3 years ago

What is the best way to randomly choose these 500 members?

1 answer:

8 0

The best way to randomly pick would be to enter all the names into a computer and let it pick the names.
The last choice is the correct answer

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2 years ago

you purchase 723 shares of Nike at $47.75 per share and one year later you are ready to sell your 723 shares for the current mar

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The answer to this question is "you gained profit". The amount of money you gain from selling the stocks now is higher compared to the amount you spent a year ago. The amount you gain from the shares is ($62.25) x 723 = $45006.75. The amount you spent last year is ($47.75) x 723 = $34523.25. The difference between the values is $10483.47. Thus, you gained $10483.47.

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3 years ago

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

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3 years ago