A charitable organization is having a raffle for a single prize of $7000. Each raffle ticket costs$3, and 9000 tickets have been sold. (a) Find the expected gain for the purchaser of a single ticket. (b) Find the expected gain for the purchaser of two tickets.

Determine by substitution which of the given numbers, if any, satisfy the given equation. $10-7 x=-x^{2} ; 2,4$

Find the slope and the y-intercept of the graph of the linear equation. y = -3.5x - 2

A 5.0 kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is $3.0 \mathrm{m} / \mathrm{s}^{2}$, find the force exerted by the rope on the bucket of water.

Evaluate each function over the domain {-2, -1, 0, 1, 2, 3}. As the values of the domain increase, do the values of the range increase or decrease? $y=2.5^{x}$

Kevin's office cubicle measures 8 ft by 12 ft. Write an equation to find the amount x that should be added to the current length and width to double the area.

Add commas where necessary. Cross out incorrect commas using the delete symbol. Like most summer camps, this one offers swimming canoeing and hiking.

Which compound forms the higher concentration of hydrate at equilibrium, PhCOCHO or $\mathrm{phCH}_{2} \mathrm{CHO}$? Explain your reasoning

Determine the radius and interval of convergence of the following power series. $\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{k}}{5^{k}}$

What alkene would yield 2,2-dimethoxycyclopentane-1,3-dicarbaldehyde on treatment with $O_3$ followed by $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{S}$?

Determine whether the following series converge absolutely, converge conditionally, or diverge. $\sum_{k=1}^{\infty} \frac{(-2)^{k+1}}{k^{2}}$

Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth.

$$3 x^{2}+47 x=-30$$

Find the general solution. of the following equations. Express the solution explicitly as a function of the independent variable. $x^{2} y^{\prime}(x)=y^{2}$

Add commas where necessary. Cross out incorrect commas using the delete symbol. On Saturday morning I need to mow the lawn, pull the weeds and sweep the front porch.