Professor Jones Professor Smith
A 3 9
B 11 12
C 14 8
D 9 4
F 8 4
B. What are the conditions required to use this test? Have the conditions been satisfied? Explain.
Answer:15 seniors served on the student council during their freshman year, 14 seniors served during their sophomore year, 16 seniors served during their junior year, and 3 seniors have never served before.
Step-by-step explanation:
Using inclusion and exclusion principles, we find that 2 seniors served on the student council during each of the four years in high school.
The problem can be solved using the Principle of Inclusion and Exclusion (PIE), a common technique in combinatorial mathematics. First, we add the number of seniors serving in their freshman, sophomore, and junior years: 3 (never served) + 10 (junior) + 9 (sophomore) + 11 (freshman) giving us 33.
Then, we subtract the number of seniors who served during both sophomore and junior years, freshman and junior years, and freshman and sophomore years: 33 - 5 (sophomore and junior) - 6 (freshman and junior) - 4 (freshman and sophomore). This results in 18.
However, from the initial condition we know that there are 20 seniors in total. Therefore, the two 'extra' seniors must have served all four years in high school. Thus we find that 2 seniors served on the student council during each of the four years in high school.
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B. 1/4
C. 3/8
D. 2/3
Answer: C:3/8
Step-by-step explanation:
Answer: C. 3/8
Step-by-step explanation:
Answer:
Parallel lines have the same slope, so any line parallel to y = 7x - 3 will have slope 7. If your y intercept is 5, the line must go through (0,5), giving you y = 7x + 5.
Step-by-step explanation:
Answer:
$46325 in total for the car
Step-by-step explanation:
Answer:
sinθ = 12/15 -> 4/5
cosθ = 9/15 -> 3/5
tanθ = 12/9 -> 4/3
cscθ = 15/12 -> 5/4
secθ = 15/9 -> 5/3
cotθ = 9/12 -> 3/4
Step-by-step explanation:
The theta is where you would use to identify the numbers for the trig functions. The adjacent side is the one closest to the theta (but not the diagonal line, that is the hypotenuse), and the opposite line is the line next to the adjacent line.
For the first three trig functions, would use the method Soh Cah Toa.
Sin = opp/hypotenus, Cosine = adjacent/hypotenuse, and Tangent = opposite/adjacent. Then, there is cosecant(csc) = hyp/opp, secant = hyp/adj, and cotangent = adj/opp.