Statistics

Probability Solutions

Although rare, tied swimming races occur with some frequency. In fact, at the 2016 Olympics there was a three-way tie for second position in the men's 100 m butterfly event. Find the number of different ways four swimmers can finish a race if (a) there are no ties (b) we include the possibility of ties.

Math - Others

Functions Solutions

Without graphing the function y = - 10 sin(6x), determine its amplitude and period. Leave answers in exact form; type pi for π . amplitude = period =

Given the equation y = 4 sin(5x - 35) + 2 The amplitude is: The period is: The horizontal shift is: The midline is: y =

Given the equation y = 2 sin(3(x + 6)) + 7 The amplitude is: The period is: The horizontal shift is: The midline is: y =

Basic Math Solutions

During a research experiment, that the number of bacteria in a culture grew at a rate proportional to its size. At 7:00AM there were 6,000bacteria present in the culture. At noon, the number of bacteria grew to7,100.How many bacteria will there be at midnight?

Trigonometry Solutions

sketch the graph of f(x)=sin(1/7x). show all the work to get the points of the graph.

Algebra

Matrices & Determinants Solutions

Use the following vectors to answer parts (a) and (b). 1 -4 3 v₁ = -3, v₂ = 12, v₃ = 5 4 -16 h (a) For what values of his v₂ in Span(v₁. v₂)? (b) For what values of h is (v₁. v₂. v₃) linearly dependent? (a) For what values of h is v₃ in Span(v₁, v₂)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i) h= (Use a comma to separate answers as needed.) ii) All values of h iii) No values of h

Geometry

Heights & Distances Solutions

The piston moves from the Top dead center as a result of a change O crank angle O ratio of crank radius to connected length O connected length O crank radius the distance from TDC to the crank center equal to O a=crank radius O b= connected length O a*b O a+b the piston travel changed with O connected rod length O crank angle O R/L O crank radius

Calculus

Limits & Continuity Solutions

Simplify [csc(t)-sin(t)]/cot(t) to a single trig function with no fractions.

Solve 2cos²(x)-7cos(x)+5=0 for all solutions. where Select an answer Give your answer as an exact value.

Vector Calculus Solutions

Find t for the following terminal points, 0 < t < 2π (a) P(0, 1), t = (b) P ( - V2/2 , V2/2),t= (c) P(-1,0), t = (d) P ( - V2/2, - V2/2), t= (e) P(0, - 1), t = (f) P(-V2/2, - V2/2).,t=

Without using a calculator, find the exact value of the expression: 15 tan² (π/3)+12 sec²(π/6)

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