Trig Functions Quiz, Help please

Mathematics

1 answer:

34kurt3 years ago

5 0

Answer:

angle C is 67.38⁰

Step-by-step explanation:

Given;

length AB = 36

length AC = 39

length BC = 15

The angle C can be calculated using cosine rule;

$c^2 = a^2 + b^2 - 2ab\times cos(C)\\\\2ab\times cos(C) = a^2 + b^2 -c^2 \\\\cos(C) = \frac{a^2 + b^2 -c^2}{2ab} \\\\cos(C) = \frac{(15)^2 + (39)^2 -(36)^2}{2(15)(39)} \\\\cos(C) = 0.3846\\\\C = cos^{-1} (0.3846)\\\\C = 67.38^0$

Therefore, angle C is 67.38⁰

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In a city school, 60% of students have blue eyes, 55% have dark hair, and 35% have blue eyes and dark hair. What is the probabil

gulaghasi [49]

Answer:

58%

Step-by-step explanation:

This is a problem of conditional probability.

Let A represent the event that student has dark hair.

So P(A) = 55% = 0.55

Let B represents the event that student has blue eyes.

So, P(B) = 60% = 0.60

Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35

We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:

$P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58$