Answer:
The probability that Joe's stock will go up and he will win in the lottery is 0.00005.
Step-by-step explanation:
Let the events be denoted as:
<em>X</em> = the stock goes up
<em>Y</em> = Joe wins the lottery
Given:
P (X) = 0.50
P (Y) = 0.0001
The events of the stock going up is not dependent on the the event of Joe winning the lottery.
So the events <em>X</em> and <em>Y</em> are independent of each other.
Independent events are those events that can occur together at the same time.
The joint probability of two independent events <em>A</em> and <em>B </em>is,

Compute the value of P (<em>X ∩ Y</em>) as follows:

Thus, the probability that Joe's stock will go up and he will win in the lottery is 0.00005.
Unit rate means how much does it cost for 1 unit
2.64 for 12 pencils
find 1 pencil
divide both sides by 12
0.22 for 1 pencil
0.22 per pencil
What’s the numbers or do you have a picture?
First, recall that Gaussian quadrature is based around integrating a function over the interval [-1,1], so transform the function argument accordingly to change the integral over [1,5] to an equivalent one over [-1,1].



So,

Let

. With

, we're looking for coefficients

and nodes

, with

, such that

You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).
Using the quadrature, we then have

6 because if thet are doing it togather jhon will speed things up