Graph and compare the two functions.

$$f ( x ) = | x - 1 | + 2 ; g ( x ) = 4 | x - 1 | + 8$$

Let f(x)=

$$x^8$$

-2x+3; find

$$\lim _ { w \rightarrow 2 } \frac { f ^ { \prime } ( w ) - f ^ { \prime } ( 2 ) } { w - 2 }$$

Write the quotient in scientific notation: (4 × 10^12)/(8 × 10^4)

Mr. Doody, at age 70, is expected to live for 15 years. If he can invest at 4% per annum compounded monthly, how much does he need now to guarantee himself $300 every month for the next 15 years?

Ms. Rosenbaum buys 5 crates of apples at the market. Each crate costs $12.50. She also buys one crate of pears for$18.75. What is the total cost of the apples and pears?

In an ideal Brayton cycle, air is compressed from 100 kPa and $25^{\circ} \mathrm{C}$ to 1 MPa, and then heated to $927^{\circ} \mathrm{C}$ before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is (a) $349^{\circ} \mathrm{C}$ (b) $426^{\circ} \mathrm{C}$ (c) $622^{\circ} \mathrm{C}$ (d) $733^{\circ} \mathrm{C}$ (e) $825^{\circ} \mathrm{C}$

Use an inverse matrix to solve the linear system. 4x + y = - 2, -6x + y = 18

Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded by the cone

$$z = \sqrt { x ^ { 2 } + y ^ { 2 } }$$

and the plane z=2.

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in.. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.5% or largest 2.5%. Find the minimum and maximum head breadths that the helmets will fit.

Two male and 2 female students from each of the 9th, 10th, 11th, and 12th grades comprise the Student Council. If a Student Council representative is chosen at random to attend a board meeting, what is the probability that the student will be either an 11th grader or male?

1-(0.2+0.48)

Find the missing dimension of each figure. rectangular prism: V=80

$$m^3$$

; length=5 m; width=4 m h=

Find the mean, median, mode, and range of each data set. 19, 25, 31, 19, 34, 22, 31, 34

Determine whether each statement is sometimes, always, or never true. Justify your reasoning using a counterexample or proof. In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.