Answer: There are 35 spellers participated in the spelling bee.
Step-by-step explanation:
Since we have given that
Rank of Anish's placement at the highest = 11 th
Rank of Anish's placement at the lowest = 25 th
We need to find the number of spellers participated in the spelling bee.
So, Number of spellers participated in the spelling bee is given by
Highest + Lowest - 1
= 11 + 25 - 1
= 36 - 1
= 35
Hence, there are 35 spellers participated in the spelling bee.
For starters, create an equation to show David's earnings. We can do this using Danielle's as a basis, which is set up as y=(# of hours)x+(bonus). This gives us y=12x+80. Now, as we need both their ys to be equal, we just set both equations equal to each other, making 15x+50=12x+80. Now, we solve for x, starting with 15x+50=12x+80, subtracting 12x from both sides to get 3x+50=80, subtracting 50 from both sides to get 3x=30, and dividing three from both sides to get x=10. To check, we just plug in our answer to both equations and see if the ys match up. With Danielle's equation, we get y=15(10)+50=150+50=200 and with David's equation, we get y=12(10)+80=120+80=200, proving that our answer is correct.
To check for continuity at the edges of each piece, you need to consider the limit as
approaches the edges. For example,

has two pieces,
and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have

By definition of
, we have
, and the limits are


The limits match, so
is continuous.
For the others: Each of the individual pieces of
are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
C is your correct answer. Good luck.
The cost function is
c = 0.000015x² - 0.03x + 35
where x = number of tires.
To find the value of x that minimizes cost, the derivative of c with respect to x should be zero. Therefore
0.000015*2x - 0.03 = 0
0.00003x = 0.03
x = 1000
Note:
The second derivative of c with respect to x is positive (= 0.00003), so the value for x will yield the minimum value.
The minimum cost is
Cmin = 0.000015*1000² - 0.03*1000 + 35
= 20
Answer:
Number of tires = 1000
Minimum cost = 20