Simple interest is the amount of money the borrower pays based on the amount borrowed (the principal) for a given period of time (months or years) It is calculated this way: $I = p r t .$ If a person borrows $20,000 ( p ) to buy a car, pays 6.95% interest ( r ), and takes 5 years ( t ) to repay the loan, how much will the borrower pay in simple interest?

Murietta is planning a party at a bowling alley. She wants to rent two lanes. The rental fee for the two lanes is $40 plus the rental of$2 per pair of bowling shoes. a. Write an equation in slope-intercept form to represent this situation. b. Murietta is renting two lanes and inviting 9 people. If everyone including herself rents shees, what will the cost of the party be?

In international play, the maximum length of a soccer field is $\frac { 525 x + 100 } { 5 x + 1 }$ meters and the maximum width is $\frac { 400 x + 85 } { 5 x + 1 }$ meters. Each linesman is responsible for watching half of the field's perimeter. How many meters along the border of the field must the linesman watch during the game?

A rectangular window has a length of $\frac { 6 a } { 3 a - 1 }$ meters and a width of $\frac { 4 } { 3 a - 1 }$ meters. How many feet of trim will be painted if the trim goes around three sides of the window (both lengths and one width)?

Find the slope of the line passing through the given pair of points.

$(3,2)$ and $(-1,2)$

John is 500 miles from home. He is traveling toward home at a constant rate of 65 miles per hour. The distance d ( in miles ) away home after t (in hours) is given by the equation $d = 500 - 65 t .$ a. Use a graphing calculator to make a table of values with the values of t from 0 to 5 in increments of 1. b. How far away from home John is after 4 hours?

A communication satellite with a 24-h period hovers over a fixed point on Earth. Why is it placed in orbit only in the plane of Earth’s equator? (Hint: Think of the satellite’s orbit as a ring around Earth.)

State whether each statement is true or false and briefly explain why. If the statement is false, try to “fix it” by modifying the given statement to a new statement that is true. For the partial derivative $\frac{\partial^{2} f}{\partial x \partial y}$, the order of partial derivatives does not matter.

If possible, find the absolute maximum and minimum values of the following functions on the region R. $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 4 ; R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \lt 4 \right\}$

Write the equation $5x + 3y = 9$ in slope intercept form.

According to a city bylaw, the area of a store's sign cannot exceed 900 square decimeters. Write and graph an inequality to represent the situation.

Determine if the premise and the conclusion use inductive or deductive reasoning. Explain your choice. Premise: The measures of two angles in a triangle add up to $80 ^ { \circ } .$ Conclusion: The third angle is $100 ^ { \circ } .$

Luca and Paolo buy old bikes for a few dollars each, and then fix them up so that they can sell them for a profit. If they bought a rare tandem bike for $8, spent an additional$150 on the bike for paint and parts, and sold it at a 285% profit, then how much money did they sell the bike for? a. If profit means the amount of money Luca and Paolo made affer taking into account what they spent, write an equation to find how much the bike sold for. b. Solve the equation to find the sale price of the bike.

Write the converse of the following statement: If a number is a whole number, then the number is a natural number. Then determine whether the new statement is true or false. If false, give a counterexample.