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stira [4]
3 years ago
14

Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the proba

bility that its first 39 characters (including spaces) will be "to be or not to be that is the question." (Leave your answer as a formula.)
Mathematics
2 answers:
Leona [35]3 years ago
8 0

|\Omega|=27^{39}\\|A|=1\\\\P(A)=\dfrac{1}{27^{39}}

In case you want it as a fraction

P(A)=\dfrac{1}{66555937033867822607895549241096482953017615834735226163}

:D

slava [35]3 years ago
3 0

Step-by-step answer:

There are 27 possibilities for each character typed.

The keys are striked randomly, so we assume independence between letters.

So the probability of hitting a specified character is 1/27.

Here the length of the string (excluding the final period, since it is not on the monkey's keyboard) is 39.

By the multiplication law of probability, the probability of multi-step independent events is the product of the probability of the individual events.

So probability of random typing resulting in the phrase

"to be or not to be that is the question"

= (1/27)^39

= 1/66555937033867822607895549241096482953017615834735226163

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In Ryan coorporation the first shift produced 5 1/2 times as many lightbulbs as the second shift. if the total lightul.bs produc
dimaraw [331]

Answer:

  • first shift: 13,750 bulbs
  • second shift: 2500 bulbs

Step-by-step explanation:

The production ratio is ...

  shift 1 : shift 2 = 5.5 : 1 = 11 : 2

so, the production on shift 1 as a ratio to the total is ...

  shift 1 : total = 11 : (11+2) = 11 : 13

The first shift produced ...

  (11/13)(16,250 bulbs) = 13,750 bulbs . . . . first shift

and the second shift produced ...

  (2/13)(16,250 bulbs) = 2,500 bulbs . . . . second shift

_____

Of course, once you have one of the numbers, you can also find the other by using the 5.5 factor or by subtracting from total production.

3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%28%7B%20%7Bx%7D%5E%7B2%7D%20%20-%204%7D%29%5E%7B5%7D%20%28%20%7B4x%20-%205%7D%29%5E%7B4%7D
Makovka662 [10]

Let u=x^2-4 and v=4x-5. By the product rule,

\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=\dfrac{\mathrm d(u^5)}{\mathrm dx}v^4+u^5\dfrac{\mathrm d(v^4)}{\mathrm dx}

By the power rule, we have (u^5)'=5u^4 and (v^4)'=4v^3, but u,v are functions of x, so we also need to apply the chain rule:

\dfrac{\mathrm d(u^5)}{\mathrm dx}=5u^4\dfrac{\mathrm du}{\mathrm dx}

\dfrac{\mathrm d(v^4)}{\mathrm dx}=4v^3\dfrac{\mathrm dv}{\mathrm dx}

and we have

\dfrac{\mathrm du}{\mathrm dx}=2x

\dfrac{\mathrm dv}{\mathrm dx}=4

So we end up with

\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=10xu^4v^4+16u^5v^3

Replace u,v to get everything in terms of x:

\dfrac{\mathrm d((x^2-4)^5(4x-5)^4)}{\mathrm dx}=10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3

We can simplify this by factoring:

10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3=2(x^2-4)^4(4x-5)^3\bigg(5x(4x-5)+8(x^2-4)\bigg)

=2(x^2-4)^4(4x-5)^3(28x^2-57)

7 0
3 years ago
If y = 2x2 – 4x, what is the value of y when x equals 5. <br> A.10 <br> B.30 <br> C.80 <br> D.480
Ainat [17]

Answer:

The value of y in the given equation is B. 30.

Step-by-step explanation:

y = 2x² - 4x             x = 5

y = 2(5)² - 4(5)        Plug 5 in for x

y = 2(25) - 20         Square 5 and multiply 4 by 5

y = 50 - 20             Multiply 2 by 25

y = 30

Hope this helps,

❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤

6 0
3 years ago
A pencil costs $0.25 more than an eraser. If the cost of eight pencils is $6.80, what is the cost of one eraser?
Sever21 [200]
6.80/8 = 0.85 + 0.25= 1.10
4 0
2 years ago
Read 2 more answers
-4 times a number plus 16 is -116. find the number and show work.
pav-90 [236]
-4*25 = -100+16 = -116
6 0
3 years ago
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