Question 12. For the following card that might appear when deck is dealt. There are total of 52 cards. Use the data in the following table. P(X) is the probability. 10 5 P(X) a. Calculate mean b. Calculate variance c. Calculate standard deviation

Cloud seeding, a process in which chemicals such as silver iodide and frozen carbon dioxide are introduced by aircraft into clouds to promote rainfall, was widely used in the 20th century. Recent research has questioned its effectiveness ["Reassessment of Rain Enhancement Experiments and Operations in Israel Including Synoptic Considerations," Journal of Atmospheric Research (2010, Vol 97(4), pp. 513-525)]. An experiment was performed by randomly assigning 52 clouds to be seeded or not. The amount of rain generated was then measured in acre-feet. The data for the unseeded and seeded clouds are given below. For each group, perform the following steps. a. Calculate the sample mean, sample variance, and standard deviation. b. Find the median and quartiles for the data. c. Construct a box plot of the data. d. Find the interquartile range, determine the number of outliers and identify them. Seeded 81.2 26.1 95.0 41.1 28.6 21.7 11.5 68.5 345.5 321.2 1202.6 1.0 4.9 163.0 372.4 244.3 47.3 87.0 26.3 24.4 830.1 4.9 36.6 147.8 17.3 29.0 Unseeded 274.7 302.8 242.5 255.0 17.5 115.3 31.4 703.4 334.1 1697.8 118.3 198.6 129.6 274.7 119.0 1656.0 7.7 430.0 40.6 92.4 200.7 32.7 4.1 978.0 489.1 2745.6

The tangent plane to the surface with equation \[ z=x \ln (y)+x^{4} y+1 \] at the point \( (x, y, z)=(2,1,17) \) has the equation \( z= \) (write the appropriate function of \( x \) and \( y \) ) The tangent plane to the surface with equation z=xln(y)+x4y+1 at the point (x,y,z)=(2,1,17) has the equation z= (write the appropriate function of x and y )

To help them find their prey in the dark, most bat species have developed a remarkable navigation system called echolocation. Using echolocation a bat can determine where an object is, how big it is, in what direction it is moving and at what speed. For this discussion topic address the following (using the same guidelines as for the prior Discussions): What properties of sound does a bat use to navigate and hunt insects? How is a bat's anatomy uniquely designed to process sound waves? Amazingly, some people have also learned how to use echolocation to navigate. Discuss how a blind person could use sound to "see" his or her surroundings. Do an internet search for this phenomena.

Static and Flexible Budgets Graham Corporation used the following data to evaluate its current operating system. The company sells items for $10 each and used a budgeted selling price of $10 per unit. Actual Budgeted Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400,000 units 430,000 units Variable costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,250,000 $1,500,000 Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,500,000 $1,290,000 c. What is the flexible budget variance for variable costs?

James (mass 90.0 kg) and Ramon (mass 60.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. When James has moved 6.0 m toward the mug, how far and in what direction has Ramon moved?

A function is a probability density function if it satisfies the following definition: s(t)dt = 1. The probability that a random variable z lies between a and B is given by Pſa 5 osu) = *50.. A. Determine which of the following is a probability density function: if SO if 2 > 0 • f(a) = { 0 if Of(x) Thaif SO >0 0" B. For the one that is a probability density function, find the probability that is between 0 and 0.2.