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2 years ago

What is the equation of the line that passes through the point (3,6) and has a slope of -1/3

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

4 0

$\Large\texttt{Answer\::}$

Please consult the "Calculations" section of this ans .

$\Large\texttt{Calculations\::}$

The information we're given is below :

slope : -1/3
Point crossed by the line : (3, 6)

As per given information , we can do the following :

Write the line's equation in point slope form

Point - slope form looks like so :

y-y₁=m(x-x₁)

y-6=-1/3(x-3)

y-6=-1/3x+1

y=-1/3x+1+7

y=-1/3x+6

↑ $\small\textsc{EQUATION OF THE LINE}$

$\small\textit{hope\:helpful~}$

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shusha [124]

Answer:

(a) 1.6197

(b) 1.3803

Step-by-step explanation:

(a) Let X denote the number of games the Reds win. If Reds win exactly one it means that in the other two games Reds lost i.e Cubs won. Now, the probability of the Reds losing is determined by $1 -\text{probability of winning} = 1-0.54 = 0.46$ . So, if X wins exactly $i$ times, then we should multiply the probabilities associated with

$P(X=0) = \binom{3}{0} \times 0.46 \times 0.46 \times 0.46 = 0.0973$

$P(X=1) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429$

$P(X=2) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023$

$P(X=3) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574$

Now,

$E(X) = \sum_{i=0}^{3} i \times P(X=i) = 1.6197$

(b) Let Y denote the number of games won by Cubs. Then by the similar logic as above,

$P(Y=3) = \binom{3}{0} 0.46 \times 0.46 \times 0.46 = 0.0973$

$P(Y=2) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429$

$P(Y=1) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023$

$P(Y=0) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574$

Now

$E(Y) = \sum_{j=0}^{3} j \times P(Y=j) = 1.3803$

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