There are 100 students at a college who have taken a course in calculus, 110 who have taken a course in discrete mathematics, an
1 answer:
Answer:
110 students
Step-by-step explanation:
The number of students who have only taken calculus is given by the number of students who have taken calculus minus the students who have taken both classes:
The number of students who have only taken discrete mathematics given by the number of students who have taken discrete mathematics minus the students who have taken both classes:
The number of students that have taken a course in either calculus or discrete mathematics is:
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Answer:
A
Step-by-step explanation:
Recall that the sum of an arithmetic series is given by:
Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>x</em>_<em>n</em> is the last term.
We know that the initial term <em>a</em> is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find <em>n</em>.
First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:
Since the initial term is 13 and the common difference is 7:
Substitute:
We are given that the initial term is 13 and the sum is 2613. Substitute:
Solve for <em>n</em>. Multiply both sides by two and combine like terms:
Distribute:
Simplify:
Isolate the equation:
We can use the quadratic formula:
In this case, <em>a</em> = 7, <em>b</em> = 19, and <em>c</em> = -5226. Substitute:
Evaluate:
Evaluate for each case:
We can ignore the second solution since it is negative and non-natural.
Therefore, there are 26 terms in the arithmetic series.
Our answer is A.