Which statement BEST explains the relationship between the numbers divisible by 6,2 and 3?

Mathematics

2 answers:

love history [14]3 years ago

8 0

A. A number that is divisible by 6 is also divisible by 2 and 3 because 2 and 3 are factors of 6.

Anuta_ua [19.1K]3 years ago

6 0

Answer:

A. A number that is divisible by 6 is also divisible by 2 and 3 because 2 and 3 are factors of 6.

Step-by-step explanation:

2 and 3 are prime numbers, whose product is equal to 6. Besides, 2 is an even number, while 3 is an odd number, and the product of an even number and an odd number is equal to an even number. Therefore, All number that is divisible by 6 are also divisible by 2 and 3, both prime numbers. In conclusion, the right answer is A.

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A standard deck of cards contains 52 cards. One card is selected from the deck.(a)Compute the probability of randomly selecting

Aneli [31]

a. There are four 5s that can be drawn, and $\binom43=4$ ways of drawing any three of them. There are $\binom{52}3=22,100$ ways of drawing any three cards from the deck. So the probability of drawing three 5s is

$\dfrac{\binom43}{\binom{52}3}=\dfrac4{22,100}=\dfrac1{5525}\approx0.00018$

In case you're asked about the probability of drawing a 3 or a 5 (and NOT three 5s), then there are 8 possible cards (four each of 3 and 5) that interest you, with a probability of $\frac8{52}=\frac2{13}\approx0.15$ of getting drawn.

b. Similar to the second case considered in part (a), there are now 12 cards of interest with a probability $\frac{12}{52}=\frac3{13}\approx0.23$ of being drawn.

c. There are four 6s in the deck, and thirteen diamonds, one of which is a 6. That makes 4 + 13 - 1 = 16 cards of interest (subtract 1 because the 6 of diamonds is being double counted by the 4 and 13), hence a probability of $\frac{16}{52}=\frac4{13}\approx0.31$ .