Mathmatics and Statistics

A circle with center (2,4) and a point on the circle of (5,8) can be described by which of the following equations: A. (x − 4)^2 + (y − 2)^2 = 5 B. (x + 2)^2 + (y + 4)^2 = 25 C. x(x − 4) + y(y − 8) = 25 D. x(x − 4) + y(y − 8) = 5

(x-h)^2 + (y-k)^2 = r^2 r = ((x-h)^2 + (y-h)^2)^0.5 r = ((5-2)^2 + (8-4)^2)^0.5 r = 5 (x-2)^2 + (y-4)^2 = 5^2 x^2 - 4x + 4 + y^2 - 8y + 16 = 25 x^2 - 4x + y^2 - 8y = 5 x(x-4) + y(y-8) = 5

The derivative dy/dx of the following equation is equivalent to which of the following equations. y = cos(2x)*e^(4x) A. − 8 sin(2x)*e^(4x) B. 8 sin(2x)*e^(4x) C. e^(4x)*(4 cos(2x) − 2sin(2x)) D. 8e^(4x)*(cos(2x) − sin(2x))

1) -2sin(x)e^(4x) + 4cos(2x)e^(4x) Factor e^(4x) -> C. e^(4x)*(4 cos(2x) − 2sin(2x))

For vectors A = 5i + 4j − 3k and B = 2i − 3j + 4k the unit vector for the sum of A + B is: A. 10i + 12j − 12k B. 7i + j + k C. 0.78i + 0.11j + 0.11k D. 0.98i + 0.14j + 0.14k

A + B = 7i + j + k = c Mag(c) = (7^2 + 1^2 + 1^2)^0.5 = 7.14 c/Mag(c) = (7/7.14)i + (1/7.14)j + (1/7.14)k = D. 0.98i + 0.14j + 0.14k

The solution to the three linear equations shown is which of the following points in coordinate form: 4x + 4y + z = −2 Equation 1 2x + y + z = 8 Equation 2 x + 2y + 2z = 4 Equation 3 A. (4, -6, 6) B. (2, 2, 4) C. (2, -3, 4) D. (-4, 6, -2)

A. (4, -6, 6) Note: use the 2nd equation function on the calculator.

The enclosed area ABCD shown below is most nearly: A. 74 m2 B. 76 m2 C. 78 m2 D. 80 m2

A1 (trapezoid) A2 (Horizontal Curve) A1 = ((12+6)/2)*8 = 72 m^2 A2: Transportation Section R = LC/(2*sin(I/2)) 11 = 10/(2*sin(1/2)) I = 54.07° Circular Segment: NOTE: RADIAN A = (r^2 ( I - sin(I)))/2 = (11^2 ((54.07*(pi/180)) - sin(54.07*(pi/180)))/2 = 8.07 m^2 D. 80 m2

A bag contains three blue marbles and two red marbles. If a marble is selected five times out of the bag with replacement after each pick, the probability of obtaining at least four blue marbles is most nearly: A. 19% B. 21% C. 25% D. 34%

Binomial Dist. P(4 blue or 5 blue marbles) PB: 3/5 PR: 2/5 Pn(x) = (n!/(x!(n-x)!))*p^x * q^(n-x) Binomial Probability Table Binomial is either or (red or blue) (even or odd) 1 - P(3 blue marbles) = 1 - 0.6630 (taken from the table) = 0.34 = 34% D. 34%

The value of cos x is not equivalent to which of the following when x = π/2 radians: A. tan(2x) B. sec(2x) + 1 C. 2(sinx)^2 − 1 D. csc(x) − 1

C. 2(sinx)^2 − 1

For vectors A = 5i + 4j − 3k and B = 2i − 3j + 4k the cross product A × B is: A. 10i + 12j − 12k B. 25i − 14j − 23k C. 7i − 26j − 23k D. 7i + 26j − 23k

Calculator: 2nd, Vector, Edit, Plug in Values, 2nd, Vector, Cross, (U,V), enter: C. 7i − 26j − 23k

For vectors A = 5i + 4j − 3k and B = 2i − 3j + 4k the dot product A ∙ B is: A. 10i + 12j − 12k B. 10i − 12j − 12k C. 10 D. -14

Calculator: 2nd, Vector, Edit, Plug in Values, 2nd, Vector, Dot, (U,V), enter: D. -14

A sample of 6 concrete cylinders were broken at 28 days to estimate the concrete's compressive strength. The test results in psi were: 3900, 4150, 4450, 4275, 4350 and 4250. The sample mean and standard deviation are most nearly: A. 4,229 psi and 173 psi B. 4,229 psi and 190 psi C. 4,263 psi and 173 psi D. 4,263 psi and 190 psi

Calculator: Data, Enter Given Data (3900, 4150, 4450, 4275, 4350, 4250) into table 1, 2nd, data, 1-Var: L1, 1 Note: remember it says sample mean Sx B. 4,229 psi and 190 psi

Given vectors A = 2i + 4j and B = −i + 3j, what is true about the vectors? A. A is perpendicular to B B. A is parallel to B C. A is the same length as B D. A is at an angle of 45° to B

Draw Vectors A is perpendicular to B: A ∙ B = 0 A is parallel to B: A × B = 0 A is the same length as B Mag(A) = Mag(B) Mag(A) = (2^2 + 4^2)^0.5 Mag(B) = (-1^2 + 3^2)^0.5 A is at an angle of 45° to B A∙B = Mag(A)*Mag(B)*cos(θ) 2*-1 + 4*3 = 4.47*cos(θ) 10 = 4.47*cos(θ) θ = 45 D. A is at an angle of 45° to B

The points below can be modeled using a best-fit linear regression model. Point: (2, 2) (4, 5) (5, 12) (8, 16) The value estimated by the linear regression model for x = 10 is most nearly: A. 20 B. 21 C. 22 D. 23

Hit Data 2x to clear data: Click Data Table 1 (2,4,5,8), Click Data Table 2 (2,5,12,16), 2nd, data, linear regression y = 2.44x - 2.84 y = (2.44*10) - 2.84 = 21.6 C. 22

The functions below intersect in two locations and create an enclosed area. f1(x) = −x^2 + 4x + 1 Function 1 f2(x) = x + 1 Function 2 The area bounded by these two functions is most nearly: A. 3.0 units^2 B. 4.5 units^2 C. 7.5 units^2 D. 10.5 units^2

Integral: (0-a) ∫ (f1 - f2) dx a = f1 = f2 x^2 + 4x + 1 = x + 1 x^2 + 3x = 0 x = 0, 3 (0-3) ∫ -x^2 + 4x + 1 -x - 1 dx = (0-3) ∫ -x^2 +3x dx NOTE: can just enter it into the calculator: B. 4.5 units^2

A concrete mix design produces normally distributed concrete with a mean strength of 4,400 psi and standard deviation of 200 psi. The probability that a sample would be greater than 4,000 psi is most nearly: A. 98% B. 97% C. 96% D. 94%

Normal Distribution: x = 0 Zvar = (mean - x) / (standard deviation / (n)^0.5) = (4400 - 4000) / (200/(1)^0.5) = 400/200 = 2 F(x) = 0.9772 when x = 2 A. 98%

The following integral is equivalent to which of the following equations ∫ sec^2(x) − 1 A. tan2 x + C B. tan x − x + C C. tan (x/2) + x + C D. (tanx)/2 − x + C

Note: go to derivative section to find derivative of sec^2(x): tanx B. tan x − x + C

A line with a slope of 12/5 and passes through the point (5,3) also passes through all the following points except: A. (-5, -21) B. (-3, -16) C. (10, 15) D. (15, 27)

Point Slope: y = mx + b y - y1 = m*(x - x1) y - 3 = (12/5)*(x - 5) y = (12/5)x - 9 Calculate to see the slope ex: A. (3+21) / (5+5) = 24/10 = 12/5 B. (3+16) / (5+3) = 19/8 B. (-3, -16)

In the right triangle below AM is perpendicular to BC. The ratio of AM:BM:CM is most nearly: See Goodnotes Question 7 A. 12: 5: 13 B. 60: 25: 144 C. 81: 36 :169 D. 90: 121: 169

Similar Triangles: ABM and AMC AM/5 = AC/BC AM/5 = 12/13 AM = 60/13 BM/5 = 5/13 BM = 25/13 CM/12 = 12/13 CM = 144/13 B. 60: 25: 144

The trigonometric expression below is equivalent to which of the following: cos x + sin x tan x A. sec x B. cos x C. csc x D. sin x

cosx + sinx * tanx cosx + sinx *((sinx)/(cosx)) = cosx + ((sinx)^2)/((cosx)*(sinx)) (sinx)^2 = 1 - (cosx)^2 cosx + (1 - (cosx)^2)/(cosx) = cosx + (1/cosx) - cosx = secx A. sec x

The functions below define a parabola and line segment where the value b is unknown. f1(x) = x^2 − 4x + 2 Function 1 f2(x) = 2x + b Function 2 The value of b that will make the line tangent to the parabola is: A. -7 B. -3 C. 1 D. 3

f1'(x) = 2x - 4 f1'(x) is slope equation 2 = 2x -4 x = 3 f1(3) = 3^2 - (4*3) + 2 = -1 (3, -1) f2(x) = 2x + b -1 = (2*3) + b b = -7 A. -7

The inverse of y = 3^x can be written as which of the following: A. y = e^3x B. y = 3 log (x) C. y = log3 (x) D. y = logx (3)

x = 3^y log(x) = log (3^y) log(x) = y*log(3) y = log(x)/log(3) y = log3(x) C. y = log3 (x)