Luca and Maria are debating about how to evaluate the integral

A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(x)=\left\{\begin{array}{ll} 0 & x<0 \\ 0.02 & 0 \leq x<1 \\ 0.18 & 1 \leq x<2 \\ 0.35 & 2 \leq x<3 \\ 0.65 & 3 \leq x<4 \\ 0.85 & 4 \leq x<5 \\ 0.98 & 5 \leq x<6 \\ 1 & 6 \leq x \end{array}\right. Calculate the following probabilities directly from the cdf: (a) P(2), that is, P(X = 2) (b) P(X > 3) (c) P(2 S X s 5) (d) P(2 < x < 5)

9. The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month's production output. The table below shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer. A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer.

. A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 45 minutes? (b) When will the turkey have cooled to 100°F?

The length of each square on the grid represents 1 cm. The scale from an actual rectangle to the drawing is 24 in. to 1 cm. Make anew scale drawing where each centimeter represents 16 in.Label the length and width of your drawing in centimeters.

The following circuit operates if and only if there is a path of functional devices from left ta right. The probability of each device functions is as shown. Assume that the probability that a device functions does not depend on whether or not other devices are functional. What is the probability that the circuit operates Round your answer to four decimal places (e.g. 98.7654).

The table gives estimates of the world population, in millions,(b) 1750 to 2000. (a) Use the exponential model and the population figures for1750 and 1800 to predict the world population in 1900and 1950. Compare with the actual figures. (b) Use the exponential model and the population figures for1850 and 1900 to predict the world population in 1950.Compare with the actual population. (c) Use the exponential model and the population figures for1900 and 1950 lo predict the world population in 2000.Compare with the actual population and try to explain the discrepancy.10.

(10 points total) A small community organization consists of 20 families, of which 4 have one child, 8 have two children., 5 have three children, 2 have four children and 1 has five children. (a) (5 points)If one of these families is chosen at random, what is the probability that it has i children i = 1, 2, 3, 4, 5? (b) (5 points)If one of the children is randomly chosen, what is the probability that they came from a family of i children i = 1,2, 3, 4, 5?

3. A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide.What is the length of the longest pipe that can be carried horizontally around the corner? (Refer the diagram exercise 74 on page 269.)

-When written out in full, the number (102020 + 2020)² has 4041 digits. What is the sum of the digits of this 404 1-digit number? А 9 В 17 С 25 D 2048 E 4041

Write the composite function in the form f(g(x)). [Identify the inner function u =g(x) and the outer function y = f(u).] (Use non-identity functions for f(u) and g(x).) (f(u), g(x))= y=\cos (\sin (x)) \text { Find the derivative } \frac{d y}{d x}