The volume of the cone is
one-third of the volume of the cylinder which is equal to the product of area
of the base and the height. The equation is,
<span> V = (1/3)(pi)(r^2)h </span>
Dividing both sides of the
equation by (1/3)(pi)(h) will give us,
<span> 3V/(pi)(h) = r^2</span>
Taking the square-root of
both sides,
<span> r = sqrt(3V/(pi)(h))</span>
The rate of change is simply the derivative of a function with respect to the other variable. In this case the rate of change with respect to x is desired. Therefore
f(x) = x^3 - 3x^2
f'(x) = 3x^2 - 6x
therefore the rate of change of y with respect to x is dy/dx = 3x^2 - 6x
He used 11/12 of sugar.
(1) I multiplied the factors and denominators by eachothers denominators
(2) I ended up with the two converted fractions: 8/12 and 3/12. The reason for this step is because if the two fractions have the smae denominator, it helps make it easier to add the fraction.
(3) I added the fractions, getting the sum of 11/12
Good question!
Answer:
4 to the -2 power divided by 4 to the 4th power

<h3>(1/4096) is the right answer.</h3>
<h2>
Answer with explanation:</h2>
Let
be the population mean.
By analyzing the given information, we have the following hypothesis:-

Since the alternative hypotheses is left tailed so the test is a right-tailed test.
Also, the accuracy ratings of people in the general population are normally distributed.
Given : Sample size : n=51 , since n>30 so we use z-test.
Sample mean : 
Standard deviation : 
Test statistic for population mean :-


Critical value (one-tailed) corresponds to the given significance level :-

Since the observed value of z (-3.195) is less than the critical value (1.645) , so we do not reject the null hypothesis.
Hence, we conclude that we do not have enough evidence to accept that people are less able to identify emotions correctly when they are extremely tired .