Answer:
A 4/605
Step-by-step explanation:
mathematics = 11 letters
P(m) = number of m's/total = 2/11
we replace it so we have mathematics = 11 letters
P(s) = number of s's/total = 1/11
not replacing it
we replace it so we have mathematic = 10 letters
P(vowel) = number of vowel/total = 4/10 = 2/5
P(m, replace,s, no replace, vowel) = 2/11* 1/11 * 2/5 = 4/605
To figure ut the roots use the quadratic formula
x = [-b +- sqrt(b^2-4ac)]/2a
x = [-k +- sqrt(k^2-4(1)(5)]/2(1)
x = [-k + sqrt(k^2 - 20)]/2 or [-k - sqrt(k^2 - 20)]/2
So the question says these roots differ by sqrt 61, so let's subtract each
[-k + sqrt(k^2 - 20)]/2 - [-k - sqrt(k^2 - 20)]/2
well the k's cancel in the beginning and we are left with 2sqrt(k^2 - 20)/2, and the 2 on top and bottom reduce to
sqrt(k^2 - 20), so this equals sqrt 61
Set equal and solve
sqrt(k^2 - 20) = sqrt(61)
k^2 - 20 = 61
k^2 = 81, so k = +9 or -9
The greatest value therefore is k = +9.
It is 6 units because you find the absolute value of the two different coordinates, in this case it is 4 and -2. Since they belong in different quadrants (one x or y value is positive and the other is negative) you add them. If they are both in the same quadrant, you subtract them.
Answer:
Bobcats
Step-by-step explanation:
The wins-to-losses ratio for the Cougars is 12:10. This can also be written as 12/10; writing this as a decimal, we would have 1.2.
The wins-to-losses ratio for the Bobcats is 20:10. This can also be written as 20/10, which is the same as 2.0.
The wins-to-losses ratio for the Bulldogs is 8:5. This can also be written as 8/5, which is the same as 1.6.
The wins-to-losses ratio for the Tigers is 3:5. This can also be written as 3/5,l which is the same as 0.6.
The largest of these decimals is 2.0; this means the Bobcats have the greatest ratio of wins to losses.
990 as 85 is closer to 90 and 8 is the tenth