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3 years ago

Is the product of 3⅝ x ⅔ greater than or less than 3⅝? explain without multiplying

2 answers:

3 0

So the question is
number times 2/3 is greater than or less than the sasme number
so let's say x
x times 2/3 is greater than or less than x
since 2/3 is less than 1, 2/3 is a fraction,
anything times a fraction will become smaller

therefor
3 and 5/8 times 2/3 is less than 3 and 5/8

the answer is LESS THAN

gizmo_the_mogwai [7]3 years ago

3 0

You are multiplying a number by a fraction, or something that is less than 1. Anytime you multiply a number by a fraction, it will become smaller. Therefore it will be less than.

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3 years ago

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seropon [69]

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5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

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3 years ago