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dexar [7]
1 year ago
15

A line is parallel to y = 3x - 2 and

Mathematics
2 answers:
Inessa [10]1 year ago
7 0

Answer:

A) The slope is 3

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts, so the slope of the line is also 3.

djyliett [7]1 year ago
5 0

Answer:

A, 3

Step-by-step explanation

two parallel lines have the same slope

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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
Solve for x.3(3x - 1) + 2(3 - x) = 0
mote1985 [20]
9x-3+6-2x=0
7x+3=0
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5 0
3 years ago
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Evaluate this expression what is <br> b=-6 and c=7.c-7b
VLD [36.1K]

Answer:

49

Step-by-step explanation:

substitute b = - 6 and c = 7 into the expression and evaluate

c - 7b = 7 - (7 × - 6) = 7 - (- 42) = 7 + 42 = 49


7 0
2 years ago
Find the area of the regular polygon below and round your answer to the nearest tenth.
stira [4]
The 9-sided polygon will have a central angle between the vertex and the center of one side of 360°/(2*9) = 20°. Then the apothem is
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The perimeter is 9*6 in = 54 in, so the area is
  A = (1/2)Pa = (1/2)*(54 in)*(8.242432 in) ≈ 222.5 in²
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3 years ago
8) The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?​
nirvana33 [79]

Answer:

120 pounds I think

Step-by-step explanation:

6 0
2 years ago
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