4).

(a) Calculate the five-number summary of the land areas of the states in the U.S. Midwest. (If necessary, round your answer to the nearest whole number.)

(b) Explain what the five-number summary in part (a) tells us about the land areas of the states in the midwest

(c) Calculate the five-number summary of the land areas of the states in the U.S. Northeast. (If necessary, round your answer to the nearest whole number.)

(d) Explain what the five-number summary in part (c) tells us about the land areas of the states in the Northeast

(d) Contrast the results from parts (b) and (d).
-----------------------------------------

5).Find the five-number summary for the data on highway mileage shown below.

Earth’s orbit around the Sun is an ellipse that is almost a circle. The Sun is at one focus, the major axis is 299,190,000 km in length, and the minor axis is 299,148,000 km in length. What are the minimum and maximum distances from Earth to the Sun?

The vertices of a triangle determine a circle, called the circumcircle of the triangle. Show that if P is any point on the circumcircle of a triangle, and X, Y, and Z are the feet of the perpendiculars from P to the sides of the triangle, then X, Y and Z are collinear.

How do I prove (step by step) Thales' Theorem?

Find the oblique asymptote for the rational function f(x)= 3x³ - 27x² + 60x / 2x² + 2x - 40

Find the composite function g o f when f(x)= 3x-5 / x-1 and g(x)= x+6 / 4x-9 (I got 9x-11 / 3x-11)

Modeling with Functions

In this course you have learned the characteristics of different types of functions and have practiced solving application problems involving modeling with these functions. For each scenario below, decide what type of function would best model the situation. Explain why you chose that type of function. Show your work in writing the function to model the situation. Be sure to state what the independent variable represents. Then use your model to answer the questions for that scenario.

1. Susan decides to take a job as a transcriptionist so that she can work part-time from home. To get started, she has to buy a computer, headphones, and some special software. The equipment and software together cost her $1000. The company pays her $0.004 per word, and Susan can type 90 words per minute.

   1. What type of function would be best to model this scenario? Choose one of the following: linear, quadratic, polynomial of degree 3 or higher, rational, exponential, or logarithmic. Explain why you chose this answer.

   2. Write a formula for the function you chose to model this scenario. What does the independent variable in your function represent?

   3. How many hours must Susan work to break even, that is, to make enough to cover her $1000 start-up cost? Show how you found the answer.

   4. If Susan works 4 hours a day, 3 days a week, how much will she earn in a month? Show how you found the answer.

a basketball coach was criticized in a newspaper for not trying out every combination of players. if the team roster has 14 players and every player can play every position how many 5-player combinations are possible?

Consider Cardano's problem of finding two numbers whose sum is 10 and whose product is 40.

a) Cardano knew beforehand that no such (real) numbers existed. How did he know? Can you prove it?

b) Solve the system of equations x+y=10 and xy=40 to find Cardano's complex solution.

c) Check that this solution does work-that is, thatb the sum of your complex numbers is 10 and that their product is 40.

189. An altitude of a triangle is a segment that joins one of the three vertices to a point on the line that contains the opposite side, the intersection being perpendicular. For example, consider the triangle whose vertices are A = (0, 0), B = (8, 0), and C = (4, 12). (a) Find the length of the altitude from C to side AB. What is the area of ABC? (b) Find an equation for the line that contains the altitude from A to side BC. (c) Find an equation for the line BC. (d) Find coordinates for the point F where the altitude from A meets side BC. It is customary to call F the foot of the altitude from A. (e) Find the length of the altitude from A to side BC. (f) As a check on your work, calculate BC and multiply it by your answer to part (e). You should be able to predict the result. (g) It is possible to deduce the length of the altitude from B to side AC from what you have already calculated. Show how.

Suppose that in an assortment of 30 calculators there are 5 with defective switches. Draw with and without replacement. (Enter the probabilities as fractions.)

(a) If one machine is selected at random, what is the probability it has a defective switch?

with replacement

without replacement

(b) If two machines are selected at random, what is the probability that both have defective switches?

with replacement

without replacement

(c) If three machines are selected at random, what is the probability that all three have defective switches?

with replacement

without replacement

Within your family, find an example of a Universal set and at least 3 subsets of that universal set. Describe each sets with the roster method. What relationships exist between the subsets? (Find the union and intersection of the sets. Are any of the sets disjoint?) Represent the sets in a Venn diagram.

A toy racecar races along a circular race track that has a radius of 29 meters. The racecar starts at the 3-o'clock position of the track and travels in the CCW direction. Suppose the car has swept out 2.55 radians since it started moving.

The racecar is how many radius lengths to the right of the center of the race track?

radius lengths   

The racecar is how many meters to the right of the center of the race track?

meters   

The racecar is how many radius lengths above the center of the race track?

radius lengths   

The racecar is how many meters above the center of the race track?

meterss   

Two

thousand

tickets

were

sold

for

entry

to

the

Heritage

Village

,

generating

$

19

,

700

.

The

prices

of

the

tickets

were

$

5

for

children

,

$

10

for

local

adults

,

and

$

12

for

foreign

adults

.

There

were

100

more

tickets

foreign

adults

sold

than

for

local

adult

s

a

.

Derive

a

system

of

three

equations

showing

the

information

given

.

b

.

Use

퐂퐫퐚퐦퐞퐫

′

퐬

퐑퐮퐥퐞

to

find

the

number

of

each

type

of

tick

For the following, give constructions using a straightedge and a compass with memory. You must prove that your construction works.

We say that a positive real number a is constructible if whenever we are given a line segment of length c , we can construct a line segment of length ac . Suppose that a and b are constructible real numbers. Show that ab is also constructible.

The cost of a can of Coca Cola in 1960 was $ 0.10 . The exponential function that models the cost of a Coca Cola by year is given below, where t is the number of years since 1960 . C ( t ) = 0.10 e^0.0576t Find the expected cost of a can of Coca Cola in 1990 , 2000 , 2015 and 2040 (rounded to the nearest cent). They expected the cost of Coca Cola to be $-------- in 1990 , $ --------in 2000 , $-------- in 2015 , and $ -------in 2040 .