CubeyThePenguin

Similarly, we have a rhombus with short diagonal 2(10/3) = 20/3 and long diagonal 2(10) = 20. From there it shouldn't be too hard to calculate the area.

There are a total of 4 choose 2 = 6 pairs that can be chosen. This number is small enough to go through each pair one by one.

(1, 2), (1, 3), (1, 4): one divides into every number, so all of these work

(2, 3): 2 does not divide evenly into 3

(2, 4): 2 divides evenly into 4

(3, 4): 3 does not divide evenly into 4

This gives 4 pairs that work for an overall probability of 4/6 = 2/3.

3.141 * 15^2 * 18/3 = 4240.35

This is the exact answer, so there is actually no need for rounding.

According to the Triangle Inequality, the sum of any two sides of a triangle is greater than the third side. Let's call the third side x.

8 + 15 > x --> x < 23

8 + x > 15 --> x > 7

15 + x > 8 --> always true

x has to be between 8 and 22 inclusive, giving us 15 possible side lengths.

Let x be the number of months.

35 + 3x = 40 + 2x

3x = 5 + 2x

x = 5

It will take 5 months for the trees to be the same height, which is 35 + 3(5) = 50 inches tall.

Monomials are algebraic expressions consisting only of one term.

A) x^23 is a monomial

B) 2x + 2 is NOT a monomial; it has 2 terms

C) 19 is a monomial

D) 13^9 + 12 is NOT a monomial; there are two terms but they can be combined into one single number

E) x^9 + y^9 is NOT a monomial- it has 2 terms

F) y is a monomial

a_1, a_2, a_3, ... can also be written as a_1, a_1 + d, a_1 + 2d... where d is the common difference of the sequence.

a_4/a_2 = (a_1 + 3d)/(a_1 + d) = 2

a_1 + 3d = 2a_1 + 2d

d = a_1

a_5/a_3 = (a_1 + 4d)/(a_1 + 2d)

= 5d/3d

= 5/3

You can use the shoelace theorem.

-1      0

0       1

-2      0

0       -3

-1      0

-----------------

left side sum: 0 * 0 + 1 * (-2) + 0 * 0 + (-3)(-1) = 1

right side sum: -1 * 1 + 0 * 0 + (-2)(-3) + 0 * 0 = 5

area: (1/2) * |1 - 5| = 2

The four girls initially received 4/5 * 50 = 40 cents to divide among themselves. Whoever got the question correct got an extra 1/2 * 1/5 * 50 = 5 cents.

total number of committees = \(\binom{20}{4} = 4845\)

number of committees without any boys = \(\binom{10}{4} = 210\)

probability: \(1 - \frac{210}{4845} = \frac{4635}{4845} = \boxed{\frac{309}{323}}\)