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1 year ago

Geometry boy yo please help

Mathematics

1 answer:

densk [106]1 year ago

4 0

Answer:

x=12

Step-by-step explanation:

ab=dc so 15=x+3 you subtract 3 from both sides... x=12

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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.

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2 years ago

What does $42,690e(0.03)×(20) equal

Mice21 [21]

Answer:

77,786.251

Step-by-step explanation:

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Jack’s dog has a rectangular pen.The length is 2 feet longer than the width. The width is 6 feet. What is the distance around th

Marizza181 [45]

Answer:

L=W+X X=2 feet, W=width, L=length

if you were to solve it then you would get L=8

Step-by-step explanation:

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What is the value of Y ??

lilavasa [31]

Answer:

but where is the diagram

Step-by-step explanation:

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1 year ago

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The perimeter of a rectangular field is 74 yards. The length of the field is 27 yards. What is the width in yard of the field

KonstantinChe [14]

Answer:

width = 10 yds

Step-by-step explanation:

perimeter = 2L + 2W

74 = 2(27) + 2W

74 = 54 + 2W

subtract 54 from both sides of the equation:

2W = 20

divide both sides by 2:

W = 10

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