Evaluate csc (3pi/14) and cot (5pi/12) using a calculator.

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

(c) 1/4

(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

According to historical records, the Great Pyramid of Giza was originally about 147 meters tall. Assuming it was built with its

vivado [14]

Answer:

115m

Step-by-step explanation:

Note that one of the face of a pyramid is a right angled triangle.

Since the pyramid was about 147m tall, the height of triangle will be 147m. If one of the faces is built with one of its faces at 52° to the incline, we can find the original length of one of its sides using SOH CAH TOA

tan(theta) = opposite/adjacent

Given theta = 52°, opposite = 147m (the side directly opposite the angle)

Substituting we have;

Tan52° = 147/adjacent

Adjacent = 147/tan52°

Adjacent = 114.8m

= 115m

Therefore 115m is the original length of one of its side

6 0

4 years ago

Find the common ratio of the geometric sequence: −320,80,−20,5,…−320,80,−20,5,… A. −14−14 B. 1414 C. -4 D. 4

vredina [299]

I'm assuming the sequence is: -320, 80, -20, 5

Divide each term by the previous term to get the common ratio r

r = (term 2)/(term 1) = 80/(-320) = -1/4
r = (term 3)/(term 2) = -20/80 = -1/4
r = (term 4)/(term 3) = 5/(-20) = -1/4

No matter which term you pick (as long as it's not the first one) dividing it by the previous term leads to -1/4 or -0.25 as the common ratio

Answer: -1/4

It seems like none of the answer choices have -1/4 but it could be choice A was supposed to show "-1/4" instead of "-14"? Perhaps the division sign didn't show up for some reason?

3 0

3 years ago

The random variable X has a uniform distribution with values between 16 and 24. What is the mean and standard deviation of X

N76 [4]

Answer:

$Mean = 20$