Question

In: Advanced Math

Each of the faces of a regular tetrahedron can be painted either black or white. Up...

Each of the faces of a regular tetrahedron can be painted either black or
white. Up to rotation, how many ways can the tetrahedron be painted? Please provide
all the necessary computations and explanations. (hint : idea of abstract algebra can be used)

Solutions

Expert Solution


Related Solutions

Imagine an urn with two balls, each of which may be either white or black. One...
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn. Suppose that in the first two draws white balls have been drawn. What is the probability of drawing a white ball on the third draw?
I have four socks in a drawer; each is either black or white. Suppose that my...
I have four socks in a drawer; each is either black or white. Suppose that my null hypothesis is H0 : There are exactly two black socks. We decide on the following test: we take out two socks at random (all at once and without replacement). We reject H0 if the two socks are the same color. [Note: this test doesn’t make a whole lot of sense; this is just to practice the ideas.] a) What is the significance level...
Determine the number of DISTINCT colorings of the four faces of a tetrahedron, where each face...
Determine the number of DISTINCT colorings of the four faces of a tetrahedron, where each face is a color from the set { orange, purple, black} - Frobenius Orbit counting
In a particular species of salamander, the skin can either be black or brown. The black...
In a particular species of salamander, the skin can either be black or brown. The black phenotype is recessive to the brown phenotype. Within a population of 1000 salamanders, 640 have the brown phenotype. Calculate the allele frequencies for this population. Show all of your work. How many heterozygotes are there? Make up an environmental change that could occur (not an oil spill or something we’ve talked about, invent your own) that would cause a shift in the allele frequencies....
1. Given: A 4-inch cube with all 6 faces painted is cut up into 64 1-inch...
1. Given: A 4-inch cube with all 6 faces painted is cut up into 64 1-inch cubes. A cube is picked at random. What is the probability that (a) It is unpainted: ________________________________ (b) It has at most 1 face painted: _________________________
Consider a box with 24 beads that have either black or white color. The beads cannot...
Consider a box with 24 beads that have either black or white color. The beads cannot be distinguished otherwise. Each time you can take one bead from the box. The only thing you know is the following: in order to be certain that you pick 3 white beads, you have to take 11 beads from the box A) What is the smallest number of beads you have to take from the box in order to be sure that at least...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim...
A soccer ball has 32 faces, each of which is a regular pentagon or hexagon. Because...
A soccer ball has 32 faces, each of which is a regular pentagon or hexagon. Because of the angles involved, exactly three faces meet at each corner. Without looking at the ball, determine how many of each type of face there are.
Decision making in finance is rarely black and white and one decision can be appropriate for...
Decision making in finance is rarely black and white and one decision can be appropriate for one situation and not appropriate for another. Point and counter-point discussions should highlight this as well as expand upon the ability to support a decision that may not be supported by others in the same department. Initial Post Instructions Consider the following point and counter-point arguments then use the Internet to learn more about the issue. Which argument to you support? Explain why and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT