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2 years ago

Solve for x. Round answer to the nearest tenth, if necessary

Mathematics

1 answer:

Nady [450]2 years ago

4 0

Answer:

x=15

Step-by-step explanation:

9²+12²=c²

81+144=c²

225=c²

√225=√c

15=c

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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

Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 3 oz of chips and drank 2 cups of soda for a t

Diano4ka-milaya [45]

Answer:

200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

Step-by-step explanation:

Let x mg sodium is in 1 oz of chips and and y mg is in 1 cup of soda.

∵ Bryan ate 3 oz of chips and drank 2 cups of soda for a total of 700 mg of sodium.

i.e. 3x + 2y = 700 --------(1),

Jadyn ate 1 oz of chips and drank 3 cups of soda for a total of 350 mg of sodium.

i.e. x + 3y = 350 ---------(2),

Equation (1) - 3 × equation (2),

We get,

2y - 9y = 700 - 1050

-7y = -350

$\implies y = \frac{-350}{-7}= 50$

From equation (1),

3x + 2(50) = 700

3x + 100 = 700

3x = 700 - 100

3x = 600

$\implies x = \frac{600}{3}=200$

Hence, 200 mg sodium is in 1 oz of chips and 50 mg sodium is in 1 cup of soda.

7 0

3 years ago

I'm making a table.

Ivenika [448]

Well I think I can help you out ...
if you assume input x=2
the output will be as following :
y= -1/3(2)+2
=-2/3+2
=-2/3+6/3
=(-2+6)/3
=4/3
=1.333

3 0

3 years ago

1. 12 more than_____

quester [9]

Answer:

11 through 0

Step-by-step explanation:

3 0

2 years ago

I PROMISE BRAINLIST PLZZ HELLLPPPP ASAPPPP!!!!!!!!!!!!!!!!!

Black_prince [1.1K]

I think the answer is a. -3x^2-x-5

6 0

3 years ago