Answer:
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one <em>c</em> within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a <em>c</em> in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to <em>x: </em>
<em />![\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20-7x%5E3%20%2B91x%5E2%20-280x%20-%209%5Cright%5D)
<em />
Differentiate:
Let g'(x) = 0:
Solve for <em>x</em>. First, divide everything by negative seven:
Factor:
<h3>
</h3>
Zero Product Property:
Solve for each case. Hence:
Since the first solution is not within our interval, we can ignore it.
Therefore:
All of these would be perfectly fine represented by a pie chart except A, which doesn't add to 100%.
The question seems to be getting at the idea that a pie chart might be better when the slices are all visually different sizes. I don't really think that's right; a pie chart for D say, where the two slices are about the same, gives the correct impression of the relative frequencies, which are about the same.
Answer they're looking for: C
Answer:
1) ven diagram #1
2)160
3) 420
4)16
Step-by-step explanation:
1) lets make a ratio table:
(look at image below, sorry for the horrible writing)
the original ratios are 18 and 17, and 18+17=35 35 is the number of students who play either or both sports. 30 is the number who play either sport:
so 35-30=5
5 students play both sports:
18-5=13(baseball)
17-5=12(basketball)
2) add up all the students who do band or sports and subtract from the total number of students
so
89/464+215/464= 304/464 students play in band or orchestra or both, to find the number of students who dont:
464-304=160
3) 630/1000+420/1000=1050/1000
1050/1000-210/1000=840/1000
840/1000-420/100=420/1000
420 ppl use brand p
4) 15+9=24
40-24=16
16 ppl
hope this helps!
In the number 14,423, the digit '4' comes up twice, in the thousand and hundred position.
The farther to the left a digit is, the higher that number is compared to another digit to the right of it.
This is why 1,000 is higher than 999.
In the number 14,423, there are two values for four: thousand (four thousand) and hundred (four hundred)
