An importance of mathematical proofs is that they elucidate on why a conjecture is false (untrue).
<h3>The importance of mathematical proofs.</h3>
Generally, some of the importance of mathematical proofs include the following:
- They elucidate on why a conjecture is false (untrue).
- It provides a rational and logical justification for a theory.
In geometry, some of the consequences of the inaccuracy in the conclusion within a proof are:
- It leads to the misinterpretation of concepts and theories.
- It produces wrong results.
Outside the world of geometry, there are different kinds of proofs and these include:
- The Big Bang theory.
- Reflection of light by a plane mirror.
- Surface tension in water.
Basically, if there were to be an unjustified conclusion in the proofs above, the study of the properties of matter might not be possible. Also, the end users of various materials are most likely to be affected.
Read more on proofs here: brainly.com/question/26283907
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First, multiply both sides by y to get rid of that y in the denominator.
Then, rearrange it to put it into standard form so you can easily see the values for a, b, and c.
Plug into quadratic formula, and you get this result:
So, y=4, y=8/3
Answer:
The probability of winning directly is, as you calculated, 8/36, and the probability of losing directly is (1+2+1)/36=4/36.
For the remaining cases, you need to sum over all remaining rolls. Let p be the probability of rolling your initial roll, and q=6/36=1/6 the probability of rolling a 7. Then the probability of rolling your initial roll before rolling a 7 is p/(p+q), and the probability of rolling a 7 before rolling your initial roll is q/(p+q). Thus, taking into account the probability of initially rolling that roll, each roll that doesn't win or lose directly yields a contribution p2/(p+q) to your winning probability.
For p=5/36, that's
(536)25+636=2511⋅36,
and likewise 16/(10⋅36) and 9/(9⋅36) for p=4/36 and p=3/36, respectively. Each of those cases occurs twice (once above 7 and once below), so your overall winning probability is
836+236(2511+1610+99)=244495=12−7990≈12−0.007.
Step-by-step explanation:
Suppose you throw a 4 and let p(4) your winning probability. At your next roll you have a probability 3/36 of winning (you throw a 4), a probability 6/36 of losing (you throw a 7) and a probability 27/36 of repeating the whole process anew (you throw any other number). Then:
p(4)=336+2736p(4),so thatp(4)=13.
Repeat this reasoning for the other outcomes and then compute the total probability of winning as:
ptot=836+336p(4)+436p(5)+…
Answer:
113.04
Step-by-step explanation:
To find the area of a circle, you multiply 3.14 times the radius squared. To find the radius, you divided the diameter by 2. You get 6. You square 6 and get 36. Multiply that by 3.14 and you'll get 113.04 as your area.
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