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egoroff_w [7]
3 years ago
14

PLEASE HELP PLEASEEEEEE

Mathematics
1 answer:
svet-max [94.6K]3 years ago
6 0

Step-by-step explanation:

Volume =

1/3πr²h

= 1/3×3.14×2²×9

= 37.68 units ³

Hope it will help :)❤

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Two professors are applying for grants. Professor Jane has a probability of 0.61 of being funded. Professor Joe has probability
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Answer:

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Step-by-step explanation:

By definition, if two event A and B are independent, then

P(A\cap B) = P(A) \cdot P(B). (P(A\cap B) is the probability that the outcome of both event A and event B are true.)

<h3>a.</h3>

Since the outcome of these two events are independent,

\begin{aligned}P(\texttt{Jane} \cap \texttt{Joe}) &= P(\texttt{Jane}) \cdot P(\texttt{Joe})\\ &= 0.61 \times 0.27 \\&= 0.1647\end{aligned}.

<h3>b.</h3>

The logic not operator \lnot or the prime superscript ^{\prime} denotes that an event does not happen.  

P(\texttt{Jane}^{\prime}) = 1 - P(\texttt{Jane}) = 1- 0.61 = 0.39.

P(\texttt{Joe}^{\prime}) = 1 - P(\texttt{Joe}) = 1- 0.27 = 0.73.

Since the two events \texttt{Jane} and \texttt{Joe}, \texttt{Jane}^{\prime} and \texttt{Joe}^{\prime} are also independent. Probability that neither professor got funded:

P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = P(\texttt{Jane}^{\prime}) \cdot P(\texttt{Joe}^{\prime}) = 0.39 \times 0.73 = 0.2847.

Probability that at least one professor got funded- in other words, it is not true that neither professor got funded:

P((\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime})^{\prime}) = 1- P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = 0.7153.

<h3>c.</h3>

Similarly, since the two events \texttt{Jane} and \texttt{Joe}, \texttt{Jane} and \texttt{Joe}^{\prime} are also independent. Probability that Jane but not Joe got funded:

P(\texttt{Jane} \cap (\texttt{Joe}^{\prime})) = P(\texttt{Jane}) \cdot P(\texttt{Joe}^{\prime}) = 0.61 \times 0.73 = 0.4453.

4 0
3 years ago
P(0,-1) that is parallel to the line y= -2x+3​
Mandarinka [93]

Answer:

y=2x+3

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8x+8=2(L+x)

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