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tino4ka555 [31]
1 year ago
12

a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expre

ssed asmn, wheremandnare relativelyprime positive integers. what ism n?
Mathematics
1 answer:
AveGali [126]1 year ago
3 0

The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

<h3>What exactly is meant by probability?</h3>
  • Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event.
  • The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.

Given: Randomly, a positive integer divisor of 12! is selected.

Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11

Total divisors of 12! = 11 × 6 × 3 × 2 × 2

  • Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor.
  • In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!.
  • There are 6 × 3 × 2 perfect squares as a result.

The probability that the divisor chosen is a perfect square is given as:

(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)

= 1/22

=m/n

Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

Learn more about probability here:

brainly.com/question/24756209

#SPJ4

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What is the solutions to the equation w/2w-3=4/w
labwork [276]

Answer:

{2, 6}

Step-by-step explanation:

w/2w-3=4/w  is ambiguous.  Did you mean

   w            4

---------- = ------     ?  If so, please enclose "2w - 3" inside parentheses.

2w - 3       w

Cross multiplying, we get w² = 8w - 12.

Putting this into standard form, we get:

w² - 8w + 12 = 0, which factors into (w - 2)(w - 6) = 0.

The solutions are found by setting each factor = 0 separately and solving the resulting equations for w:  {2, 6}.

7 0
3 years ago
What value of x makes the equation 66x = 6 true
KatRina [158]

Answer:

66 x 1/11 = 6

or

66 x 0.09 = 6

So x = either 1/11 or 0.09

3 0
3 years ago
Read 2 more answers
Iodine-131, a radioactive substance that is effective in locating brain​ tumors, has a​ half-life of only 8 days. A hospital pur
Aloiza [94]

The mass of substance left after 7 days is 13.09 g

The mass of substance left, N is given by

N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time

Also, λ = 0.693/t' where t' = half-life of iodine = 8 days

So, λ = 0.693/t'

λ = 0.693/8

λ = 0.086625/day

Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 7 days,

N = N₀exp(-λt)

N = 24 gexp(-0.086625/day × 7 days)

N = 24 gexp(-0.606375)

N = 24 g × 0.5453

N = 13.09 g

So, the mass of substance left after 7 days is 13.09 g

Learn more about radioactive decay here:

brainly.com/question/23705307

7 0
3 years ago
Monyne Phillips three coins. What is the probability that the first second and third Cornwall in the same way (either all heads
nasty-shy [4]

Answer:

1 in 8 chance.

Step-by-step explanation:

When a coin flips is has two outcomes: heads or tails, obviously.

Whenever you have a 50/50 probability, in this case a coin, every time you add another coin the amount of outcomes squares, or multiplies by the number of outcomes, and since we are using a coin, two. To reiterate, say we were using a die, a die is a cube, a six sided shape, so there are six outcomes. The chances of getting all sixes with one die is 1 in 6. Add another die and try to get all sixes, the chances become 1 in 36. We got this by multiplying our out comes by our outcomes

1 coin: 2 outcomes

2 coins: 4 outcomes

3 coins: 8 outcomes

Another thing:

Don't be fooled by questions being specific by saying "all heads" or "all tails"...

This is a wording trick, no matter the outcome, the chances will always be equal.

Good luck :)

8 0
3 years ago
I need help with this
muminat

Answer:

abcs

Step-by-step explanation:

abcdefghijklmnopqrstuvwxy and z

7 0
3 years ago
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