I don’t understand how to do this math.
1 answer:
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Given that the difference between the roots of the equation 
is 
.
Recall that the sum of roots of a quadratic equation is given by
.
Let the two roots of the equation be
and 
, then
. . . (1)
Also recall that the product of the two roots of a quadratic equation is given by
, thus:
. . . (2)
From (1), we have:
Substituting for alpha into (2), gives:
Recall that the sum of roots of a quadratic equation is given by
Let the two roots of the equation be
Also recall that the product of the two roots of a quadratic equation is given by
From (1), we have:
Substituting for alpha into (2), gives:
Answer:
Louis has faster pitch when compared to each of their teams.
Step-by-step explanation:
We have two pitchers which we need to compare to each of their teams.
To calculate this, we will approximate the distributions to a normal distribution, and calculate the z-score, to know what proportion of players of their team fall below their score.
For Jerry, he has a speed of 86 and his team has a mean speed of 93 and standard deviation of 3.
We can calculate the z-score for Jerry speed as:
The proportion of players that are below Jerry speed is approximated by the standard normal distribution:
For Louis, his speed is 84 and his team has a mean speed of 89 and standard deviation of 3.5.
We can calculate the z-score for Jerry speed as:
The proportion of players that are below Louis speed is approximated by the standard normal distribution:
As the proportion of players of Louis team that are below Louis speed is much bigger than the proportion of players of Jerry's team that are below Jerry speed, we can say that Louis has faster pitch when compared to each of their teams.