why me?

A boy mentions that none of the 21 kids in his 3rd grade class has had a birthday since school started 56 days previously. Assume that kids in the class are drawn from a population whose birthdays have the same probability on all days of the year. What is the probability that 21 kids would not yet have a birthday in 56 days?

can someone help me with integrating (y/(3-y))^2? I have no idea where to start and the answer key is confusing the heck out of me.

Please help!

my friend scanned me pages that were originally printed on green paper. When I try to print these pages out, the whole page is green, which is kinda ink wasting, so is there a way to get it so that only the words get printed and the background stays white? I tried printing in greyscale and the whole page turns grey instead.

I am a Canadian domestic student filing my taxes for the first time. I was told by the volunteers who did my taxes on campus that as a first time filer, I have to send my return to the international taxes office in Ottawa instead of my local office. I tried looking on the Canadian Revenue Agency website and contacting them via phone, but I can't seem to find any information relating to that. Does anyone know anything about this?

In situations like Newton's method, I can find out what the next term of x is based on my current term and I can do iterations to whatever accuracy I need. But is there a way for me to go backwards to go back to the original term? How do I do that?

Determine whether the sequence a_n = (1^1)/(n^2) + (2^1)/(n^2) + ... + (n^1)/(n^2) converges or diverges. If it converges, find the limit.

i'm trying to solve the differential equation dP/dt = -0.1P+500 with the initial P of 12000. I ended up with P(t) = -7000e^(-0.1t) +5000, which is not correct. Can someone show me where I went wrong?

Paramecia in a pond sample are growing according to the principle of Malthusian growth (i.e. unlimited growth, with no food or space limitations). Initially, there are 1100 Paramecia. Four hours later, the population has 1400 individuals. Find the population of Paramecia as a function of time.

I tried exponential growth, but it doesn't seem to work. Please help!

A spherical bead of radius R cm is made by drilling a round hole of radius r cm through its center?

https://webwork.elearning.ubc.ca/webwork%E2%80%A6

What is the volume of the bead? To assist in setting up the integral, the shaded region in the sketch above depicts a cross-section of the bead through the centre of the hole that was drilled along the x-axis.

How do you solve the integral above? I used integration by parts and I used the following substitutions:

u = arctan (4x) du = 1/(16x^2 +1)

v = 1/3 x^3 dv = x^2

Plugging these in, I have, 1/3x^3 * arctan (4x) - integral of (1/3x^3 * (1/16x^2 +1)

Apparently I'm supposed to use long division inside that integral that I just got, but how exactly does that work? Please explain!

if g(1)= -4 and g(5) =2, the integral of g(x) from 1 to 5 = -8. What's the integral of xg'(x) from 1 to 5?

I realized this is an integration by parts problem, but I don't know which to assign as u and v, please help.

The hypotenuse of an isosceles right triangle is 11 centimeters. The midpoints of its sides are connected to form an inscribed triangle, and this process is repeated. Find the sum of the areas of these triangles if this process is continued infinitely.

Consider a diatomic molecule with the x-axis as the bond axis. Which of the following atomic orbitals on adjacent atoms can form a pi bond?

a. 3d xz and 3d xy

b. 3d xz and 3s

c. 2p y and 3d x2-y2

d. 3d x2-y2 and 3d x2-y2

e. 3d xy and 2p y

The correct answer is apparently e, but I don't understand how that works, I picked d. Can someone explain why e is the correct answer?

A 29.0cm -long wire with a linear density of 30.0g/m passes across the open end of an 88.0cm -long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the tension in the wire?

A violin string is 36.0cm long. It sounds the musical note A (440 Hz) when played without fingering.

How far from the end of the string should you place your finger to play the note C (523 Hz)?

https://webwork.elearning.ubc.ca/webwork2_course_f...

For the graph in the link, what are the x values where there are maxima and minima in the interval (0, 8)?

What are the values of the absolute maximum and minimum of the function in the interval [0, 8]?

Shark Inc. has determined that demand for its newest netbook model is given by lnq−5lnp+0.001p=7, where q is the number of netbooks Shark can sell at a price of p dollars per unit. Shark has determined that this model is valid for prices p≥100. You may find it useful in this problem to know that elasticity of demand is defined to be E(p)=dq/dp * p/q

I took the derivative and got dq/dp = (5/p -0.001)q, i then multiplied by p/q, q cancels out and i'm left with E(p) = (5/p - 0.001)p, and p cancels out with 5/p and i'm left with 5-0.001p. but apparently this isn't the right answer, and i have no idea of how to do the second part. please help.

a quantity grows exponentially according to y(t) = y(0)e^kt. what is the relationship between m, n, and p such that y(p)=(y(m)y(n))^0.5?

Some time in the future a human colony is started on Mars. The colony begins with 20000 people and grows exponentially to 140000 in 200 years. What is the rate of change of the size of the population 150 years after the founding of the original colony?

An oscillator with a mass of 600g and a period of 1.00s has an amplitude that decreases by 1.20% during each complete oscillation. If the initial amplitude is 9cm, what will the amplitude be after 31 oscillations?

How do I calculate the damping constant of this problem?