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3 years ago

8. There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random without replacement.

Mathematics

1 answer:

PIT_PIT [208]3 years ago

5 0

Answer:

a. 720

b. 0.3

Step-by-step explanation:

Three balls are selected at random without replacement.

First ball can be selected in 10 ways

Second ball can be selected in 9 ways

Third ball can be selected in 8 ways

Thus, there are 10×9×8 =720 different ways of selecting three balls.

There are three cases that satisfy this condition

first ball picked is 5, the others are not
first ball is not 5, second is 5, third is not
first and second ball is not five, third ball is 5

Each probabilities are:

$\frac{1}{10} * \frac{9}{9} *\frac{8}{8} =\frac{1}{10}$
$\frac{9}{10} *\frac{1}{9} *\frac{8}{8} =\frac{1}{10}$
$\frac{9}{10} *\frac{8}{9} *\frac{1}{8} =\frac{1}{10}$

Thus, one of the balls selected is the number 5 is then $\frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10}$

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The graph shows a function. Find the value of b and d.

True [87]

Answer:

The required values are b=-6 and d=4

Step-by-step explanation:

The graph corresponds to the function

$r(x) =x^2+bx^2+8x+d$

We are required to find the values of b and d.

They can be found by using two points that are clearly visible on the graph. For example, the points (0,4) and (2,0) belong to the function. Substituting their values in the function:

$4 =0^2+b*0^2+8*0+d$

Simplifying:

4 = d

d = 4

Now use the point (2,0):

$0 =2^2+b*2^2+8*2+d$

Since d=4, and calculating

$0 =4+4b+16+4$

Simplifying:

$4b = -24$

Dividing by 4:

$b = -24/4 = -6$

$b = -6$

The required values are b=-6 and d=4

5 0

2 years ago

Please show the work for it as well thank you

AlexFokin [52]

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

=2( x^2+1)^2

= 2( x^2 +2x^2 +1)

= 2x^4+4x^2+2

4 0

3 years ago

Five cards are randomly selected without replacement from a standard deck of 52 playing cards. what is the probability of gettin

EastWind [94]

Ok so it is a standard deck of 52 cards. Theres 4 suites: Hearts, Spades, Clubs and Diamonds.
In each suite there is 13 cards: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2. The probability of you choosing 5 hearts is most likely to be 5/52.

3 0

2 years ago

If (2i/2+i)-(3i/3+i)=a+bi, then a= A. 1/10 B. -10 C. 1/50 D. -1/10

Verizon [17]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

$\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi$

We need to find the value of a.

The LCM of (2+i) and (3+i) is (2+i)(3+i)

$=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}$

Now rationalize the denominator by multiplying by 5-5i/5-5i

$=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}$