Study the entries and answer the question that follows.

The root spir means "to breathe."

The root hal means "to breathe."

The root neur means "nerve."

The prefix con- means "together."

The prefix ex-means "out."

The prefix a-means "towards."

The suffix -osis means "sickness," "condition," or "process."

If per means "through," then perspire literally means ___________.

Root $+$ combining vowel $=$ combining form. Deconstruct the following term to determine the correct combining form (CF). Finding the root(s) (Rs) first will put you on the right track. Fill in the blanks.

gynecologic:

$Root(s)$ $\rule{2cm}{0.15mm}$

$Combining~Vowel$ $\rule{2cm}{0.15mm}$

$Combining~Form$ $\rule{2cm}{0.15mm}$

The solution to the equation $x^{3}=64$ is called the cube root of 64. The idea is similar to the square root, except that the value must be cubed (multiplied by itself three times) to become 64. One way to write the cube root of 64 is using the notation $\sqrt[3]{64}$. Evaluate each of the following expressions. $\sqrt[3]{64}$

An unmanned satellite orbits the earth with a perigee radius of 10,000 km and an apogee radius of 100,000 km. Calculate (a) the eccentricity of the orbit; (b) the semimajor axis of the orbit (kilometers); (c) the period of the orbit (hours); (d) the specific energy of the orbit (kilometers squared per seconds squared); (e) the true anomaly at which the altitude is 10,000 km (degrees); (f) $v_{r}$ and $v_{\perp}$ at the points found in part (e) (kilometers per second); and (g) the speed at perigee and apogee (kilometers per second).

The average body temperature for 15 randomly selected polar bears was $97.5^{\circ} \mathrm{F}.$ Assume that the standard deviation from a recent study was $2.8^{\circ} \mathrm{F}.$ Find the maximum error of estimate for a 95% confidence level. Then estimate the mean body temperature for all polar bears in that region using a confidence interval.

In the definite integral $\int_{a}^{b} a(t) d t$, where a represents acceleration measured in meters per second squared and t is measured in seconds, what are the units of $\int_{a}^{b} a(t) d t$?

Your friend claims 72 and 75 cannot be part of a Pythagorean triple because 72² + 75² does not equal a positive integer squared. Is your friend correct? Explain your reasoning.

Study the entries and answer the question that follows.

The prefix ortho- means "straight" or "correct."

The prefix hetero- means "different."

The prefix homo- means "same."

The roots dogm and dox mean "belief."

The root gen means "type."

The suffix -logy means "word."

Using literal translations as guidance, define the following word without using a dictionary: heterodox

Study the entries and answer the question that follows.

The roots mit and miss mean "send."

The root duct means "to lead."

The prefix dis- means "away."

The prefix ad- means "toward."

The prefix ab- means "away from."

The prefix in- means "into."

The prefix trans- means "across."

List as many words as you can think of that contain the prefix trans-.

Use the fact that a falling body with friction equal to velocity squared obeys the equation $d v / d t=g-v^{2}$. Show that $v(t)=\sqrt{g} \tanh (\sqrt{g }t)$

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity $I_{0}=2 I_{\mathrm{ave}}),$ using either the fact that $E_{0}=\sqrt{2} E_{\mathrm{rms}},$ or $B_{0}=\sqrt{2} B_{\mathrm{rms}},$ where rms means average (actually root mean square, a type of average).

Employee Ages. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.

b. If the population standard deviation is $\sigma=8.2$ years, compute the standard error both with and without the finite population correction factor. What is the rationale for ignoring the finite population correction factor whenever $n / N \leq .05$ ?

Identify the function as belonging to the linear, quadratic, square root, cubic, cube root, or absolute value family. Then sketch the graph using shifts of a parent function and a few characteristic points. $f(x)=x^3-1$

Determine whether the statement is true or false. Justify your answer. "" $8$ less than $z$ cubed divided by the difference of $z$ squared and $9 ""$ can be written as

$$\frac{z^3-8}{(z-9)^2} .$$