Pls help I'm confused, oh and can you also explain it. 15pts
1 answer:
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Answer:
Δy = 0.822
dy = 0.6
Step-by-step explanation:
Let us use the rules:
If f(x) = y, then
- dy = f'(x) . dx
- Δy = f(x + Δx) - f(x)
∵
- Differentiate it (remember the differentiation of is
∴
∴
∵ dy = y' . dx
∴
∵ x = 0
∵ dx = Δx
∵ Δx = 0.6
∴ dx = 0.6
- Substitute x by 0 and dx by 0.6 in y'
∴
- Remember any number to the power of 0 is 1 except 0
∵ = 1
∴ dy = 0.6
∵ Δy = f(x + Δx) - f(x)
∵ x = 0
- Substitute x by
∴ f(0) =
∴ f(0) = 1
∵ Δx = 0.6
∵ x + Δx = 0 + 0.6
∴ x + Δx = 0.6
- Substitute x by 0.6
∴ f(0.6) =
∴ f(0.6) = 1.8221188
∵ Δy = f(0.6) - f(0)
∴ Δy = 1.8221188 - 1
∴ Δy = 0.8221188
- Round it to the nearest 3 decimal places
∴ Δy = 0.822
It is given the probability that a dancer like ballet is 0.35
So, P(B) = 0.35
It is given the probability that a dancer like tap is 0.45
So, P(T)= 0.45
The probability that he likes both ballet and tap is 0.30
So,
the probability that the dancer likes ballet if we know she likes tap. This is the case of conditional probability.
So,
= 0.666
= 0.67
Therefore, the probability that the dancer likes ballet if we know she likes tap is 0.67.
Option 3 is the correct answer.