OC userin Mathematics·30 May 2018Suppose we wish to test the hypotheses Ho:u= 10 versus H.: u<10, where u represents the mean age of non-high school aged children who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with o=2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be X = 8.76. 35. What is the value of the P-value? A) 0 B) 0.0066 C) 0.1075 D) 0.2676
OC userin Mathematics·29 May 2018For each part, clearly indicate your final short answer in the appropriate BOX provided marks, 1 mark for each part, with NO part marks for incorrect final answers.] Given the function f(x)=- e) For what value(s) of x does this function have a point of inflection? Indicate if it has none.
OC userin Mathematics·27 May 2018b. What is the probability that at least four of the people are left-handed?
OC userin Mathematics·28 May 20182. Find the equation of the slant asymptote of the following function as x++oo, if there is one: 5.23 +2:02 - 1 f(x):=- 22 +23 (5x-8) xt zx 15x3+2x?_ Write your answer in the form y=mx + b.
OC userin Mathematics·29 May 20187. If g() = 2.73 +62 then (a) g has an inflection point at x = -1 (c) g has a relative maximum at x = 2 (e) both (a) and (c) are true (b) g has a relative minimum at x = 2 (d) both (a) and (b) are true
OC userin Mathematics·27 May 2018(5) Among all cylinders that can be inscribed in a sphere of radius R find the dimensions of the one with the largest volume. (Your final answer should involve R.) Hint: The volume of a cylinder of heighth and radiasis given by V . Let re radius of cylinder h= height of cylinder V = volume of cylinder By Pythagorus: V=Th= ( Rh) v=tu/p?h ) dom V= (0,2R) VETR 3 ) = No DNE crit pts. 120 x 22.30 - 3 ph=ZER (can omit ha sind so it is a max rº: R - S = P2-R2 = 2p? ms rtt R. The options and en bestand sales a R _V3N RI The cylinder of maximal volume has beight 12 Continues on the next page →
OC userin Mathematics·25 May 201810. Recall that the half-life of Carbon-14 (C-14) is 5730 years. (a) Give the radioactive decay model for the amount of C-14 that remains after t years.
OC userin Mathematics·28 May 20185. (8 points) A flu epidemic follows the curve given by V(t) = 150 1 + 15.000e-0.350 million people, where F is the number of people infected by flu t weeks after the start of the epidemic. How fast is the epidemic growing 30 weeks after the start of the epidemic?
OC userin Mathematics·26 May 20182. (16 pts) EXPLANATION IS NOT REQUIRED! The graph of a function g' (t), the derivative of g is given below. Assume that the function gis continuous on its domain (-2, 4). y =gt) y = g' (t) -2 o (I) Find all critical points of g. (II) on what interval (or intervals) is the function g increasing? 2. (CONTINUED) (III) At what point (or points) does the function g have a LOCAL MAXIMUM ? (IV) on what interval (or intervals) is the function g CONCAVE UP ? (V) Find all inflection points of g.
OC userin Mathematics·25 May 2018Suppose we wish to test the hypotheses Ho:u= 10 versus H.: u<10, where u represents the mean age of non-high school aged children who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with o=2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be X = 8.76. 34. What is the value of the test statistic? A) Z=-0.62 B) z=-1.24 C z =-2.48 D) Z=-9.92
OC userin Mathematics·27 May 2018Problem 5. Determine which of the following matrices are in reduced form. 110 -4 0 0 A=1 01 10 09 0 0 0 1 3 /1 0 01 B=1 0 0 12 0 1 0 3 1 C= /10 -4 03 0 0 0 12 0 0 0 18 A) Matrices A and C only; B) Matrix A only; C) All three matrices. D) Matrix B only; E) Matrices A and B only; F) none of these.
OC userin Mathematics·25 May 20181. Short Answer Problems a) State the precise mathematical definition of lim f(x) = -0 b) State the Fundamental Theorem of Calculus. c) Find the exact value of tan(sec-1(4).
OC userin Mathematics·25 May 2018[4] 7. (a) A function f is said to grow exponentially when f'(x) = kf() for some non-zero constant k and all x in R. If f grows exponentially, prove that the function g(t) = is a constant function. [1] (b) If (b) If f grows exponentially, use part (a) to show that f(x) = Aek for some constant A. [5] (c) The population in a dish of bacteria is growing exponentially. At the start there are 8 micro- units of bacteria in the dish and the population doubles every 3 hours. How long will it take for the population to reach 20 micro-units?
OC userin Mathematics·24 May 2018It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 km/hr, the mean stopping time in fresh snow is known to be 215 meters with a standard deviation of o = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of 9 snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of t = 212.9 meters. 28. What is the P-value? A) 0.012 B) 0.050 C) 0.025 D) 0.006 E) Not within +0.002 of any of the above.
OC userin Mathematics·25 May 2018(x+y54 E. Given the constraints: y22) 821 Ez) When you maximize Z= 2x + 2y, subject to the constraints given above, the maximum value is: