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2 years ago

Five times the sum of a number and 3 is 15

Mathematics

1 answer:

lara [203]2 years ago

3 0

Answer:

the answer is 30 ok my friend your welcome

Step-by-step 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

TiliK225 [7]

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

$\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024$

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.

4 0

3 years ago

30 pts.!! Which expression is equivalent to (4√5^3)^1/2? 5^3/8 5^6 5^16/3 5^2/3

vampirchik [111]

it would be 5^6 5^16/

5 0

3 years ago

Evaluate the expression Show your work b) -10 -5h for h = -6

vazorg [7]

Answer:

Step-by-step explanation:

-10-5x(-6)

-10+30

4 0

3 years ago

HELPPPPPP THIS IS DUE IN A LITTLE BIT!!!!!!!!!Roberto earns $7.00 an hour at a grocery store. If he works 20 hours each week, wh

vaieri [72.5K]

Answer:

Step-by-step explanation:

hope I'm right sorry if I'm not lol.

5 0

2 years ago

Read 2 more answers

Suppose the profit a honda dealership makes on the next 5 accords it sells are:564, 1,000, 848, 1,495, 1,348. calculate the stan

stepladder [879]

First we have to find the mean (average)
mean = (564 + 1000 + 848 + 1495 + 1348) / 5 = 5255 / 5 = 1051

now we subtract the mean from every data point, then square it
564 - 1051 = -487......-487^2 = 237169
1000 - 1051 = -51......-51^2 = 2601
848 - 1051 = -203......-203^2 = 41209
1495 - 1051 = 444......444^2 = 197136
1348 - 1051 = 297......297^2 = 88209

now find the mean of the results.....but know when ur dealing with a sample instead of the whole population, u divide by 1 number less...so instead of dividing by 5, u divide by 4.
(237169 + 2601 + 41209 + 197136 + 88209) / 4 = 566324 / 4 =
141581.....this is called ur variance

now take the square root of the variance and u have ur standard deviation
sqrt (141581) = 376.272 rounds to 376.27 <==

5 0

3 years ago