the perimeter of a rectangle id 34 units. Its width is 6.5 units. Write an equation to determine the length of the rectangle

Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a

Ipatiy [6.2K]

After 9months it will cost $1770

5 0

3 years ago

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 poli

Strike441 [17]

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 <em>NOT </em>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.

6 0

3 years ago

One ship leaves a port at 1 pm traveling at 12 mph at a heading of 70 degrees . at 2 pm another ship leaves the port traveling a

vampirchik [111]

<span>28.4 miles.
This problem effectively creates a triangle with the data you're giving being SAS (side, angle, side) and then asks you for the length of the 3rd side. So let's first determine the sides and angle of the triangle.
1st side, the ship leaves at 1 pm and travels for 4 - 1 = 3 hours at 12 mph. So the length of the side is 12 * 3 = 36 miles.
2nd side, the ship leaves at 2 pm and travels for 4-2 = 2 hours at 15 mph. So the length of the side is 15 * 2 = 30 miles
The included angle. The key thing to realize is that the angle isn't either of the ship headings. It's the difference between the headings. So we have one ship with a heading of 70 degrees and the other ship with a heading of 120 degrees. So there's a difference of 120 - 70 = 50 degrees between the two ships.
So we have side 1 = 36 miles, side 2 = 30 miles, included angle = 50 degrees.
Since we we only know the lengths of the adjacent sides to the known angle, we should use the law of cosines to solve for the unknown side (if we had a known angle and knew the length of the opposite side to the angle, we would use the law of sines).
The law of cosines is:
c^2 = a^2 + b^2 - 2ab cos Î¸
where a,b = adjacent sides to known angle
c = side opposite to known angle
Î¸ = known angle
Let's substitute the known values and calculate
c^2 = a^2 + b^2 - 2ab cos Î¸
c^2 = 36^2 + 30^2 - 2*36*30 cos 50
c^2 = 1296 + 900 - 2160*0.64278761
c^2 = 1296 + 900 - 1388.421237
c^2 = 807.5787631
c = 28.41793031
So at 4 pm, the distance between the ships is 28.4 miles.</span>

4 0

3 years ago

The total surface area is _ square inches

Fantom [35]

Answer:

169

Step-by-step explanation:

(19×3)+(8×5)+(9×8)=169

8 0

3 years ago

Two 4-sided dice are tossed 10 times. What is the expected number of times a sum of 3 should occur?

Irina-Kira [14]

The expected number of times a sum of 3 should occur is 1.25.

<h3>How to illustrate the information?</h3>

It should be noted that from the information given, two 4-sided dice are tossed 10 times.

The probability of getting a sum of 3 will be 1/8.

Therefore, the expected number will be:

= 10 × 1/8

= 1.25

Therefore, the expected number is 1.25.

Learn more about sum on:

brainly.com/question/10577562

#SPJ1

6 0

1 year ago