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2 years ago

Please help guys.......equation practice

Mathematics

1 answer:

nignag [31]2 years ago

7 0

Answer:

Step-by-step explanation:

m∠AOC = 180 as it is straight line

m∠AOC = m∠AOB + m∠BOC

m∠AOB + m∠BOC = 180

3x + 124 + 6x + 29 = 180

9x + 153 = 180

9x = 180 - 153

9x = 27

x = 27/9

x = 3

m∠BOC = 6x +29 = 6*3 + 29 = 18 +29 = 47

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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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3 years ago

Please help me!! Solve for 'a'. <br> b=(4*a)-3<br> ----------<br> 4

lilavasa [31]

here u go! i hope this is correct :)

8 0

2 years ago

Read 2 more answers

David has a garden with dimension 11 feet long x 9 feet wide. he wants to enlarge the garden to an area of 126. How much farther

kipiarov [429]

Length = 11
Width = 9
Area we need = 126
So Area = length * width
126 = 11 * 9
Now.. this is obviously wrong.. they want us to find the correct length..
126 = L * 9
126/9 = L
L = 14
Now since they ask about how much farther you need to extend, take the final and subtract from the original
14 - 11 = 3
Answer is 3.

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2 years ago

A student bought 5 coats at $86 each and paid for them with only $20 bills. How many bills did it take ?

aleksandr82 [10.1K]

It took 22 $20 bills . $86 x5= $430
Then $430 divide by 20 = 21.5
So you can’t have half a bill do the answer has to be rounded up to 22 twenty dollar bills

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2 years ago

Which of the following is the factored form of 9y2-121

lukranit [14]

It's the first one.

If you work backwords, I'd say it's easier. 3y swuared is 9y2, and 11 squared is 121. Then just keep the sign the same

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2 years ago

Please help guys.......​equation practice

Please help guys.......equation practice