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2 years ago

Alex flips a fair coin four times. What is the probability that he flips heads four times in a row?

Mathematics

1 answer:

sdas [7]2 years ago

4 0

1/16

the probability of flipping head on the first flip is 1/2

the probability of flipping head on the second flip is 1/2 of that, or 1/4

the probability of flipping head on the third flip is 1/2 of that, or 1/8

the probability of flipping head on the fourth flip is 1/2 of that, or 1/16

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How many 5-digit numbers can be formed that do not contain the digits 0 or 8?

alexandr402 [8]

Answer:

27218

34578

44444

21387

12345

87654

34343

56843

76432

68345

Step-by-step explanation:

and many more

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2 years ago

Write the Taylor Series for f(x) = sin(x)center

tangare [24]

Answer:

Taylor series of sin(x) centered at x = 0.

Step-by-step explanation:

Taylor series expansion:

$\sum_{n=0}^N f^n(a)\displaystyle\frac{(x-a)^n}{n!}$

Here, f(x) = sin (x) and a = 0

$f(x) = \sin x, f(0) = 0\\f'(x) = \cos x, f'(0) = 1\\f''(x) = -\sin x, f''(0) = 0\\f'''(x) = -\cos x, f'''(0) = -1\\f^4(x) = \sin x, f^4(0) = 0\\f^5(x) = \cos x, f^5(0) = 0$

Putting all the values and expanding, we get,

$f(x) = f(a) + \displaystyle\frac{f'(a)(x-a)}{1!} + \displaystyle\frac{f''(a)(x-a)^2}{2!} + \displaystyle\frac{f'''(a)(x-a)^3}{3!} + \displaystyle\frac{f^4(a)(x-a)^4}{4!} + \displaystyle\frac{f^5(a)(x-a)^5}{5!} + ...\\\\= \sin 0 + \displaystyle\frac{x}{1!} + \displaystyle\frac{(0)x^2}{2!} + \displaystyle\frac{(-1)x^3}{3!} + \displaystyle\frac{(0)x^4}{4!} + \displaystyle\frac{(1)x^5}{5!} + ...$

Solving, we get

$\sin x = x - \displaystyle\frac{x^3}{3!} + \displaystyle\frac{x^5}{5!} - \displaystyle\frac{x^7}{7!} + ...\\\\\sin x = x - \displaystyle\frac{x^3}{6} + \displaystyle\frac{x^5}{120} - \displaystyle\frac{x^7}{5040} + ...$

3 0

3 years ago

Find the z value for x=40 for a normal distribution with μ=30 and σ=5

DedPeter [7]

Answer: z = 2
solution:
formula of z value is
z = x - μ / σ

so z = 40-30 / 5 = 10/5 = 2#

7 0

3 years ago

I need the statement and reasons <br>and whether its a sss sas asa hl

andrew-mc [135]

Answer:

it's sas

Step-by-step explanation:

statement: angle pqr is congruent to angle sqt. reason: they are vertical angles

statement: line pq is congruent to line qt

reason: definition of midpoint

statement: line sq is congruent to line qr

reason: definition of midpoint

hope this helps

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2 years ago

The graphically and algebraically

sertanlavr [38]

Graphically is intersect i believe

6 0

2 years ago