With a partner or a group, toss a number cube $30$ times and record the number showing on each toss. Compare the histograms. Describe how the distribution of the mean changes as the number of tosses increaes.

Find a power series for the solution of the following differential

If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. f(x)=

$$\sin ^ { - 1 } x$$

; [0, 1/2]

Consider u = i - 2j + k and v = 3i + pj - k. Show that no value of p exists such that v - u and u are parallel.

Is a weak Bronsted-Lowry base necessarily a weak Lewis base? Explain with an example.

What effects did the Open Door policy have on U.S. interests in Asia?

Graph the linear equation. y = 3x + 1

Evaluate the expression

$$(3/2)^{-2}$$

Why were Japanese missions to Tang China so important?

Estimate the following solutions using Euler’s method with n = 5 steps over the interval t = [0, 1]. If you are able to solve the initial-value problem exactly, compare your solution with the exact solution. If you are unable to solve the initial-value problem, the exact solution will be provided for you to compare with Euler’s method. How accurate is Euler’s method? y’ = 3t – y, y(0) = 1. Exact solution is $y=3 t+4 e^{-t}-3$

If the vector v has initial point P, what is its terminal point? v = (23, -5, 12), P(-6, 4, 2)

Changes in the DNA sequence that affect genetic information are known as a. replications b. mutations c. transformations d. prokaryotes

Find the first partial derivatives of the following functions. f(x, y)=

$$y ^ { 8 } + 2 x ^ { 6 } + 2 x y$$

If $x+3=15$, then find the value of $18+6x$.