To find the average value of the function f(x, y) = 7xy over the triangular region defined by vertices (0, 0), (1, 0), and (1, 8), compute the area of the triangle and then calculate the double integral of the function over the region, divided by the area. The bounds for the double integral will be defined by the region.
Explanation:To find the average value of f over the given triangular region, we first need to find the area of the region. The given region is a triangle with vertices (0, 0), (1, 0), and (1, 8). This triangle has a base of 1 (the difference in x coordinates) and a height of 8 (the difference in y coordinates), so its area is (1/2)*base*height=(1/2)*1*8=4.
Next, we integrate the function f(x, y) = 7xy over the triangular region, and divide by the area of the region, to find the average value. Setting up and computing the double integral will provide the total value of the function over the region. The bounds for the double integral will be defined by the region, so we will integrate x from 0 to 1 and y from 0 to 8. The average value is then given by the total value divided by the area, or (1/4)*double integral of f(x, y) dy dx.
Without performing the actual calculation, this is the best process to solve the problem as presented.
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Jessica is measuring two line segments. The first line segment is 30 cm long. The second line segment is 500 mm long. How long are the two line segments together? (answer in cm)
convert mm to cm
1mm = 0.1 cm
500 * 0.1 = 50cm
50 +30 = 80cm total length
The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. Which ratio represents the number of votes for hot dogs to chicken? 1/5 2/5 3/5 5/2
The answer is 2/5 because hot dogs to chicken is 2/5
suppose someone tells you that she has a triangle with sides having lengths 2.6,8.1 and 8.6. Is this a right triangle? why or why not? Is there an angle in the triangle larger than 90 degree?
a girl scout has (5x-12) boxes of cookies and sells (3x+18) of them. Write an expression to represent the amount of boxes she has left. Also can you show me the work that gets this answer not just the answer
The width of a rectangle is equal to m cm, but its length is five times greater than the width. Find the area of the rectangle.
The area will be 5m^2
How do you write .625 as a fraction
To turn a decimal into a fraction, first notice that the number to the right of the decimal point is 625. The 6 represents the tens, the 2 represents the hundreds, and the 5 represents the thousands. So, we can put 625 over 1000 or 625/1000.
Notice that the fraction [tex]\frac{625}{1000}[/tex] is not in lowest terms. To turn the fraction into lowest terms, we can divide both the numerator and the denominator by 125.
[tex]\frac{625}{1000}[/tex] ÷ [tex]\frac{125}{125}[/tex] = [tex]\frac{5}{8}[/tex]
Therefore, .625 can be written as the fraction 5/8, which is in lowest terms.
Divide.
3 5/9 ÷ -2 2/3
Enter your answer as a mixed number, in simplified form, in the box.
Show that for the same shear angle, there are two rake angles that give the same cutting ratio.
Charlie's father is 41 years old. His age is two years more than three times Charlie's age. What is Charlie's age?
Final answer:
By setting up a linear equation, it is determined that Charlie is 13 years old based on the given information that his father is two years more than three times Charlie's age and is 41 years old.
Explanation:
The problem presented is a classic example of a linear equation in the subject of mathematics. We are given that Charlie's father is 41 years old, and his age is two years more than three times Charlie's age.
To determine Charlie's age, we can set up the equation as follows: Let x represent Charlie's age. The father's age is then described by the expression 3x + 2.
Since we know the father is 41 years old, we have:
3x + 2 = 41
Subtract 2 from both sides of the equation to isolate the terms with x:
3x = 39
Now, divide both sides by 3 to solve for x:
x = 39 / 3
x = 13
Therefore, Charlie is 13 years old.
9x-5y=-32 in slope intercept form
The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:
y = a + bxb is the slopea is a constant term. It is the y intercept, the place where the line crosses the y axis.
Example 1
y = -13 + 7x
This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.
Example 2
4x + 3y = 12
Rewrite this equation in slope intercept form.
3y = 12 - 4xThe equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.
Example 3
5x - 3y - 15 = 0
Rewrite this equation in slope intercept form.
3y = -15 + 5xThe equation is now in slope intercept form. The y intercept is (0,-5) and the slope is
5/3.
Example 4
The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is
1.5.
At a school, 126 students play at least one sport. This is 40% of the students at the school. How many students are at the school?
What is the quotient?
-5 1/4 ÷ 2 3/4
Enter your answer as a mixed number, in simplified form, in the box.
To divide -5 1/4 by 2 3/4, convert both numbers to improper fractions, multiply the first fraction by the reciprocal of the second fraction, and simplify the result. The quotient is -1 10/11.
Explanation:To divide -5 1/4 by 2 3/4, first convert both mixed numbers to improper fractions. -5 1/4 can be written as -21/4, and 2 3/4 can be written as 11/4. Next, divide -21/4 by 11/4. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (-21/4) * (4/11) = -21/11. This quotient can be written in mixed number form as -1 10/11, which is the simplified answer.
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What is the slope of y=1/5x - 4?
If ( f ∘ g)(x) = x2 - 6x + 8 and g(x) = x - 3, what is f(x)?
Determine the unit rate. Use mental math when you can. 6 golf balls for $15. 2 dozen tennis balls for $36. 4lb meat for $18. 24 tickets for $480.
To determine the unit rate for each item, divide the total cost by the number of units. This gives us $2.50 per golf ball, $1.50 per tennis ball, $4.50 per pound of meat, and $20 per ticket.
Explanation:The question involves determining the unit rate of different items. A unit rate is the cost per one unit of an item. To calculate each unit rate, we divide the total cost by the number of units.
For 6 golf balls for $15, the unit rate is $15 ÷ 6 = $2.50 per golf ball.For 2 dozen (24) tennis balls for $36, the unit rate is $36 ÷ 24 = $1.50 per tennis ball.For 4lb of meat for $18, the unit rate is $18 ÷ 4 = $4.50 per pound of meat.For 24 tickets for $480, the unit rate is $480 ÷ 24 = $20 per ticket.These calculations can often be made using mental math, especially when dealing with simple numbers or common multiples.
At one university, the students are given z-scores at the end of the each semester, rather than the traditional gpas. the mean and standard deviation of all students' cumulative gpas, on which the z-scores are based, are 2.7 and 0.5, respectively
The students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is 1.9.
Given data:
To translate z-scores to corresponding GPAs, you can use the formula:
GPA = (z * standard deviation) + mean
Given:
Mean (μ) = 2.7
Standard Deviation (σ) = 0.5
Let's calculate the corresponding GPAs for the given z-scores:
For z = 2.0:
GPA = (2.0 * 0.5) + 2.7
= 1.0 + 2.7
= 3.7
For z = -1.0:
GPA = (-1.0 * 0.5) + 2.7
= -0.5 + 2.7
= 2.2
For z = 0.5:
GPA = (0.5 * 0.5) + 2.7
= 0.25 + 2.7
= 2.95
For z = -2.5:
GPA = (-2.5 * 0.5) + 2.7
= -1.25 + 2.7
= 1.45
Now, to determine the corresponding probationary GPA for z = -1.6:
GPA = (-1.6 * 0.5) + 2.7
= -0.8 + 2.7
= 1.9
Hence, students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is approximately 1.9.
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The complete question is attached below:
At one university, the students are given z-scores at the end of each semester rather than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.
- translate each of the following z-scores to corresponding GPA: z=2.0, z=-1.0, z=.5, z =-2.5.
- Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA?
what is absolute value of these set of numbers?
A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours. What is the distance of the entire trip? How long does the entire trip take?
12x = 10x + 3
Subtract 10x from both sides
2x = 3
Divide by two on each side
x = 3/2 or 1 1/2 hours
Distance of the trip:
12 * 2 * 3/2 = 36 miles
How long does the trip take:
3/2 + 3/2 + 3/10 = 3 3/10 hours
3 hours
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How did you calculate the price of each nickel to begin with? Thanks
5y-x=10 (solve for y).
To solve 5y - x = 10 for y, add x to both sides and then divide by 5, resulting in the solution y = (x + 10) / 5.
To solve the equation 5y - x = 10 for y, follow these steps:
Add x to both sides of the equation to isolate terms with y on one side: 5y = x + 10.
Now, divide both sides of the equation by 5 to solve for y:
y = (x + 10) / 5.
The solution for y when given an equation of the form 5y - x = 10 is y = (x + 10) / 5.
A carpenter has a 6-foot long board. He wants to cut the board into pieces that are 4/5 foot long. How many pieces of length 4/5 foot can the carpenter cut from the board? What length of the original board will be left after the carpenter has cut all the pieces that are 4/5 foot long?
Answer:
Number of pieces=7
Length of board remaining=[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
We are given that a carpenter has board of length=6 foot
Length of each piece of board=[tex]\frac{4}{5}[/tex] foot
We have to find the number pieces of given length of piece can be made from given board.
In order to find the number of pieces we will divide the total length of board by the length of each piece.
Therefore, number of pieces =[tex]\frac{6}{\frac{4}{5}}[/tex]
Number of pieces=[tex]7\frac{1}{2}[/tex]
Length of each piece =[tex]\frac{4}{5}[/tex]
Therefore, number of pieces=7
Length used in 7 pieces =[tex]7\times\frac{4}{5}=\frac{28}{5}[/tex]
Length of board remaining=[tex]6-\frac{28}{5}=\frac{2}{5}[/tex]
The expression 1/3b−1/3 factored is
Answer:
[tex]\frac{1}{3}[b-1][/tex]
Step-by-step explanation:
we have
[tex]\frac{1}{3}b-\frac{1}{3}[/tex]
Factor the coefficient [tex]\frac{1}{3}[/tex] of both terms
[tex]\frac{1}{3}b-\frac{1}{3}=\frac{1}{3}[b-1][/tex]
Find the dimensions of the rectangle with area 120 square inches and smallest possible perimeter
There are 5 slots, each containing the letters w, r, l, d or o. one letter is picked at random from each slot. what are the odds that the letters stored in these slots read the word world?
The probability of the 5 letter slots randomly making the word 'world' is calculated by finding the product of the probability of choosing each letter correctly, which for this problem, is (1/3125).
Explanation:To calculate the probability of picking the letters 'w', 'o', 'r', 'l', 'd' in that order, we understand that we are dealing with a probability problem regarding independent events. This scenario means that the outcome of each selection does not affect the others.
Here, each slot contains 5 distinct letters. The probability of picking a specific letter correctly is 1/5 (1 way to pick a correct letter divided by 5 total letters). So, the probability of picking each letter correctly and in the order of 'world' is the product of the probabilities of choosing each letter correctly i.e P(choosing all five correct letters) = P(choosing 1st correctly) X P(choosing 2nd correctly) X P(choosing 3rd correctly) X P(choosing 4th correctly) X P(choosing 5th correctly) = (1/5) X (1/5) X (1/5) X (1/5) X (1/5) = (1/3125).
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A bag contains 90 marbles some red and some transparent the ratio of red marbles to transparent ones is 1:4. how many red marbles are there? andwer
If bethany earned $51,740 last year, how much did she earn per week?
All real numbers at least 3 units from -2
You are building a new house on a cartesian plane whose units are measured in miles. Your house is to be located at the point (2,0) . Unfortunately, the existing gas line follows the curve y= √(16 x^2 +5x+16). It costs 400 dollars per mile to install new pipe connecting your house to the existing line. What is the least amount of money you could pay to get hooked up to the system?
Leo has 421 prize tickets. He can get 1 prize for every 100 tickets. How many prizes can Leo get? How many tickets will he have left over?
421 / 100 = 4.21
so he will win 4 prizes and have 21 tickets left over.
Emily bought a video game console and some games for $350. The video game console cost $200. Each game cost $25. How many games did Emily purchase?