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2 answers:
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Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
=
n = 9
r = 3
= ⁹P₃
=
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 ×
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
Answer:
Step-by-step explanation:
Given
Required
Find all product of real values that satisfy the equation
Cross multiply:
Subtract 7 from both sides
Reorder
Multiply through by -1
The above represents a quadratic equation and as such could take either of the following conditions.
(1) No real roots:
This possibility does not apply in this case as such, would not be considered.
(2) One real root
This is true if
For a quadratic equation
By comparison with
Substitute these values in
Add 56 to both sides
Divide through by 4
Take square roots
Hence, the possible values of r are:
or
and the product is: