As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The international Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano international Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comn1ent on the accuracy of this estimate. Use a 95% confidence interval to support your inference.

Evaluate the multiple integrals. $\int_{2}^{3} \int_{0}^{2 x} y d y d x$

In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject ( International Journal of Obesity , January 2007). The study revealed that the overall physical activity of obese young adults has a mean of

$$\mu = 320 \mathrm { cpm }$$

and a standard deviation of

$$\sigma = 100 \mathrm { cpm }$$

(In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 obese young adults, consider the sample mean counts per minute,

$$\overline { x }$$

a. Describe the sampling distribution of

$$\overline { x }$$

b. What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm? c. What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?

Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well-ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (Dec. 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted. The radon levels-measured in becquerels per cubic meter $(Bq/m^3)$-in the inner chambers of a sample of 12 tombs were determined. For thís data, assume that $\bar{x}=3,643 \mathrm{Bq} / \mathrm{m}^{3}$ and $s=1,187 \mathrm{Bq} / \mathrm{m}^{3}$. Use thís information to estímate, with 95% confidence, the true mean level of radon exposure in tombs in the V alley of Kings. Interpret the resulting interval.

Radon exposure in Egyptian tombs. Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted. The radon levels-measured in becquerels per cubic meter $\left(\mathrm{Bq} / \mathrm{m}^3\right)$-in the inner chambers of a sample of 12 tombs were determined. Summary statistics follow: $\bar{x}=3,643 \mathrm{~Bq} / \mathrm{m}^3$ and $s=4,487 \mathrm{~Bq} / \mathrm{m}^3$. Use this information to estimate, with $95 \%$ confidence, the true mean level of radon exposure in tombs in the Valley of Kings. Interpret the resulting interval.

If every nonzero element of R is either irreducible or a unit, prove that R is a field.

Use determinants to decide if the matrix is invertible.

$$\left[\begin{array}{rr} 1 & 3 \\ 5 & -2 \end{array}\right]$$

If the subset $T=\left\{u_{1}, \ldots, u_{s}\right\}$ of V is linearly independent over F, then prove that any nonempty subset of T is also linearly independent.

The vector v has initial point $P_{1}$ and terminal point $P_{2}$. (a) Write each vector v as a position vector. (b) Write each vector v in terms of the standard basic vectors. (c) Graph the vector v and the corresponding position vector. $P_{1}=(0,5)$ and $P_{2}=(-1,6)$

Find an equation of the tangent line to the curve $y=3+x-5 x^{2}+x^{4}$ when x=0

If N is a normal subgroup of a group G and if every element of N and of G/N has finite order, prove that every element of G has finite order.

Write an iterated integral of a continuous function f over the region R. Use the order dy dx. Start by sketching the region of the integration if it is not supplied. R is the region in quadrants 2 and 3 bounded by the semicircle with radius 3 centered at (0, 0).

A multiple choice exam has 20 questions each with 4 possible answers and 10 additional questions each with 5 possible answers. How many different answer sheets are possible?

Subtract in binary. Place a 1 over each column from which it was necessary to borrow. (a) 10100100 − 01110011 (b) 10010011 − 01011001 (c) 11110011 − 10011110