Let f be a function from R to

$÷{\sqrt[gn]{fvbfb}}_3$

A bag of 11 marbles contains 7 marbles with red on them, 3 with blue on them, 5 with green on them, and 4 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Graph the polynomial function. Factor first if the expression is not in factored form.

f(x)=x³+7x²+4x-12

The formula s=√18d$s=\sqrt{18d}$ can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after stepping on the brakes. If it took a car 25 feet to come to a complete stop after stepping on the brakes, estimate the speed of the car. Estimate the value of √18d$\sqrt{18d}$, when d=25$d=25$, to the tenths place.

Write an R function using Euclidean algorithm not only computes
the greatest common divisor d of a and b, but also two numbers s and t
such that d = s a + t b. (i.e solves Bezout's identity).

draw the hasse diagram representing the partial ordering {(a,b)|a<=b} on {1,2,3,4,6,8,12},is it a lattice justify

Triangle J K L is shown. The length of J K is 13, the length of K L is 11, and the length of L J is 19.Law of cosines: a2 = b2 + c2 – 2bccos(A)

Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree.

30°
34°
42°
47°

let c be the distance between Carlisle and Wellesley ,let b be the distance between Carlisle and Stonebridge, let a be the distance between Wellesley and Stonebridge. if you did a circuit, traveling from Carlisle to Wellesley to Stonebridge  and back to Carlisle you would travel 73 miles. the distance from Stonebridge to Carlisle is 12 miles farther than the distance from Wellesley to Carlisle. if you drove from Stonebridge to Carlisle and back to Stonebridge and then continue to Wellesley then back to Stonebridge you would travel 102 mile. 

1.write a system of linear equations to represent the situation

2. solve the system of equations. explain the meaning of the solutions in the context of the situations.

Is A« B an ideal of R?

Solve the recurrence relations together with the initial conditions given. a. an = 7an−1 − 10an−2 , for n ≥ 2 , a0 = 2 , a1 = 1 .

We define 𝐶[𝑎, 𝑏] as the set of all continuous functions 𝑓:[𝑎, 𝑏] → ℝ. Let 𝑊 = ቄ𝑓 ∈ 𝐶[𝑎, 𝑏]: ∫ 𝑓(𝑥)𝑑𝑥 ௕ ௔ = 0ቅ. Show that 𝑊 is a subspace of 𝐶[𝑎, 𝑏].

Determine which point is part of the solution set to the following
system of inequalities: f(x) <x + 4; f(x) > -x - 3; and f(x) < 5.