Determine whether you think the given pair of events is independent.

You frequent casinos. You have lost money gambling.

What are the postulates that define Spherical Geometry?

1) Create a 3-dimensional figure. Label all of the relevant dimensions. Calculate the area of each face, the number of vertices, the perimeter of each face, the total surface area, and the volume. Express your results in both the English and the Metric system.PLEASE TYPE

Find the symmetries of the Platonic Solids: Cube, Tetrahedron, Octahedron, Icosahedron, and Dodecahedron.

I. You need to describe with words the planes of reflectional symmetry and identify how many there are in any of the categories found.

II You need to describe with words the axes(lines) of rotational symmetry. For each type of axis, determine how many there are and the order of rotation.

Prove the necessary part of Ceva’s Theorem for the case where D and E are ideal but F is ordinary.

The case is where:  D and E are ideal but F is ordinary.

Lately I feel as though the people working for Chegg prematurly take on questions they cannot answer. If you do not know the answer that is ok but please do not accept the question if you do not think you can answer it. Someone anonymously accepted this question and then said the description of the case is needed.... It is frustrating to get this response when it is clearly stated in the prompt: for the case where D and E are ideal but F is ordinary. I feel that the only reason they would respond like this is if they have no idea what the question is asking. This is becoming a regular occurence on this site so I feel someone should start monitoring the questions being asked by their so called "expert" tutor. FYI I already soved this problem I just think that this should be brought to Chegg's attention.

The area of a particular rectangle is 12 times the area of a certain square, and the width of the rectangle is three times the length of a side of the square. The perimeter of the rectangle is 30 units greater than the perimeter of the square. Find the dimensiuons of both the rectangle and the square.

Derive the point-slope form of a line using the fact that similar triangles have proportional sides.

Assume that a 3D polygon is tranformed by a transformation matrix T. Assume the normal vector of the polygon is n. Can we use the formula Tn to compute the normal vector of the transformed polygon? If not, drive the correct formula.

Prove that an isometry takes a (poylgon) unicorn to a congruent unicorn.

Please Consider the function f : R -> R given by f(x, y) = (2 - y, 2 - x).

(a) Prove that f is an isometry.

(b) Draw the triangle with vertices A = (1, 2), B = (3, 1), C = (3, 2), and the triangle with vertices f(A), f(B), f(C).

(c) Is f a rotation, a translation, or a glide reflection? Explain your answer.

Using Euclid's Propositions:

1. Prove that the regular octagon is constructible.

2. Prove that the regular decagon is constructible.

Small triangle. Answer the following.

a. State a definition for small triangle that would eliminate a counterexample to ASA.

b. Explain why using this definition eliminates the possibility of a counterexample to ASA.

Suppose that ABCD is cyclic, so there is a circle through all four of its vertices. Prove that (?A) + (?C) = 180? and (?B) + (?D) = 180?.

Business

The annual average natural gas price (in dollars per million BTUs) can be approximated by the function
h(x) = 69.54e^?0.264x

where x = 8 corresponds to the year 2008.

(Data from: Energy Information Administration.)

(a) What was the average price per million BTUs in the year 2010?

(b) According to the model, in what year did the average price per million BTUs hit $3.00?