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Darya [45]
2 years ago
9

What's the distance between the points (7,3) and (7,–8)?

Mathematics
2 answers:
iris [78.8K]2 years ago
8 0
Answer:

The distance between (7, 3) & (7, -8) is 11

Step-by-step explanation:

I used distance formula for the following explanation attached with an image.

Hope this explanation helps!

Maru [420]2 years ago
3 0

Answer:

11

Step-by-step explanation:

The distance is found by

d =sqrt ( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( ( 7-7)^2 +(3 - -8)^2)

   = sqrt(0 +(3+8)^2)

  = sqrt( 11^2)

  = 11

 

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Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is:
professor190 [17]

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is \{1,2,3,4\}.

a) We need to find a relation R reflexive and transitive that contain the relation R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

  • 1R4 and 4R1, then 1 must be related with itself.
  • 4R1 and 1R4, then 4 must be related with itself.
  • 4R1 and 1R2, then 4 must be related with 2.

Therefore \{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\} is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

  • since 1R2, then 2 must be related with 1.
  • since 1R4, 4 must be related with 1.

and the analysis for be transitive is the same that we did in a).

Observe that

  • 1R2 and 2R1, then 1 must be related with itself.
  • 4R1 and 1R4, then 4 must be related with itself.
  • 2R1 and 1R4, then 2 must be related with 4.
  • 4R1 and 1R2, then 4 must be related with 2.
  • 2R4 and 4R2, then 2 must be related with itself

Therefore, the smallest relation containing R1 that is symmetric and transitive is

\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

  • 1 must be related with 1,
  • 2 must be related with 2,
  • 3 must be related with 3,
  • 4 must be related with 4

For be symmetric

  • since 1R2, 2 must be related with 1,
  • since 1R4, 4 must be related with 1.

For be transitive

  • Since 4R1 and 1R2, 4 must be related with 2,
  • since 2R1 and 1R4, 2 must be related with 4.

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}

5 0
3 years ago
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Answer:

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Step-by-step explanation:

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Students received grades with or - (example B ). Of all students who received one or more plus grades, 92% were undergraduates a
MrMuchimi

Answer:

The probability that a student is an undergraduate student, given that the student received a plus grade is 0.92

Step-by-step explanation:

The conditional probability of an event <em>B</em> given that another event <em>A</em> has already occurred is:

P(B|A)=\frac{P(A\cap B)}{P(A)}

Denote the events as follows:

<em>X</em> = a students is a graduate

<em>Y </em>= a students is a under-graduate

+ = a student received one or more plus grades

- = a student received one or more minus grades

Consider the tree diagram below.

According to the tree diagram, the probability that a student is an undergraduate student, given that the student received a plus grade is:

P (+ | Y) = 0.92

Thus, the probability that a student is an undergraduate student, given that the student received a plus grade is 0.92.

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