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3 years ago

What is the value of B-A, as a fraction?

Mathematics

1 answer:

Nikolay [14]3 years ago

8 0

I’m pretty sure you can just do 1/2! since B is 0.75 and A is 0.25 so 0.75-0.25=0.5=1/2

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Let X equal the number of flips of a fair coin that are required to observe

Nataliya [291]

Answer:

(a) I attached a photo with the diagram.

(b) $f(x) = \big( \frac{1}{2} \big)^{x-1}$

(d) 4

(e) $k^2/2$

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

1 - Your first outcome is HEADS and all the others are different except the last one.

2 - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

$f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}$

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

$E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}$

(d)

Remember that this is a geometric distribution therefore

$E[X] = p/(1-p)$ , in this case $p = 1/2$ so $E[X] = 1$ and

$E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4$

Also

(e)

This is a geometric distribution so its variance is

$Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2$

And using properties of variance

$Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2$

3 0

4 years ago

Does this graph represent a function? Why or why not?

artcher [175]

Answer:

Yes, this graph represents a function.

Functions can have a maximum of one y-value for every x-value. On a graph, this means it passes the vertical line test.

Step-by-step explanation:

The vertical line test is when a vertical line is passed though the graph. If at any point the vertical line touch more than one point on the graph, the graph is not a function. Vertical line test is also known as VLT.

6 0

3 years ago

18x + 24 = 12x +14. Find the value of (x)

densk [106]

Answer:

X = -10/6

X = -1,666666666666667

Step-by-step explanation:

First at all you join the X's

18x-12x = 14-24

Then you simplified:

6x = -10

X = -10/6

X = -1,666666666666667

3 0

3 years ago

Read 2 more answers

Zoey knit a total of 24 centimeters of scarf over 3 nights. How many nights will Zoey have to spend knitting in order to knit a

Drupady [299]

Answer:

Step-by-step explanation:

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3 years ago

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Hezekiel runs 1000 m at a rateof 3 minutes per km. how long does he take to run 500 m

lana66690 [7]

Step-by-step explanation:

1 km = 1000 m

(hence the term "kilo" which means 1000).

so. he runs 1000 m at the rate of 3 minutes per km, that means 3 minutes per 1000 m.

now, we can see the solution already with our eyes.

but let's do it formally :

the rate or ratio between time and distance must be the same for the same speed.

so,

3 min / 1000 m = x min / 500 m

500 m × 3 min / 1000 m = x min

1/2 × 3 min = x min

3/2 = 1.5 min = x min

so, it takes him 1.5 minutes (90 seconds) to run 500 m.

3 0

3 years ago