Consider the sequence: 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1,...
How many times does the number '1' occur in the first 63 terms?
The vertices of a triangle are (-1, 3), (1, 1), and (7, 1). Find its area.
In the diagram, all the dots are equally spaced. Segment `bar(AB)` is drawn. How many ways are there to choose point C from the remaining points so that triangle ABC is isosceles with AB=AC?
In the expression `(a)/(b)+(c)/(d)+(e)/(f),` each letter is replaced by a different number from 1, 2, 3, 4, 5, 6.
What is the largest possible value of the expression?
A certain company allows employees to retire when the sum of their age and number of years worked equals 85. Amie is 45 years old and has worked 18 years. If she works continuously until she retires, how old will she be when she can retire?
A 1 litre carton for juice uses 500 cm2 of cardboard to make and costs $5.25 to buy.
A mathematically similar 500 ml carton for juice uses 300 cm2 of identical cardboard to make and costs $2.60 to buy.
Which size carton is better for the environment in terms of cardboard use?
If `x=1440-:3` , `y=x-:3` , and `z=x+y` , then the value of `z` is
Triangle `ABC` is a right triangle with `/_C=90^O` . If `bar(AB)=13` , `bar(BC)=5` and `bar(AC)=3xxDC` , find `bar(BD)` .