What are the first four terms of this sequence, beginning with n = 0 An = (-1)n (n+1)! Solution n=0 —> A0 = 1/1! = 1 n=1 —> A1 = -1/(2!) = -1/2 n=2 —> A2 = 1/(3!) = 1/6…
A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain 120 gallons of a mixture that contains 80% pure antifreeze, how many gallons…
Important to note Required Characteristics 1.) Has 2 vertical asymptotes 2.) Has a horizontal asymptote at y=0 3.) Has a positive y-intercept 4.) Has a hole in the fourth quadrant 5.) Passes through (2,5) 6.) Has exactly 1 x-intercept…
-8x-24=-8y 1=-1/3x+3/10y Solution -8x + 8y = 24 (-1/3)x + (3/10)y = 1 Divide the first equation by -8 and multiply the second equation by 30: x – y = -3…
2log(base 3)(x-4)+log(base 3)3=3 Solution Answer: x=7, 1 First, use the properties of logarithms to move the 2 up front. It can become an exponent: log3(x-4)2 + log33=3 Use properties of logarithms again to combine the two logs, since they have…
(a) 68% of the data ______ cm — ______ cm (b) 95% of the data ______ cm — ______ cm (c) 99.7% of the data _______cm — _______ cm Solution Given: normal distribution, μ = 177 cm, σ = 7.4 cm In a normal distribution: 68% of…
sin^2(x) – 3sin(x) + 2 = 0 within [-4π, 4π] Solution Let y = sin(x) Then the given equation becomes y2 – 3y + 2 = 0 (y – 1)(y – 2) = 0 y = 1 (Note that 2…
The distance between each street and each avenue is one block. Each block is 2 miles. You drive on Broadway from A to B in a car that uses 24 mpg. Approximately how many gallons did you use? It’s a…
Find tan(x-y) if sin(x) = 1/5, cos(y) = 2/5, tan(x) < 0 tan(y) > 0 Solution In the triangle containing x the remaining side is -2sqrt(6) and in the triangle containing y the remaining side is sqrt(21). Therefore tan x…
The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced: What is the length of the wood that is needed to replace AD? A. 8.1 B. 6.2…
