The best approximation to the solution of the system of equations is (2, 3)
How to determine the best approximation to the solution?From the question, we have the following parameters that can be used in our computation:
Equation 1 is 5 x plus 2 y equals 16.
Equation 2 is x plus 3 y equals 12.
Rewrite the equations properly
So, we have the following representation
5x + 2y = 16
x + 3y = 12
Make x the subject in the second equation
So, we have
x = 12 - 3y
Substitute x =12 - 3y in the equation 5x + 2y = 16
So, we have
5(12 - 3y) + 2y = 16
Open the brakects
This gives
60 - 15y + 2y = 16
Evaluate the like terms
-13y = -44
Divide both sides by -13
y = 3.39
Substitute y = 3.39 in x = 12 - 3y
x = 12 - 3 * 3.39
Evaluate
x = 1.83
Approximate the solutions
x = 2 and y = 3
Hence, the solution is (2, 3)
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Consider a political discussion group consisting of 6 Democrats, 7
Republicans, and 2 Independents. Suppose that two group members are
randomly selected, in succession, to attend a political convention.
Find the probability of selecting no Independents.
(Type an integer or a simplified fraction.)
Answer:
13/15×13/14
Step-by-step explanation:
13/15 are not independents and then 12/14 aren't independants
when graphing x is greater than or equal to 1, where does the shading occur
Edmund is designing his garden. For every yellow tulip, he plans to plant two whites lilies. Using only these two types of flower, he plans to plant 12 flowers in his garden. How many of each type of flower will Edmund plant in his garden? Edmund will plant _______ tulips and _______ lilies.
Answer:
4 yellow tulips and 8 white lilies.
Step-by-step explanation:
Ratio is 1:2:3 for yellow tulips, white lilies and the total.
Set up a proportion
[tex]\frac{yellow}{total}[/tex] = [tex]\frac{yellow}{total}[/tex] Three of these numbers you know, Solve for the unknown
[tex]\frac{1}{3}[/tex] = [tex]\frac{x}{12}[/tex] Cross multiply and solve for x
3x = 12 Divide both sides by 3
x = 4 This is the number of yellow tulips
Set up another proportion:
[tex]\frac{white lilies}{total}[/tex] = [tex]\frac{white lilies}{todal}[/tex]
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{12}[/tex] I can see that 3 x 4 = 12 so I will multiply the top number to 2 by 4 to get 8.
When attempting to do his homework Mark incorrectly uses the addition property of equality below which statement would correct Mark's error?
The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.
Mark incorrectly uses the addition property of equality, below which statement would correct Mark's error?Mark's statement: 4 = 2 + 5Correct statement: 4 = 5 + 2The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.
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Which function is represented in the graph? A.) y = sinx
B.) y = cosx
C.) y = sin-1x
D.) y = cos-1x
From the given information, we can that y = [tex]sin^{-1}x[/tex] function is represented in the graph.
What is inverse sine function?The opposite of the sine function is the inverse sine function, commonly referred to as the arcsine function. Since the sine (or sine function) of an angle is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of that ratio will provide the angle's measurement.
According to graph
Domain is [-1, 1]
Range = [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex]
Set an interval to limit [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex] the sine-scope function's so that it is one to one and not unlimited.
The limited function is one to one since it satisfies the horizontal line test.
[tex]Each range value (-1 to 1) is within the limited domain (-\frac{\pi }{2} \frac{\pi }{2})[/tex]
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Some people active cult like status after their death, such as Jimi Hendrix. Brad has a list of thirteen such people and would like to propose some documentaries about four of them. If there are thirteen people to choose from on the list, in how many ways could brad pick groups of four?
The number of ways that Brad can pick groups of four is 715 ways.
How many ways could Brad pick groups of four?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula is given as:
= n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Based on the information, Brad has a list of thirteen such people and would like to propose some documentaries about four of them. This will be:
n! / ((n – r)! r!)
= 13! / (13 - 4)!4!
= 13! / 9!4!
= 13 × 12 × 11 × 10 / 4 × 3 × 2
= 715
There'll be 715 ways.
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The marked price of an article is Rs. 8000. After allowing a certain percent of discount with 13% Value Added Tax (VAT) levied, the articles is sold at Rs 7684. Find the difference between discount amount and VAT amount.
Answer:
$1200.00
Step-by-step explanation:
Let x = the discounted priced
x + .13x = 7684 Combine like terms.
1.13x = 7684 Divide both sides by 1.13
[tex]\frac{1.13x}{1.13}[/tex] = [tex]\frac{7684}{1.13}[/tex]
x = 6800
$6800 is the cost of the discounted article before tax.
8000 - 6800 = 1200
I need help on this question it’s really difficult please
Answer:
See attached
Step-by-step explanation:
You want the graphed figure dilated by different scale factors around different center points.
DilationTo find the image of a dilated point, figure how far it is from the center of dilation, then multiply that distance by the scale factor. Plot the image point at that distance from the center of dilation in the same direction as the original point.
Dilation by a factor of 1/2 cuts all the distances in half. 2 grid squares become 1; 4 grid squares become 2.
Dilation by a factor of 2 multiplies all the distances by 2. 2 grid squares become 4; 4 grid squares become 8.
GraphIn the attached graph, the points are labeled with subscripts a, b, c according to the dilation they correspond to. Note that the center of dilation doesn't move, so Q and Q_a are the same point, and S and S_c are the same point.
In the video, it was remarked that for small values of the equation of motion for the pendulum, 9 sin 0 = 0 is similar to the linear spring equation. If we take two nonzero terms of the L series for sin into account, the model is even more spring-like, but this time to a non-linear spring. From this perspective, which of the following kind of spring is the pendulum most like?
O ideal linear spring
O hard spring O soft spring
Hard spring
What is Spring?
They swing back and forth around a stationary point. Classic examples of this type of vibrating motion are a simple pendulum and a mass on a spring. The use of motion detectors demonstrates that the vibrations of these items have a sinusoidal character, even if this is not obvious from plain viewing.
Let θ be A,
[tex]A''+(g/l)sinA=0\\sinA=A - (A^{3} /3!)+(A^{5} /5!)....\\[/tex]
taking first 2 terms,
[tex]A'' +(g/l)(A-A^{3}/3!)\\[/tex]
intergrating both sides,
[tex]A'+(g/l)(A^{2}/2 -A^{4}/24)=c[/tex]
integrating again,
[tex]A+(g/l)(A^{3} /6-A^{5}/120)=ct+c_{1}[/tex]
power is 5= non linear spring
Additionally, a larger degree indicates that the displacement over time diminishes more quickly.
Hence its a hard spring.
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thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. each student was given a choice between the macaroni and cheese and the cajun potato barrels. from the sample, 20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
Given that,
36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).
We have to find which of the following keeps this study from being an experiment with a sound design.
Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.
Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
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which would be the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! where: if n
The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .
Given :
the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .
Base case :
The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .
we know that ,
def func ( n ) :
if n == 0 :
return 1
Here the base case is clearly n = 0
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Simplify completely.
(h12/h4)3
Enter your answer in the box.
After solving the given expression using exponents properties, the resultant answer is h²⁴.
What are exponents?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bⁿ and is pronounced as "b to the n."
Positive, negative, zero, and rational exponents are the four different categories. Positive exponents indicate the number of times a base should be multiplied by itself.
So, we have:
(h¹²/h⁴)³
Now, solve as follows using properties:
(h¹²/h⁴)³
(h¹²)³/(h⁴)³
h³⁶/h¹²
h³⁶⁻¹²
h²⁴
Therefore, after solving the given expression using exponents properties, the resultant answer is h²⁴.
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A random sample of 45 door-to-door encyclopedia salespersons were asked how long on average they were able to talk to the potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes.
Construct a 95% confidence interval for mu, the time it takes an encyclopedia salesperson to talk to a potential customer.
What is the upper confidence limit?
If the mean is 8.5 minutes and the variance is 9 minutes then the upper confidence limit is 9.3765 .
In the question ,
it is given that ,
the number of sales person in the random sample (n) = 45 ,
the mean = 8.5 minutes
the variance is = 9 minutes .
So , the standard deviation is = 3.
For the 95% confidence interval the level of significance (α) is 0.05 .
So , α/2 = 0.05/2 = 0.025 .
So , from Z table ;
the value of [tex]Z_{\frac{\alpha }{2} }[/tex] is = 1.96 .
The formula for the confidence interval is
= [ mean ± [tex]Z_{\frac{\alpha }{2} }[/tex](SD/√n)]
Substituting the values from above ,
we get ,
= [8.5 - 1.96*0.4472 , 8.5 + 1.96*0.4472]
Simplifying further ,
we get ,
= [ 7.6235 , 9.3765 ]
Therefore , the upper limit of the 95% confidence interval is 9.3765 .
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A total of 50 people play darts.
Each player is given 3 darts to try and
hit the bullseye. If 21 of the darts hit
the bullseye, then what percent of
the darts hit the bullseye?
The percentage of the darts hit the bullseye will be 14%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A sum of 50 individuals plays darts. Every player is given 3 darts to attempt to stir things up around town. Assuming 21 of the darts hit the bullseye.
The total number of dart is calculated as,
Total dart = 50 x 3
Total dart = 150
The percentage is given as,
P = (21 / 150) x 100
P = 0.14 x 100
P = 14%
The percentage of the darts hit the bullseye will be 14%.
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x4 = -x2 + 5. as they are quadratic equations.
What are quadratic equations?A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be straightforward or difficult.
How do you identify a quadratic equation?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" form.
What is not quadratic equation?Due to the absence of an x2 component, bx 6 = 0 is NOT a quadratic equation. Because there is an x3 term, x3 x2 5 = 0 is NOT a quadratic equation (not allowed in quadratic equations).
The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x4 = -x2 + 5.
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If you are at - 15 on the number line and you wanted to move toward the positive integers, which direction along the number
line would you need to move?
O To the right.
O To the left.
O Start at zero on the number line and then move to the left.
O The positive integers are not a part of the same number line as the negative integers.
Answer: The number line that you really want to move is the right side. Then, at that point, the right choice is C.
What is a number line?
A number line alludes to a straight line in science that has numbers organized at customary stretches or divides along its width. A number line is frequently shown on a level plane and can be delayed toward any path.
On the off chance that you are at - 15 on the number line and you needed to push toward the positive numbers
The number line that you need to move in the right side. Then the correct option is C.
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Step-by-step explanation:
Tell Emily safe for trip look back over her spending habits on this page and page 9 what changes do you think she should make to save enough money for her trip explain your answer?
Answer: She could make those two changes to save money for her trip. Also, she could save a little bit of her salary to have enough money to go.
Step-by-step explanation:
This is just a guess but PLEASE GIVE ME BRAINLIEST if you're pleased with my answer.
Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes, that can be inscribed in the ellipse given by x^2/144+y^2/16=1
The dimensions of the rectangle of maximum area are the length of 12√3 units and width of 4 units
How to find the dimensions of the rectangle of maximum area?
Given that the ellipse has the equation: x²/144 + y²/16 = 1
Make x the subject:
x²/144 + y²/16 = 1
(x²+9y²)/144 = 1
x² + 9y² =144
x² = 144-9y²
x = √(144-9y²)
The rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Thus, the rectangle has a length and width of 2x and 2y respectively
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4(√(144-9y²))y
A = 4y√(144-9y²)
A = 4√(144y²-9y⁴)
The maximum area of the rectangle is at dA/dy = 0
dA/dy = 4[144-18³y/ (√(144y²-9y⁴))]
4[144-18y³/ (√(144y²-9y⁴))] = 0
144-18y³= 0
18y³ = 144
y³ = 144/18
y³ = 8
y = ∛8
y = 2
x = √(144-9y²)
x = √(144 - 9(2)²)
x = √108
x = 6√3
Thus, the dimensions are the length = 2x = 2×(6√3) = 12√3 units, the width = 2y = 2×2 = 4 units
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How much more does Amy need to make each month to cover her costa?
well, let's get Amy's expenses and income to see how much is leftover, hmmm let's recall she's going to be a Resident living off campus, so her total costs will pretty much be the Total Costs of a Resident, now since this is for 9 months, whatever is leftover, we'll have to divide it by 9, Check the picture below.
What function has an inverse which is also one-to-one?
If a function is defined as z = f(x), then the inverse of the function f is x = f-1 (x) i.e. f-1 defined from z to x.
In mathematics, function is an expression that explains the relationship between the variable and other variable. In this expression, one variable is independent and the other is dependent. unction and into function.
There are four types of functions. There is one to one function, many to one function, onto function, one to one and onto function.
Inverse function refers to the expression where the original output becomes the opposite.
These are the expressions used in mathematics to solve the problems and equations. In other fields of science, inverse function is also used.
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What must be true for lines A and B to be parallel lines?; Which lines are parallel justify your answer lines a and b are parallel because their?; Which lines are parallel justify your answer ABEF?; Are parallel lines congruent?
Parallel lines are straight lines that never meet each other no matter how long we extend them
Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).
The fundamental characteristics listed below make it simple to recognise parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
No matter how far apart they are from one another, parallel lines can never intersect.
I've answered in general as the question is incomplete
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what is the expression?
Bill Roundy bought 800 shares of a mutual fund with an NAV of $14.10. This fund has a load charge of 3%.
a. What is the offer price? (Round your answer to the nearest cent.)
b. What did Bill pay for the investment?
1. The offer price of the 800 shares of a mutual fund with a NAV of $14.10 that Bill Roundy bought is $11,280.
2. For this investment, Bill paid $11,618.40, including the load charge of 3%.
What is a load charge?A load charge is a sales commission that investors pay when they buy (front-end load) or redeem (back-end load) shares in a mutual fund.
What is NAV?NAV means net asset value.
NAV refers to the difference between the investee company's total assets and its total liabilities.
The total number of mutual fund shares bought by Bill = 800
The net asset value of the shares = $14.10
Load charge = 3%
Offer price = $11,280 (800 x $14.10)
Amount Bill paid for the investment = $11,618.40 ($11,280 x 1.03)
Thus, with an offer price of $11,280 for the mutual fund, Bill Roundy paid a total of $11,618.40, including the load charge.
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Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie's points per basketball game are normally distributed. Let X = the number of points per basketball game. Then X ~ N(23,4) Provide your answer below: The mean is Suppose Annie scores 34 points in the game on Sunday. The z-score when x-34 is This z-score tells you that x=34 is standard deviations to the right of the mean.
This z-score tells you x = 34 is 2.75 standard deviations to the right of mean. And the mean is 23.
What is standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
Given:
Annie averages 23 points per basketball game with a standard deviation of 4 points.
Suppose Annie's points per basketball game are normally distributed.
Let X = the number of points per basketball game.
By Notation,
X ~ N(23,4) means E(X) = 23, SD(X) = 4
Mean = 23 , Standard deviation = 4
So,
[tex]Z_s_c_o_r_e = \frac{Value - Mean}{Sd}\\Z_s_c_o_r_e = \frac{34-23}{4}\\ = \frac{11}{4} Z_s_c_o_r_e = 2.75[/tex]
mean = 23
This z-score tells you x = 34 is 2.75 standard deviations to the right of mean.
Hence, this z-score tells you x = 34 is 2.75 standard deviations to the right of mean. And the mean is 23.
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change .350 to hundredths
Answer:
.35
Step-by-step explanation:
Just drop the zero .350 is 350 thousandths = 35 hundredths
The horizontal and vertical movement of the graph.
A vertical shift is a movement up or down the y-axis, and it's represented by a change in the value of the y-intercept. A horizontal shift is a movement left or right along the x-axis, and in the equation of a function it's a change in the value of x before it's multiplied by the slope.
Vertical Shifts
One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function
g(x) =f(x)+k, the function f(x) is shifted vertically k units.
Horizontal Shifts
We just saw that the vertical shift is a change to the output, or outside, of the function. We will now look at how changes to input, on the inside of the function, change its graph and meaning. A shift to the input results in a movement of the graph of the function left or right in what is known as a horizontal shift,
Given a function f, a new function g(x)=f(x−h) , where h is a constant, is a horizontal shift of the function f . If h is positive, the graph will shift right. If h is negative, the graph will shift left.
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2. A train leaves Alphaville at 13 27. It travels at an average speed of 56 Km/h.
If it arrives in Eastwich at 16 12, What is the distance between the two
towns?
Answer: 13 27 to 15 27 = 2 hours
15 27 to 16 00 = 33 mins
1600 to 16 12 = 12 mins
Total = 2hours + 33 mins + 12 mins = 2 hours 45 mins = 2.75 hours
Distance = Speed x time = 56 x 2.75 = 154 km
Answer: 154 km
Step-by-step explanation:
Triangles PQR and XYZ are similar triangles. Which are the other two angle measures of triangle XYZ?
The other two angle measures of triangle XYZ are 35° and 75°.
We are given that the triangles PQR and XYZ are similar.
Also, ∠ZXY = 70° and ∠PRQ = 35°.
Now, we know that when two triangles are similar, then the corresponding angles are same.
Therefore, ∠XZY = ∠PRQ = 35°
Now, in triangle XYZ, we have ∠XZY = 35° and ∠ZXY = 70°.
Since, we know that the sum of the angles of a triangle is 180°.
So, ∠XZY + ∠ZXY + ∠ZYX = 180°
i.e. 35° + 70° + ∠ZYX = 180°
i.e. ∠ZYX = 180° - ( 35° + 70° )
i.e. ∠ZYX = 180° - 105°
i.e. ∠ZYX = 75°
Hence, the other two angle measures of triangle XYZ are 35° and 75°.
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The answer is 35 and 75 which is A and C
Check all properties that the following relations on the set of positive integers have: The relations are defined by (x, Y) € R if and only if the indicated condition is satisfied x and Y have a common prime factor A. reflexive B. symmetric C. irreflexive D. transitive E: antisymmetric (b) x _ y is a multiple of 3 A. symmetric B. antisymmetric C: irreflexive D. reflexive E. transitive (c) x and y are both prime A. transitive B. irreflexive C. symmetric D. reflexive E: antisymmetric (d) x and y are twin primes (they are primes and their distance is 2) A. symmetric B. irreflexive C.antisymmetric D. reflexive E: transitive
If x and y have a common prime factor then y and x also have a common prime factor,so x and y are symmetric.
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Step-by-step explanation:
Part a: x and y have a common prime factor
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
Reflexive: x and y are not reflexive since {1,1}∉ R(1 has no prime factor)
Symmetric: If x and y have a common prime factor then y and x also have a common prime factor , so x and y are symmetric.
Irreflexive: refer point A(above)
Transitive: x and y are not transitive since {2,9}∉ R(has no common prime factor)
Anti symmetric: x and y are not anti symmetric [Refer point B(above)]
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
b) x - y is a multiple of 3
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
Symmetric: If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric.
Antisymmetric x-y is not anti symmetric (refer above)
Irreflexive refer point D
Reflexive : x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.
Transitive: if x-y,y-z is multiples of 3 then x-z is also multiples of 3.so it is also transitive.
(c) x and y are both prime
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
Transitive: If x,y and y,z are primes then x,z are also primes.So it is transitive.
irreflexive Refer It is not reflexive since {4,4}∉ R(4 is not a prime)
Symmetric: If x,y are primes then y,x are also primes.So it is symmetric..
Reflexive:It is not reflexive since {4,4}∉ R(4 is not a prime)
Antisymmetric: Refer point C
(d) x and y are twin primes (they are primes and their distance is 2)
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Symmetric: x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Irreflexive Refer point D
Antisymmetric Refer point A
Reflexive: It is not reflexive since {4,4}∉ R
Transitive: It is not transitive because (3,5)∈R and (5,3)∈R but (3,7)∉ R
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(1 point) determine whether the line integral of each vector field (in blue) along the oriented path (in red) is positive, negative, or zero.
Through the graph we will determine if the line integral of each vector field is positive, negative, or zero. The answer to this question is:
-Positive
-Negative
-Zero
-Negative
-Zero
-Zero
What is the Line integral?
A line integral, also known as the route integral, curve integral, or curvilinear integral, is used to find the surface's area in three dimensions. In this integral, the function is evaluated along a curve. There are several applications of line integrals, such as in the field of electromagnetics, to find the force applied on a charged particle moving along a curve in a force field created by a vector field.
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