from Empirical Rule, approximately 98% of the scores (98% of 40 = 39.2 ---> 39) lie within 2 standard deviations of the Mean

chapter 3 exercise 3.3 (answer)

from Empirical Rule, approximately 98% of the scores (98% of 40 = 39.2 ---> 39) lie within 2 standard deviations of the Mean

H/36 = 6/4 = 3/2; H = 3(36)/2 = 3(18) = 54 inches

weight of 15 cases of oranges = 15m kg

Factor. 7a^2 + 50a + 7 (answer)

7a^2 + 50a + 7 = (7a + 1)(a + 7)

Factor. 7b^2 + 22b + 3 (answer)

7b^2 + 22b + 3 = (7b + 1)(b + 3)

Factor. 49x^2 − 28x + 3 (answer)

use AC Method: compute 3(49) = 3(7)(7) form the following products and sums: -1 -3(49) -[1 + 3(49)] -3 -49 -(3...

from x = 0.5(a)(t^2), we have 18 = 0.5(a)(5^2) = 0.5(25)a, or a = 2(18)/25 = 36/25 m/s^2; then, if T = tension in rope attached to block A, then T = 15(a) = 15(36)/25 = 108/5 Newtons = 21.6 Newtons; if F denotes the applied force (applied to block B), then: F - T...

setting up word problems to solve (answer)

let A = Alvin's age; and let E = Elga's age; then: A = E + 11, and A + E = 103; then (substituting): (E + 11) + E = 103; or 2E + 11 = 103; or 2E = 103 - 11 = 92; or E = 46; A = 46 + 11 = 57

let area of rectangular field be A = xy, where x = length, y = width; then: A = 3,000,000 = xy ---> y = 3,000,000/x = 3,000,000 x^(-1); ---> L = length of fencing = 2x + 2y + y = 2x + 3y = 2x + 3(3,000,000)[x^(-1)] = 2x + (9,000,000)[x^(-1)]; compute...

x - y^2 = 0 ---> x = y^2 ( parabola opening to the right, vertex at (0,0)) ; let point on parabola that minimizes distance from (0,3) be (a,b); then, slope of line joining (0,3) and (a,b) = m = -(3 - b)/a = (b - 3)/a; using a = b^2, we have the following: m = (b...

evaluate the definite integral (answer)

I agree with Kenneth S. that since the integrand is an odd function of x, and the integral, call it I, is between symmetrically placed limits, -a and a, the result should be, even without any detailed calculations, I = 0.

find the total area bounded (answer)

perhaps the two curves were f(x) = 2sin((π/2)x), and g(x) = cos((π/2)x); if so, then that would seem to imply that the area in question is: b ∫ [(f(x) -...

Answer: 9 < A < 11; note that exact answer (area of trapezoid) is: A = 10 details of the above answer, with f(x) = 2x + 3: using inscribed rectangles: A1 = 0.5[f(0) + f(0.5) + f(1) + f(1.5)] = 0.5[3 + 4 + 5 +...

what's the question?

note the following: n 2n 2n-1 0 0 -1 1 2 1 2 ...

actually, the work done on a body, W = (component of force in direction of motion)(distance) = increase...

measures of angles (answer)

let x = measure of first angle; let y = measure of second angle; let z = measure of third angle; then: x = 2y; z = y + 96; and x + y + z = 180 ---> 2y + y + y + 96 = 180 ---> 4y + 96 = 180 ---> 4y = 180 - 96 --->...

what is the question? is the question the following: after one second, what is the velocity of the 10kg mass? if this is the question, then: F = ma ---> 5 = 10a ---> a = 0.5 meters/sec^2; in which case, assuming initial...

SOLVE WORD PROBLEM (answer)

let x = cost of one donut; and let y = cost of one large coffee; then 2x + 4y = 5.10; and ---> 2x + 4y = 5.10 6x + 3y = 6.39 --------->...

write sin(7*pi/12) = sin[(3*pi/12 + 4*pi/12) = sin(pi/4 + pi/3) = sin(pi/4)cos(pi/3) + sin(pi/3)cos(pi/4) = [sqrt(2)/2](1/2) + [sqrt(3)/2][sqrt(2)/2], where we have used sum formula: sin(x + y) = sin(x)cos(y) + sin(y)cos(x)