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Semenov [28]
3 years ago
15

NEED ANSWERED ASAP PLEASE.

Mathematics
2 answers:
MAXImum [283]3 years ago
5 0
<span>Write out what the statements represent:

"the quotient of a number and 7" -> (y / 7)
</span><span>"Two less than" -> -2
</span><span>"equals 8" -> = 8

The sentence will be translated into the following equation:

</span>\boxed{(y \div 7) - 2 = 8}<span>
</span>
MariettaO [177]3 years ago
3 0
Answer: 
\boxed {y \div7 -2 =8}
<span>
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>
Solution-
What we already know:
<span>"Two less than the quotient of a number and 7 equals 8."
</span><span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━<span>━━</span></span>
How to translate the sentence into an equation:
We will translate the sentence into an equation by using our mathematical knowledge and applying the statements provided into our equation.
<span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>
Statement: "the quotient of a number and 7<span>"
</span>Expression: y \div 7

Statement: "two less than:
Visual: "-2"

Statement: "equals 8"
Visual: "=8"
<span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>
Solve:
After we apply all of the above together, the equation would look like. 
y \div7 -2 =8
<span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>
Hence, the answer would be \boxed {y \div7 -2 =8}

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May I also have an explanation?
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A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one
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In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are \binom44\binom{48}1=48 possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by \binom{13}1=13. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

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There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing \binom41\binom{48}4=778,320 possible hands. Exactly 2 aces are drawn in \binom42\binom{48}3=103,776 hands. And so on. This gives a total of

\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656

possible hands containing at least 1 ace, and hence B occurs with probability

\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. P(A\cap B)=P(A)P(B). This happens if

  • the hand has 4 aces and 1 non-ace, or
  • the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So A\cap B consists of 96 possible hands, which occurs with probability

\dfrac{96}{\binom{52}5}\approx0.0000369

and so the events A and B are NOT independent.

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