Answers
The output of the definite integral and summation expression can be presented as follows;
[tex](\frac{\int\limits^1_0 {(\sum\limits_{n=5}^5 n\cdot 5 \cdot \sqrt{25} )} \, dx }{\int\limits^1_0 {(\sum\limits_{n=2}^5 2 + 6)} \, dx } ) = \frac{125}{32} =3\frac{29}{32}[/tex]
What is the difference between definite and indefinite integral?An indefinite integral is an antiderivative of a function, while a definite integral is the limit of a sum of areas of rectangles.
The steps to integrate the specified definite integral expression can be presented as follows;
The integrals and the summations in the question are simplified thus;
Sum n = 5 to 5 n × 5 × √(25) is the sum of n times 5 times √(25) over the range [5, 5], which is the same as 5 × 5 × √(25) = 125
Sum n = 2 to 5, 2 + 6 is the sum of (2 + 6) over the range [2, 5], which, based on the operation is (2 + 6) + (2 + 6) + (2 + 6) + (2 + 6) = 32
The integration of the above summations are found as follows;
Integrate 125 dx from 0 to 1 is the definite integral of the constant function, 125, over the interval [0, 1], which is the same as 125 × (1 - 0) = 125.
The integration of 32 dx from 0 to 1 is the definite integral of the constant function 32 over the interval [0, 1], which is just 32 × (1 - 0) = 32
Plugging in the above values into the original expression, we get;
[tex]\frac{\int\limits^1_0 ({\sum\limits_{n=5}^5}n\cdot 5\cdot \sqrt{25} ) \, dx }{\int\limits^1_0 (\sum\limits_{n=2}^5 2+6) \, dx } = \frac{125}{32}[/tex]
Learn more on evaluation of integrals here: https://brainly.com/question/29853090
#SPJ1
Related Questions
What is the length of side JN and JS (Round your answer to the nearest tenth.)
Answers
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
I really need the answer to this question(PLEASE I REALLY NEED IT)
Answers
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.
The installer is completing a bid for a job that will total 295 square feet. The tile comes in boxes of 20 12-inch by 12-inch tiles (meaning that each tile is 1 square foot), and they cost $72 per box. Profit = 84.25x 35 +0.15m 6. Now that you know the installer will need to buy 15 boxes of tile, use the expression you developed for profit to calculate how much money the installer will make on the job. Round to the nearest cent.
Answers
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.
What is cost?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.
To know more about cost click-
https://brainly.com/question/25109150
#SPJ1
thanks if you answer
Answers
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
Given the growth formula f(t) = 5(1.25)^x what is the growth rate?
Answers
The equation for growth is [tex]f(t) = 5. (1.25)[/tex] x can be stated in the formula f(t) = abx, where a = 5 and b = [tex]1.25[/tex] . The growth rate in this case is the value of b, which is the quantity by which the function increases over time.
What is the growth formula?The given growth formula is:
[tex]f(t) = 5(1.25)^t[/tex]
Here, t represents time, and f(t) represents the value of the function at time t.
The growth rate of a function is the rate at which its value increases over time. In this case, the growth rate is determined by the base of the exponential function, which is 1.25. The base represents the factor by which the function grows at each time step.
The growth rate can be calculated as follows:
Growth rate = (1 + growth factor) - 1
where the growth factor is the factor by which the function grows at each time step, which in this case is [tex]1.25[/tex] .
Therefore, the growth rate can be calculated as:
Growth rate [tex]= (1 + 1.25) - 1 = 0.25 or 25%[/tex]
Therefore, the growth rate of the given function is [tex]25%.[/tex]
Learn more about growth rate here:
https://brainly.com/question/13870574
#SPJ1
The interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan
find the formula relating I and P
a) I when P = 800 b)P when I = 72
Answers
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.
Learn more about interest rate here
brainly.com/question/29486301
#SPJ4
Construct a residual plot of the amount of money in a person’s bank account and their age that would indicate a linear model
Answers
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.
To know more about Residual Plot, visit: brainly.com/question/2876516
#SPJ4
Adam solved 12 math problems in 42 mins if he continues at this pace how many minutes will it take him to solve 20math problems
Answers
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
to know more about denominator click here:
https://brainly.com/question/19249494
#SPJ4
Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 8 meters above the center of the river (see the figure). Write 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. Type the left side of the equation below.
Answers
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
Learn more about Equation
brainly.com/question/29657983
#SPJ11
modeling real life find the height of the roller coaster using two different methods. round your answers to one decimal place.a roller coaster. a right triangle is formed by taking the length of the roller coaster, 283 feet as the hypotenuse. the height of the triangle measures x feet. the angle between the hypotenuse and the height of the triangle measures 45 degrees.
Answers
The height of the roller coaster is 199.9 feet.
According to the information provided,
There are two methods you can use to find the height of the roller coaster.
Method 1: Trigonometric ratios
To use this method, we can use the fact that the angle between the hypotenuse and the height of the triangle measures 45 degrees.
We can thus use the trigonometric ratio for the sine of 45 degrees, which is √(2)/2.
Setting up the equation, we have,
⇒ sin(45 degrees) = x/283
Solving for x, we get:
⇒ x = 283sin(45 degrees)
= 199.9 feet
Therefore,
The height of the roller coaster is 199.9 feet.
Method 2: Pythagorean theorem
To use this method,
we can use the fact that the length of the roller coaster, 283 feet, is the hypotenuse of the right triangle.
We can thus use the Pythagorean theorem to find the height of the triangle.
Setting up the equation, we have,
283² = x² + h²
where h is the height of the triangle.
Rearranging the equation, we get,
h = √(283² - x²)
Substituting x = 283/√(2) (since the angle between the hypotenuse and the height of the triangle measures 45 degrees), we get,
h = √(283² - (283/√(2))²)
= 199.9 feet
Therefore, using either method, we can say that the height of the roller coaster is 199.9 feet.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ12
Los salarios mensuales de los empleados en una tienda minorista tenía un valor medio de
US$3500 y una desviación estándar US$250. En el fin de año todos recibieron un
aumento de US$100. Escriba el valor de la nueva media y la nueva desviación estándar
Answers
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.
Learn more about desviación estándar here:
https://brainly.com/question/23033292
#SPJ4
Find The surface area of the composite figure
Answers
Answer: It should be 470 cm^2
Step-by-step explanation:
Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument, writing premises first and conclusion last. List the premises in the order in which they make the most sense (usually the order in which they occur), and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusion have been appropriately labeled. The exercises marked with a star are answered in the back of the book.
Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim.
(Aristotle, Nicomachean Ethics)
Answers
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.
for such more questions on eudaimonia
https://brainly.com/question/28580624
a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Answers
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?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.
To know more about Foot visit:
brainly.com/question/14230645
#SPJ1
This question has two parts. First, answer Part A. Thenanswer Part B
Part A
BAKERY Aisha can work up to 20 hours per week Working at a bakery, she earns $7 per hour most of the time and $ 8.50 per hour during the early morning shift. Aisha needs to earn at least $150 this week to pay for a trip with her friends. Determine the number of regular and early morning hours that Aisha could work
Part A Select the correct system and graph. Let r=regular hours and m = early morning hours
R<20
7r+8.5m>=150
R+m <=20
r+m<=150
r+m<= 20
7r+ 8.5m >= 150
7r+8.5m>20
7r+8.5m>= 150
Part B
Drag every viable solution to the bin.
Answers
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).
What is an illustration of a workable solution?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)
To know more about amount visit:-
brainly.com/question/28193995
#SPJ1
Can anyone help? It says to refer to functions n and p. Find the function and write the domain in interval notation. Write any number in the intervals as an integer or a simplified fraction.
Answers
The domains of both functions may be expressed in interval notation as follows: [tex]n(x):[/tex](-∞, ∞) and [tex]D(x):[/tex] (-∞, ∞)
What mathematical interval examples are there?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]
How do you represent the domain and range in interval notation?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] (-∞, ∞)
To know more about interval notation visit:
https://brainly.com/question/29059564
#SPJ1
what is the value of x?
Answers
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
A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 110 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answers
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
Learn more about substitution method here
brainly.com/question/14619835
#SPJ4
need help with this question
Answers
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.
What is a translation?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:
N represents an integer.g(x) and f(x) represent a function.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
Read more on translation here: brainly.com/question/4521517
#SPJ1
Convince Me! How does the unit rate describe Sergio's cycling speed? How is the unit rate helpful in determining how much farther Sergio must cycle in a given amount of time each time he increases his target speed?
Answers
The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.
What is the formula for Speed?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.
To know more about Unit rate, visit:
https://brainly.com/question/29781084
#SPJ1
let x1 and x2 be two independent random variables both with mean 10 and variance 5. let y 2x1 x2 3 2. find the mean and the variance of y.
Answers
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.
what is variable ?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.
To know more about variable visit :-
https://brainly.com/question/2466865
#SPJ1
25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answers
Answer: 25:68
Step-by-step explanation:
If 68 is the total number of students, and 25 is the number of students who have vanilla, the ratio of the number of students who have vanilla to the total number of students is 25:68.
The ratio of the number of students who have chocolate to the total number of students is [tex]\frac{43}{68}[/tex]
In the above question it is given that,
There are students some of them have gotten the vanilla ice-cream and some have chocolate ice-cream
The total number of students are = 68
The number of students who had vanilla ice-cream are = 25
The number of students who had chocolate ice-cream are = 68 - 25 = 43
We need to find the ratio of the number of students who have chocolate to the total number of students
Therefore, the ratio of the number of students who have chocolate to the total number of students = [tex]\frac{43}{68}[/tex]
Hence, the ratio of the number of students who have chocolate to the total number of students is [tex]\frac{43}{68}[/tex]
To learn more about, ratio, here
https://brainly.com/question/13419413
When calculating a confidence interval for the difference between two means proportions How do you determine whether or not the results indicate a significant difference?
Answers
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.
Learn more about Hypothesis
brainly.com/question/20165896
#SPJ11
Helpp me plss
Explain how to solve the given equation for “x”.
Answers
By answering the presented question, we may conclude that Therefore, equation the solution to the equation [tex]8^x = 25[/tex] is approximately [tex]x = 1.5473[/tex] .
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex] states that the word [tex]"2x + 3"[/tex] corresponds to the number [tex]"9"[/tex] .
The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.
For example, in the equations [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.
Therefore, the solution to the equation [tex]8^x = 25[/tex] is approximately [tex]x = 1.5473[/tex]
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Help me with this question
Answers
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
What is the divide by five rule?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)
To know more about prime numbers visit:-
https://brainly.com/question/30358834
#SPJ1
based on the t-test assuming unequal variances on the t-testunequal worksheet, is the difference in mean mpg between 4 and 8 cylinder cars statistically significant?a. Yes, the means appear to be similarb. No, the ratio of the variances is not greater than 4:1c. No, the calculated t Stat value is less than the critical t valued. Yes, the calculated t Stat value is greater than the critical t value
Answers
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)
To know more about t-test here
https://brainly.com/question/15870238
#SPJ4
Investment centre.
Compute return on assets for each of the three NIKE shoe divisions below (each division is an investment centre).
Division
Basketball
Soccer
Cross-trainer
Net Income
$4,000,000
$1,500,000
$ 750,000
Assets
$20,000,000
$15,000,000
$10,000,000
Return on Assets
M10/MO.
Answers
ROA = Net Income / Assets
For the Basketball division, the ROA is:
ROA = $4,000,000 / $20,000,000 = 0.20 or 20%
For the Soccer division, the ROA is:
ROA = $1,500,000 / $15,000,000 = 0.10 or 10%
For the Cross-trainer division, the ROA is:
ROA = $750,000 / $10,000,000 = 0.075 or 7.5%
Therefore, the return on assets for the Basketball division is 20%, for the Soccer division is 10%, and for the Cross-trainer division is 7.5%.
the area under the entire probability density curve is equal to___a. 0b. -1c. 1d. [infinity]
Answers
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.
Learn more about area here
brainly.com/question/30066972
#SPJ4
(5x^2+2x-7)-(3x^2+6x-9)
Answers
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
Can someone help me with this
Answers
Answer:
corn dogs: $1.25fries: $3.50Step-by-step explanation:
You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.
SetupThe cost of each purchase can be represented by the equations ...
2d +3f = 134d +f = 8.50SolutionSubtracting the second equation from twice the first gives ...
2(2d +3f) -(4d +f) = 2(13) -(8.50)
5f = 17.50 . . . . . . simplify
f = 3.50 . . . . . . . divide by 5
4d = 8.50 -f = 5.00 . . . . use the second equation to find d
d = 1.25 . . . . . . divide by 4
Corn dogs cost $1.25; chili-cheese fries cost $3.50.
__
Additional comments
Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.
The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.