3 years ago

Jeremy will roll a number cube, numbered 1-6, twice. What is the probability of rolling an even number than the number 3?

1 answer:

3 0

There are 6 possible outcomes on a dice. Meaning when you roll it it could be any of them. Because 3 is one of the 6 the answer would be 1/6

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In a group of 25 girls, 8 ran for the cross country team, 13 are on the math league team, and 6 are on both teams. How many of t

Anna11 [10]

Answer:

10 girls are not on either team

Step-by-step explanation:

first subtract 6 from 8 to get 2 (since it's easier) because those 6 girls are on the math league team as well

next add 2 and 13 to get 15

last subtract 15 from 25 to get 10

8 0

3 years ago

Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)

aleksandr82 [10.1K]

$\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}$

Notice that if $f(x)=e^{\sin x}$ , then $f(\pi)=e^{\sin\pi}=e^0=1$ . Recall the definition of the derivative of a function $f(x)$ at a point $x=c$ :

$f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$

So the value of this limit is exactly the value of the derivative of $f(x)=e^{\sin x}$ at $x=\pi$ .

You have

$f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1$