Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
- If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.
- (Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.
If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
Answer:
x = 22
Step-by-step explanation:
Answer:
And if we solve for a we got
The highest total cholesterol level a woman in this 20–34 age group can have and still be in the bottom 1% is 91.771 mg per deciliter
Step-by-step explanation:
Let X the random variable that represent the cholesterol level of a population of women between 20-34, and for this case we know the distribution for X is given by:
Where and
We want to find the highest value for the bottom 1% in the distribution, so we need to find a value a who satisfy the following conditions:
(a)
(b)
We can find a z value that satisfy the condition with 0.01 of the area on the left and 0.99 of the area on the right it's z=-2.33. And we can verify that on this case P(Z<-2.33)=0.01 and P(z>-2.33)=0.099
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
The highest total cholesterol level a woman in this 20–34 age group can have and still be in the bottom 1% is 91.771 mg per deciliter
Answer:
17a) Joanne is not correct because 8+8+8+5=29 cups of punch
17b) it will fit because 29 cups=7.25 quarts and 8 1-quart containers will be more than enough
Step-by-step explanation:
17a) REMEMBER TO COVERT THE QUARTS,GALLONS,and pints to cups
4 pints=8 cups
5 cups=5 cups
1/2 gallon=8 cups
2 quarts=8 cups
add the "cup" measurements together
17b) convert 29 cups into quarts
29 cups=7.25 quarts
7.25<8
Answer X= 0.6
Step-by-step explanation: