When finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation.
One approach to finding an antiderivative of a function is the method of guess and check. This involves making an educated guess for the antiderivative and then verifying it by taking the derivative of the guess and comparing it to the original function.
To find the antiderivative of f(x) = sin(x)cos(x), we can start with a guess based on the product rule for differentiation: d/dx (uv) = u * dv/dx + v * du/dx
Since f(x) = sin(x)cos(x), we can write: d/dx (sin(x)cos(x)) = cos^2(x) + sin^2(x) = 1
This suggests that the antiderivative of f(x) = sin(x)cos(x) might be: F(x) = sin(x)sin(x) + C, where C is an arbitrary constant of integration.
To check our guess, we need to take the derivative of F(x) and compare it to the original function f(x): d/dx (sin(x)sin(x) + C) = cos(x)sin(x)
If our guess is correct, the derivative of F(x) should equal f(x). However, in this case, our guess does not match the original function f(x), so we need to make another guess. A second guess could be:
F(x) = -cos(x)cos(x) + C
Taking the derivative: d/dx (-cos(x)cos(x) + C) = -sin(x)cos(x)
This time, the derivative of F(x) does match the original function f(x), so our guess is correct and the antiderivative of f(x) = sin(x)cos(x) is:
F(x) = -cos(x)cos(x) + C.
Thus, In conclusion, when finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation. By checking the derivative of the guess and comparing it to the original function, we can determine whether or not our guess is correct.
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using a 52 card deck, how many different collections (hands) of 5 cards are there?
There are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.
What is Combinations ?
A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.
The number of different collections (hands) of 5 cards from a standard deck of 52 cards is calculated using combinations. In combinatorics, the number of ways to choose k items from a set of n items is given by the formula:
C(n, k) = n! / (k! (n-k)!)
where n! represents the factorial of n, which is the product of all positive integers less than or equal to n.
In this case, n = 52 and k = 5, so the number of different hands is:
C(52, 5) = 52! / (5! (52-5)!)
= 52! / (5! 47!)
= 2598960
Therefore, there are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.
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........help..........
Answer:
a. $2,125
b. $2,000
Step-by-step explanation:
a. profit = 25%
[tex]\frac{x - 1700}{1700}[/tex] = 25%
Multiply 1700 to both sides
x - 1700 = 425
add 1700 to both sides
x = 2125
b. [tex]\frac{2500 - x}{x}[/tex] = 25%
multiply x to both sides
2500 - x = 0.25x
add x to both sides
2500 = 1.25x
1.25x = 2500
x = 2000
classify these events. selecting a king from a deck of cards, replacing it and selecting a queen from the same deck. these events would be considered:
Random selection events.The two number of events involve selecting cards randomly from a deck and can thus be said to be random selection events.
The two events involve randomly selecting cards from a deck of cards. The first event is selecting a king, while the second event is replacing the king and selecting a queen. These two number of steps can be classified as random selection events, as the cards are chosen without any specific pattern or criteria. Random selection events involve selecting something at random, without any pre-defined criteria.
This can include flipping a coin, rolling a dice, or, in this case, selecting a card from a deck. Since the two events involve randomly selecting cards from a deck of cards, they can be classified as random selection events.
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find a positive angle less than 2 that is coterminal with the given angle.
350° and 350° - 360° are coterminal angles with magnitudes less than 2π.
What is coterminal?
In mathematics, two angles are called coterminal if they have the same magnitude (measure) but different orientations. This means that they represent the same angle but start from different points on the unit circle.
An angle is coterminal with another angle if it has the same magnitude but a different orientation. To find a positive angle less than 2π that is coterminal with a given angle, you can add or subtract multiples of 2π until you get an angle in the desired range.
For example, if the given angle is 350 degrees, you can subtract 2π from it to get a positive angle less than 2π:
350° - 360° = -10° + 360° = 350°
So, 350° and 350° - 360° are coterminal angles with magnitudes less than 2π.
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How Do You Evaluate Sin π/2
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/π), π/2 radians= π/2 × (180°/π) = 90° or 90 degrees. Therefore sinπ/2 = sin (90°) = 1. The Value of sinπ/2 is given as 1.
How do you evaluate?When an algebraic expression is evaluated, the value of the expression is determined when the variable is replaced by a given number.
To evaluate an expression, we substitute the given number for the variable in the expression, then simplify it using the order of operations.
Evaluation is a method of studying a program, practice, intervention, or initiative in order to determine how well it achieves its objectives.
Evaluations aid in determining what works well and where improvements can be made in a program or initiative.
Top evaluation tips: Making preparations for your evaluation, As, you gather your data, As you examine your data, Having reached your conclusions, Writing the report and presenting your findings.
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what dictionary value would we use to perform a grid search to determine if normalization should be used and for testing the following values of alpha? 1,10, 100
A dictionary with keys 'normalize' and 'alpha' and values [True, False] and [1, 10, 100] respectively can be used to perform a grid search.
Grid search is a technique used to find the optimal hyperparameters for a machine learning model. In the case of determining if normalization should be used and testing different values of alpha, we need to provide the algorithm with a range of values for each hyperparameter. This can be done using a dictionary.
The keys in the dictionary would be 'normalize' and 'alpha', representing the hyperparameters we want to search for. The values for 'normalize' would be [True, False], representing the options for normalizing the data or not. The values for 'alpha' would be [1, 10, 100], representing the different values of alpha to test.
This dictionary can then be passed as an argument to the grid search algorithm, which will then perform a search through all possible combinations of these hyperparameters, evaluating the performance of the model for each combination and determining the optimal set of hyperparameters.
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this is called the principle of superposition. use this principle to find the general solution of (a) y″ 4y = 4 cos 2x 6 cos x 8x2 − 4x;
The general solution of the differential equation is given by: [tex]y(x) = c1*sin(2x) + c2*cos(2x) + c3*x + c4*cos(x) + c5*sin(x) + c6*x^2[/tex]
1. The equation is of the form y” + 4y = f(x), which is a second order linear differential equation with constant coefficients.
2. By the principle of superposition, the general solution of the equation is the sum of the solutions of the homogeneous equation y” + 4y = 0 and the particular equation y” + 4y = f(x).
3. The homogeneous equation has two linearly independent solutions, [tex]y1 = sin(2x) and y2 = cos(2x)[/tex]
4. The particular equation has three linearly independent solutions, [tex]y3 = x, y4 = cos(x) and y5 = sin(x).[/tex]
5. Hence, the general solution of the equation is[tex]y(x) = c1*sin(2x) + c2*cos(2x) + c3*x + c4*cos(x) + c5*sin(x) + c6*x^2[/tex], where c1, c2, c3, c4, c5 and c6 are arbitrary constants.
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complete the table below given f(x)=x 3/√1−x−2
x = -3.1, -3.01, -3.001, -2.999, -2.99, -2.9; f(x) undefined, undefined, undefined, 2.8069, 2.8068, 2.8067 respectively.
What do you mean by function?A function is a mathematical object that assigns a unique output (or "value") to each input in its domain. It is a rule that takes an input (or "argument"), performs some operations on it, and returns a corresponding output. Functions are often written using the notation f(x), where x is the input, and f(x) is the corresponding output. For example, the function f(x) = x^2 maps the input value x to its square. Functions are a key concept in mathematics and are used to model various phenomena in science, engineering, economics, and more.
To complete the table, we need to evaluate f(x) for each value of x:
x -3.1 -3.01 -3.001 -2.999 -2.99 -2.9
f(x) undefined undefined undefined 2.8069 2.8068 2.8067
We can see that f(x) is undefined when x = -3.1, -3.01, and -3.001 because the square root of a negative number is undefined. For other values of x, we can evaluate f(x) by plugging in the values and simplifying:
f(-2.999) = (-2.999 + 3)/√(1 - (-2.999) - 2) = 0.001/√0.999 = 0.001/0.999 = 0.001 * (1/0.999) = 0.001 * 1.001 = 0.001001
Similarly, we can find f(-2.99) and f(-2.9) as follows:
f(-2.99) = (-2.99 + 3)/√(1 - (-2.99) - 2) = 0.01/√0.99 = 0.01/0.9950 = 0.01 * (1/0.9950) = 0.01 * 1.0050 = 0.01005
f(-2.9) = (-2.9 + 3)/√(1 - (-2.9) - 2) = 0.1/√0.9 = 0.1/0.9487 = 0.1 * (1/0.9487) = 0.1 * 1.0543 = 0.10543
So, rounding the results to four decimal places, we have:
x -3.1 -3.01 -3.001 -2.999 -2.99 -2.9
f(x) undefined undefined undefined 2.8069 2.8068 2.8067
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the four cities on the map form a square. about how many miles is the most direct route from washington to springfield? round to the nearest tenth, only if needed.
Answer: 50 miles man
Step-by-step explanation: im just that guy
On the basis of change in proportion; which amongst the following is a type of correlation: Select one: a. none of these b. Simple c. Multiple d. Zero'
The type of correlation is determined by the relationship between variables in terms of the proportion of change between them that is multiple proportion.
A proportion is the relationship between two quantities, often expressed as a ratio or fraction.
"Simple correlation" refers to the relationship between two variables, where a change in one variable is associated with a change in the other variable in a consistent manner.
"Multiple correlation" refers to the relationship between three or more variables. In this type of correlation, the proportion of change in one variable is associated with the proportion of change in other variables.
"Zero correlation" refers to the absence of any relationship between two variables. In this type of correlation, there is no consistent proportion of change in one variable that is associated with a change in the other variable.
Therefore correct option is (b).
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Natalie wants to join a gym. She has two choices. Gym A that costs $ 50 a month for unlimited visits per month. She can also choose Gym B that charges a flat monthly fee $10 plus $4 per visit. Write an equation, in terms of, v, visits per month, to find out when the two gyms cost the same price.
Let v be the times visited:
Answer: 50 = 10 +4(v)
40 = 4(v)
10 = v
10 visits
please give me brainliest. ty!
f (x) = x2 − 2x − 8 f ( x) = x 2 - 2 x - 8. Find the properties of the given parabola.
The equation of the parabola is give as;
f (x) = x² − 2x − 8
Let y = x² − 2x − 8
Complete the square on right sides of the equation.
y = (x - 1)² + 9
Comparing with the standard equation of the parabola.
y = a(x - h)² + k
a = 1h = 1k = -9Thus, vertex of the parabola are found as:
(h, k) = (1, - 9)
Since 'a' has a positive value, the parabola opens upwards.
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A box has the shape of a rectangular prism with height 31 cm. If the height is increased by 0. 8 cm, by how much does the surface area of the box increase?
Use pencil and paper. Show your work. Then show a second way to solve the problem. Explain which way you like better and why.
39.52 cm² of the surface area of the box increase.
What is the rectangular prism?A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces).An object must have all six faces be rectangles, the opposite faces must be equal, and the cross-section throughout the length must be the same for it to be a right rectangular prism.Rectangular prisms have surfaces equal to the sum of their side areas, and their volumes are equal to their length times breadth times height.Given data :
H = 31 cm
the surface area of the box increase ;
= 2( 31 x 8.7 + 31 x 16 + 16 x 8.7) + 2 ( 31.8 x 8.7 + 31.8 x 16 + 16 x 8.7 )
= 2 ( 8.7 + 16 ) x ( 31.8 - 31 )
= 2 x 24.7 x 0.8
= 39.52 cm²
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Question 3 of 10
What are the more appropriate measures of center and spread for this data
set?
0 2
4
5 8 10
H
14
24
6 8 10 12 14 16 18 20 22 24 26 28 30
Select two choices: one for the center and one for the spread.
A. Better measure of spread: the standard deviation
B. Better measure of center: the median
C. Better measure of spread: the interquartile range (IQR)
D. Better measure of center: the mean
The more appropriate measures of center and spread or the data set would be:
B. Better measure of center: the medianC. Better measure of spread: the interquartile range (IQR)When should median and interquartile range be used ?The median and interquartile range (IQR) should be used when analyzing data that has a non-normal distribution. They are particularly useful when working with data sets that contain outliers or skewness.
The median provides an indication of the central tendency of the data, representing the value that separates the data into two equal parts, with half the data being below and half the data being above that value. The IQR, on the other hand, provides information about the spread of the data and can be used to identify outliers.
The data here has the extreme figure of 24 which is an outlier and so not compatible with the mean. The median is therefore better. The interquartile range would be better for spread due to the outlier as well.
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A wheat farmer plows 5 acres of land and collects 135 bushels of wheat. The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat. Is there a proportional relationship between the number of bushels of wheat collected and the number of acres plowed over the two days? explain.
Yes, there is a proportional relationship between the number of bushels of wheat collected and the number of acres ploughed over the two days.
This can be seen by calculating the average number of bushels of wheat collected per acre for each day, and seeing if they are equal.
For the first day,
The average is 135 bushels / 5 acres = 27 bushels per acre.
For the second day,
The average is 216 bushels / 8 acres = 27 bushels per acre.
Since the two averages are equal, it can be concluded that there is a proportional relationship between the number of bushels of wheat collected and the number of acres ploughed.
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22.
The following ordered pairs represent a function.
(-2, 2), (-1, 1), (0, 0), (1, 1), (2, 2)
Which ordered pair can be added to the given set and still have the set represent a
function?
The only ordered pair that can be included in the given set and yet have it represent a function is (-3, -6), or (3, 6).
what is function ?vast quantities and their modifications, equations and parts, shapes and their placements, and locations where they can found are all included in the study of mathematics. The relationship between a group of inputs, each of which has a collective agreements, is referred to as a "function." A utility is a linkage between both inputs and outputs where each input produces a single, unique result. Every function has a domain but a codomain, often termed as a scope. F is typically utilised denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, another functions, so several functions, within functions, and then on functions.
given
A value of x cannot have two outputs, or y-values, therefore start by using the process of elimination to eliminate the response options where the x coordinates have already been utilized in the relation. You now have two choices.
(-2, 2), (-1, 1), (0, 0), (1, 1), (2, 2)
so ( -3 , -6), ( 3, 6 ) as it has both different values of x and y .
The only ordered pair that can be included in the given set and yet have it represent a function is (-3, -6), or (3, 6).
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Austin had to make a scale drawing of the school cafeteria for his architecture class. He used a scale that equaled 4 feet for every 1 inch depicted. If the scale drawing he made identified the cafeteria as being 16 inches in length, how long was the actual cafeteria?
A.
64 ft
B.
12 ft
C.
4 ft
D.
256 ft
The actual length of a cafeteria is 64 ft. Therefore, the option A is the correct answer.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, Austin used a scale that equaled 4 feet for every 1 inch depicted.
The scale drawing he made identified the cafeteria as being 16 inches in length.
Now, 4×16
= 64 feet
Therefore, the option A is the correct answer.
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If b= the number of baseballs which algebraic expression represents the phrase below? The number of baseballs minus 3 lost during practice
If b= the number of baseballs , then b-3 ,this algebraic expression represents the phrase, The number of baseballs minus 3 .
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
If b= the number of baseballs
now,
The number of baseballs minus 3
i.e. the number = b-3.
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A +2 μC charge is at the origin. A +5 μC charge is on the x-axis at +1.0 m. At what point between the charges is the electric field zero? A. +10 cm
B. +18 cm
C. +39 cm
D. +45 cm
So Condition 1 has reduced the possibilities for existing Enet = 0 positions to Region (I) (to the left of both charges) and Region (III) to the right of both charges.
What does X-axis mean?The X-axis is sometimes known as the horizontal axis, and the Y-axis is the vertical axis.
There are a few main approaches to this issue. I'll explain it in terms of electric fields. This is due to the defining equation's ability to link the electrostatic force's expression, FE, to a region's net electric field, E:
FE = qE
where q is a charge that has been added to the electric field; in this case, it is a charge of 1 C. The only way FE can equal zero at some place when q is not zero (and q=0 would be a simple case, anyway) is if the net electric field E is zero at that location.
This is true regardless of the size and nature of the charge you were putting there.
Therefore, given this scenario, where can the net electric field E = 0? At every point in space surrounding the charge, each charge generates its own electric field, which either points in the direction of the charge (for negative charges) or away from the charge (for positive charges). The following equation determines the size of the electric field, |E|, produced by a point charge at a distance r from the charge:
|E| = kq/r2
At every point in space surrounding the two charges stated in the issue, an electric field is produced by one of them. The vector sum of the field from each charge present at a given point is the net electric field at that location. There are two requirements for the two fields to cancel each other out:
1. Each charge's electric fields must be directed in opposite directions.
2. Each charge's electric fields must be of equal strength.
We can examine the two situations independently. Since the first one (regarding directions) may frequently weed out a lot of potential responses through scrutiny, I frequently start there.
For instance, if you were to create a diagram with the two charges as indicated on the x-axis and then choose any location off of the x-axis, it would be clear that this position does not satisfy Condition 1. This is so that the (+)10 C charge's electric field will point away from the 10 C charge from that location. And from there, the -5 C charge's electric field will point in its direction. These two electric field vectors won't even coincide for any position off the x-axis. Since they cannot point in the same direction, even if their magnitudes are equal, they cannot cancel out. Thus, the third response from above is disproved.
Therefore, let's examine the x-axis. The electric fields for points on this line point in the same direction, so they could potentially point in different directions. But how is that even possible? We can divide a line with two charges into three regions: (I) to the left of both charges, (II) in the space in between the charges, and (III) to the right of both charges.
Therefore, So Condition 1 has narrowed the range of potential locations where Enet = 0 is present to Region (I) (to the left of both charges) and Region (III) (to the right of both charges).
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What is R? (percent)
The initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.
Given that, an exponential function with rate of decay, h(t) = [tex]1250(0.865)^t[/tex]
Here we need to identify the initial amount, rate and the value of function when t = 3
The general formula of exponential decay is given by,
A = P(1-r)ⁿ
Where A is final amount
P is initial amount
r = rate of decay
n = years or time
Comparing with general formula,
P = 1250
1-r = 0.865
r = 1-0.865
r = 0.135
r % = 13.5
h(3) = 1250(0.865)³
= 809
Hence, the initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809
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James is buying a new shirts.He has a coupon that will give him 20% discount off of the original price(p) of the shirt which expression could be used to find the new coast of the shirt after the discount 0.2p 0.8p 1-0.2p 100p-20p
The expression for the new cost of the shirt is 0.8p. Option B
What is price discount?Price discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product
To get the expression for the new cost of the shirt,
1 - 0.2 = 0.8
We then multiply the new percentage with the price to get the new price. And this can be expressed as: 0.8p
Hence, 0.8p is the new expression for the price discount
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Hi, can anyone pls help. It’s based on variation. The question is in the picture attached
The value of v in the variation is 21.1
How to determine the value of VFrom the question, we have the following parameters that can be used in our computation:
Joint variation from p to s and v^2
So, we have
p = ksv^2
Substitute the known values in the above equation, so, we have the following representation
18 = k * 9 * 15^2
So, we have
k = 2/225
When s = 81 and p = 32, we have
32 = 2/225 * 81 * v^2
This gives
v^2 = 72000/162
So, we have
v = 21.1
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A credit card holder owes $5,498 on a credit card with a 26.99% interest rate compounded monthly. Assuming no additional purchases are made with the card, what is the monthly payment the cardholder should make to pay off the debt in 5 years? Round your answer to the nearest penny. A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. $91.63 $123.66 $167.85 $215.29
The monthly payment is $167.85.
The correct option is C.
What is a loan calculation formula?The formula:
PV = PMT/i[1 - {1/(1+i)ⁿ]
PV denotes the loan sum.
PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)
Given:
A credit card holder owes $5,498 on a credit card with a 26.99% interest rate compounded monthly.
Assuming no additional purchases are made with the card.
PV = 5498
n = 60
i = 0.2699/12 = 0.02
PMT={PVi(1+i)ⁿ}/{(1+i)ⁿ−1}
PMT = {5498(0.02)(1 + 0.02)⁶⁰/{(1 + 0.02)⁶⁰ - 1}
PMT = $167.85
Therefore, PMT = $167.85
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Question 3 (5 points)
(02. 01 MC)
Which of these is a positive externality of carpooling with friends to work?
оа
Reduced commute time
Ob
Reduced driving focus
Ос
Reduced traffic on the road
Od
Reduced time to socialize
The positive externality of carpooling with friends is reduced traffic on the road. Hence, option C is the correct option.
Carpooling is a very useful method of reducing traffic as well as pollution and is quite simple as well. It involves the usage of only one common vehicle that can be used by people who commute to the same destination. It's helpful since it means a lot of people will use only one vehicle and hence, there will be less traffic and pollution.
In the given problem as well, since these friends are gonna carpool to work, they will use the same vehicle and so, lead to less traffic. So, option C is the correct option.
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What is the sum?
(42x-23) + (13x+43)
Answer:
55x+20
Step-by-step explanation:
Answer:
Simplification 5(11x+4)
Step-by-step explanation:
42x-23+13x+43
42x +20 + 13x
Combine like terms
42x+20+13x
55x+20
Common factor
55x+20
5(11x+4)
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable y represent the number of defects on a fat quarter that can be sold by company f. (a) construct the probability distribution of the random variable y.
The probability distribution's mean and standard deviation, Y, will be 0.4899 and 0.699, respectively, based on the information provided.
What is meant by probability distribution?A probability distribution is a statistical function that enumerates all the potential probabilities and values for a random variable within a certain range.
A key idea in statistics is the probability distribution. They are applied both theoretically and practically. Probability distributions can be used to compute critical regions for hypothesis tests and confidence intervals for parameter values, among other useful applications.
Each possible result of a random experiment or occurrence is shown by the probability distribution in statistics. It offers the odds of many potential events.
It should be noted that the likelihood that y will occur will follow the probability distribution given:
Let the given data be
Y 0 1. 2
Probability 0.63. 0.25. 0.12
Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)
simplifying the above equation, we get
Mean = 0 + 0.25 + 0.25
Mean = 0.49
Let the variance be 0.4899.
standard deviation = ✓0.4899
Standard Deviation = 0.699
The complete question is:
Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution. If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F. (a) Construct the probability distribution of the random variable Y
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help im stuck on this
The pair of slopes of -3/4 and 4/3 represent perpendicular lines
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Two lines are said to be perpendicular if the product of their slope is -1.
Given two lines with slope of -3/4 and 4/3:
Product of their slope = (-3/4) * (4/3) = -1
The lines with slope of -3/4 and 4/3 is perpendicular
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Find the value of f(-6) y = f(x)
y=f(x)
f(-6)
Answer : y=-6
36 were undergraduates, and 3 were undergraduates living off campus. find the number of these students who were a undergraduates, were living off campus, or both. b undergraduates living on campus. c graduate students living on campus.
(a)The number of students who were undergraduates, living off campus, or both is 42
(b)The number of students who were undergraduates living on campus is 33
(c)The number of graduate students living on campus is 18
What is Sample?
A sample is a subset of people drawn from a larger group. Sampling is the process of identifying the group from which you will gather data for your research. For example, if you want to learn about the thoughts of students at your university, you may poll 100 of them.
Let us define the following sets:
S = The sample space of the students in the survey
O = The students living off campus
U = Undergraduate students
According to the question, we have:
n(s) = 60
n(o) = 9
n(u) = 36
n (u ∩ o) = 3
a) The number of students who were undergraduates, living off campus, or both is given by:
n (u ∪ o) = n(u) + n(o) - n(u ∩ o)
36 +9-3
n (u ∪ o) = 42
b) The number of students who were undergraduates living on campus is given by:
n (u ∩ o) = n(u) - n(∩ o)
=36-3
=33
c) The number of graduate students living on campus is given by:
n (u ∩ o) = n(∩ o)
n(s) - n (u ∪ o)
=62-42
=18
(a)The number of undergraduate students living off campus or both is 42. (b)The number of undergraduate students living on campus is 33.
(c)The number of graduate students living on campus is 18.
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(a)The number of students who were undergraduates, living off campus, or both is 42
(b)The number of students who were undergraduates living on campus is 33
(c)The number of graduate students living on campus is 18
What is Sample?
A sample is a subset of people drawn from a larger group. Sampling is the process of identifying the group from which you will gather data for your research. For example, if you want to learn about the thoughts of students at your university, you may poll 100 of them.
Let us define the following sets:
S = The sample space of the students in the survey
O = The students living off campus
U = Undergraduate students
According to the question, we have:
n(s) = 60
n(o) = 9
n(u) = 36
n (u ∩ o) = 3
a) The number of students who were undergraduates, living off campus, or both are given by:
n (u ∪ o) = n(u) + n(o) - n(u ∩ o)
36 +9-3
n (u ∪ o) = 42
b) The number of students who were undergraduates living on campus is given by:
n (u ∩ o) = n(u) - n(∩ o)
=36-3
=33
c) The number of graduate students living on campus is given by:
n (u ∩ o) = n(∩ o)
n(s) - n (u ∪ o)
=62-42
=18
(a)The number of undergraduate students living off campus or both is 42. (b)The number of undergraduate students living on campus is 33.
(c)The number of graduate students living on campus is 18.
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I need help... Ainsley works for the owners of a bookstore. Her starting salary is $24,500, and she gets a 3% raise each year.
a. Write an equation in function notation to represent Ainsley's salary as a function of the number of years she has been working at the bookstore.
b. What will Ainsley's salary be when she begins her fourth year working at the bookstore? Show your work.
Thanks for helping me : )
Answer:
y = $24,500 * (1 + 0.03x)
Step-by-step explanation:
Please find the attachment for detail
Answer:
26771.8115
Step-by-step explanation:
24500(1.03)=25235 then continue doing this 2 more times and you get 26771.8115