y first, giving the limits of integration for x as y/3 to 243^(1/3). The second iterated integral integrate over x first, giving the limits of integration for y as 0 to 3x^(1/3).

a) To express the area element dA as a double integral using vertical cross-sections, we can integrate with respect to x and y separately. Since the region R is bounded by the lines y = Vx, y = 0, and x = 243, the limits of integration are:

- For y, the lower limit is 0 and the upper limit is Vx.

- For x, the lower limit is 0 and the upper limit is 243.

Therefore, the iterated integral for dA using vertical cross-sections is:

∫[from 0 to 243]∫[from 0 to Vx] dy dx

b) To express the area element dA as a double integral using horizontal cross-sections, we can also integrate with respect to x and y separately. However, the limits of integration are different:

- For x, the lower limit is 0 and the upper limit is y/V.

- For y, the lower limit is 0 and the upper limit is 243.

Therefore, the iterated integral for dA using horizontal cross-sections is:

∫[from 0 to 243]∫[from 0 to y/V] dx dy

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1. The proportion P of green Skittles in your data is approximately 0.2094 or 20.94%. 2. The standard deviation of the sample proportions based on your data is approximately 0.0266. 3. The estimated true proportion of green Skittles in the population, based on your data, is 20.94% [tex]^+_-[/tex] 4.07%. 4. The data supports your initial guess that the percentage of green Skittles in a bag is approximately 20%-25%.

1. To find the proportion P, divide the number of green Skittles by the total number of Skittles in your sample:

P = Number of green Skittles / Total number of Skittles

In this case, you found 49 green Skittles out of a sample size of 234, so:

P = 49 / 234 = 0.2094 (rounded to four decimal places)

Therefore, the proportion P of green Skittles in your data is approximately 0.2094 or 20.94%.

2. To calculate the standard deviation of the sample proportions, you can use the following formula:

Standard Deviation = [tex]\sqrt{(P * (1 - P)) / n}[/tex]

Where P is the proportion and n is the sample size.

Using the given values:

= sqrt((0.2094 * (1 - 0.2094)) / 234) = 0.0266 (rounded to four decimal places)

Therefore, the standard deviation of the sample proportions based on your data is approximately 0.0266.

3. To estimate the true proportion p in the population, including a margin of error, you can use the confidence interval formula:

[tex]p ^+_- z * \sqrt{(p * (1 - p)) / n}[/tex]

Where p is the sample proportion, z represents the z-score based on the desired confidence level (such as 95% confidence), and n is the sample size.

Since you didn't mention a specific confidence level, we'll assume a 95% confidence level, which corresponds to a z-score of approximately 1.96.

Using the values from your data:

p = 0.2094

z = 1.96

n = 234

Calculating the margin of error:

The margin of Error =[tex]z * \sqrt{(p * (1 - p)) / n}[/tex]

[tex]= 1.96 * \sqrt{(0.2094 * (1 - 0.2094)) / 234}[/tex]

= 0.0407 (rounded to four decimal places)

The estimated true proportion p in the population, including the margin of error, is:

p [tex]^+_-[/tex] Margin of Error = 0.2094 [tex]^+_-[/tex] 0.0407

Therefore, the estimated true proportion of green Skittles in the population, based on your data, is 20.94% [tex]^+_-[/tex] 4.07%.

4. Comparing the estimated true proportion with your initial guess of 20%-25%, we can see that the proportion you found in your data (20.94%) falls within the estimated range of 20.94% [tex]^+_-[/tex] 4.07%. This means that the data support the initial guess that the percentage of green Skittles in a bag is approximately 20%-25%.

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Statement: ∠ABC ≅ ∠EDC

Reason: Given (or Angle equality postulate)

In line 5, we can state that ∠ABC is congruent to ∠EDC because it is given in the paragraph proof. The reason for this statement is the "Given" or "Angle equality postulate," which states that if two angles are given to be congruent, then they are congruent.

Statement: Triangle ABC and Triangle EDC are congruent.

Reason: ASA (Angle-Side-Angle) congruence criterion.

In a two-column proof, each line consists of a statement and a reason. To complete the proof, we need to determine the appropriate statement and reason for line 5.

The given paragraph proof should provide information leading to the conclusion that Triangle ABC and Triangle EDC are congruent. The most likely reason for this congruence would be the ASA (Angle-Side-Angle) criterion.

The ASA criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Therefore, in line 5, we can state "Triangle ABC and Triangle EDC are congruent" and provide the reason as "ASA (Angle-Side-Angle) congruence criterion." This indicates that the two triangles are congruent based on the given information and the ASA criterion.

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y=x-10 is the equation of the line.

We can use the point-slope form of a linear equation to find the equation of the line that passes through two given points.

First, we need to find the slope of the line:

slope = (change in y) / (change in x) = (0 - (-8)) / (-6 - 2) = 8 / 8 = 1

Now we can use one of the given points, say (2, -8), and the slope, m = 1, to write the equation of the line in the point-slope form:

y - y1 = m(x - x1)

y - (-8) = 1(x - 2)

y + 8 = x - 2

y = x - 10

Therefore, an equation of the line that passes through the points (2, -8) and (-6, 0) is y = x - 10.

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Answer:

Divided by 2; next terms would be 2.5 and then 1.25

Step-by-step explanation:

It keeps dividing by 2.

40 / 2 = 20

20 / 2 = 10

10 / 2 = 5

So the next term would be:

5 / 2 = 2.5 = [tex]2\frac{1}{2}[/tex]

Then it would be 2[tex]\frac{1}{2}[/tex] / 2 = 1 [tex]\frac{1}{4}[/tex]

This does not imply that there is a one-to-one correspondence between dorm rooms and students.

A one-to-one correspondence between sets A and B if pairing of each object in A with one and only one object in B, and also another statement is when we counting one- to - one or like counting, one, two, three and so on.

In the question says that : Each and Every student assigned per room then we would be able to guarantee that there is a one-to-one correspondence between dorm rooms and students.

However, the possibility that two students could be assigned per one room, there is no way to imply that there is a guaranteed one-to-one correspondence between dorm rooms and students. It is follows only one student assign one room it is able to guarantee a one-to-one correspondence between dorm rooms and students.

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We can verify that QTAQ = D, which shows that A has been orthogonally diagonalized.

To orthogonally diagonalize the matrix A, we need to find the eigenvectors and eigenvalues of A. The eigenvalues are the solutions to the characteristic equation det(A-λI) = 0, where I is the identity matrix and det denotes the determinant. Once we have the eigenvalues, we can find the eigenvectors by solving the equation (A-λI)x = 0, where x is the eigenvector.

Using these methods, we find that the eigenvalues of A are λ1 = 50 and λ2 = 7. The eigenvectors corresponding to λ1 and λ2 are [1, 11] and [-1, 1], respectively.

To orthogonalize the matrix, we normalize the eigenvectors to length 1 and form the matrix Q by taking them as columns. Thus, Q = [[1/√122, -1/√2], [11/√122, 1/√2]]. The diagonal matrix D is formed by placing the eigenvalues on the diagonal, i.e. D = [[50, 0], [0, 7]].

Finally, we can verify that QTAQ = D, which shows that A has been orthogonally diagonalized.

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The diameter, circumference, and area of the circle will be 22.4 units, 70.336 units, and 393.88 square units, respectively.

Given that:

Radius, r = 11.2 units

The diameter of the circle is calculated as,

d = 2r

d = 2 x 11.2

d = 22.4 units

The area of the circle will be given as,

A = πr²

A = 3.14 x 11.2²

A = 393.88 square units

The circumference of the circle will be given as,

C = 2πr

C = 2 x 3.14 x 11.2

C = 70.336 units

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A positive association on a scatter plot indicates that as the value of one variable increases, the value of the other variable also tends to increase. In other words, when the values of two variables increase together, they have a positive relationship.

For example, if we create a scatter plot of temperature and number of clothing people wear, a positive association would mean that as the temperature increases, people tend to wear more clothing.

This is because higher temperatures lead to increased discomfort, which in turn leads people to wear more clothing to stay comfortable.

Similarly, if we create a scatter plot of time and money earned, a positive association would mean that as the amount of time spent working increases, the amount of money earned also tends to increase.

This is because more time spent working often leads to more opportunities to earn money, through increased productivity or more hours worked.

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The total number of possible outcomes in this two-player game is 12 Option C

Game theory is a branch of mathematics that studies decision-making in situations where multiple players are involved.

In this particular game, one player has four available strategies,

1 x 4 = 4

While the other player has three available strategies

1 x 3 = 3,

This problem can be solved by using Unitary Method. To determine the total number of possible outcomes, we need to consider all the possible combinations of strategies that each player can use. We can do this by multiplying the number of strategies available to each player.

4 x 3 = 12

Using the multiplication rule, the total number of outcomes is equal to the product of the number of strategies available to each player. Therefore, the number of outcomes in this game is 12.

This means that there are twelve possible outcomes when the two players choose their strategies independently. Each outcome represents a different combination of strategies chosen by both players.

The total number of possible outcomes in this two-player game is 12, Option C which is equal to the product of the number of strategies available to each player.

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Complete Question

In a two-player game in which one player has four available strategies and the other player has three available strategies, how many outcomes can there be?

A. 8

B. 10

C. 12

D. 16

E. 64

Answer:

Six rotations around the unit circle correspond to 2160 °.

Step-by-step explanation:
We know that One rotation around a circle is equal to 360 degrees :

i.e.          1 rotation     =     360 ° ........(i)
Hence,   6 rotations  =    ( 6 × 360 ° )

So for 6 rotations, we have 2160 °.

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To find the value of x that maximizes f(x) = z x^2 x1t21, we need to take the derivative of f with respect to x and set it equal to zero.

First, we use the product rule to differentiate f(x):

f'(x) = z [2x x1t21 + x^2(∂/∂x)(x1t21)]

Next, we set f'(x) equal to zero:

0 = z [2x x1t21 + x^2(∂/∂x)(x1t21)]

Simplifying, we get:

0 = 2x x1t21 + x^2 (∂/∂x)(x1t21)

0 = 2x x1t21 + x^2 x2t22 (since ∂/∂x(x1t21) = x2t22)

0 = x(2x1t21 + x x2t22)

Therefore, either x = 0 or 2x1t21 + x x2t22 = 0. Since we are interested in finding the maximum value of f(x), we focus on the second equation.

To solve for x, we can use the quadratic formula:

x = (-2x1t21 ± sqrt((2x1t21)^2 - 4(x2t22))(1))/2

Simplifying, we get:

x = -x1t21 ± sqrt((x1t21)^2 - x2t22)

So the value of x that maximizes f(x) is:

x = -x1t21 ± sqrt((x1t21)^2 - x2t22)

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Answer:

Step-by-step explanation:

The quotient (integer division) of 733/38 equals 19; the remainder (“left over”) is 11. 733 is the dividend, and 38 is the divisor.

Answer:

5%

Step-by-step explanation:

100 - 95 = 5