Balls are placed in a large box. Each ball is marked with a whole number from 1 to 20; each even number is represented by two balls, and each odd number is represented by one ball.

Two balls are drawn without replacement. Give the probability that both balls will be marked with an odd number.

(a)  

The measures of the angles of a quadrilateral are x, x + 10, x + 30, and x + 40 degrees. What is the largest angle, in degrees?

(Note: No need to include degrees symbol)

(a)  

In how many ways can the letters of the word EVENT be arranged so that the two Es are not all together?

(a)  

What is the sum of the roots of $$4x^2-2022x-2023=0?$$ Express your answer in lowest terms (improper fraction). 

(a)  

If $$a\ -b+c=1$$  , $$b-2c=0$$   $$2a+c=5$$  , what is the sum of $$a^2+b^2+c^2?$$  

(a)  

A cardboard manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 8 inches by 16 inches by cutting equal squares from the four corners and turning up the sides.

What is the volume (in cubic inches) of the box, if the length of the side of the square cut is 2 inches?

(a)  

For how many integers $$x$$  from 1 to 150 inclusive, is the fraction $$\frac{x}{150}$$  already in lowest terms?

(a)  

Let u and v be the roots of $$8x^2-3x+1=0$$  . Find the value of $$\log_2u+\log_2v.$$  

(a)  

In triangle ABC, D is the midpoint of BC. If the sides AB, BC, and CA have lengths 4, 12, and 8 respectively, then what is the numerical value of AD?

(a)  

A trapezoid has parallel sides of lengths 10 and 15; its two other sides have lengths 3 and 4.Find its area.

(a)