we know that
The probability that "at least one" is the probability of exactly one, exactly 2, exactly 3, 4 and 5 contain salmonella.
The easiest way to solve this is to recognise that "at least one" is ALL 100% of the possibilities EXCEPT that none have salmonella.
If the probability that any one egg has 1/6 chance of salmonella
then
the probability that any one egg will not have salmonella = 5/6.
Therefore
for all 5 to not have salmonella
= (5/6)^5 = 3125 / 7776
= 0.401877 = 0.40 to 2 decimal places
REMEMBER this is the probability that NONE have salmonella
Therefore
the probability that at least one does = 1 - 0.40
= 0.60
the answer is
0.60 or 60%
For this case, what we must do is fill squares in all the expressions until we find the correct result.
We have then:
x2 + y2 − 4x + 12y − 20 = 0 x2 + y2 − 4x + 12y = 20
x2 − 4x + y2 + 12y = 20
x2 − 4x + (12/2)^2 + y2 + 12y + (-4/2)^2 = 20 + (12/2)^2 + (-4/2)^2
x2 − 4x + (6)^2 + y2 + 12y + (-2)^2 = 20 + (6)^2 + (-2)^2
x2 − 4x + 36 + y2 + 12y + 4 = 20 + 36 + 4
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
x2 + y2 + 4x + 6y − 5 = 0
x2 + y2 + 4x + 6y = 5
x2 + 4x + (4/2)^2 + y2 + 6y + (6/2)^2 = 5 + (4/2)^2 + (6/2)^2
x2 + 4x + (2)^2 + y2 + 6y + (3)^2 = 5 + (2)^2 + (3)^2
x2 + 4x + 4 + y2 + 6y + 9 = 5 + 4 + 9
(x + 2)2 + (y + 3)2 = 18
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 − 12x − 8y − 4 = 0
x2 + y2 − 12x − 8y = 4
x2 − 12x + (-12/2)^2 + y2 − 8y + (-8/2)^2 = 4 + (-12/2)^2 + (-8/2)^2
x2 − 12x + (-6)^2 + y2 − 8y + (-4)^2 = 4 + (-6)^2 + (-4)^2
x2 − 12x + 36 + y2 − 8y + 16 = 4 + 36 + 16
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 2x − 12y − 9 = 0
x2 + y2 + 2x - 12y = 9
x2 + 2x + y2 - 12y = 9
x2 + 2x + (2/2)^2 + y2 - 12y + (-12/2)^2 = 9 + (2/2)^2 + (-12/2)^2
x2 + 2x + (1)^2 + y2 - 12y + (-6)^2 = 9 + (1)^2 + (-6)^2
x2 + 2x + 1 + y2 - 12y + 36 = 9 + 1 + 36
(x + 1)2 + (y − 6)2 = 46
<span>h = Williams hours
h + 2.5 = Jose's hours because he worked 2.5 hours more than William, so you add 2.5 to William's hours (which is represented by h) to get Jose's hours
then you add them together..</span><span>
</span>
We meet again
so first divide 60 by 5
this gives 12
then multiply 12 by 4
giving a final answer of 48
When you say "at the same ratio", you mean that you consume the same amount of gas for the same amount of miles.
We know that everytime you drive 75 miles, you use 3 gallons of gas.
Since 12 gallons of gas is four times 3 gallons of gas, if the ratio remains the same, you can drive four times the distance:
You drive 75 miles, and use 3 gallons.
You drive 75 more miles (so you are at 
miles) and use 3 more gallons, so you use 
gallons.
You drive 75 more miles (so you are at 
miles) and use 3 more gallons, so you use 
gallons.
You drive 75 more miles (so you are at 
miles) and use 3 more gallons, so you use 
gallons, and you're done.
