Complete each analogy by choosing the word that creates the same relationship between both pairs of words. Use a dictionary if you are uncertain about a word's meaning. vogue : anachronism :: obtuse : (a) dull, (b) cheerful, (c) acute, (d) angle

The percentage p(t) of children who can speak in sentences of five or more words by the age of t months can be approximated by the equation $p(t)=100\left(1-\frac{5.27 \times 10^{17}}{t^{12}}\right) \quad(t \geq 30)$ a. Give a technology formula for p. b. Graph p for $30 \leq t \leq 45$ and $0 \leq p \leq 100$. c. Create a table of values of p for t=30, 31, ..., 40 (rounding answers to one decimal place). d. What percentage of children can speak in sentences of five or more words by the age of 36 months? e. By what age are 75% or more children speaking in sentences of five or more words?

Find the greatest common factor of the numbers. Then tell whether the numbers are relatively prime.

Complete each analogy by choosing the word that creates the same relationship between both pairs of words. Use a dictionary if you are uncertain about a word's meaning. roof : gable :: poem : (a) haiku, (b) prose, (c) rhyme, (d ) stanza

$$\begin{array} { c } {\text { calculate } \mu \text { and } \sigma , \text { where } \sigma \text { is the standard deviation} } \\ { \sigma ^ { 2 } = \int _ { - \infty } ^ { \infty } ( x - \mu ) ^ { 2 } p ( x ) d x } \end{array}$$

$$p ( x ) = \frac { 1 } { \pi \sqrt { 1 - x ^ { 2 } } } \quad \text { on } ( - 1,1 )$$

What nominal interest rate per year is equivalent to 11.5% per year, compounded monthly?

Find an equation of the tangent line at the given point.

$$2 x ^ { 1 / 2 } + 4 y ^ { - 1 / 2 } = x y , \quad ( 1,4 )$$

Air is expanded in an adiabatic turbine of 90 percent isentropic efficiency from an inlet state of 2800 kPa and $400^{\circ} \mathrm{C}$ to an outlet pressure of 150 kPa. Calculate the outlet temperature of air, the work produced by this turbine, and the entropy generation.

A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)? Explain how you found your answer.

A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport?

Evaluate the expression when x = 2.

$$6 x + 8$$

Expand each expression. (4+2x)(4-2x)

Sketch the asymptotes and the graph of each equation. $y=\frac{1}{x-3}+4$

A student said that one should never allow bacteria near any foods. Explain whether this conclusion is appropriate.