Math128 Exam 2. Name. Signature. Student ID Number (all 8 digits)

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1 Math128 Exam 2 April 13 th, 2017 Special Code: Name Signature Student ID Number (all 8 digits) Please shut off all electronics Please put everything away except a #2 pencil and a calculator that is not attached to a cell phone You will have 90 minutes to complete the twentyfive multiple choice questions on this exam It is very important that you fill in your answers (the bubbles ) on the answer sheet correctly so that the grading machine reads your answers correctly Please be conscientious in filling out the bubble sheet 1 Please fill in the information at the top of this page 2 On the bubble sheet where it says Name, please print your last name, leave a space, and then print your first name in the rectangles Then fill in the bubbles underneath 3 On the bubble sheet, where it says Identification Number, please CAREFULLY write your entire Student ID number in the rectangles and fill in the bubbles underneath Please double check to make sure you bubbled in your ID # correctly 4 On the bubble sheet, where it says Special Code please write the number in the rectangles and fill in the bubbles underneath 5 On the bubble sheet, where it says Grade or Educ bubble in your section number Section 1 Calden Tues/Thurs 830AM Section 2 Calden Tues/Thurs 10 AM Section 3 Hayes MWF Lastly do not write anything in the sections labeled Sex or Birth date Please double check that you bubbled your answers correctly on the bubble sheet and circle your answers on your test booklet before you hand it in When you are finished, quietly gather your belongings and come to the front of the room Have your student ID card ready to show us Grades will be posted on your MOODLE page just as soon as they are done Please do not call or asking for your grade We cannot give grades out by phone or GOOD LUCK!!

2 Yes Special Code: The following graph is of a population density function The function equals 0 for x < 0 and x > b Based on the graph, which of the following is false? a p(x) b (A) This is a uniform distribution PDF Yes, (B) The product of a and b must be 1 Yes (C) The area under the curve must be 1 Ye 's, (D) The total population is a times itisacoustautonafiniteinterod sinaph/)isapdf true of any PDF 2 Any exponential distribution PDF can be written in the form p(x) ae bx If b 5, what must the value of a be? amustequalb (A) 5 (B) 5 (C) 1 5 (D) 1 5 p( )KEk+ so C) or a5 3 Which of the following is false about the probability density function, p(x) and cumulative distribution function, P(x) if they are for the same set of data? FALSE@ a) p(x) is the derivative of P(x), b) The limit PK/)p/x, as x goes to infinity of p(x) is the same as the limit as x goes to infinity of P(x) c) The area under the curve of p(x) from to t equals P(t) Yes! d) The area under the curve from a to b of p(x) equals P(b) minus P(a) Illd / t Yes! fabpnndx limilh1 x o but lim Pm 0 x o Ila ) ftpph ( part a) ) since

3 6,z3 o Special Code: The distribution of heights of tomato plants is given in the PDF below What fraction of the tomatoes have a height less than 6 feet? (g c) PM is LINEAL through p(x) 'zx (0,07 and (8) c) x (feet) areanftiidngientaotita XHHXNWHHN 6 (0,07 8 ) pnndxf axdx so CY4 Prlxeo linethroatn#ad8h (A) 1 4 area of green triangle (B) (D) ( where the 8 C I pix )fzx cnecklfindthelinedo4pthfotphdxftatx2dxor@o4at 5 Let p(x) be the PDF and P(t) be the CDF for some set of data For the PDF below, find the value of t to the nearest thousandth if P(t) 04 0 if x < 0 1 p(x) { 9 x2 if 0 x 3 0 if x > 3 (A) 0002 (B) 1026 (C) 2210 (D) 'fht,h3 ) or + (

4 Special Code: A study in public transportation is done looking at the amount of time students wait at bus stop 1 and bus stop 2 The graph below was made of the CDFs for each stop Which of the following can be concluded based on the graph? P(t) 1 2 : I 5 10 t (minutes) (A) All students at stop 2 wait longer than students at stop 1 (B) More students wait less than 5 minutes at stop 2 than at stop 1 (C) Students at stop 1 are generally more satisfied with the bus service than at stop 2 (D) More students wait less than a minute at stop 2 than at stop 1 & Ipad " < Imd ) 7 Which of the following is false about the median and mean of a set of data? (A) The median is the t value where area under the curve of p(x) from to t is 5 (B) The median is the t value such that P(t) 5 (C) The mean is the area under the curve from to of p(x) (D) The mean and median of a uniform distribution are equal to each other mean µ Xpixldx not fotpnndx 8 The height of corn in a field can be modeled with a normal distribution where the mean is 75 inches and the standard deviation is 3 inches What percent of the corn would you expect to be over 80 inches? Give answer to the nearest µ75, (A) 5% (B) 10% (C) 37% (D) 42% 63 TAME " d or a 47890

5 5) AX Special Code: Find the mean and median of the following exponential distribution: p(x) 3e 3x (A) The Mean is 033 and the Median is The Mean is 333 and the Median is 231 (C) The Mean is 333 and the Median is 062 (D) The Mean is 033 and the Median is 231 KEKX mean kt 1<03 median HUI means # mediant 3333 ' ' The total revenue, R(d, l, t), in dollars of Jack s lemonade stand is a function of the number of lemonades he sells, l, the number of iced teas he sells, t, and the number of hot dogs, d, he sells Interpret the statement R(15, 26, 35) 91 The professor got it wrong! Q (A) If Jack sells 15 lemonades, 26 iced teas, and 35 hot dogs his revenue is $91 (B) If Jack sells 26 lemonades, 15 iced teas, and 35 hot dogs his revenue is $91 (C) If Jack sells 35 lemonades, 26 iced teas, and 15 hot dogs his revenue is $91 (D) If Jack sells 26 lemonades, 35 iced teas, and 15 hot dogs his revenue is $91 : 11 Suppose z f(x, y) 3x 2 y 4 5xy 3, which of the following statements is TRUE? (A) z is an increasing function of x and a decreasing function of y for x > 0 & y > 0 (B) z is an increasing function of y and a decreasing function of x for x > 0 & y > 0 (C) z is an increasing function of x and an increasing function of y for x > 0 & y > 0 (D) z is a decreasing function of x and a decreasing function of y for x > 0 & y > 0 5y3y3( Gxy 3, ), 12 For a function z f(x, y) we are given that f(40,120) 512 and f x (40,120) 05 and f y (40,120) 021 Use this to estimate f(43,124) 15 1/ (A) & 578 (B) 428 fl (C) ,124) flyqkdtfx (40, )+4,140, : ) + (D) 278 f fx + fy Ay )( 4) y 6 y K n( 2) K

6 Special Code: If z f(x, y) is given in the contour diagram below then find z f(15,0) The point 0 on the z4 Contour P (A) z f(15,0) 2 (B) z f(15,0) 4 (C) z f(15,0) 6 (D) z f(15,0) 8 1,5 14 Find a possible linear equation for the function with the contour diagram below: We so see 10,04 it is not (A) Hix/y) 4 tax t by 6411,o)4t a 1+60 (A) H(x, y) 4 + 2x 2y (B) H(x, y) 4 + x y 0(C) H(x, y) 4 + 2x y (D) H(x, y) 4 + x + y 4 + a 0,254 a 2 tenfold

22 C Hk Special Code: 041317 15 Consider the function given in the graph below which represents the temperature, H(x, t), of a bowl of milk placed x, feet from a fire, measured after t, minutes

7 22 C Hk Special Code: Consider the function given in the graph below which represents the temperature, H(x, t), of a bowl of milk placed x, feet from a fire, measured after t, minutes +15,HAA# tf ni# H 15,40 ),s ) 8 yo df{ Estimate H t (5,8) (A) H t (5,8) 5 32 (B) H t (5,8) 1 5 (C) H t BEST Estimate! A# a 1++15,81 at 0 #tauten Modisette (5,8) (D) H t (5,8), The concentration, C, of bacteria in the blood (in millions of bacteria/ml) following the injection of an antibiotic is a function of the dose x(in gm) injected and the time (in hours) since the injection Suppose we are told that C f(x, t) te xt Calculate f x (1,2) to the nearest hundredths place (A) 114 F text t ) (B) 054 (C) 432 text (D) 214 E " 2 #f}iii? 11,2 ) 4E2

Special Code: 041317 17 Z f(w, s) has data represented below with w, weight, in pounds and s, speed, in miles per hour Which statement about this function is FALSE?

8 Special Code: Z f(w, s) has data represented below with w, weight, in pounds and s, speed, in miles per hour Which statement about this function is (A) f w is negative (B) f s is positive (C) f w (140,8) 005 (D) f s (140,8) 16 flu,s ) increases as w increases! 18 Given z g(x, y) ln(xy) sin(x) + cos(y) e xy then g y (A) 1 cos(x) sin(y) exy y (B) 1 sin(y) gyx y, (C) 1 sin(y) xyexy xy (D) 1 cos(y) yexy xy o siny siny e Y e Yx 19 Suppose z f(x, y) 3x 2 y 3 find f xy (A) 18x 2 18xy 2 (C) 27xy (D) 9x 2 20 Which of the following is a critical point of z f(x, y) y 2 4y + x 2 2x + 8? (A) (1,2) (B) (2,1) (C) (0,1) (D) (2,0) Fx 32 1/3 6 1,3 F y(fx)y ( 6xy3)y _ Problems 18 1/ is material not covered on Exam 2 spring 2018

9 Special Code: Which of the following is true? (A) For there to be a critical point at (x 0, y 0 ), both f x (x 0, y 0 ) and f y (x 0, y 0 ) are either 0 or undefined (B) A critical point is always a maximum or minimum (C) You can test xvalues around a critical point to see if it is a maximum or minimum (D) The second derivative test will tell you if it is a maximum or minimum 22 Which of the following is true for f(x, y) x 3 27x y y? (A) There are 4 critical points one is a local maximum, one is a local minimum, and two are neither (B) There are 4 critical points two are local maximums and two are local minimums (C) There are 2 critical points both are local maximums (D) There are 2 critical points one is a local maximum and one is a local minimum 23 Find A, B, and C such that f(x, y) x 2 + Ax + y 2 + By + C and f(2,3) is a local miniimum with a value of 10 What is A + B + C? (A) 0 (B) 3 (C) 13 (D) Use Lagrange Multipliers to find the maximum for the following f(x,y) subject to the constraint f(x, y) xy, 4x + 6y 64 (A) 333 (B) 533 (C) 1667 (D) 4267

10 Special Code: It is determined that with a constraint of $65,000 in production costs, the maximum amount of production is given by f(125, 200) 500 The Lagrange Multiplier is 002 If the constraint is lowered to $60,000 estimate the new maximum production (A) 300 (B) 400 (C) 450 (D) 490

Math128 Exam 2. Name. Signature. Student ID Number (all 8 digits)

Math128 Exam 2. Name. Signature. Student ID Number (all 8 digits) Math128 Exam 2 April 13 th, 2017 Name Signature Student ID Number (all 8 digits) Please shut off all electronics Please put everything away except a #2 pencil and a calculator that is not attached to a