Alan

"2. The terms $140, a, \frac{45}{28}$ are the first, second and third terms, respectively, of a geometric sequence. If $a$ is positive, what is the value of $a$?"

"1. Consider the infinite arithmetic sequence $A$ with first term $5$ and common difference $-2$. Now define the infinite sequence $B$ so that the $k^{th}$ term of $B$ is $2$ raised to the $k^{th}$ term of $A$. Find the sum of all of the terms of $B$."

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To get f^-1 rewrite f as:

   \(f=\frac{a}{x+2}\\x+2=\frac{a}{f}\\x=\frac{a}{f}-2\)

Now change f into x and x into f^-1:

\(f^{-1}=\frac{a}{x}-2\)

We have: \(f(0)=\frac{a}{2}\text{ and }f^{-1}(3a)=\frac{a}{3a}-2\rightarrow-\frac{5}{3}\)

I'm sure you can take it from here!

Like so:

"Mr. Z gave a test in Physics. Scores for the class are as follows: 76, 55, 73, 93, 29, 74, 57, 34, 54, and 75 out of a possible 100 points. Assume scores from this test are normally distributed.

If this set of scores is representative of all Physics classes Mr. Z has (in other words, with the same mean and same standard deviation), on average what percent of students pass this test? (Passing is 60% minimum.) Use technology or Standard Normal table to find probabilities and show all your reasoning to answer the question. List z-score and percent probability to 2 decimal places or decimal probability to 4 decimal places"

I think the following is what is meant:

z = (x - x_av)/sd.  So 

Here we have: x = 105, x_av = 103, sd = 2.7

You can crunch the numbers!

I suspect this means something like:

X is a matrix with, say, N rows and M columns.  Subscript i runs from 1 to N; subscript j runs from 1 to M.

\(\Sigma_iX_{ij}^2\) returns the sum of the squares of all elements from row 1 to row N in column j.

You can enter both e and pi from the calculator on the home page here (top line near the left hand side).

"A human resources department manager is tallying recent statistics regarding the relationship between an applicant being offered a job and the applicant having a job interview. Of 200 people applying for a job, 10 had an interview. Of those who had an interview, 7 are offered a job. If an applicant was not interviewed, he or she did not have an opportunity to get the job. Fill in the two-way frequency table below."
 

                      Job    No Job    Total

Interview         7            3           10

No Interview    0         190         190

Total                7          193         200

"What is the probability (rounded to the nearest whole percent) that an applicant does not get a job if he or she has an interview?"

Interview but No Job/Interview Total

3/10 or 30%

If the centre values of the histogram bars are x_i and the heights of the histogram are h_i, then assuming the widths are all the same:

\(x_{ave}=\Sigma_ix_ih_i/\Sigma_ih_i\)