Working with the symmetry of a pentagonal pyramid.

Determine the number of planes of symmetry and the rotational symmetry (including the number axes) of a right regular pentagonal pyramid.

Working with permutations and combinations.

If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects taken r at a time, determine the value of r. Is there enough information to determine the value of n? Why or why not?

Finding the percentage of a number.

What is 20% of 40% of 500?

Venn Diagram to solve Probability Problem

Dr. Hawk works in an allergy clinic, and his patients have the following allergies:68 are allergic to diary products , 93 are allergic to pollen , 91 are allergic to animal fur, 31 are allergic to all three, 29 are allergic only to pollen,12 are allergic only to dairy products, 40 are allergic to to dairy products and pollen. ...continues

Probability

You roll a dice twice. What is the probability that you will roll each of the following pairs of numbers. Please answer with explanation, and show formula. 1. 6 then 5 2. 6 then 2 or 5 3. 6 then number less than 4 4. even number then 2 or 5 5. 1 and 1 6. even number then odd number

Solutions to a system: Algebraic Method

Find all solutions of the following system algebraically. Express answers in decimal form, accurate to two decimal places. Show all work. System: x^2 - y - 4 = 0 x^2 + y^2 = 9

Working with scientific notation and error bounds.

The population of a town is given in scientific notation 1.75 x 10^4. Choose the one option giving the population together with the implied error bound. Options A. 1750, with an error bound of 0.005 B 1750, with an error bound of 5. C. 1750, with an error bound of 50 D. Seventeen and a half thousand with an error ...continues

Working with outcomes of probability.

I have been given a question to break a pin code of 5 digits, and to list all the outcomes. The numbers are between Zero and Nine. How do I go about doing this?

Show that multiplication of an absolutely convergent series and bounded series is convergent.

Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded. Show that the series ak*bk converges absolutely.

Using proportional relationships.

Assume that male snakes of a particular species are all scaled versions of the same basic shape. (i) (a) Describe in words the sort of relationship that you might expect there to be between the volume and the length of a snake. What relationship would you expect there to be between the mass and the length of a snake ?. ...continues