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Ivenika [448]
3 years ago
14

If p(a) = 1/3, p(b) = 2/5, and p(a ∪ b) = 3/5, then p(a ∩ b) =

Mathematics
1 answer:
Mumz [18]3 years ago
8 0
P(a ∪ b) = p(a) + p(b) - p(a ∩ b)
p(a ∩ b) = p(a) + p(b) - p(a ∪ b)
p(a ∩ b) = 1/3 + 2/5 - 3/5
p(a ∩ b) = 2/15
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2 years ago
What is the slope of the line through the points (6,-8)And (3,- 4)​
Nina [5.8K]

Answer:

y=(-4/3)x

Step-by-step explanation:

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(y2-y1)/(x2-x1)

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7 0
3 years ago
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a fr
Naily [24]
\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\
\begin{array}{llll}
\stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\
\qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t}
\end{array}

\bf f=k\sqrt{t}\quad \textit{we also know that }
\begin{cases}
f=300\\
t=8
\end{cases}\implies 300=k\sqrt{8}
\\\\\\
\cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k
\\\\\\
\textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k

\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\
-------------------------------\\\\
\textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}
5 0
3 years ago
Read 2 more answers
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