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2 years ago

Find the 9th term of the geometric sequence 8,32,128,

1 answer:

7 0

$\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}$

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Given a standard deck of 52 cards, 3 cards are dealt without replacement. Using this situation, answer the questions below.<b

kherson [118]

Given that 3 cards are dealt without replacement in a standard deck of 52 cards.

Part A:

There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.

Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given by 3 / 51 = 1 / 17

Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.

Therefore, the probability that all three cards are queens is given by

$\frac{1}{13} \times \frac{1}{17} \times \frac{1}{25} = \frac{1}{5525}$

Part B:

Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.

Part C:

Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.

Therefore, if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17

Part D:

Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.

Therefore, if two of the three cards are queens ,the probability that you will be dealt three queens is given by 2 / 50 = 1 / 25 = 0.04

Part E:

Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.

Therefore, if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96

8 0

3 years ago

Can someone find x for these questions

Maurinko [17]

Answer:

8, 36, -12

Step-by-step explanation:

41 = 8x - 23

8x = 41 + 23

8x = 64

x = 8

11 = x/2 - 7

22 = x - 14

22 + 14 = x

x = 36

3(x - 8) = -60

x - 8 = -20

x = -12

8 0

3 years ago

George bought 7 quarts of cleaning fluid: x quarts at $3.00 per quart & y quarts at $2.00 per quart. Find x & y if the t

PolarNik [594]

Answer:

3x + 2y = 16

x = 2 , y = 5

Step-by-step explanation:

Given that George bought x quarts at $3.00 per quart & y quarts at $2.00 per quart and he bought 7 quarts for $16.00

Considering the total cost

3x + 2y = 16

For the cost of each

x + y = 7

solving the 2 equations simultaneously be substitution

x = 7 - y

3(7 - y) + 2y = 16

21 - 3y + 2y = 16

-3y + 2y = 16 - 21

-y = - 5

Divide both sides by -1

y = 5

x = 7 -y

x = 7 - 5

= 2

7 0

3 years ago

A shop uses cone-shaped coffee filters in its coffee pots. Each filter has a diameter of 5 inches and a height of 4 inches. What

KengaRu [80]

Answer:

26.2 inches cubed

Step-by-step explanation:

The volume of a cone is denoted by: $V=\frac{1}{3} \pi r^2h$ , where r is the radius and h is the height.

Here, we are given that the diameter is 5. Remember that the radius is simply 1/2 the diameter, so the radius is r = 5/2 = 2.5. We are also given that the height is h = 4. Plug these into the equation:

$V=\frac{1}{3} \pi r^2h$

$V=\frac{1}{3} *3.14* (2.5^2)*4$ ≈ 26.2

Thus, the volume is about 26.2 inches cubed.

Hope this helps!

5 0

4 years ago

Which expression can be used to convert 65in in meaters

Rainbow [258]

Answer:

idkcorsica

Step-by-step explanation:

idkhb4n4ut Henry

6 0

3 years ago