<u>Complete Question</u>
The table shows the number of grade 7 and grade 8 students on the student council at Jeremy’s school.
Number of Students
- Grade 7 - 17
- Grade 8 - 34
Answer:
C- The number of outcomes representing each grade level does not change after the first student is chosen.
Step-by-step explanation:
The ratio of Grade 7 students to Grade 8 students is:
17:34
This written in reduced form is 1:2
Therefore, initially, the six parts of the cube can be divided into the ratio 2:4 which Jeremy did.
However, after the first selection of a student, the ratio of Grade 7:Grade 8 student changes since the same student cannot be chosen more than once.
Therefore the cube rolls represent only the first student choice and may not be accurate for subsequent rolls.
The correct option is C.
Let the constant of variation be c.
We are given that y varies inversely with 2.5x, this means that:
y = (c) / (2.5x)
This can be written as:
2.5xy = c
Now, we a re given that y = 5.6 at x = 30.
Substitute with these values in the equation to get the value of c as follows:
2.5xy = c
2.5(30)(5.6) = c
c = 420
Therefore, the equation that describes the relation is:
2.5xy = 420
Splitting up the interval [0, 6] into 6 subintervals means we have
![[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]](https://tex.z-dn.net/?f=%5B0%2C1%5D%5Ccup%5B1%2C2%5D%5Ccup%5B2%2C3%5D%5Ccup%5Ccdots%5Ccup%5B5%2C6%5D)
and the respective midpoints are
. We can write these sequentially as
where
.
So the integral is approximately
Recall that
so our sum becomes
Given profit,
p(t)=0.4t^2+5.3t-8
After the first year, t=1
p(1)=0.4*(1^2)+5.3*1-8=-2.3
Answer: the annual loss of the coffee shop after the first year (i.e. the second year) is $2,300.
