The double integral of 6y * 4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3
A double integral is used to calculate the total amount of a quantity that is distributed over a two-dimensional region. In this case, the quantity being integrated is 6y*4x^5 + 1. To evaluate the integral, we need to integrate with respect to x and y.
The first step is to evaluate the inner integral with respect to y. The limits of integration for y are 0 and x^2.
∫(6y4x^5 + 1) dy from 0 to x^2 = ∫(6y4x^5) dy + ∫1 dy = [6/7y^74x^5] from 0 to x^2 + [y] from 0 to x^2 = (6/7)x^5x^2 + x^2 = (6/7)*x^7 + x^2The second step is to evaluate the outer integral with respect to x. The limits of integration for x are 0 and 1.
∫((6/7)*x^7 + x^2) dx from 0 to 1 = [x^8/7 + x^3/3] from 0 to 1 = 1/7 + 1/3 = 20/21 + 10/21 = 30/21 = 20/3Therefore, the double integral of 6y*4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3.
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Suppose that 10% of all students at a local college have tattoos. Suppose that a simple random sample of 10 students is obtained. What are the probabilities that (a) none of the 10 students have a tattoo, (b) the first student chosen has a tattoo, but the rest do not, and (c) exactly one student has a tattoo?
The probability of none of the 10 students having a tattoo is 0.3486784401, the probability of the first student chosen having a tattoo and the rest not having one is 0.03162277660, and the probability of exactly one student having a tattoo is 0.3162277660.
(a) P(none of the 10 students have a tattoo)
= P(no tattoos) = P(no tattoos in the first student) * P(no tattoos in the second student) * ... * P(no tattoos in the tenth student)
= 0.9 * 0.9 * ... * 0.9 = 0.9^10
= 0.3486784401
(b) P(first student chosen has a tattoo, but the rest do not)
= P(tattoo in the first student) * P(no tattoos in the second student) * ... * P(no tattoos in the tenth student)
= 0.1 * 0.9 * 0.9 * ... * 0.9 = 0.1 * 0.9^9
= 0.03162277660
(c) P(exactly one student has a tattoo)
= P(tattoo in the first student and no tattoos in the others) + P(no tattoos in the first student and tattoo in the second student) + ... + P(no tattoos in the first nine students and tattoo in the tenth student)
= 10 * 0.1 * 0.9^9
= 0.3162277660
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A worker takes 1 week to fill up 7 crates at this rate how will it take for it to fill up 280 crates
Answer:
40 weeks
Step-by-step explanation:
This question is meant to be solved using direct proportion.
7 crates = 1 week
I crate = 1/7 week
280 crates = 1/7 * 280
Answer = 40
|Calculations|
( 280÷7)
Which function depicts f (x)
We have depicted the function f(x).
If the function is stretched vertically by a factor of 5 -> 5f(x).
If the function is shrunk horizontally by a factor of 5 -> f(5x).
If the function is shifted to the right five units -> f(x) - 5
If the function is shifted to the down five units -> f(x - 5)
If the function is shifted to the up five units -> f(x) + 5
If the function is shifted to the right five units -> f(x + 5)
What is a function?
A function is a mathematical relationship between a set of inputs, known as the domain, and a set of outputs, known as the range. In other words, it's a rule that assigns a unique output to each input.
If the function is stretched vertically by a factor of 5 -> 5f(x).
If the function is shrunk horizontally by a factor of 5 -> f(5x).
If the function is shifted to the right five units -> f(x) - 5
If the function is shifted to the down five units -> f(x - 5)
If the function is shifted to the up five units -> f(x) + 5
If the function is shifted to the right five units -> f(x + 5)
Hence, we have depicted the function f(x).
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Factor this expression 9y - 36
Answer:
(3y - 12)(3)
Step-by-step explanation:
Since both 9x and 36 divide by 9 you can put 9 as one factor: 9x −36 = 9 ⋅ x −9 ⋅ 4 = 9 ⋅ (x −4)
What is the horizontal example?
The horizontal example is a line that runs from side to side, such as the horizon or the x-axis of a graph.
A horizontal relationship is a type of relationship between two or more entities that are on the same level. This type of relationship is often characterized by competition. For example, two companies which are both competing for the same market share would be in a horizontal relationship with each other. This type of relationship usually involves collaboration on certain projects, but ultimately the two entities are in direct competition with each other. This type of relationship can be seen in business, politics, and other areas of life. It is important to remember that a horizontal relationship does not have a hierarchical structure, which is often seen in vertical relationships. This type of relationship is based on mutual interests and is usually characterized by competition and the drive to be better than the other entity.
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The triangles are congruent by sss or hl. Triangles m n q and p q n are connected at side q n. Triangle m n q is rotated about point n and then is shifted to the left to form triangle p q n. Which transformation(s) can map trianglemnq onto trianglepqn?.
The combination of a rotation and a translation transformation can map triangle mnq onto triangle pqn.
It is possible to map triangle mnq onto triangle pqn by performing a combination of rotation and translation transformations.
First, triangle mnq can be rotated about point n by a certain angle to form a new triangle that is congruent to triangle mnq. This rotation transformation preserves the size and shape of the triangle but changes its orientation.
Next, the rotated triangle can be shifted to the left to form triangle pqn. This translation transformation moves the triangle to a new position without changing its size or shape.
Therefore, the combination of a rotation and a translation transformation can map triangle mnq onto triangle pqn.
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Answer:
D
Step-by-step explanation:
just took the test on edg
In a regression analysis, the error term ε is a randomvariable with a mean or expected value of
a) Zero
b) One
c) any positive value
d) any value
In a regression analysis, the error term ε is a random variable with a mean or expected value of zero. The correct option is a.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
Analysis is a regression analysis.
And the error term in regression analysis:
The error term, which refers to the total of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.
ε = Epsilon or error term.
The variation in the dependent variable that the independent factors do not explain is taken into account by the error term.
The values of the error term should be determined by random chance.
The average value of the error term must be equal to zero in order for your model to be impartial.
Therefore, error term is zero.
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Directions: Solve each problem using the correct algebraic rules. 1. Write an expression for each of the following: a. the sum of 6 and z b. the difference between 20 and x c. 8 less than the quotient of x divided by 6 d. x increased by 5 divided by 4
The algebraic expressions are defined as follows:
a. 6 + z.
b. 20 - x.
c. (x/6) - 8.
d. (x + 5)/4.
How to define the algebraic expressions?The sum of two terms is defined by an addition operation, hence the sum of 6 and z is given as follows:
6 + z.
The difference between two terms is given by the subtraction of the two terms, hence the difference between 20 and x is given as follows:
20 - x.
The quotient of x and 6 is given as follows:
x/6.
Eight less than the quotient means that it is subtracted by eight, hence:
(x/6) - 8.
The increase of x by 5 is given as follows:
x + 5.
Then the division by 4 is of:
(x + 5)/4.
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Which equation has no solution?
|4x - 2| = - 6, |-2 - x| = 9, |3x + 6| = 6, |-2x + 8| = 0
What is the slope of the equation 5/4x-7/4
Answer:
3rd option ==> 5/4
Step-by-step explanation:
5x/4 means that for every time x increases by 1, y increases by 5/4.
5/4 is the coefficient for x.
Answer:
[tex]\dfrac{5}{4}[/tex]
Step-by-step explanation:
The general slope-intercept form of a line equation is
[tex]y = mx + b[/tex]
where m is the slope and b the y-intercept
The given line has the equation:
[tex]y = \dfrac{5}{4}x - \dfrac{7}{4}[/tex]
Comparing the general equation to this equation tells us that the slope
[tex]\textr{m } = \dfrac{5}{4}[/tex]
and y-intercept
[tex]b = -\dfrac{7}{4}[/tex]
You go shopping and buy a gift for a friend, but on the day before you're going to give it to him, you notice that he already has exactly what you bought him! You take the gift back to the mall, but you lost your receipt. The cashier says that you can only get back cash for the lowest amount that the item sold for. The item was originally $50 and sales tax in your area is 9.5%. It went on sale on four different occasions. Keep in mind that when an item goes on sale, it is taxed first and then the discount is taken. The first sale was 10% off. The second sale was no tax. The third sale was buy 3, get 1 half off. The last one was buy anything over $40 and get a $5 gift card. How much cash will you get back? Activate Windove Go to Settings to active
The total cashback you will get back is[tex]$ 49.75}[/tex]
The Given, original price [tex]$=\$ 50$[/tex] Sales fax[tex]$=9.5 \%$\\[/tex]
For first sale
[tex]\begin{aligned}\text { Price of item } & =\$ 50 \\\text { sales tax } & =+\$ 4.75 \\10 \% \text { discount } & =\frac{-\$ 5}{\$ 49.75}\end{aligned}[/tex]
A sale is a transaction between two or more parties that involves the exchange of tangible or intangible goods, services, or assets for money. In some cases, assets other than cash are paid to a seller.
In the financial markets, a sale can also refer to an agreement that a buyer and seller make regarding a financial security, its price, and specific arrangements for its delivery.
Regardless of the context, a sale is essentially a contract between a seller of a particular good or service and a buyer who is willing to pay for that good or service.
for second Sale:-
There is no tax
So price[tex]$=\$ 50$[/tex]
For third sale: - Buy 3 and get 1 half of
[tex]\begin{aligned}\text { Price }=50 \times 3 & =\$ 150 \\\text { Sales tax }= & +\$ 14.25 \\\text { Discount } & =\frac{-\$ 25}{\$ 139.25}\end{aligned}[/tex]
So, price of 1 piece [tex]$=\$ 46.42$[/tex]
for fourth Sale; - Buy anything over [tex]\$40[/tex] and get [tex]$\$ 5$[/tex] gift card.
[tex]& \text { Price }=\$ 50 \\& \text { sales tax }=+\$ 4.75 \\& \text { Gift card }=\frac{-\$ 5}{\$ 49.75}\end{aligned}[/tex]
Therefore, the cashback you will get back is [tex]$ 49.75}[/tex]
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What is a function of the form f/x Logbx?
The logarithmic function [tex]f(x)=\log _{x} b[/tex] is the inverse of the exponential function [tex]g(x)= b^{x}[/tex].
The logarithm function is of the form [tex]f(x)=\log _{x} b[/tex] where [tex]x[/tex] is the base and [tex]b > 0[/tex].
The exponential function is of the form [tex]g(x)= b^{x}[/tex] where [tex]x[/tex] represents variable and [tex]b[/tex] represents constant. [tex]b[/tex] is also called the base of the function and must be greater than 0.
The inverse of a function exists if and only if the function is one-one and onto function. When the function has inversed the range of the function changes to the domain of the inversed function and the domain of the function changes to the range of the inverse function.
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What is the domain of the relation graphed below?
Domain of the given graph is {x/-4≤x≤4}
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The domain of a function or relation is the set of all possible independent values the relation can take.
The graph is passing through the points (4, 0)(-4, 0)(0, 1) and (0, -1)
Four comma zero, minus four comma zero, zero comma one and zero comma minus one.
The x is between -4 and 4
The domain of the given graph is {x/-4≤x≤4}
Hence, domain of the given graph is {x/-4≤x≤4}
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a basketball team's players were successful on $50\%$ of their two-point shots and $40\%$ of their three-point shots, which resulted in 54 points. they attempted $50\%$ more two-point shots than three-point shots. how many three-point shots did they attempt?
The team attempted 30 three-point shots.
Let x be the number of three-point shots the team attempted.
We know that the team attempted 50% more two-point shots than three-point shots, so the number of two-point shots is 1.5x.
We also know that 50% of the two-point shots were successful and 40% of the three-point shots were successful, so we can set up the following equation:
(1.5x)(0.5) + (x)(0.4) = 54
Solving for x yields x = 30.
Therefore, the team attempted 30 three-point shots.
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4 A piece of wire is 30 cm long.
It is cut into two unequal pieces.
One piece is bent into a circle.
The other is bent into a square enclosing the circle, as
shown in the diagram.
Find the length of each piece of wire in cm to 3 s.f.
Step-by-step explanation:
When an iron rod is cut into equal pieces of 30 cm each, a piece of 4 cm is left out. When cut into equal pieces of 29 cm, a piece of 13 cm is left out. The minimum length of rod is
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A 5 metre long piece of cloth is cut into three smaller pieces. How long is the longest of the three pieces? Given that:
I. One piece is 2.90 metre long.
II. One piece is 90 cm longer than another piece and the remaining piece is 20 cm long
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A piece of wire 12 m long is cut into two pieces, one piece is 4.29 m long. What is the length of the other piece?
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A rope 5 m 75 cm long is cut into two pieces. If one piece is 2.25 m long find out the length of the other piece.
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A piece of wire. 2
4
3
metres long, broke into two pieces. One piece is
8
5
metre long. How long is the other piece?
I am so confused on this question and do not understand how to do the topic.I need help so bad.What I need help with is like how do I get the answer on the right.
Answer:
Below
Step-by-step explanation:
Take the first set of numbers 2 seconds 24.4 yds
24.4 yds / 2 s = 12.2 yards per second
You can take any of the other sets and should get this same value
73.2 yards in 6 seconds 73.2/6 = 12.2 yards per second ( as we found)
So for 8 seconds : 12.2 yds/s * 8s = 97.6 yds
In which of the following options does x varies inversely as y?
x+y=5x plus y is equal to 5
x=5yx is equal to 5 y
x=5yx is equal to 5 over y
x=5y+5
Answer: The meaning of the statement “ x vary inversely as y “ is “x is inversely proportional to y".
Final Answer // x=5yx is equal to 5 over y
Step-by-step explanation:
Pancho goes to the movies with $18 in his wallet. He buys
a ticket for $5.75 and three snacks for $1.50 each. How
much money does he have left?
Select the correct expression.
A. 18-3(5.75 +1.50)
B. 18-5.75 +3.1.50
C. 18-(5.75 +3.1.50)
D. 18-5.75 -1.50
The Numerical expression that will represent the money that is left is 18-[ 5.75 + 3(1.50)] and the amount is $ 7.75.
Numerical expressions:Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
By mixing numbers with different mathematical operators, we can create a numerical expression. There is no restriction on how many operators can be used in a numerical expression.
Here we have
Pancho goes to the movies with $18 in his wallet. He buys a ticket for $5.75 and three snacks for $1.50 each.
The total amount that he spent = 5.75 + 3(1.50)
The amount that will be left = Initial amount - The total amount spent
= 18 - [ 5.75 + 3(1.50)]
= 18 - 5.75 - 4.5
= 7.75
Therefore,
The Numerical expression that will represent the money that is left is 18-[ 5.75 + 3(1.50)] and the amount is $ 7.75.
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Solve the equation. 1 1 ²x+3-2x = 4+²x+5 4 If necessary: Combine Terms Apply properties: Add Multiply To start over: Subtract Reset Divide
Answer:
13x would be the right answer, here is a cookie
Step-by-step explanation:
The Johnson family is getting a new fence around their circular pool. If the pool has a radius of 15.6 feet, approximately how many feet of fencing do they need to surround the pool?use 3.14 for pi
The points ( – 10,1) and (k,6) fall on a line with a slope of 5. What is the value of k?
Answer:
slope(m) =y2-y1 / x2-x1
Step-by-step explanation:
5=5/k+10
50 + 5k = 5
5k = -45
k= -9
n2+6n-4= Evaluate the expression when n=2. and n2 is n to the power of two
The polygons are similar. x = ___ Write your answer as a decimal
Answer:
Step-by-step explanation:
+5
. A soccer team spent $183 on 15 new soccer balls. Each ball cost the same. Find the exact cost of each soccer ball. Show all work.
Answer:
Each soccer ball cost $12.20
Step-by-step explanation:
183/15 = 12.20
The thin‑layer chromatography (TLC) plate shown was developed with 20% ethyl acetate in hexanes. (4)
Suppose the plate had instead been developed with 5% ethyl acetate in hexanes. Determine whether each plate is a possible result of the adjusted development process
The solvent characteristics of the formed plate would probably change from those of the unaltered plate development process if it had been developed with 5% ethyl acetate in hexanes.
Hexanes are nonpolar while ethyl acetate is polar, therefore mixing the two together would probably produce a more polar solvent solution.This might alter the chemicals' solubility and movement on the plate, possibly resulting in various separation patterns and band intensities.Additionally, it's feasible that the 5% ethyl acetate in hexane solution will improve the separation of the chemicals on the plate since the solvents' polar and nonpolar characteristics.
May combine to do so.However, it would rely on the different kinds of compounds on the plate and each one's unique solubility characteristics.
Conclusion: The 5% ethyl acetate in hexanes produced plate may have varied solvent characteristics, which may result in different separation patterns and band intensities, but it is impossible to know for sure without additional testing and analysis of the precise substances on the plate.
Complete question:
The thin‑layer chromatography (TLC) plate shown was developed with 20% ethyl acetate in hexanes. (4) Suppose the plate had instead been developed with 5% ethyl acetate in hexanes. Determine whether each plate is a possible result of the adjusted development process and its conclusion.
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Find the x -intercept of a line with a slope of - 2 and a point ( 3 , 4 ) .
let's firstly get its equation and then find the x-intercept, keeping in mind that the x-intercept occurs when y = 0.
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 2}(x-\stackrel{x_1}{3}) \qquad \implies\quad \stackrel{\textit{setting y = 0}}{0-4=-2(x-3)} \\\\\\ -4=-2x+6\implies -10=-2x\implies \cfrac{-10}{-2}=x\implies 5=x~\hfill \boxed{\stackrel{x-intercept}{(5~~,~~0)}}[/tex]
Which 2 numbers give you -70 when multiplied but when added give you 9?
The numbers for the condition are 14 and -5.
What is an expression?What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given two numbers,
let the numbers be a and b,
and the product of a and b is -70.
a x b = -70
a = -70/b
addition of numbers is 9
a + b = 9
substitute value of a
-70/b + b = 9
b² - 9b - 70 = 0
factors of equation are
b² + 5b - 14b - 70 = 0
(b + 5)(b - 14) = 0
b = -5 and b = 14
when b = -5, a = 14
and when b = 14, a = -5
Hence the numbers are -5 and 14.
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Implementing a new system into an organization module by module is called a ____________.
A.
pilot study
B.
phased approach
C.
module strategy
D.
parallel strategy
E.
direct cutover strategy
Implementing a new system into an organization module by module is called a phased approach.
A phased approach is one of two common methods used to develop an ERP system solution. In this strategy, the system's functionalities are introduced in a certain order, gradually replacing previous systems and processes.
This frequently indicates that a business starts off with core functionality that is given top attention, and then other applications are gradually added in stages over time. An alternative implementation strategy, however, uses an all-at-once model in which the system and all apps "Go Live" simultaneously.
The optimal implementation plan for your firm will depend on the needs, goals, and strategies you have for it. This might involve a hybrid strategy where crucial functionality is added to the core ERP programs first, and then desirable features are added later on in a staged implementation. By considering all of your options, your firm can decide which will serve its interests the most effectively.
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Given that x y=60, the maximum value of x2y is the value of x for this maximum value is answer
The maximum value of x2y is 3600 and the value of x for this maximum value is 60.
The given equation is xy = 60. This equation can be rearranged to x = 60/y. Therefore, the maximum value of x2y is when x is at its maximum value.
xy = 60
x = 60/y
To find the maximum value of x, we substitute the value of y with 1, as 1 is the lowest possible value for y. Thus, x = 60/1 = 60. Therefore, the maximum value of x2y is 60 x 60 = 3600 and the value of x for this maximum value is 60.
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Find the x-intercept of the line 18x–5y=12.
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
The x-intercept of the line 18x – 5y = 12 is 2/3
How to determine the x-intercept of the line?From the question, we have the following parameters that can be used in our computation:
A linear equation
The linear equation is represented as
18x–5y=12
Express properly
So, we have the following representation
18x – 5y = 12
Set y to 0 to determine the x-intercept of the line
So, we have the following representation
18x – 5 * 0 = 12
Evaluate the products
18x = 12
Divide by 18
So, we have
x = 12/18
Simplify
x = 2/3
Hence, the intercept is 2/3
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