MATHEMATICS COLLEGE

The table shows the price for different numbers of notebooks:Number of Notebooks Price (in dollars)
2 12
3 18
4
5 30

Answers

Answer 1

Answer: If you are looking for what it is multiplied by it is 6. But for the number 4 it is 24 because 6 times 4 is 24

Answer 2

Answer:

Answer:

The answer would be 24$

Step-by-step explanation:

If the relationship is proportional then it would be equal so if were adding 12 plus a number (which is 6) adds up which is 12 plus 6 = 18 plus 6 is our answer 24 then plus 6 is 30 as you can see we were adding by six proportionally and so the answer was 24

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Let P be the relation defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party. Not being registered or being registered as an independent also counts as a registration. Check all properties that P has.anti-symmetric

reflexive

transitive

symmetric

Answers

Answer:

This relation is symmetric, reflexive and transitive, but not anti-symmetric. Therefore it is an equivalence relation.

Step-by-step explanation:

Let's first prove that it is reflexive:

$\forall x : xRx \quad ?$

The explanation is as follows: let x be some american citizen, $xRx$ means that this person x is registered for the same political party as himself. This is obviously truth, because we are talking about the same person.

Next comes symmetry:

$xRy \iff yRx$

What does this statement mean? It means that if a is in the same party as b, then b is in the same party as a, and viceversa. This must be true, for the statement $xRy$ tells us that x is in the same party as y, which can also be stated as "x and y are both in the same party". This last statement also implies that y is in the same party as x, which is written as: $yRx$ . That proves that:

$xRy \implies yRx$

And the converse follows from the same reasoning.

Now for Transitivity:

$aRb \, \wedge bRc \implies aRc$

What this statement means in this context is that if a,b and c are american citizens, and we have that it is simultaneously true that both a and b are in the same party, and that also b and c are in the same party, then a and c must be also in the same party. This is true because parties are exclusive organisations, you cannot be both a democrat and a republican at the same time, or an independent and a republican. Therefore if a and b belong to the same party, and b and c also belong to the same party, it must be true that a belongs to the same party as b, and the same holds for c, therefore a and c belong to the same party (b's party). which we write as: $aRc$ . Thus it is true that R is a transitive relation.

Finally, Antisymmetry is NOT a property of this relation.

Let's see why, antisymmetry means:

$xRy \wedge x \neq y \implies \neg yRx$

That would mean that if x and y are two distinct american citizens $x\neq y$ , then if x is in the same party as y ( $xRy$ ), then it is not true that y is in the same party as x! ( $\neg yRx$ )

Clearly this isn't true, for example if x and y are two distinct democratic party members, we can say that $xRy$ that is, x and y are registered for the same party, and given that this relation is symmetric, as we have shown, we can also say $yRx$ , but this comes in conflict with the definition of antisymmetry. Thus we conclude that the relation R is not antisymmetric.

On a final note, it's interesting to point out that reflexivity, symmetry and transitivity are the requirements for a relation to be an equivalence relation, which is a very useful concept in maths.

Final answer:

The relation P defined on the set of all American citizens by xPy is reflexive and symmetric, but not transitive.

Explanation:

The relation P defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party has the properties of reflexivity, symmetry, but not transitivity.

Reflexivity means that every element is related to itself. In this case, every American citizen is registered for the same political party as themselves, including those who are registered as independent or not registered at all.

Symmetry means that if x is related to y, then y is related to x. In this case, if two American citizens are registered for the same political party, they are related to each other.

However, the relation P does not have the property of transitivity. Transitivity means that if x is related to y and y is related to z, then x is related to z. In the case of the relation P, if two American citizens are registered for the same political party and another two American citizens are registered for the same political party, it is not necessarily true that the first two citizens are also registered for the same political party as the second two citizens.

Learn more about Relation properties here:

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Im still stuck.... help? :',)

Answers

The answer should be B.

This is because if you multiply, you’ll get the answer of 3/8 which is less than 1/2 (4/8) but not close to zero, thus leaving B as the best option.

Hope this helps!

Please, I need help! a positive integer is subtracted from its square. The sum is 56. Write and solve a quadratic equation to find the number. Thank you!

Answers

Answer:

Step-by-step explanation:

x² − x = 56

x² − x − 56 = 0

(x − 8) (x + 7) = 0

x = -7 or 8

x is positive, so x = 8.

The expression below is a sum of cubes. 125x3 + 169

Answers

Answer:

$\text{The expression }125x^3+169\text{ is not the sum of cube}$

Step-by-step explanation:

Given the expression

$125x^3+169$

we have to tell the above expression is the sum of cube

The sum of cube is of the form

$a^3+b^3$ → (1)

$Expression: 125x^3+169$

125 is the cube of 5 and 169 is the square of 13

$125x^3+169$

$(5x)^3+13^2$

Comparing above with equation (1), we see the given expression is not the sum of cube

125x^3 = (5x)^3
125x^3 is the cube of 5x.

169 = 13^2
169 is the square of 13, but not the cube of a rational number.

The statement is false.

Caroline can sketch 8 cartoon strips in two hours. How long will it take her to sketch 12 strips?

Answers

So start with subtracting 12 and 8 to get 4. You know it takes 2 hours to sketch 8 of the 12 which leaves the 4 left. There are half the strips so, it will take half the time. In the end, it will take them 3 hours.

Jared ate 1/4 of a loaf bread. He cut the rest of loaf into slices. How many slices of bread did he cut?