8. [0/1 Points] PREVIOUS ANSWERS SCALCET9 15.4.032. ASK YOUR TEACHER PRACTICE ANOTHER (a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean ,4 = 1,700, nd the probability that both of the lamp's bulbs fall within 1,800 hours. (Round your answer to four decimal places.) 0.4286 x (b) Another lamp has just one bulb of the same type as In part (a). If one bulb burns out and is replaced by a bulb of the same type, nd the probability that the two bulbs fail within a total of 1,800 hours. (Round your answer to four decimal places.) 0.3132 x Need Help? 7. [0.8/1 Points] PREVIOUS ANSWERS SCALCET915.4.031. ASKYOUR TEACHER Suppose X and Y are random variables with the given joint density function. ale(0'5" + My) ifx a o, y 2 o x = K ' y) {0 otherwise (a) Is fa joint density function? 0 Yes ' No q! (b) Find P(Y z 4). (Round your answer to four decimal places.) 0.4493 Find P(X S 3, Y S 3). (Round your answer to four decimal places.) 0.5499 x (c) Find the expected value of X. 2 J Find the expected value of Y. 5 8. [-/1 Points] DETAILS SCALCET9 15.6.028. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x, y, z) is evaluated at the center (x;, y,, Zx) of the box Bijk. Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to two decimal places.) 5 V x2 + yz+ 27 dV, where B = ( x, y, 2) 1 0 s x 54, 0 sys 4, 05zs 4) Need Help? Read ItConsider the following. f( x, y, z) = 2x Z z=1- x2 y +z = 2 E i (a) Express the triple integral f(x, y, z) dV as an iterated integral for the given function f and solid region E. 1 - x2 2-y X 2x dy dz dx (b) Evaluate the iterated integral. 05. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 15.7.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use cylindrical coordinates. Evaluate fj/ '/ x2 + y2 dV, where E is the region that lies inside the cylinder X2 + y2 = 25 and between the planes 2 = 3 and z = 13. E 31251: x Need Help? 8. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 15.8.025.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following integral. (/ /(x2 + 2) dv, where E lies between the spheres x- + y" + 2" = 4 and x2 + y + 27 = 25 Write an equivalent integral using spherical coordinates. p*sin' (4) * dp de do A = B = 5 Evaluate the integral.5. [0.34/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 15.9.018.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following integral and transformation. (16x + 16y) dA, where R is the parallelogram with vertices (-2, 6), (2, -6), (5, -3), and (1, 9); x = =(u + v), y = = (v - 34) Use the transformation to write an equivalent integral in terms of u and v. Lol ( $ ( - 8u + 8v ) : av du A = 12 Evaluate the integral. 23047. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 15.9.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the given transformation to evaluate the integral. 8y2 dA, where R is the region bounded by the curves xy = 5, xy = 7, xy = 5, xy2 = 7; u = xy, V = xy2 768 35 X8. [-I1 Points] DETAILS SCALCET9 15.9.025.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the given integral by making an appropriate change of variables. ff 5 g; 8:: dA, where R is the parallelogram enclosed by the lines x 8y = 0, x 8y = 6, 3x y = 1, and 3x y = 2 R _ Need Help? 9. [0/1 Points] PREVIOUS ANSWERS SCALCET915.9.027. ASK YOUR TEACHER Evaluate the integral by making an appropriate change of variables. // 9 cos(7 (y l X dA where R is the trapezoidal region with vertices (4, 0), (10, 0), (0, 10), and (0, 4) R Y X lsin 10 2( ) x Need Help