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Nutka1998 [239]
3 years ago
11

Write an equation in slope-intercept form perpendicular to the given equation through the given point

Mathematics
1 answer:
Irina18 [472]3 years ago
6 0

Answer:

y = (1/3)x - 4

Step-by-step explanation:

Any line perpendicular to the given equation y = -3x + 4 will have a slope which is the negative reciprocal of -3; that is, +1/3.

Start with the general slope-intercept form y = mx + b.

Insert the coordinates 6 and -2 into y = mx + b:  -2 = (1/3)(6) + b, or

-2 = 2 + b.  Thus, b = -4, and the desired equation is

y = (1/3)x - 4

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Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive
PtichkaEL [24]
Looks like the PMF is supposed to be

\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65

Next,

\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25

\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5

\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2
\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5
\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}

If Y=X^2+1, then X^2=Y-1\implies X=\sqrt{Y-1}, where we take the positive root because we know X can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that Y can take on the values 1^2+1=2, 2^2+1=5, and 5^2+1=26. At these values of Y, we would have the same probability as we did for the respective value of X. That is,

\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}

Part (5) is incomplete, so I'll stop here.
8 0
3 years ago
Can someone help me pls
Wittaler [7]

Answer:

3 cm

Step-by-step explanation:

  • V_{cylinder} = 189\pi \: cm^3 (Given)

  • h_{cylinder} = 21\: cm (Given)

  • Formula for V_{cylinder} is given as:

  • V_{cylinder} = \pi r^2h

  • \implies  189\pi = \pi r^2(21)

  • \implies \frac{ 189\pi}{21\pi} = r^2

  • \implies 9 = r^2

  • \implies \pm\sqrt 9 = r

  • \implies \pm 3 = r

  • Length of radius can not negative

  • \implies r = 3 \: cm

Hope it helps you in your learning process.

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2 years ago
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Multiply the expression (1/3 m-n)^2​
nataly862011 [7]

Answer:

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2 years ago
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Slope is -2/3 and ordered pair is (3,-4)
konstantin123 [22]

Answer:

Step-by-step explanation:

3 0
3 years ago
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Find the quotient.<br><br> n7 divided by n3
bogdanovich [222]
The answer is n^4. This is calculated by just subtracting the exponents. Hope this was what you were asking.
8 0
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