Answer:
4(2a + b)
and
8a + 4b
Step-by-step explanation:
Hope this helped :)
The explicit formula of the sequence is given by a_n = -4n(n-1).
We have to find the first five terms of the sequence.
The first term:
![\begin{gathered} a_1=-4\times(1)(1-1) \\ =-4(0) \\ =0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_1%3D-4%5Ctimes%281%29%281-1%29%20%5C%5C%20%3D-4%280%29%20%5C%5C%20%3D0%20%5Cend%7Bgathered%7D)
The second term:
![\begin{gathered} a_2=-4(2)(2-1) \\ =-8(1) \\ =-8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_2%3D-4%282%29%282-1%29%20%5C%5C%20%3D-8%281%29%20%5C%5C%20%3D-8%20%5Cend%7Bgathered%7D)
The third sum:
![\begin{gathered} a_3=-4(3)(3-1) \\ =-12(2) \\ =-24 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_3%3D-4%283%29%283-1%29%20%5C%5C%20%3D-12%282%29%20%5C%5C%20%3D-24%20%5Cend%7Bgathered%7D)
The fourth term:
![\begin{gathered} a_4=-4(4)(4-1) \\ =-16(3) \\ =-48 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_4%3D-4%284%29%284-1%29%20%5C%5C%20%3D-16%283%29%20%5C%5C%20%3D-48%20%5Cend%7Bgathered%7D)
The fifth term:
![\begin{gathered} a_5=-4(5)(5-1) \\ =-20(4) \\ =-80 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_5%3D-4%285%29%285-1%29%20%5C%5C%20%3D-20%284%29%20%5C%5C%20%3D-80%20%5Cend%7Bgathered%7D)
Thus, option D is correct.
Answer:
a) 0.857
b) 0.571
c) 1
Step-by-step explanation:
Based on the data given, we have
- 18 juniors
- 10 seniors
- 6 female seniors
- 10-6 = 4 male seniors
- 12 junior males
- 18-12 = 6 junior female
- 6+6 = 12 female
- 4+12 = 16 male
- A total of 28 students
The probability of each union of events is obtained by summing the probabilities of the separated events and substracting the intersection. I will abbreviate female by F, junior by J, male by M, senior by S. We have
- P(J U F) = P(J) + P(F) - P(JF) = 18/28+12/28-6/28 = 24/28 = 0.857
- P(S U F) = P(S) + P(F) - P(SF) = 10/28 + 12/28 - 6/28 = 16/28 = 0.571
- P(J U S) = P(J) + P(S) - P(JS) = 18/28 + 10/28 - 0 = 1
Note that a student cant be Junior and Senior at the same time, so the probability of the combined event is 0. The probability of the union is 1 because every student is either Junior or Senior.
Answer:
2x+12
Step-by-step explanation:
We have a square patio, then each side of the patio has the same lengt. As we know the perimeter of a square is the sum of all sides. Then to know the length of the patio we just need to divide by 4 the perimeter.
![\dfrac{(8x+48)}{4}=\dfrac{8x}{4}+\dfrac{48}{4}=2x+12](https://tex.z-dn.net/?f=%5Cdfrac%7B%288x%2B48%29%7D%7B4%7D%3D%5Cdfrac%7B8x%7D%7B4%7D%2B%5Cdfrac%7B48%7D%7B4%7D%3D2x%2B12)
Then each side of the square patio has a length of 2x+12
You did not complete your question but I think this is what you are looking for. View the image.