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2 years ago

Match the expression to its simplified form.

Mathematics

1 answer:

omeli [17]2 years ago

4 0

Answer:

Step-by-step explanation:

5³ = 5 × 5 × 5 = 125

$2^{5}$ = 2 × 2 × 2 × 2 × 2 = 32

$5^{-2}$ = $\frac{1}{5^{2} }$ = $\frac{1}{25}$

$2^{-4}$ = $\frac{1}{2^4}$ = $\frac{1}{16}$

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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

Which arc is a minor arc? SQ PSR PS

laila [671]

Answer:

probably would say PS would be your best

4 0

2 years ago

Which one is 25%? please help me

Vinvika [58]

So first of all you count all the blocks, so it will be 16 blocks (4x4) sideways and horizontal.

A = 16/4 marked blocks = 25%

B = 16/8 marked blocks = 50%

C = 16/6 marked blocks = ?

D = 16/10 marked blocks = 62,5%

So answer would be A

3 0

2 years ago

Solve by factoring: 5t=t ^2

elena-14-01-66 [18.8K]

Answer:

t=0 and t=5

Step-by-step explanation:

5t = t^2

Subtract 5t from each side

5t-5t = t^2 -5t

0= t^2 -5t

Factor out a t

0= t(t-5)

Using the zero product property

t=0 and t-5 =0

t=0 and t-5+5=0+5

t=0 and t=5

7 0

2 years ago

That is the screen shot for questions 5.

Klio2033 [76]

It's choice C as the root overhead bar goes over all of (x-7) and not just the x. So you have the correct answer.

f(x) = x^4+7
y = x^4+7
x = y^4+7
y^4 = x-7
y = FourthRoot(x-7)

$y = \sqrt[4]{x-7}$

7 0

3 years ago