Timbo Slice

x = (a/b)^(2/3)

What is dx / d(a/b) ?

I don't understand the notation :O how can you take the derivative with respect to (a/b) ?

I'll omit the subscript so Z*α/2 becomes Z* for readability

I have the following confidence interval from a difference of proportions

[0.012, 0.148] = [0.08 - 0.0693Z*, 0.08 + 0.0693Z*]

What are the confidence/significant levels?

I believe you get Z* = 0.9809? Now I just need to find confidence (1 - α) and significance α using the right table. I'm just confused about which table, since we have the α/2 division of 2.

V = s^(3)

s(t) = t

Then s'(t) = 1 and V'(t) = 3t^(2)

Now let V(t) = t

Then V'(t) = 1

And s'(t) = ?

Why is s'(t) = (1 / (3t^(2/3))?

f(x) = e⁴ˢᶦⁿ⁽ˣ⁾ - 3x

What is the maximum angles we can rotate this about the origin and still have a proper function?

My work

f'(x) = e⁴ˢᶦⁿ⁽ˣ⁾*4cos(x) - 3

f''(x) = [ e⁴ˢᶦⁿ⁽ˣ⁾*4cos(x)*4cos(x) ] - [ 4e⁴ˢᶦⁿ⁽ˣ⁾*sin(x) ] = 0

From symbolab online calculator, solving for x in the interval [-2pi, 2pi]

x = 1.08175 + 2pi, and pi - 1.08175 + 2pi

Plugging these into f'(x),

The maximum slope = 61.19

The minimum slope = -67.19

My questions

Q1) What is the maximum acute angle through which the graph can be rotated counter-clockwise? Why is it 90 - arctan (61.19) = 0.936?

Q2) What is the maximum acute angel through which the graph can be rotated clockwise? Why is it 90 - arctan (-67.19579) = 179.147?TL;DR, Why do we calculate 90 - arctan for rotating the graph? I have no idea what rotating a graph even means...

lim x --> 1

[ √(x) - x² ] ÷ [ 1 - √(x) ]

Is it possible to solve this limit without using L'hospital rule, since it hasn't been taught in class yet?

Thank you

You have 3 coins tossed independently.

If your first coin toss is a head, you get one dollar.

Q) What is the probability you get one dollar, given that you get 3 heads?

*The word given shouldn't be used, rather we're interested in the joint probability. Does the word given matter?

The answer is 1/8

I don't understand why, wouldn't it be 1, since if you have 3 coins and 3 heads, the first coin MUST be a head?

From 20 components, 18 are good, 2 are defective.

If I take 5, the probability all 5 are good is:

r = 18, N-r = 2, n = 5

P(Y = 5) = 0.553.

Now, it takes 2 minutes to install these components if they are good, and 10 minutes to install if they are defective.

What is the mean and variance of the time to install 5 components?

E(X) = 4.5 good components

4.5*2 + .5*10 = 9.5 minutes to install 5 components on average

V(X) = ?

The solution is V(T) =

We have a 1000 base pair insertion in some gene.

Consequences?

The mRNA is longer by 1000 base pairs.

1)The same amount of mRNA is transcribed. Why isn't it more?

Protein may be longer or shorter depending on start/stop codons altered.

Probably causes non-functional protein.

2) The same amount of protein is translated. Why is it the same amount?

A plant has 3 genes? that control colour.

P purple > p1 light purple > p white.

The number of leaves is controlled by 2 genes?

F five leafs > f four leafs

I cross a purple leaf with five leafs to white flower with four leafs.

F1 Progeny:

35 purple and five leafs

36 light purple and five leafs.

1) What is the genotype of the parents crossed?

I just had this on a test, hopefully I have all the information!

I guessed the parents :(

The dot means we don't know if genes are linked.

My punnet square for the hypothesized parent genotype:

P/p1 ⋅ F/F x p/p ⋅ f/f

.........P ⋅ F...........P ⋅ F...........p1 ⋅ F............p1 ⋅ F

p ⋅ f...P/p ⋅ F/f......P/p ⋅ F/f......p1/p ⋅ F/f......p1/p ⋅ F/f

Hope the above is understandable!

Progeny is 1/4 for all:

P/p ⋅ F/f

P/p ⋅ F/f

p1/p ⋅ F/f

p1/p ⋅ F/f

So half are Purple with five leafs

Other half are light purple with five leafs!

Parents must be: P/p1 ⋅ F/F and p/p ⋅ f/f?

Nuclear radiation energy is much larger than visible light energies.

So instead of just being absorbed and increasing an objects temperature, nuclear radiation ionizes matter and breaks molecular bonds.

Explanation was because:

"These energies are much larger than ionization energies of atoms and molecules".

"The ionization energies of an atom is about 10 eV, while alpha or beta particles are around 1 MeV".

How does an atom's ionization energy and ionizing radiation fight? Atom ionization energy is energy needed to rid of an electron.

Nuclear radiation just damages everything.

I don't see how they connect?