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2 years ago

The endpoints of a side of rectangle ABCD in the coordinate plane are at A (3,9) and

Mathematics

1 answer:

Montano1993 [528]2 years ago

5 0

Answer:

Step-by-step explanation:

A(3, 9)

B(5, 1)

$m_{AB}$ = $\frac{1-9}{5-3}$ = - 4

CD║AB

C(9, 2)

y - 2 = - 4(x - 9)

<em>y = - 4x + 38</em>

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A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactl

Andrew [12]

Answer: $\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$ or $\dfrac{228}{91885}$ .

Step-by-step explanation:

Given : A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 12

Number of cards not face cards = 40

The total number of combinations of drawing 9 cards out of 52 cards = $^{52}C_9$

Now , the combination of 9 cards such that exactly 6 of them are face cards = $^{12}C_{6}\times^{40}C_3$

Now , the probability that the hand contains exactly 6 face cards will be :-

$\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$

$=\dfrac{\dfrac{12!}{6!6!}\times\dfrac{40!}{3!37!}}{\dfrac{52!}{9!\times43!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{228}{91885}$

Hence, the probability that the hand contains exactly 6 face cards. is $\dfrac{228}{91885}$ .

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3 years ago

Translate the word phrase into a math expression. nine more than five times a number

levacccp [35]

The number is 'n'.

Five times the number is 5n .

Nine more than that is 5n + 9 .

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3 years ago

Jason receives some money for his birthday. He spends 15 of the money and has $14.40 left. Calculate how much money he received

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He had $14.40 + $15 =39.40

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3 years ago

Julian spends 85 min on HW each day. If 20% of the time is spent on math HW, how many minutes a day is Julian spending on math H

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3 years ago

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Henry is conducting an experiment with 800 bacteria. He found the exponential growth rate to be 2.7% per hour. What is the amoun

joja [24]

Let's formulate an equation first. For exponential growth, we follow the formula. b = 800, r - 0.027. Hence,

y = 800(1+0.027)^t

Then, at t = 21, y will be determined
y = 800 (1+0.027)^21
y = 1399.81 = 1400

Thus, the amount of bacteria present after 21 hours is 1400.

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3 years ago