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3 years ago

What are the comman factors of 4 and 8

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

4 0

First list out the factors of 4 and 8:

4: 1, 2, 4
8: 1, 2, 4, 8

The common factors of 4 and 8 are 1, 2, and 4

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Which of the following functions has the steepest slope?

Nonamiya [84]

The one with the steepest slope would be the equation that will have the highest value of m regardless of the sign. From the choices, I believe the correct answer is option C. It is <span>y=-4x+1 that has the steepest slope where m is equal to -4, the negative would indicate the direction of the slope.</span>

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4 years ago

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Aleksandr [31]

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3 years ago

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jonny [76]

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3 years ago

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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

Pls help me! Pls pls pls pls

k0ka [10]

Answer:

5. A.

6. F

Step-by-step explanation:

5. Perpendicular lines have slopes that are negative reciprocals of one another, so slope is 3

y = 3x + b

using coordinates (-6,3)

3 = 3(-6) + b

b = 21

y = 3x + 21

6. I think F is the right answer

3 0

2 years ago