Maths Mixture Trivia Quiz

Answer: 0

Anything times zero equals zero.

Answer: 6

Plug in 3 for x into 2x and you get 2(3) = 6.

Answer: 0.21

1/5 = 0.20 and 1/4 = 0.25. So 0.21 is between 1/5 and 1/4.

Answer: 60 percent

The total number of marbles in the bag equals 5. So the percentage of blue marbles is 3/5 = 0.60 or 60 percent.

Answer: 30 degrees

The sum of the three angles of a triangle equal 180 degrees. So if two angles sum to 150 degrees, then the third angle is 180 - 150 = 30 degrees.

Answer: 4(2x - 3)

Use the chain rule and you get 2(2x - 3)(2) which equals 4(2x - 3).

Answer: ellipse

The standard form of an ellipse centered at the origin is x^2/a^2 + y^2/b^2 = 1.

Answer: (1.5, 2.6)

In converting polar coordinates to rectangular coordinates, x=rcos(theta) and y=rsin(theta). In this problem, x=3cos60 which is 3(0.5) which equals 1.5. And y=3sin60 which is 3(0.866) which equals 2.6. So the rectagular coordinate is (1.5, 2.6).

Answer: 1

In order to calculate i raised to a large number, take the exponent, divide by 4 and see what the remainder is once you do the division. This remainder is the equivalent exponent to the large exponent (since the exponents of i are periodic). So, in this problem, 160/4 equals 40. The remainder is 0. Therefore, i^160 = i^0 which equals 1.

Answer: 25

The magnitude of a vector is calculated by taking the square root of the sum of the squares of the values multiplying i, j and k. So in this problem, magnitude = square root [15^2 + (-12)^2 + 16^2] = square root(625) = 25.

Answer: 15

In a poisson distribution, the mean equals the variance. Plus, the standard deviation is the square root of the variance. So, twice the mean less one standard deviation equals 2(9)-square root(9) = 18 - 3 = 15.

Answer: $674.43

Since this is convertible monthly, you have to convert the 6 percent interest rate to a monthly rate. So, .06/12 = 0.005. Then take 1.005, raise it to the power of 12 times 5, or 60, which is the number of months in 5 years. Then multiply by 500. So, 500(1.005)^60 = 674.43.

Answer: pi/10

The general formula for calculating the volume of an area between two equations rotated about the y-axis is the integral from a to b of 2pi times x[f(x)-g(x)]dx. In this problem, the two curves intersect at x=0 and x=1. So the integral is from 0 to 1 of 2pi times x[x^2 - x^3]dx.

This equals the integral from 0 to 1 of 2pi times (x^3 - x^4)dx. This equals 2pi(x^4/4 - x^5/5)from x=0 to x=1. Plugging in x=1 and then subtracting when you plug in x=0 gives you 2pi[(1/4)-(1/5)] which equal 2pi(1/20) which equals pi/10.

Answer: 0.896

This is a binomial random variable. At most one defective means finding the probability that zero are defective plus the probability that one is defective. The probability that zero is defective is (3 "choose" 0 times)*(0.2)^0(0.8)^3 + (3 "choose" 1 times)*(0.2)^1(0.9)^2 which is 0.512 + 0.384 = 0.896.

Answer: 2.175

The variance of an aggregate distribution is Var(S)=E[N]Var(X)+ {(E[X])^2}Var(N). E[N] is the expected value of the number of day of rain in a month of 30 days. This is 30(0.1)=3 since it is binomial. The variance of the binomial function is Var(N)=30(0.1)(0.9)=2.7. It is given that E[X]=0.5 and Var(X)=0.5. So, Var(X)=(3)(0.5)+(0.5)^2(0.5)=2.175.