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KengaRu [80]
3 years ago
15

What is the translation from quadrilateral IJK to quadrilateral I'J’K’

Mathematics
1 answer:
liberstina [14]3 years ago
6 0

Answer:

The translation from triangle IJK to triangle I'J'K' is T_{(2, 6)} which is 2 units to the right and 6 units up

Step-by-step explanation:

The coordinates of triangle JKI are;

J has coordinates (1, - 1)

K has coordinates (1, - 4)

I has coordinates (-3, - 2)

While, the coordinates of translation triangle J'K'I' are;

J' has coordinates (3, 5)

K' has coordinates (3, 2)

I' has coordinates (-1, 4)

Which give the translation as follows

Translation in the y-coordinate (y values);

For J = 5 - (-1) = 6

For K = 2 - (-4) = 6

For I = 4 - (-2) = 6

Translation in the x-coordinate (x values);

For J = 3 - 1 = 2

Therefore, the translation from triangle IJK to triangle I'J'K' is T(2, 6) which is 2 units to the right and 6 units up

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A student who is trying to write a paper for a course has a choice of two topics, A and B. If topic A is chosen, the student wil
algol13

Answer:

P(Topic A) = 0.91

P(Topic B) = 0.9163

The student should choose Topic B to maximize the probability of writing a good paper because P(Topic B)>P(Topic A).

Step-by-step explanation:

If Topic A is chosen, 2 books will be ordered (n=2)

If topic B is chosen, 4 books will be ordered (n=4)

Probability that a book arrives in time (p) = 0.7

Probability that a book does not arrive in time (q) = 1 - p = 1 - 0.7 = 0.3

We will <u>use the binomial distribution</u> to find out which topic should the student choose to maximize the probability of writing a good paper. The binomial distribution formula is:

P(X=x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

           q = probability of failure

           n = total no. of trials

           x = no. of successful trials

For Topic A, n = 2, p=0.7 and q=0.3. If topic A is chosen, the student will use at least half the books i.e. he will use either 1 or 2 books. So,

P(Topic A) = P(X=1) + P(X=2)

                 =²C₁ (0.7)¹(0.3)²⁻¹ + ²C₂ (0.7)²(0.3)²⁻²

                 = 0.42 + 0.49

P(Topic A) = 0.91

For topic B, n=4, p=0.7 and q=0.3. If topic B is chosen, the student will choose 2 or more books i.e. 2, 3 or 4 books.

P(Topic B) = P(X=2) + P(X=3) + P(X=4)

                  = ⁴C₂ (0.7)²(0.3)⁴⁻² + ⁴C₃ (0.7)³(0.3)⁴⁻³ + ⁴C₄ (0.7)⁴(0.3)⁴⁻⁴

                  = 0.2646 + 0.4116 + 0.2401

P(Topic B) = 0.9163

The student should choose Topic B to maximize the probability of writing a good paper because P(Topic B)>P(Topic A) as calculated above.

3 0
3 years ago
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