BuilderBoi

The only possibilities are: 69,78,87,96. Of these, the only one that works is 69. nice :)

it is all the intervals of which the value of the function either goes up(increases) or goes down(decreases)

Your answer is incorrect guest. You need to account for the side lengths OQ and PO, each of which have a side length of 15. 

The circumference of a complete circle would be $30\pi$, so the circumference of $3 \over 4$ of the circle would be $22.5\pi$

We also have to add 30 to the circumference, so the circumference is $\color{brown}\boxed{22.5\pi+30}$

15 out of 50 = 30%

30% of 4,500 = $\color{brown}\boxed{1,350}$

There are 3 x 2 ways to choose 2 red marbles

There are 11 x 10 ways to choose 2 marbles

So, the answer is $\color{brown}\boxed{{3 \times 2} \over {11 \times 10}}$. You have to simplify the fraction.

$a$ = adult tickets sold

$s$ = student tickets sold

$2a+9s=68$

$10a+s=76$

Solve for the system, and you find that a student ticket costs $\color{brown}\boxed{6}$, and you can find what an adult ticket costs by subsituting.

Every 12 days, they ate $1 \over 4$ of the rice. 

This means that they ate $1 \over 8$ of the rice every 6 days. 

So, ${3 \over 4} - {1 \over 8} = {5 \over 8}$.

This means that ${5 \over 8} = 21$. By solving the ratios, we find that Jason originally had $\color{brown}\boxed{33.6}$ kg of rice.

cos = $\text{adjacent}\over\text{hypotenuse}$

The hypotenuse is always the longest side, and adjacent is the one side that is next to the relative position of the vertice that is being "cos'ed". For example:  $\color{brown}\boxed{{\cos A} = {5\over 9}}$. You can solve the rest from here. Good Luck!

Plug 27 in to the quadratic: $27 = -6t^2+43t$. 

Subtract 27 from both sides to make it a quadratic: $0 = -6t^2+43t-27$

Plug it in to the quadratic formula: $t ={-43 \pm \sqrt{43^2-4\times -6 \times -27} \over 2\times -6}$

There are 2 solutions, one at $t\approx6.5$ seconds, and the other at $t\approx0.7$ seconds. 

We want the smaller answer, so  $\color{brown}\boxed {t \approx 0.7}$

Make a system of equations: 

x + y = 5

15x+10y=60

x = 2 y = 3

So, 2 gallons of 15% alcohol and 3 gallons of 10% alcohol.