Please help, I can’t figure this out

The equation of the ellipse is (x2/100) + (y2/50) = 1. The left side of the equation is:x2/100 + y2/50 = 1The equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch is x2/100 + y2/50 = 1.

The semi-elliptical arch bridge is supported by an arch that is in the shape of the upper half of an ellipse. To find an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch, we have to use the given dimensions and the equation of the ellipse, which is (x2/a2) + (y2/b2) = 1. Here a is the length of the semi-major axis and b is the length of the semi-minor axis.Given,

The width of the river is 20 meters.The center of the arch is 8 meters above the center of the river. The semi-elliptical arch is symmetric. Hence, the center of the arch is (0, 8).Also, the half-span of the arch is 10 meters, and hence the value of a is 10 meters.

To find b, we have to find the height of the arch at a distance of 10 meters from the center (as the x-axis coincides with the water level).Using the equation of the ellipse, we get:(102/102) + (y2/b2) = 1b2 = (100 - y2)(x2/a2) + (y2/b2) = 1(20/2)2 = x2 + (y2/b2)(10)2 = y2 + (y2/b2)(100/b2) = y2 + y2b2b2 + y2 = 100b2 = 100/2b2 = 50

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The interval does not include the null hypothesis value, then the results are significant.

When calculating a confidence interval for the difference between two means or proportions, the significance level must be considered to determine whether the results suggest a significant difference.What is a confidence interval?A confidence interval (CI) is an interval estimate that quantifies the uncertainty associated with the unknown population parameter. Confidence intervals are used to express how confident we are about the accuracy of an estimated population parameter.The significance level is the level at which the results of a statistical test are considered statistically significant. The significance level is frequently represented as alpha, and its value is usually set to 0.05 (5%) in most statistical analyses. This implies that there is a 5% chance that the statistical test findings will indicate a significant difference when, in fact, there is no such difference. The significance level is the probability of rejecting a true null hypothesis.Therefore, in order to determine whether or not the results of a confidence interval for the difference between two means or proportions indicate a significant difference, we must compare the interval with the significance level (alpha) that was established before the test. If the interval contains the null hypothesis value (usually 0), then the results are not significant. If the interval does not include the null hypothesis value, then the results are significant.

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The graph of the function h(x) can be obtained using a horizontal stretch by a factor of 4, a horizontal translation to the right by 2 units, and a vertical translation 3 units up of the graph of g(x).

The graph of the function g(x) is a translation of the function f(x) 3 units up and 6 units to the left.

The graph of the function f(x) moves 6 units above the origin.

In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented or modeled by the following mathematical equation g(x) = f(x) + N.

Where:

Based on the information provided about the functions, we have the following:

f(x) = (x - 6)²

g(x) = x² + 3

h(x) = 4(x - 2)² + 3

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As a result, with the US$100 increase, the average monthly wage for employees would be US$3600, while the standard deviation would remain at US$250.

After the increase of US$100, the following will be the new average for employee monthly salaries:

Nueva media = previous media plus an increase, or US$3500 plus US$100, or US$3600.

The standard deviation does not change with an increase in sueld, so the new standard deviation would continue to be:

new standard deviation = previous standard deviation equals $250

As a result, with the US$100 increase, the average monthly wage for employees would be US$3600, while the standard deviation would remain at US$250.

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The installer will make a profit of $868.75 on the job. This amount is calculated by multiplying the price of each box of tile ($72) by the number of boxes needed (15 boxes) to cover the 295 square feet.

Cost is the total amount of money that is expended or invested in order to produce and/or acquire a good or service. It is usually measured in terms of the amount of money spent to produce a unit of a good or service, and is usually expressed in terms of units of currency, such as dollars, euros, or pounds. Cost is an important factor in determining the price of a good or service and can be used to evaluate the effectiveness of a company's operations. Additionally, cost can be used to determine the profitability of a company by measuring the amount of money it spends in relation to the amount of money it earns.

That results in a total cost of $1,080. From that, the installer then subtracts the cost of materials ($840). The remaining amount of $240 is the installer's profit. With a markup of 84.25%, this leaves the installer with a total profit of $868.75.

This profit is possible by factoring in the markup of materials, labor, and overhead costs. The installer is able to cover these costs and make a profit by charging a slightly higher price per square foot. This allows them to cover the cost of materials and labor, as well as make a profit. Additionally, they can also cover overhead costs such as insurance, taxes, and other miscellaneous costs that are associated with running their business. By charging a slightly higher price per square foot, the installer is able to make a profit on the job and remain competitive in the market.

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As per the given question, we have to identify the premises and conclusions of different passages in the text of Aristotle's Nicomachean Ethics. It is a philosophical text that explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. Here are the premises and conclusions of some of the passages:

Passage 1:

Premises: (P) All human beings have a natural desire for knowledge. (C) Therefore, philosophy is an important pursuit for all human beings.

Conclusion: Philosophy is an essential activity for all people because all humans have an innate desire for knowledge.

Passage 2:

Premises: (P) Virtues are habits that are formed by repeatedly practicing virtuous actions. (C) Therefore, becoming a virtuous person requires a lot of practice.

Conclusion: Being virtuous requires lots of practice because virtues are habits that are formed through repeated actions.

Passage 3:

Premises: (P) Moral virtues are acquired by habituation. (C) Therefore, becoming virtuous requires practicing virtuous actions.

Conclusion: One becomes virtuous by practicing virtuous actions because moral virtues are acquired through habituation.

Passage 4:

Premises: (P) Happiness is the highest good that humans can achieve. (C) Therefore, all human actions aim at achieving happiness.

Conclusion: All human actions are aimed at achieving happiness because happiness is the highest good that humans can attain.

Passage 5:

Premises: (P) All humans have a natural desire to be happy. (C) Therefore, achieving happiness is the ultimate goal of all human actions.

Conclusion: The ultimate goal of all human actions is to achieve happiness because all humans have a natural desire to be happy.

In summary, the text of Aristotle's Nicomachean Ethics explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. The premises and conclusions of different passages have been identified in the given question, and we have explained them in detail.

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The cost of each nachos is $2.50 and the cost of each water bottle is $1.50.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the cost of each water bottle and y be the cost of each nachos.

Two bottled water and an order of cheese nachos costs $5.50.

So, 2x+y=5.50 -------(I)

Three bottled water and two orders of cheese nachos costs $9.50​

3x+2y=9.50 -------(II)

Multiply equation (I) by 2, we get

4x+2y=11 -------(III)

Subtract equation (II) from equation (III), we get

4x+2y-(3x+2y)=11-9.50

x=$1.50

Substitute x=1.50 in equation (I), we get

2(1.50)+y=5.50

y=$2.50

Therefore, the cost of each nachos is $2.50.

Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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Answer:

[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]

Answer:

A- 2

B- 4,100

C- 82

D- 4,182

22 gallons of the first brand (35% pure antifreeze) and 88 gallons of the second brand (60% pure antifreeze) to make 110 gallons of a mixture that contains 55% pure antifreeze.

Let x be the number of gallons of the first brand (35% pure antifreeze) needed, and y be the number of gallons of the second brand (60% pure antifreeze) needed to make the desired mixture.

We know that the total volume of the mixture is 110 gallons and the desired concentration of antifreeze is 55%.

We can set up two equations based on the amount of antifreeze and the total volume of the mixture:

0.35x + 0.6y = 0.55(110) (amount of antifreeze)

x + y = 110 (total volume)

Simplifying the first equation, we get:

0.35x + 0.6y = 60.5

Now we can use substitution or elimination to solve for x and y. Here's one way to use substitution method

x + y = 110 (equation 1)

x = 110 - y (solve for x)

0.35x + 0.6y = 60.5 (equation 2, substitute x)

0.35(110 - y) + 0.6y = 60.5 (substitute x into equation 2)

38.5 - 0.35y + 0.6y = 60.5 (distribute 0.35)

0.25y = 22 (combine like terms)

y = 88 (divide both sides by 0.25)

So we need 88 gallons of the second brand (60% pure antifreeze). To find the amount of the first brand (35% pure antifreeze), we can substitute y back into equation 1:

x + y = 110

x + 88 = 110

x = 22 gallons

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So, the statements that are true are: This study uses a repeated measures design. This study uses random sampling. This study uses a control group.

An equation is a mathematical statement that asserts that two expressions are equal. It typically contains variables, constants, and mathematical operators, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations are used to solve problems and find the values of the variables that make the equation true. For example, the equation 2x + 3 = 7 is true when x equals 2, because 2(2) + 3 = 7. Equations can be represented using mathematical notation.

by the question.

This study uses a repeated measures design because each subject experiences each of the four treatments.

This study uses random sampling because the 100 children were randomly selected.

This study uses a control group because the first group, which has no screen time, serves as the control group for comparison.

This study does not use blinding because there is no mention of hiding the treatment groups from the children or the researchers.

This study does not use blocking because there is no mention of grouping the children based on certain characteristics (e.g., age, gender) and then randomly assigning them to the treatment groups within each block.

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The probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

Let X be the number of students who choose UNC, and Y be the number of students who choose Duke. Then X follows a binomial distribution with n = 5 and p = 0.6, and Y follows a binomial distribution with n = 5 and p = 0.1.

(a) The event a 2 UNC corresponds to choosing exactly 2 out of 5 students to attend UNC. This can be written as:

A UNC = {X = 2}

The indicator random variable for a 2 UNC is

UNC = 1, if X = 2 , 0, otherwise

(b) Similarly, the events  a 2 Duke, a 2 NCS, and a 2 Hogwards-NC correspond to choosing exactly 2 out of 5 students to attend Duke, NC State, and Hogwarts-NC, respectively. These can be written as:

A 2 Duke = {Y = 2}

A 2 NCS = {Z = 2}, where Z is the number of students who choose NC State

A 2 HCS = {W = 2}, where W is the number of students who choose Hogwarts-NC

The indicator random variables for these events are:

2 DUKE= 1, if Y = 2 , 0, otherwise

2 NCS = 1, if Z = 2 , 0, otherwise

2 HNC = 1, if W = 2 , 0, otherwise

(c) To find the probability that at least two students choose UNC, we can use the complement rule:

P(at least 2 students choose UNC) = 1 - P(less than 2 students choose UNC)

= 1 - P(X = 0) - P(X = 1)

= 1 - (0.4)⁵ - 5(0.6)(0.4)⁴

≈ 0.848

(d) To find the probability that exactly 2 students choose UNC and 2 students choose Duke, we can use the joint probability:

P(2 students choose UNC and 2 students choose Duke) = P(X = 2)P(Y = 2)

= (0.6)²(0.4)³(0.1)²(0.9)³

≈ 0.0003456

For five graduating high school students from five different high schools in NC who have all been accepted to four colleges (UNC, Duke, NC State, and Hogwarts-NC), the probability that exactly two out of the five students choose UNC is approximately 0.259. Similarly, the probabilities of exactly two students choosing Duke, NC State, and Hogwarts-NC are approximately 0.008, 0.008, and 0.327, respectively.

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Answer:

4(h+3) = 20

Step-by-step explanation:

Para empesar, disculpa si mi español no es perfecto, pero igual me encataria a ayudarte.

Pues, se sabe que estas temporadas de practica vienen en groupitos de horas a la ves. Dijo que cada dia, ella practica por alguans horas, las cuales suman a 20 en total. Como la problema nos dice que ella practica 4 veces a la semana, tienemos 4 de estos groupitos de horas. Por eso, la respuesa es 4(h+3) = 20, porque ella va por estas 4 temporadas de practicar 3 horas en la manana y quien sabe cuantos en la tarde. Addicionalmente, este"quien sabe" numero de horas se representa con h.

The chance of the outcomes that are divisible by 5 is 5, and it is 0.116. The odds of the outcomes 2 and 3, which are prime numbers , are 0.043 and 0.041, respectively. P(A|B) = 1 * 0.116 / 0.084= 1.381

The last digit in the number (475) may be simply checked to see whether it is either 0 or 5 to see if it can be divided by 5. The entire integer is divisible by 5 if the last number is either 0 or 5. The outcome is the remaining digits multiplied by 2 if the number's last digit is 0.

We must determine the likelihood that the result is divisible by 5 given that it is prime in order to determine P(A|B).

We can utilize the following formula: P(A|B) = P(B|A) * P(A) / P (B).

P(A) = 0.116 (as calculated above)

P(B) = P(2) + P(3) = 0.043 + 0.041 = 0.084

P(B|A) = 1 (because any number divisible by 5 cannot be a prime number) (since any number divisible by 5 cannot be a prime number)

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Answer: x=24

Step-by-step explanation:

1. We know that both of the angles together are equal to 180 because they are alternate exterior angles; therefore, we place them in an equation equal to 180.

                 x-17+7x+5=180

2. Next, we combine like terms.

                  8x-12=180

3. Then, we add 12 on both sides, which cancels the 12 on the left side and makes the right side 192.

                     8x=192

4. Finally, we divide by 8 on both sides and get the answer of 24.

                       x=192/8 which is also x=24

The required area under the whole probability density curve is given by option C. 1.

The area under the entire probability density curve is equal to,

As the probability density function (pdf) represents the probability of a continuous random variable.

And continuous random variable taking on a specific value within a certain range.

Since the total probability of all possible outcomes must be equal to 1.

This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.

Therefore, the area under the entire probability density curve function is equal to option c. 1.

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Yes, the calculated t-test value is greater than the critical t value. (option d).

The t-test is a statistical test used to determine whether there is a significant difference between the means of two groups. In your case, you are comparing the mean miles per gallon (mpg) of 4-cylinder cars and 8-cylinder cars.

Yes, the calculated t Stat value is greater than the critical t value

This answer choice is also a possibility. If the calculated t statistic is greater than the critical t value, then the difference in means is statistically significant. This means that it is unlikely that the observed difference occurred by chance, and there is evidence to support the claim that there is a true difference in mean mpg between 4-cylinder and 8-cylinder cars.

Hence the correct option is (d)

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The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel. This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

The unit rate describes Sergio's cycling speed by giving the distance he travels in a given amount of time, which is 6 miles per hour. This means that for every hour he cycles, he travels a distance of 6 miles.

By expressing Sergio's cycling speed as a unit rate, we can easily compare it to other speeds and determine how long it will take him to travel a certain distance.

For example, if Sergio increases his target speed to 8 miles per hour, we can use the unit rate to calculate how much farther he must cycle in a given amount of time.

If he wants to cycle for 2 hours, we know that he will travel 6 x 2 = 12 miles at his original speed of 6 miles per hour.

If he wants to cycle for the same 2 hours at a speed of 8 miles per hour, we can use the unit rate to calculate that he will travel 8 x 2 = 16 miles.

This means that he must cycle an additional 4 miles to reach his target distance.

Overall, the unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

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Answer:

JN = 44.3

JS = 43.1

Step-by-step explanation:

19)  Use Law of Sines

sin53/39 = sin65/JN

JN = 39(sin65) / (sin53) = 44.26 ≈ 44.3

20)   m∠N = 180 - 65 - 53 = 62

sin53/39 = sin62/JS

JS = 39(sin62) / (sin53) = 43.12 ≈ 43.1

The domains of both functions may be expressed in interval notation as follows:  [tex]n(x):[/tex](-∞, ∞) and [tex]D(x):[/tex] (-∞, ∞)

For instance, a range between 0 to 100 would include all of the integers between them, not only [tex]1, 2, 3, 4, 5, 6, 7 and 9[/tex]

Interval notation, which employs values enclosed in brackets to represent a collection of numbers, can be used to express the domain and range. In interval writing, we place a square bracket where the endpoint is a part of the set and a parenthesis where it is not or if the gap is unbounded.

Given:

[tex]n(x) = x - 9[/tex]

The domain of this function is all real numbers, since there are no restrictions on the input [tex]x[/tex] that would make the function undefined.

The given function for the domain is:

[tex]D(x) = x^2 + 6x[/tex]

To find the domain of this function, we need to consider what values of [tex]x[/tex] would make the function undefined. The only thing that could make the function undefined is division by zero, but there is no division in this function. Therefore, the domain of [tex]D(x)[/tex] is all real numbers.

In interval notation, we can write the domain of both functions as:

[tex]n(x):[/tex] (-∞, ∞)

[tex]D(x):[/tex] (-∞, ∞)

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The other solutions are not viable because either they exceed the maximum number of hours Aisha can work (20 hours) or they do not meet the minimum amount Aisha needs to earn ($150).

If the ongoing research is successful, this approach might be an effective remedy. The only real way to resolve the problem is through negotiations between the military administration and the various opposition movements.

Part A: The correct system and graph to represent Aisha's situation is:

r + m ≤ 20 (maximum number of hours Aisha can work)

7r + 8.5m ≥ 150 (minimum amount Aisha needs to earn)

Part B: The viable solutions are:

r = 20, m = 0 (Aisha works only regular hours for 20 hours at $7 per hour)

r = 14, m = 6 (Aisha works 14 regular hours and 6 early morning hours at $7 per hour and $8.50 per hour, respectively)

r = 0, m = 18 (Aisha works only early morning hours for 18 hours at $8.50 per hour)

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Answer:

2x^2-4x+2

Step-by-step explanation:

depends what the question is telling you to do

if its askin you to simplify this is the answer

The formula relating I and P is I = kP

a) When P= $800, then I = $48

b) When I = $72, then P = $1200

If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:

I = kP

where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:

I/P = 6/100 = 0.06 = k

Now we can use this value of k to answer the given questions,

a) When P = 800, the formula relating I and P is:

I = kP

I = 0.06 × 800

I = 48

Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.

b) When I = 72, the formula relating I and P is:

I = kP

72 = 0.06P

Solving for P:

P = 72/0.06

P = 1200

Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.

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To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:

bank account = β0 + β1 * age + ε

where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.

Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:

residual = bank account - (β0 + β1 * age)

We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.

In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.

Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.

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The coordinate matrix LFE of L relative to the ordered bases E and F is given by:

LFE=12,3,0,12,3,0,0

LFE =

[[5, 1, 3, 3],

[0, 0, 3, 0],

[0, 0, 0, 0]]

This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:

LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12

LFE[1,2] = L(e2) =  = 0 + 0 + 3 + 0 = 3

LFE[1,3] = L(e3) =  = 0 + 0 + 0 + 0 = 0

LFE[2,1] = L(f1) =  = 5 + 1 + 3 + 3 = 12

LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3

LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0

LFE[3,1] = L(f4) =  = 0 + 0 + 0 + 0 = 0

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Adam solved 12 math problems in 42 mins if he continues at this pace how many minutes will it take him to solve 20 math problems:  x=70 times.

In light of the given circumstances,

plan: 12÷42= 20÷x

Assuming the division is characterized, the denominator can't approach 0: x ≠ 0

Affix the imbalance as the space: 12/42 = 20/x, x ≠ 0

Decrease the division: 2/7 = 20/x , x ≠ 0

Increase the two sides of the situation by the shared factor: 2 * 7x/7 = 20 * 7x/x, x ≠ 0

Diminish the part: 2x=20×7,x ≠ 0

Compute the item or remainder: 2x=140, x ≠ 0

Partition the two sides of the situation by the coefficient of the variable: x=140÷2, x ≠ 0

Work out the item or remainder: x=70, x ≠ 0

Track down the crossing point: x=70

obtain the outcome: x=70

Reply: x=70

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Answer:

The system has one point because when the system is graphed the lines will intersect at exactly one point. Therefore, there is only one solution to this system of equations.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.

given

To get the mean and variance of y, we can apply the characteristics of expected value and variance:

We can start by determining the expected value of y:

E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]

By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.

Next, we may determine y's variance:

Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4

Var(x1)

Var(x2) + 9

Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

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Answer:

Let's call the tens digit of the two-digit number "t" and the units digit "u".

From the problem statement, we know that:

t = u - 5 (the tens digit is 5 less than the units digit)

10t + u = 3(t + u) + 5 (the number is five more than three times the sum of its digits)

We can use the first equation to substitute for t in the second equation:

10(u - 5) + u = 3((u - 5) + u) + 5

Simplifying and solving for u, we get:

10u - 50 + u = 6u - 9

Simplifying further, we get:

5u = 41

Therefore, u = 8.2

Since u must be a whole number, we round up to 9. Then, we can use the first equation to find that t = u - 5 = 4.

So the two-digit number is 49 (with t=4 and u=9).

We can check if it satisfies the second equation:

10t + u = 10(4) + 9 = 49

3(t + u) + 5 = 3(4 + 9) + 5 = 46

49 is indeed five more than three times the sum of its digits (4 + 9), so our solution is correct.

Therefore, the two-digit number is 49.

The tens digit is 3 and the unit digit is 8. So, the number is 38.

Important information:

Let x be the tens digit and y be the unit digit.

The tens digit is 5 less than the unit digit.

[tex]x=y-5[/tex]          ...(i)

The number itself is five more than three times the sum of its digits.

[tex]10x+y=3(x+y)+5[/tex]

[tex]10x+y=3x-3y=5[/tex]

[tex]7x-2y=5[/tex]          ...(ii)

Using (i) and (ii), we get

[tex]7(y-5)-2y=5[/tex]

[tex]7y-35-2y=5[/tex]

[tex]5y=40[/tex]

[tex]y=8[/tex]

Substitute this value in (i).

[tex]x=8-5[/tex]

[tex]x=3[/tex]

Therefore, the number is 38.

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