SqltyPi

Very close, pay attention to how it does not specify the order in which the three spins have to happen. For example:

a) asks for red, blue, and yellow... but it does not have to be in that order. There is a 1/3 chance for each color to be landed on... so there is a 1/27 chance that in that order, will be the outcome.

But, since it could also be blue, red, and yellow or yellow, red, and blue. We have to account for that as well.

There are 3*2*1 different combinations. Therefore your answer is 6/27 or 2/9. (for part a)

See if you can do the rest :D..

---

Also, I can't say that I am always right, so if you think I made a mistake, just let me know :)

Actually, I just figured out what I did wrong, there are 13 terms, not 12... The correct answer is 5304.

First of all, either that dog is seriously overweight, or he/she is going through a growth spurt. If Amar's dog east 114 pounds of dry dog food every day, a 45-pound bag of dog food will only last 45/114 of a day.

---

If this is not the answer you are looking for, or it is incorrect, don't hesitate to ask, and I can look at the question again :D

There are \(\binom{10}{3} = 120 \) different combinations of 3 meerkats that have to stand guard. Therefore each meerkat has to stand guard \(\frac{120}{10} = 12 \) nights. That means each meerkat gets 108 nights of sleep.

---

If this answer is incorrect, or you are looking for a different answer, feel free to ask me and I can look at the question again :D

If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 yards long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 1/3 of a piece of string.

---

If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 feet long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 1 piece of string.

---

If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 inches long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 12 pieces of string.

---

I am not exactly sure if this is what you are looking for. If you need anything else, don't hesitate to ask :D

If the area of the original square is \(64\) square inches, then the perimeter is \(32\) inches, and each side is \(8\) inches. Each triangle will have an area of \(32\) square inches. The perimeter of the triangles is \(16\) + the hypotenuse. The length of the hypotenuse is given by the Pythagorean theorem: \(a^2 + b^2 = c^2\) so we have \(8^2 + 8^2 = c^2\) therefore the length of the hypotenuse is \(\sqrt{128}\)  so your answer is \(16 + \sqrt{128} = 16 + 8\sqrt{2}\). 

I'm not 100% sure this is the answer you want, if you need anything else, just ask :D

The volume of a cone \(V\) can be calculated by the equation \(V = \frac{bh}{3}\) where \(b\) is the area of the base. If the cone has a radius of \(5.5\) then the area of the base is \(30.25\pi\) therefore the volume of the cone is \(\frac{12 \times 30.25\pi}{3} = 121\pi \approx 380.132711084\) units^3.

Out of the five people, there is a \(\frac{2}{5} \cdot \frac{1}{4} = \frac{2}{20} = \frac{1}{10} \) chance that the commitee will have exactly two women and one man. And there is a \(\frac{1}{10} \cdot \frac{1}{3} = \frac{1}{30}\) chance that the chairperson will be a man.

I'm not 100% sure this answer is correct, someone should double check it :D

If we plug in \(-5\) to the function \(f(x) = |x + 1|\) we get \(|-5 + 1|\) which simplifies to \(|-4| = 4\)