Answer:
Step-by-step explanation:
Differentiability at a point implies no sudden changes in the slopes from one side to the other; that is, the derivative must have the same value.
Differentiating x^2 - 6 and 6 - x^2, we get 2x = -2x, whose only solution is zero (0). The two halves of the given function have the same slope (0) at x = 0.
Answer:
Step-by-step explanation:
Please find the attachment.
We have been given that a community pool that is shaped like a regular pentagon needs a new cover for the winter months.
To find the area of community pool we will use area of pentagon formula.
, where, a represents the apothem or perpendicular distance from the center of the pentagon and p represents perimeter of pentagon.
Let us find the perimeter of our given pentagon by multiplying each side length by 5.

Now let us find apothem of our pentagon by using Pythagoras theorem.





Upon substituting our given values in above formula we will get,



Therefore, the area of the pool that needs to be covered is 960.42 square feet.
Answer:
Step-by-step explanation:
Next time, please share the possible answer choices.
Since the slope and y-intercept are given here, we can immediately write out the slope-intercept form of the equation of this line:
y = mx + b becomes y = -1x - 5, where I have arbitrarily chosen the negative slope -1.
(11*5)+(4*10)=95
11+4=15
Both are equal to the constraints of the word problem and there for justified.
Answer:
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
That is z with a pvalue of
, so Z = 1.28.
Now, find the margin of error M as such

In which
is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5
The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.