A local road was designed to handle a daily mean of 187 cars. The local city council is concerned that the road it getting more traffic than it was designed to handle. A recent sample of 50 days found a sample mean of 193 cars per day and a sample standard deviation of 33 mph. We will perfrom a hypothesis test to determine if this is strong evidence that the mean number of daily cars is more than the road was designed to handle. Define your variable. O Let μ be the mean number of of cars that use the road on the sampled days. O Let p be the proprotion of cars in the sample that use the road. O Let p be the proportion of cars that use the road. Let μ be the mean number of cars that use the road on a daily basis. Write your hypotheses: Ho: HY Hevo 00187 HA 187 Find the P-value: Type your answer as a decimial rounded to three decimal places. Do not type a percentage or a percent sign. P-value= о esc K 72 .. % 925 $4 #3 9 W t y

7. (a) Find the vertex of the quadratic function S(x) = 2x² – 8r (b) Sketch the graph of the quadratic function. f(x) = 2x² – 8x -2 2 -2 -4- --6 -8 10

I want to make sure that I am working this correctly. I believe that the y-intercept is (0,0) and that the x-intercepts are (0,0), (8,0) and (-3,0)   I'm not exactly sure how to complete the rest of the problem. Any help is appreciated.

The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1800 + 12x − 0.1x2 + 0.0005x3 and the company finds that if it sells x yards, it can charge  p(x) = 37 − 0.00021x  dollars per yard for the fabric Use calculus to find the production level for maximum profit. (Round your answer to two decimal places)

In my precalculas with algebra class we are currently working on the vertexes, x-intercepts, and maximum and minimum values. I think that I have the concept understood but somehow I'm always slightly off on the homeowork assignments. The problem I'm stuck on is  f(x) = 3x2 − 36x + 96   I have correctly identified the x-intercepts as 4 and 8 but I got the vertex wrong with my answer of (6,12) when the correct answer was (6,-12). I cant seem to figure out what I'm doing wrong in the solving process.