A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 10 pounds and 12 pounds, respectively. a. Calculate the expected value and the standard deviation of this distribution. (Do not round intermediate calculations. Round your "Standard deviation" answer to 4 decimal places.) Expected value Standard deviation b. Find the probability that the weight of a randomly selected bag is no more than 11 pounds. (Round your answer to 2 decimal places.) Probability c. Find the probability that the weight of a randomly selected bag is at least 10.5 pounds. (Round your answer to 2 decimal places.)

a) The expected value is given by:

The variance is given by:

And the standard deviation is just the square root of the variance and we got:

b)

And we can use the cumulative distribution function given by:

And using this function we got:

c)

And using the complement rule and the cumulative distribution function we got:

Step-by-step explanation:

For this case we define the random variable X=quantity put in each bag , and we know that the distribution for X is given by:

Part a

The expected value is given by:

The variance is given by:

And the standard deviation is just the square root of the variance and we got:

Part b

For this case we want this probability:

And we can use the cumulative distribution function given by:

And using this function we got:

Part c

For this case we want this probability:

And using the complement rule and the cumulative distribution function we got:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length