Using the function \(f(x) = x^2 + x\) for each step, evaluate and simplify the following expressions (where \(h \neq 0\)). Make sure to combine like terms and simplify when possible.\(f(1+h) =\) [fh1]\(f(1+h) – f(1) =\) [fh2]\(\displaystyle \lim_{h \to 0} \frac{f(1+h) – f(1)}{h} =\) [fh3]Equation of the tangent line to \(f(x)\) at the point \((1, 2)\): [fh4]

(Q5.4.c)  The data given below represents the number of traffic fatalities by seat location and gender. Female Male Total Driver 32,955 11,732 44,687 Passenger 6,390 6,243 12,633 Total 39,345 17,975 57,320 Determine P(Male) and P( Male | Driver ).  Show how you found each answer. Then say if the events “Male” and “Driver” are independent and explain how you know.

The following questions cover discrete and continuous probability distributions, the binomial distribution, the normal distribution, the Central Limit Theorem, and the t-distribution.

The notation P(A|B) represents:

Using the angle \(\theta\) of the right triangle given below, find \(\sin(\theta)\). 

The mean gestation time of a litter of puppies is approximately bell-shaped with a mean of 60 days and a standard deviation of 6 days. Using technology, what percent of gestation times are between 50 and 55 days? Round your answer to the nearest tenth of a percent.  Answer: [1]%

A sputum sample submitted for Mycobacterium culture grew numerous orange-colored colonies that stained acid-fast after three weeks of incubation in 37° C in the dark.  These characteristics are consistent with identification of this isolate as a:

Match the organism with the gram-stain reaction and morphology

 In the Kirby Bauer disk diffusion test, if the density of the inoculum used to seed a plate for an antibiotic susceptibility test is less than the standard, the zone diameter will show which of the following after proper incubation?

According to the picture shown here or a special stain from a sputum specimen,  what would be an appropriate genus of an organism that would have this type of staining characteristic? final stain pic.png