Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
2 answers:
Answer:
see attached
Step-by-step explanation:
The Pythagorean theorem can be used to find the hypotenuse associated with each pair of legs. That tells you ...
c² = a² +b² . . . . . legs a, b; hypotenuse c
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<h3>alternate form of Pythagorean theorem</h3>For the purpose of this problem, it is convenient to consider a slightly different form of the equation.
For legs √a and √b, the hypotenuse √c is given by ...
(√c)² = (√a)² +(√b)²
c = a +b
That is ...
legs √a, √b ⇒ hypotenuse √(a+b)
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<h3>application to this problem</h3>Since the legs are (mostly) given in terms of square roots, the value under the radical for the hypotenuse is simply the sum of those:
legs: √1, √2 ⇒ hypotenuse √(1+2) = √3
legs: √2, √3 ⇒ hypotenuse √(2+3) = √5
legs: √5, √3 ⇒ hypotenuse √(5+3) = √8
legs: √5, √1 ⇒ hypotenuse √(5+1) = √6
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<em>Additional comment</em>
You may not see the leg lengths given as square roots very often. This is a rather unusual set of problems for hypotenuse length.
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Answer:
(a) The probability that a randomly selected parcel arrived late is 0.026.
(b) The probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.
(c) The probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.
(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.
Step-by-step explanation:
Consider the tree diagram below.
(a)
The law of total probability sates that:
Use the law of total probability to determine the probability of a parcel being late.
Thus, the probability that a randomly selected parcel arrived late is 0.026.
(b)
The conditional probability of an event A provided that another event B has already occurred is:
Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.
(c)
Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.
(d)
Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.
