The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Reports

Classify each of the studies as either descriptive or inferential. Explain your answers. In an article titled “Teaching and Assessing Information Literacy in a Geography Program” (Journal of Geography, Vol. 104, No. 1, pp. 17-23), Dr. M. Kimsey and S. Lynn Cameron reported results from an on-line assessment instrument given to senior geography students at one institution of higher learning. The results for level of performance of 22 senior geography majors in 2003 and 29 senior geography majors in 2004 are presented in the following table. Level of performance Met the standard: 36−48 items correct Passed at the advanced level: 41−48 items correct Failed: 0−35 items correct Percent in 2003 82%50%18% Percent in 2004 93%59%7% Level of performance Met the standard: 36−48 items correct
Passed at the advanced level: 41−48 items correct
Failed: 0−35 items correct
Percent in 2003
82%
50%
18%
Percent in 2004
93%
59%
7%

The equation above gives the monthly cost C, in dollars, to take care of k kittens and b bunnies. John has 3 kittens and 5 bunnies, and Jenny has 2 kittens and 3 bunnies. How much greater, in dollars, is Johns

Using "Proof by Contraposition",sho that: if n is any odd integer and m is any even integer, then, ${\displaystyle 3m^3+2m^2}$ is odd.

B. G. Cosmos, a scientist, believes that the probability is ${\displaystyle \frac{2}{5}}$ that aliens from an advanced civilization on Planet X are trying to communicate with us by sending high-frequency signals to Earth. By using sophisticated equipment, Cosmos hopes to pick up these signals. The manufacturer of the equipment, Trekee, Inc., claims that if aliens are indeed sending signals, the probability that the equipment will detect them is ${\displaystyle \frac{3}{5}}$. However, if aliens are not sending signals, the probability that the equipment will seem to detect such signals is $\frac{1}{10}$. If the equipment detects signals, what is the probability that aliens are actually sending them?

Using the Mathematical Induction to prove that: ${\displaystyle 3^{2n}-1}$ is divisible by 4, whenever n is a positive integer.

${\displaystyle {\left(x^4{y}^5\right)}^{\frac{1}{4}}{\left(x^8{y}^5\right)}^{\frac{1}{5}}=x^{\frac{j}{5}}{y}^{\frac{k}{4}}}$
In the equation above, j and k are constants. If the equation is true for all positive real values of x and y, what is the value of $j-k$?
A)3
B)4
C)5
D)6

The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $ $\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n}}{a_n}<1/2$ then ${\displaystyle \sum a_n}$ converges, while if $\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n+1}}{a_n}>1/2$ then ${\displaystyle \sum a_n}$  diverges. Let ${\displaystyle a_n=\frac{n^{\ln n}}{{\left(\ln n\right)}^n}}$. Show that $\frac{a_{2n}}{a_n}\to 0$ as ${\displaystyle n\to \mathrm{\infty }}$