The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.
Define function.A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x).
Given,
Function,
Region = [0,1] × [0,1]
Lˣ = 1/area of region ∫¹₀ ∫₀¹ f(xy) dx dy
Differentiating,
Lˣ
= 1/1 ∫₀¹ tan⁻¹ xy dxdy
= ∫¹₀ [ ∫¹₀ tan⁻¹(xy) dx ] dy
= ∫₀¹ [{x tan⁻¹ (xy) ¹₀ - 1/2 ∫ 2(x+y)/ 1 + xy₂ dx] dy
= ∫¹₀ tan⁻¹ y dy - ¹₀ log(y² + 1) 2y dy
= [ytan⁻¹ y - 1/2 log( y² + 1) ∫¹₀ - [1/4 log (y² +1) log y² +1/4log(y²+1)
= π/4 - 1/2 log 2 -π²/48
L = 1/4( π - log4) - π²/48
The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.
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a letter grade of a B+ avg in a regular class counts for how many points
The number of points that a letter grade of a B+ avg in a regular class counts for is; 3.3
How to grade undergraduate scoring system?The following should be noted as used for Undergraduate Grade Points;
- Letter grades of A, B, C, D, and F are used.
- Pluses and minuses could be assigned to grades of B and C.
- Minus may be assigned to an A, while plus may be assigned to a D.
- Temporary grades consisting of IN and AB do not affect grade point average.
- Courses that consist of a grade of PS, SP, BE, W or PL are ignored in establishing the quality point average.
Now, the grade points are assigned as follows:
A = 4.0
A⁻ = 3.7
B⁺ = 3.3
B = 3.0
B⁻ = 2.7
C⁺ = 2.3
C = 2.0
C⁻ = 1.7
D⁺ = 1.3
D = 1.0
F = 0.0
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15. Determine if the triangles are similar. If they are, write a similarity statement.
Answer:
No, they're not
Step-by-step explanation:
If two triangles have equal angles we can say they are similar, as u can see it doesn't apply for those triangle.
What are the 5 steps in dividing rational expressions?.
The 5 steps in dividing rational expressions are explained below.
What are rational expressions?Rational expression seem to be parts that have factors in their denominators (and frequently numerators as well). For instance, x 2 x + 3 \dfrac{x^2}{x+3} x+3x2 start part, x, squared, separated by, x, furthermore, 3, end portion is a reasonable articulation.
Steps to divide the rational expression,1) Take the rational expression.
2) Rewrite the division as the product of the first rational expression then, the reciprocal of the second.
3) Factor the numerators and denominators of rational expression completely.
4) Multiply the numerators and denominators together.
5) Simplify by dividing out common factors.
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(8x-1)
(3x +9)
(3x + 4)*
Find the value of x.
The value of x is 12.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
We are given a triangle with the angles (8x-1), (3x +9) and (3x + 4)
Since we know that the sum of the interior angles of a triangle is 180 degrees.
Therefore,
(8x-1) + (3x +9) + (3x + 4) = 180
8x + 6x + 12 = 180
14x + 12 = 180
14x = 168
x = 12
Hence, the value of x is 12.
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when calculating a confidence interval for the mean using a sample size of less than 30 with an unknown population standard deviation, the______ is used.
when calculating a confidence interval for the mean using a sample size of less than 30 with an unknown population standard deviation, the Binomial distribution is used.
In statistics, what is a binomial distribution?
The binomial distribution summarizes the number of trials or observations when each trial has the same chance of achieving a specific value. The binomial distribution determines the likelihood of observing a given number of successful outcomes in a given number of trials.
In a posthumous proof published in 1713, Swiss mathematician Jakob Bernoulli determined that the probability of k such outcomes in n repetitions is equal to the kth term (where k starts with 0) in the expansion of the binomial expression (p + q)n, where q = 1 p. (This is why the binomial distribution is so named.)
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Jackson sells toolboxes for farming tools. He plans on selling them during a fair this weekend. Jackson estimates he will sell the boxes for $30 each with an additional shipping fee of $10, regardless of order size. Which equation best represents this situation?.
The linear equation for the given situation is represented as:
20x + 12y = 1,300
correct answer option: b
What is a linear equation with two variables?A general linear equation in two variables is defined as an equation of the form ax + by + c = 0, where x and y are the two variables and a, b, and c are real numbers and a and b are non-zero (x and y).
Given:
We use variables to represent the cost of the big and the smaller boxes.
According to the question, let x be the selling price of the big boxes.
The selling price of the bigger boxes is y.
The total selling price of the smaller boxes is 20x.
The total selling price of the bigger ones is 12y.
Now we know he is making a profit of $1,300 on the total transaction.
Hence the linear equation in two variables for the given situation is represented as:
20x + 12y = 1,300
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I understand that the question you are looking for is:
Jackson sells two types of toolboxes. he plans on selling them during a farming fair this weekend. He estimates he will sell 20 of the smaller boxes (X) and 12 of the larger boxes (Y). if he'd like the profit to be $1300, which of the following best displays the equation that represents this information?
A- y+12=20(x-1300)
B- y=- [tex]\frac{5}{3}[/tex]x+ [tex]\frac{325}{3}[/tex]
C- 20x+12y=1300
D- 12y=20x-1300
How can you determine if the two triangles are congruent by SSS?.
How do you find the equation of a line given the slope and y-intercept?.
The equation of a line is typically written as y = MX + b where m is the slope and b is the y-intercepts.
First of all, remember what the equation of a line is:
y = MX + b
Where:
m is the slope, and b is the y-interceptAll you really have to do here is
replace m with 0, which is the slope you gave, and
replace b with 0, the y-intercept you gave,
in the equation y = MX + b.
If a point crosses the y-axis, then its miles are referred to as the y-intercept. The means of intercept of a line is the thing at which it intersects both the x-axis and y-axis.
in case you examine the graph, you may see that the factor in which Stealth is 0 and choice is 5 hits proper on the critical, vertical line - the y-axis. for the reason that this factor touches, or intercepts, the y-axis, its miles known as the y-intercept.
The x-intercept is in which a line crosses the x-axis, and the y-intercept is the thing in which the road crosses the y-axis.
y = MX + b is the slope-intercept shape of the equation of a straightaway line. inside the equation y = MX + b, m is the slope of the street, and b is the intercept. x and y represent the gap of the street from the x-axis and y-axis, respectively. The value of b is the same as y whilst x = zero, and m shows how steep the street is.
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Determine the value of x in the equation. four fifths times the quantity x plus 9 end quantity minus one fifth times x equals three fifths times the quantity x plus 12 end quantity no solution infinite solutions x = 3 x = 1
The value of x will be ∞ and the solution will be infinite.
To find the value of, we need to write the equation we get from the question. We need to transform the alphabetic demonstration into the numerical one.
Four-fifths times x= [tex]\frac{4}{5}x[/tex]
One-fifths times x= [tex]\frac{1}{5}x[/tex]
Three-fifths times x= [tex]\frac{3}{5}x[/tex]
So the equation we get will be:
[tex](\frac{4}{5}x - 9) -[/tex] [tex](\frac{1}{5}x) =[/tex] [tex](\frac{3}{5}x + 12)[/tex]
Take the variable 'x' values to the Left side of the equation.
[tex]\frac{4}{5} x \ - \frac{1}{5} x \ - \frac{3}{5}x \ = 12 - 9[/tex]
Taking the L.C.M '5' on the left-hand side, we get
[tex]\frac{4x -x-3x}{5} = 3[/tex]
Simplifying the equation,
0x = 3 x 5
x = [tex]\frac{15}{0}[/tex]
x = ∞ ∴ anything divided by zero (0) equals undefined.
So the value to x will be undefined (∞) and the solution is infinite.
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6. Find side BC.
E
B
A
4 in.
C
D
20 in.
28 in.
F
The measure of side BC is 2.3 inches.
What is congruency?
Two triangles are same to be congruent if all 3 corresponding sides ar equal and every one the 3 corresponding angles ar equal in measure. These triangles will be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The symbol of congruence is’ ≅’.
Main body:
We need to suppose that these 2 triangles are congruent.
ΔABC ≅ ΔDEF
so using it,
BC/AC = DF/EF
BC/4 = 20/28
BC = 2.3 inches
Hence the value of BC is 2.3 inches APPROX.
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Suppose that a famer planned to borrow $5,400 from the bank and repay the loan at the end of the year. The interest rate at the bank is 7.36% compounded annually.
(i) Calculate the amount of interest paid to the Iron Bank.
(ii) Calculate the effective interest rate at the Iron Bank.
(i) $397.25
(ii) 7.36%
For the given principal amount $5,400 borrowed by a farmer from the bank at the rate of interest 7.36% compounded annually for the time period of 1 year then the amount of interest paid to the bank is equal to $397.44 and the effective interest rate is equal to 7.36%.
As given in the question,
Principal amount borrowed by a farmer from the bank 'P' = $5,400
Rate of interest compounded annually 'r' = 7.36%
Time period 'n' = 1 year
Amount = P [ 1 + (r/100) ]ⁿ
= 5400 [ 1 + (7.36/100) ]¹
= 5400 [ (100 + 7.36)/100]
= 54 × 107.36
= 5797.44
Amount of Interest paid to the bank = Amount - Principal amount
= 5797.44 - 5400
= $397.44
x = number of times compounding occurs in one year.
Here 'x' = 1
Effective Interest rate = [ 1 + (r/x) ]ˣ -1
= [ 1 + ( 7.36%/1)]¹ -1
= 1 + 7.36% - 1
= 7.36%
Therefore, for the given principal amount $5,400 borrowed by a farmer from the bank at the rate of interest 7.36% compounded annually for the time period of 1 year then the amount of interest paid to the bank is equal to $397.44 and the effective interest rate is equal to 7.36%.
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Which statement about correlation is true?I. Regression based on data that are summary statistics tends to result in a higher
correlation.
II. If r2 = 0.95, the response variable increases as the explanatory variable increases.
III. An outlier always decreases the correlation.I only
Regression based on data that are summary statistics tends to result in a higher correlation is true statement about regression.
Define regression.A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable. the consequence of doing a regression analysis, which is the mathematical representation of the relationship between a dependent (outcome or response) variable and one or more independent (predictor) variables. Finding the variables that have an effect on an interest issue can be done with accuracy using regression analysis. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression.
Given,
True statement about correlation is:
Regression based on data that are summary statistics tends to result in a higher correlation.
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Which expression is an example of the Distributive Property? Select all that apply.
A 6.5(11.5)
B4.7(-8.9)+4.7(2.6)
C2.1(5.3+6.9)
D-8.4(1.5-7.3)
E-12.5(3.9) + 5.1
F1.9-6.2(9.4)
The expression that shows example of distributive property,
4.7(-8.9)+4.7(2.6)
What is distributive property?
The distributive property of binary operations generalizes the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has One says that multiplication distributes over addition.
In 4.7(-8.9)+4.7(2.6)
we can write it as 4.7(-8.9+2.6) = 4.7(-8.9)+4.7(2.6)
If in right hand side is equal to left hand side than
it holds distributive property
4.7(-6.3)=-41.83+12.22
-29.61=-29.61
Hence, this expression holds distributive property.
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Describe how to calculate each of the measures of central tendencies: mean, median, and mode. Be sure to include one description for each.
The mean is easy to calculate. Simply add all of the values together and divide by the number of observations in your dataset.
The median is the value in the middle of a list that is ordered from smallest to largest.
The mode value appears the most
How do you calculate the mean?The mean, median, and mode are the three most common measures of central tendency. The most common value is the mode. In an ordered data set, the median is the number in the middle. The mean is calculated by taking the sum of all values and dividing it by the total number of values.
The mean is the arithmetic average, and it is probably the most familiar measure of central tendency. The mean calculation takes into account all of the values in the data.
Let's assume we've the numbers 2, 5, and 5. The mean will be:
= (2 + 5 + 5) / 3
= 12/3
= 4
The median is 5 and the mode is also 5. The mode is the number that occurs most.
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Which letter choice shows the memory byte order, from low to high address, of the following data definition? BigVal DWORD 12345678h
a. 56h, 78h,12h,34h b. 12h,34h,56h,78h c. 78h,56h,34h,12h d. 34h,12h,78h,56h
The letter options indicate that option C is the memory byte order. 78h,56h,34h,12h
Given,
The data definition;-
BigVal DWORD 12345678h
We have to find the letter choices shows the memory byte order, from low to high address;
Byte order;-
A computer word's numerical order. The order of the digits in computer words with at least 16 bits is referred to as "byte order."
There are two typical approaches for the host's byte order: The least important byte comes first in little-endian byte ordering. For instance, Intel microprocessors employ this technique. The most significant byte comes first in big-endian byte ordering.
Here,
The letter choices shows the memory byte order is option C 78h,56h,34h,12h
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help
me please
am stuck
Answer: 10 cm
Step-by-step explanation:
Look at the sides with the lengths of 16cm and of 6cm. the length with the 16cm is the total of the length of the 6cm combined with the unknown side. So, you need to subtract 6 from 16, which leaves you with 10cm.
How do you find 2/3 of a number?.
The fraction 2/3 of a number is calculated by multiplying the number by 2 and then dividing the number by 3 .
Let us consider a number a.
To find 2/3 of the number a ,
we have to multiply the number by 2 = 2a
Then we have to divide the product by 3 .
Therefore 2/3 of a number will look like 2a/3 .
A number that represents a fraction of a whole is used to express fractions. Any number, amount, or portion of an object can all be regarded as a fraction.
The fractional bar is a horizontal bar that divides each fraction's numerator and denominator in half.
The numerator gives the number of selected or visible portions of the fraction. Above the fractional bar, in the upper portion of the fraction, is where it is located.
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select from the three alternative methods of overhead allocation in the drop down list so that it matches with the provided feature.
Item #1 plantwide rate
Item #2 departmental rate
Item #3 activity based costing
Overhead allocation based on one rate Plant wide rate
Overhead allocation based on at least two rates Departmental rate
Overhead allocation using activities that drive costs Activity based costing
In the given question, we have to Select from the three alternative methods of overhead allocation in the drop down list so that it matches with the provided feature.
Item #1 Plant Wide rate
Item #2 Departmental rate
Item #3 Activity based costing
Plant Wide rate: Whenever a corporation assigns all of its production overhead costs to products or cost items, it does so using a single overhead rate known as the plant wide overhead rate. In smaller companies with predictable cost structures, it is most frequently used.
Departmental rate: The overhead rate per unit of activity that is charged by a certain department is known as a departmental rate. Only the production departments charge this rate. Administrative departments don't have departmental rates because their expenses are paid as they are incurred.
Activity based costing: Activity based costing(ABC) is a mechanism for allocating overhead and indirect costs to goods and services, such as salaries and utility prices. The ABC approach of cost accounting is based on activities, which are seen as any occasion, unit of labour, or assignment with a particular goals.
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HELP HELP ME PLEASEEEEEEEEEE QUICK
Answer:
y=7x+2
Step-by-step explanation:
The standard form to represent the equation of a line is as follows:
Equation of a Line, y = mx + b
Where“m” is the slope of the line
and “b” is the y-intercept
T/F if a nevada real estate licensee who is the subject of a complaint receives notice of a hearing, they must file an answer to the charges within
Upon receiving notice of a hearing, a Nevada real estate licensee who is the subject of the complaint is required to file an answer denying the allegations made.
Within the real estate division, there is a five-member panel known as the Nevada Real Estate Commission. Within 30 days of receiving the complaint, licensees must submit an answer to it. The licensee must either admit the allegations are accurate or dispute them in their response. If the license holder disputes the allegations, they must provide the rationale for doing so. If the licensee doesn't provide an answer, they will automatically be found guilty of the allegations and subject to commission reprimand.
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What is the missing step in solving the inequality 5 8x 2 x 3?.
4/5< x is the missing step in solving the inequality 5-8x < 2x-3 .this can be obtained by simplification
We are given that an inequality
5-8x< 2x-3
We have to find the first step and missing step 2 in solving the given inequality
5-8x < 2x-3
We are given that first step
Step 1: Subtract 3 from both side of the inequality
5-2x < 8x-3
Then we get
Step 1: 5-2x -3 < 8x-3-3
Now, we are finding the second step
2-2x <8x-6
By simplification
2+6-2x < 8x -6+6
By adding 6 on both side
8-2x < 8x
Step 2: Adding 2x on both side of inequality
Step 2: 8-2x +2x < 8x+2x
8< 10x
Step 3:Divide both sides of the inequality by the coefficient of x.
Then we get
Step 3: 4/5<x
the complete question is
Step 1: Subtract 3 from both sides of the inequality. Which is a correct first step in solving 5 – 2x < 8x – 3?Step 2: __________ Step 3: Divide both sides of the inequality by the coefficient of x. What is the missing step in solving the inequality 5 – 8x < 2x + 3?
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I will mark you brainlist im begging please help me
In order to keep the Bermuda Triangle on the Flat Earth from toppling over, it was balanced on the hole which leads to the interior of the hollow Earth. If the vertices of the Bermuda Triangle are given by (1,3) , (2,7) , and (6,2). In order to find the hole we will need to find the intersection of at least 2 lines. Name 2 points through which one of those lines will pass (in the form (x,y),(x,y))
The slope-intercept representation of a linear function is given by the rule shown as follows:
y = mx + b
The coefficients of the function, along with their meaning, are listed as follows:
m is the slope, representing the rate of change of y relative to x.b is the y-intercept of the function, which is the value of y when x = 0.Given two points, only one line will pass through them.
Using a calculator, the lines are given as follows:
Points (1,3) and (2,7): y = 4x - 1.Points (2,7) and (6,2): y = -1.25x + 10.5.Then the x-coordinate of the point in which the lines intersect is obtained as follows:
4x - 1 = -1.25x + 10.5
5.25x = 11.5
x = 2.19.
The y-coordinate can be found in any of the equations, hence:
y = 4(2.19) - 1 = 7.76.
Another point on the line y = 4x - 1 has a x-coordinate of 3 and an y-coordinate obtained as follows:
y = 4(3) - 1 = 12 - 1 = 11.
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The following is a student solution to the inequality.
Part A: There are two mathematical errors in this work. Identify at what step cach
mathematical error occurred and explain why it's mathematically incorrect.
The first mathematical error occurred going from line __ to line
Why it is incorrect:
Answer:
A: line 3 to 4; distributive property was incorrectly applied
B: line 8 to 9: division by a negative number was incorrect
Step-by-step explanation:
You want to know where errors occurred in the solution of the given inequality, and what the errors were.
A. First errorThe first error occurred going from line 3 to line 4.
Expressions 2(x -2) and 3(x -4) were incorrectly evaluated as 2x-2 and 3x-4. The distributive property requires the factor to be applied to all of the terms in parentheses, not just the first one.
B. Second errorThe second error occurred going from line 8 to line 9.
The inequality -5x ≤ -11 was incorrectly divided by -5 to get x ≤ 11/5. Multiplication or division of an inequality by a negative number is an order-reversing operation, so requires the comparison symbol be reversed.
C. How to learn itDistributive property
The student could be asked to group some dissimilar objects, then tell what must happen to make two such groups, or three such groups. This can be compared to groups identified by parentheses, with 2 or 3 as a multiplier.
Ordering
The student can be asked to order a pair of numbers, then the same numbers with opposite signs. The direction of the comparison symbol should be noted in each case. (-1 > -2; 1 < 2) Multiplication or division by a negative can be seen as changing the signs of the things being compared.
A: line 3 to 4; distributive property was incorrectly applied
B: line 8 to 9: division by a negative number was incorrect
What is expression?Expression: An expression is made up of operators, constants, and variables. An expression can be made up of one or more operands and one or more operators to yield a value.
A. First error
The first error occurred going from line 3 to line 4.
Expressions 2(x -2) and 3(x -4) are incorrectly evaluated as 2x-2 and 3x-4. The distributive property requires the factor to be applied in all of the terms in parentheses, not just the first one.
B. Second error
The second error occurred going from line 8 to line 9.
The inequality -5x ≤ -11 was incorrectly divided by -5 to get x ≤ 11/5. Multiplication or division of any inequality by a negative number follow an order-reversing operation, so requires the comparison symbol to be reversed.
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Here are the equations that define three functions.
f(x) = 4x-5 g(x) = 4(x - 5) h(x) = -5
a. Which function value is the largest: f(100), g(100), or h(100)?f
b. Which function value is the largest: f(-100), g(-100), or h (-100)?
c. Which function value is the largest: (T) 9 (T) (T)?
Part A
f(100) is largest
Part B
h(-100) is largest
Part C
f(1/100) is largest
The function
f(x) = 4x-5
g(x) = 4(x-5)
h(x) = (x/4) - 5
Part A
f(100) = 4(100)-5
= 395
g(100) = 4(100-5)
= 4(95)
= 380
h(100) = (100/4) - 5
= 20
f(100) is largest
Part B
f(-100) = 4(-100)-5
= -405
g(-100) = 4(-100-5)
= 4(-105)
= -420
h(-100) = (-100/4) - 5
= -30
h(-100) is largest
Part C
f(1/100) = 4(1/100)-5
= -4.96
g(1/100) = 4((1/100)-5)
= 4(-4.99)
= -19.96
h(1/100) = ((1/100)/4) - 5
= -4.99
f(1/100) is largest
Hence,
Part A
f(100) is largest
Part B
h(-100) is largest
Part C
f(1/100) is largest
The complete question is
Here are the equations that define three functions.
f(x) = 4x - 5
g(x) = 4(x - 5)
h(x) =x/4 -5
a. Which function value is the largest: f(100), g(100), or h(100)?
b. Which function value is the largest: f(-100), g(-100), or h(-100)?
c. Which function value is the largest: f(1/100), g(1/100), or h(1/100)
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(pythagorean theorem and the coordinate plane mc) determine the length of the line segment shown. line segment from negative 3 comma 10 to 4 comma negative 1 13 units 12 units 7 units 3 units
Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.
Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.
c² = a² + b²
Let a = vertical distance between the two points
b = horizontal distance between the two points
c = distance between the two points / length of line segment
Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².
Substitute the values of x and y and solve for c.
c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²
c² = (|-1 - 10|)² + (|4 - -3|)²
c² = (|-11|)² + (|7|)²
c² = 11² + 7²
c² = 121 + 49
c² = 170
c = 13.04
length of line segment ≅ 13 units
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Rhombus JKLM is shown below. Find mZKLM.
J
M
m2KLM-
K
w for
N
(9x - 11)°
(5x
(5x + 3)°
L
how many tosses are required to be certain that the probability that at least one '6' appears is greater than or equal to 1/2?
The number of tosses required is 3.
On a fair toss of dice, outcomes are 1, 2, 3, 4, 5, 6.
So, a dice has 6 possible outcomes.
Probability refers to the measurement of the likelihood of certain events that will occur.
Probability = (Number of desired outcomes)/(Total number of outcomes)
Probability of occurrence of 6 in one toss = 1/6
We have to find that after how many trials probability of 6 becomes 1/2
Let,s say the number of trials = n
1/6 + 1/6 +1/6 ……...upto n times = ½
n*(1/6) = 1/2
n=3.
Here, we just sum up the probability of 6 in one toss n number of times to get the answer as 3.
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A lamina occupies the region inside the circle x2 + y2 = 14y but outside the circle x2 + y2 = 49. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
The mathematical expression for the function that gives the center of mass is m=[tex][tex]\int\limits \int\limits[/tex][tex]D_{p}[/tex](x, y)dA[/tex]
What is center of mass?The center of mass is a point specified relative to an object or set of things. It is the weighted average position of all the system's pieces. For simple stiff objects with homogenous density, the centroid is the location of the center of mass.
A lamina that occupies the region inside the circle x²+y²=14y
Outside the circle is x²+y²=49.m
x²+y²=[tex][tex]\int\limits[/tex]P(x, y)dA[/tex]
Where
r²=14rsinθ
x²+y²=49r=7
Therefore, the center of mass is-x=[tex](i/m) [tex]\int\limits[/tex]xp(x, y)dA[/tex]
-x=[tex](1/m)[tex]\int\limits \int\limits[/tex](r cosθ)p(r, θ)r drdθ[/tex]
-y=[tex](1/m)[tex]\int\limits \int\limits[/tex]Dyp(x, y)dA[/tex]
-y= [tex](1/m)[tex]\int\limits \int\limits[/tex]D(rsinθ)p(r, θ)r drdθ[/tex]
Therefore, the center of mass is
m=[tex][tex]\int\limits \int\limits[/tex][tex]D_{p}[/tex](x, y)dA[/tex]
The mathematical expression for the function that gives the center of mass is
m=[tex][tex]\int\limits \int\limits[/tex][tex]D_{p}[/tex](x, y)dA[/tex]
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martin is a food critic reviewing a restaurant that has 6 main courses, 3 desserts, and 5 appetizers he has yet to try. martin asks the server to surprise him with one of the remaining items. what is the probability that martin is served a main course?
3/7 is the probability that martin is served a main course.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
A = Served with main course
n(A) = 6
S = sample space total no of different courses
n(S) = 6 + 3 + 5 = 14
P(A) = n(A)/n(S) = 6/14 = 3/7
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A baby gains 11 pounds in its first year of life. The baby gained pounds during the first four months and pounds in its second four months. How much did the baby gain in the last four months? pounds pounds 4 pounds 5 pounds.
According to the first and second four months weight gain, the baby gained 3.25 pounds in the last four months.
Firstly forming the equation according the weight gain in a year. So, as per the known fact there 12 months in a year.
Total weight gain in a year = weight gain in first four months + weight gain in second four months + weight gain in third four months
Now converting mixed fraction to fraction -
Weight in first four months = 4 [tex] \frac{1}{4} [/tex]
Weight in first four months = 17/4
Weight in first four months = 3 [tex] \frac{1}{2} [/tex]
Weight in first four months = 7/2
11 = 17/4 + 7/2 + weight gain in third four months
Weight gain in third four months = 11 - 17/4 - 7/2
Taking LCM, we get 4
Weight gain in third four months = (11×4 - 17 - 7×2)/4
Weight gain in third four months = (44 - 17 - 14)/4
Weight gain in third four months = 13/4
Weight gain in third four months = 3 [tex] \frac{1}{4} [/tex]
Hence, the weight gain is 3 [tex] \frac{1}{4} [/tex] pounds.
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The complete question is -
A baby gains 11 pounds in its first year of life. The baby gained 4 1/4 pounds during the first four months and 3 1/2 pounds in its second four months. How much did the baby gain in the last four months?
