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3 years ago

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1. If a student's course grade was a B, what is the probability that a randomly selected student did at least 30 minutes of home

work at night? 2. Are the events "did at least 30 minutes of homework l" and "course grade is a B" independent? Explain your answer.

1 answer:

dlinn [17]3 years ago

5 0

Answer:

Step-by-step explanation:

i. 0.21 over 0.30

ii. Independent

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$\lim_{h \to 0} f(x)=\dfrac{f(x+h)-f(x)}{h}$

f(x) = $\sqrt x\\$

f(x+h) = $\sqrt{x+h}$

$\lim_{h \to 0} f(x)=\dfrac{\sqrt{x+h}-\sqrt x}{h}$

$=\dfrac{\sqrt{x+h}-\sqrt x}{h}\bigg(\dfrac{\sqrt{x+h}+\sqrt x}{\sqrt{x+h}+\sqrt x}\bigg)$

$=\dfrac{(x + h)-(x)}{h(\sqrt{x+h}+\sqrt x)}$

$=\dfrac{h}{h(\sqrt{x+h}+\sqrt x)}$

$=\dfrac{1}{\sqrt{x+h}+\sqrt x}$

$=\dfrac{1}{\sqrt{x+0}+\sqrt x}$

$=\dfrac{1}{2\sqrt x}$

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4 years ago