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____ [38]
3 years ago
15

PLZ HELPPPPP

Mathematics
1 answer:
QveST [7]3 years ago
4 0

Use the quadratic formula with a = 2, b = -5, and c = 1



x = -b ± sq rt b2 - 4ac
-------------------- <---------- Please note: sq rt is over entire expression of b^2 - 4ac
2a


x = - (-5) ± sq rt (-5)2 + 4(2)(1)
-------------------------------- <---------Please note: sq rt is over entire expression (-5)2 + 4(2)(1)
2(2)



x = 5 ± √17
---------
4


x = 5 + 1√17 OR x = 5 + -1√17
--- --- --- ----
4 4 4 4


Answer: x = 5 + 1√17 OR x = 5 + -1√17
--- -- -- --
4 4 4 4

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Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

A = a + (A \cap B)

In which a is the probability that he wins the first race but not the second and A \cap B is the probability that he wins both these races.

By the same logic, we have that:

B = b + (A \cap B)

The probability that he wins both races is 0.5.

This means that A \cap B = 0.5

The probability that he wins the second race is 0.6

This means that B = 0.6

B = b + (A \cap B)

0.6 = b + 0.5

b = 0.1

The probability that he wins the first race is 0.7.

This means that A = 0.6

A = a + (A \cap B)

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A) he wins at least one race.

This is

P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

P = a + b = 0.2 + 0.1 = 0.3

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

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