A polyhedron must meet three conditions in order to be regular:

All of the faces are regular polygons;

All of the faces are congruent (identical);

All of the vertex points/arrangements are congruent (identical).

Try to find three nonregular polyhedra, each of which violates a different one of these conditions. In other words, one of them should meet (1) and (2) but not (3); one should meet (1) and (3), but not (2); one should meet (2) and (3) but not (1). Describe each polyhedron using words:

number of faces and the polygons forming the faces

number of vertices and their vertex arrangements

number of edges

** Make sure to state which condition is being violated in each case

Find the dual problem for each of the following primal problems.

a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0

b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4 x1<=0,x2<=0,x3 unrestricted

You are the owner of a company that produces and sells a new tool at hardware stores. During one month, when 'x' of those new tools were produced and sold, the following were the revenue and cost (in hundreds of dollars).  

R(x)= -0.06x² +13.12x + 65.8 C(x)=3.04x+ 7.6

5.Fill-in the blanks.Be sure to read the following carefully!

HINT: do NOT use the TABLE from your graphing calculator, but DO use the graphing capabilities.

a)The profit for that month was 79 hundred dollars when ..........................of the new tool were produced and sold.

b)The profit for that month was 98 hundred dollars when ...........................of the new tool were produced and sold.

c)The profit for that month was 316 hundred dollars when...........................of the new tool were produced and sold.

d)The profit for that month was 47,600 dollars when................................of the new tool were produced and sold.

Solve these linear equations over Z₅

2x+3y =4

3x+y=2

The answer is (1,4) as unique solution, please kindly explain the reasons and show your work, much appreciated!

A national chain of clothing goods stores recently sent shipments to the following stores. The number of items shipped to each store and their total wholesale cost is shown in the table below. Find the wholesale price of one of each item.

(A) cost of a pair of jeans is?

(B) cost of a jacket is?

(C) cost of a sweater is?

(D) cost of a shirt is?

'(16) Consider the map T : P2(F) →P2(F) defined by T(p(x)) = xp'(x).

(a) Prove that T is linear.

(b) What is null(T)?

(c) Compute the matrix M(T) with respect to the bases B and B' of P2(F), where

B = {1,1 + x,1 + x + x2}, B' = {2−x,x + x2,x2}.

(d) Use the matrix M(T) to write T(7x2 + 12x−1) as a linear combination of the polynomials in the basis B'.

A chorded cycle in a graph is a cycle in the graph with one additional edge connecting two of the cycle vertices. Prove that every graph with minimum degree 3 contains a chorded cycle as a subgraph. (Hint: Consider a longest path in the graph. What does it tell you when a vertex is the end of a longest path? )

When Buying a Lotto Ticket What are my odds? a. Calculate your odds of winning if you spend $1 on an entry. b. Calculate your odds of winning if you spend $50 on an entry. c. Compare these odds to the odds of being in a car accident, plane crash, struck by lightning, or hit by a meterorite. NOTE PLEASE TYPE

How might geometry be used to build a feeling of community? type please

Assume that you have an isosceles right triangle, with legs equal to 6 units, that is rotated around on one of its legs to generate a right circular cone. Find the volume of this cone.

(1) You are estimating the cost of optical sensors based on the radius of the sensors. You decide to calculate the coefficient of determination (R2) as part of determining the goodness of fit of an equation. Using the preliminary calculations below, calculate the R2 and determine its meaning. [Image Description: Summation of (Yi-Ybar)2 = 150000, Summation of (Yhat-Ybar)2 = 125000, Summation of (Y-Yhat)2 = 25000]

16.67% of the variation in the radius is being explained by the cost.

83.33% of the variation in the cost is being explained by the radius.

16.67% of the variation in the cost is being explained by the radius.

83.33% of the variation in the radius is being explained by the cost.

(2) Given the following information, determine the equation for the unit formulation. (Round intermediate calculations to 4 decimal places) [Table Description: Table listing Unit Number (X) and Unit Cost ($Y). Unit 1 = $785.00, Unit 2 = $605.00, Unit 3 =$519.50, Unit 4=$466.27]

Unit Number (X) Unit Cost (Y) $

1 785.00

2 605.00

3 519.50

4 466.27

Y = (785)(X) -0.4941

Y = (785)(X) -0.3758

Y = (785)(X) 0.7707

Y = (785)(X) 0.7 2)

You are estimating the fuel consumption (gallons per mile) for intermediate armored vehicles based on the horsepower of the vehicle. The vehicle for which you are estimating has 4.77 hundred horsepower. Given the following equation, select the correct response from each pair.

Fuel Consumption = - 0.0494 + 0.22 (Horsepower in hundreds)

The dependent variable is Horsepower

The dependent variable is Fuel Consumption The y-intercept is 0.22

The y-intercept is - 0.0494

The estimated fuel consumption for your vehicle is 1.10 gallons per mile

The estimated fuel consumption for your vehicle is 1.00 gallons per mile

(1) Let G be a group and H, K be subgroups of G.
(a) Show that if H is a normal subgroup, then HK = {xy|x ? H, y ? K} is a
subgroup of G.
(b) Show that if H and K are both normal subgroups, then HK is also a normal
subgroup.
(c) Give an example of subgroups H and K such that HK is not a subgroup of G.

Kevin's body metabolizes caffeine at a rate of 14.4% per hour (so the amount of caffeine in Kevin's body decreases by 14.4% each hour).

1. If Kevin consumes a cup of coffee with 86 mg of caffeine in it, how long will it take for Kevin's body to metabolize half of the 86 mg of caffeine?

2. If Kevin consumes an energy drink with 200 mg of caffeine in it, how long will it take for Kevin's body to metabolize half of the 200 mg of caffeine?

3. If Kevin consumes a cup of coffee with cc mg of caffeine in it, how long will it take for Kevin's body to metabolize half of the cc mg of caffeine? (Hint: your answer will be a numerical value.)

How can geometry be used to promote responsible stewardship? Type Please

Given two circles C1 and C2 in the same plane where C1 has a radius of a and C2 has a radius of b and the centers of the C1 and C2 have a distance of c apart. In terms of a,b, and c describe when the intersection of C1 and C2 would be zero points. prove this