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2 years ago

10

Two cards are chosen at random without replacement from a well-shuffled pack. what is the probability that the second card drawn

is also a king given that the first one drawn was a king?

1 answer:

frosja888 [35]2 years ago

4 0

Having drawn one king, there are 3 kings remaining and a total of 51 cards. Therefore the probability of drawing another king is 3/51 = 1/17.

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Identify a pattern in the given list of numbers. Then use this pattern to find the next number.

Rom4ik [11]

Answer:

The given sequence is geometric sequence

In the given pattern we have next number is $a_5=\frac{1}{4}$

Step-by-step explanation:

Given numbers are 64,-16,4,-1

To identify the pattern of the given numbers :

Let $a_1=64$ , $a_2=-16$ , $a_3=4$ and $a_4=-1$

To find the next number that is $a_5$

common ratio $r=\frac{a_2}{a_1}$

$=\frac{-16}{64}$

$r=-\frac{1}{4}$

$r=\frac{a_3}{a_2}$

$=\frac{4}{-16}$

$r=-\frac{1}{4}$

Therefore the common ration is $r=-\frac{1}{4}$

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is $a_n=a_1r^{n-1}$

Now find the 5th term so put n=5 , $a_1=64andr=\frac{-1}{4}$ we have

$a_5=64(\frac{-1}{4})^{5-1}$

$=64(\frac{-1}{4})^{4}$

$=64(\frac{1}{4})^{4}$

$=64(\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4})$

$=\frac{1}{4}$

Therefore $a_5=\frac{1}{4}$

8 0

3 years ago

A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

7 0

3 years ago

Customers at Beans Coffee Shop have entered their name in a drawing for one of 4 gift cards. The gift cards each have a value of

Dimas [21]

Answer:

36,060,024 ways

Step-by-step explanation:

To choose the winner in this case, the order is very important because it determines who is chosen first out of the seventy-nine customers whose names were entered for the draw.

The above supports the reason Permutation will be used instead of Combination.

The total number of ways is given by:

⁷⁹P₄ = 79!/(79-4)!

= 79!/75!

= [79 x 78 x 77 x 76 x75!]/75!

= 79 x 78 x 77 x 76

= 36,060,024 ways

This implies that there are 36,060,024 ways the Bean Coffee Shop could choose the winners.

8 0

3 years ago

What is the measure of angle Z in the parallelogram shown?

Anarel [89]

Answer:

30 Degress

Step-by-step explanation:

8 0

2 years ago

Eva invests $6400 in a new savings account which earns 3.4 % annual interest, compounded continuously. What

cupoosta [38]

Answer:

$7821.74

Step-by-step explanation:

Eva invests $6400 in a new savings account which earns 3.4% annual interest, compounded continuously.

We have to find the value of her investment after 6 years,

Now, using the formula for the compound interest we can get the value of her investment.

So, it will be $V = 6400 (1 + \frac{3.4}{100} )^{6} = 7821.74$ Dollars (Approximate)

{Rounded to the nearest cent} (Answer)

7 0

3 years ago