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4 years ago

Convert 60 miles per hour into meters per second

1 answer:

3 0

1,609.35 meters are in a mile.
3,600 seconds are in an hour.

1,609.35meters x 60miles = 96,561 meters per hour
96,561meters per hour / 3,600seconds = 26.82 meters per second

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If 3^2x+1 = 3^x+5 what is the value of X

cupoosta [38]

Answer:

Step-by-step explanation:

Since the base is the same, 3, you can just get rid of it using the principles of log. What you're left with is:

2x + 1 = x + 5

Now just solve for x:

2x - x = 5 - 1

x = 4

7 0

2 years ago

Suri has 1 7/10 boxes of matchsticks. She give 1/4 of a box to Philip.

Trava [24]

$1 \frac{7}{10} - \frac{1}{4} = 1 \frac{9}{20}$

7 0

3 years ago

The length of the rectangle is 2x + 8 cm and the width is 2cm . The area of the rectangle is 12 cm

Ksju [112]

Answer:

x = - 1

Step-by-step explanation:

Length ( l ) = 2x + 8 cm

Width / Breadth ( b ) = 2 cm

Area ( rectangle ) = 12 cm

Formula : -

Area ( rectangle ) = lb

12 = ( 2x + 8 ) ( 2 )

Divide 2 on both sides,

12 / 2 = ( 2x + 8 ) ( 2 ) / 2

6 = 2x + 8

2x + 8 = 6

2x = 6 - 8

2x = - 2

x = - 2 / 2

x = - 1

5 0

3 years ago

Simplify the expression. 16 • 4–4 a)256 b)–256 c)1/16 d)–4,096

stepladder [879]

Answer: C) 1/16

Hope this helps :)

4 0

2 years ago

jon flips a fair coin until a head is witnessed, and independently anna flips a fair coin (a different coin than jon’s) until a

Readme [11.4K]

a) The pmf for w for certain value n is P(W = n) = 3 / 2²ⁿ⁺², b) The expected value on w, E(w) = 4 / 3, c) The expression for P(w ≥ k) = $\frac{1}{2}^{2k}$ , where k = 1, 2, 3...

Given: Jon flips a fair coin until a head is witnessed.

Anna flips a fair coin independently until a head is witnessed.

What is the probability density function?
The probability density function is a function that determines the probability for a discrete random variable X over a given sample space S for a certain value for X = x(some value).

It is also denoted as pmf and is written as P(X = x).

Let's solve the given question:

Let us assume the number of flips Jon did until he got a head to be X.

Also as Anna's flip independently so we need to consider a different random variable say Y.

So, the probability mass function for Jon (X) for a certain value of x is:

P(X = x) = $\frac{1}{2} * (1 - \frac{1}{2})^{x-1}$ , where x = 1, 2, 3, ...........

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

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

P(X = x) = $\frac{1}{2}^x$ , where x = 1, 2, 3, ........

Similarly, for Anna, we will have the same probability mass function but with a different random variable Y for a certain value of y

P(Y = y) = $\frac{1}{2}^y$ , where y = 1, 2, 3, ........

Now it is given that, w is the minimum number of flips between Jon and Anna.

w = minimum(P(X = x), P(Y = y))

Let us suppose the probability mass distribution over w is n for a certain value.

Then

P(w ≥ n) = P(minimum(P(X = x), P(Y = y)) ≥ n)

= $\frac{1}{2}^n * \frac{1}{2}^n$

= $\frac{1}{2}^{2n}$

Therefore, the probability mass function for w is

P(W = n) = P(W ≥ n) - P(W ≥ n + 1)

= $\frac{1}{2}^{2n}\\$ - $\frac{1}{2}^{2(n+1)}$

= $\frac{1}{2}^{2n}$ - $\frac{1}{2}^{2n + 2}$

= $\frac{1}{2}^{2n}$ ( 1 - $\frac{1}{2}^{2}$ )

= $\frac{1}{2}^{2n}$ ( 1 - 1 / 4)

= $\frac{1}{2}^{2n}$ (4 - 1) / 4

= 3 / 4 ( $\frac{1}{2}^{2n}$ )

= 3 / 2² ( $\frac{1}{2}^{2n}$ )

= 3 / 2²ⁿ⁺²

Now the expected value of w, E(w) is:

E(w) = ∑P(w ≥ i) where i = 0 to ∞

= ∑ $\frac{1}{2^{2i}}$ where i = 0 to ∞

= 1 + 1 / 4 + 1 / 16 + .......

This is infinite GP series. So the summation of infinite GP is

S = a / ( 1 - r )

where a is the first term, r is the power and s is the summation.

Here a = 1, r = 1 / 4

S = 1 / (1 - 1 / 4)

S = 1 / 3 / 4

S = 4 / 3

Therefore, E(w) = 4 / 3

The expression for P(w ≥ k) is:

P(w ≥ k) = $\frac{1}{2}^{2k}$ , where k = 1, 2, 3...

Hence

a) The pmf for w for certain value n is P(W = n) = 3 / 2²ⁿ⁺²

b) The expected value on w, E(w) = 4 / 3

c) The expression for P(w ≥ k) = $\frac{1}{2}^{2k}$ , where k = 1, 2, 3...

Know more about "probability density function" here: brainly.com/question/14410995

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5 0

2 years ago