tertre

90.

The total number of marbles: \(12+8+4+16=40\)

Blue Marble: \(\frac{4}{40}=\frac{1}{10}\)

Red marble: \(\frac{12}{40}=\frac{3}{10}\)

So, the answer is just \(\frac{1}{10}*\frac{3}{10}=\boxed{\frac{3}{100}}\)

89. The probability of choosing a dime first is \(\frac{2}{10}=\frac{1}{5}\) .

Next, picking a quarter without replacement is just \(\frac{3}{10}\).

Multiplying, we get \(\frac{1}{5}*\frac{3}{10}=\frac{3}{50}\)

81. (5x)^1/2=square root of 5x, which is \(\sqrt5x, B\)

No problem, 

CPhill, can I use your glasses? 

Solution:

This triangle is isosceles, and so the altitude to the side with length 6 must hit that side at its midpoint. Thus our triangle is divided into two right triangles with hypotenuse \(5\) and one side of length \(3\). Thus each of these is a \(3-4-5\)  triangle, and each one has area \(\frac{3 \times 4}{2} = 6\), for a total area of \(\boxed{12}\).

Solution:

a^2+b^2=c^2

So, 7^2+3^2=c^2

m^2=58

m=7.61- 8

7+3>m

m<10

So, 5,6,7,,8,9

Aren't there 13 diamonds?

So, 13/52*12/51=1/4*12/51=3/51 

Ah, here it is!

The vertex has to be right in between them, so the vertex is \((0, 2)\). Now, we use the equation \((x-h)^2=4p(y-k)\). \(p = -2\) , because that is the directed distance between the vertex and focus. We get than \(x^2 = -8(y-2)\), so 

\(\boxed{y = -\frac{1}{8}x^2+2}\) is the desired equation.

I'll provide a solution later:

 1. \(y = -\frac{1}{8}x^2+2\)

Is it https://www.desmos.com/calculator/tfl8wyadtm