As The Wizard of Oz drifts away from Emerald City in his hot air balloon, Dorothy watches him leave. She notices that he is traveling at a constant altitude and at a speed of 20 miles per hour. She wonders how far he is above the ground. At one instant, the Scarecrow tells her that the angle of elevation to the Wizard's balloon is 24º. Three minutes later, the Scarecrow tells her that the angle of elevation to the balloon is now 21º. Using the information provided by the scarecrow, calculate the altitude of the balloon. Give your answer in feet, rounded to 3 decimal places.

Select true or false to tell whether the following conditional p q is true or false. use the truth table if needed. if a week has seven days, then a year has twenty months.

Steve wants to develop a way to find the total cost of any item including sales tax. the sales tax in his city is 6%. his friend jenna writes the expression x + 6x where x is the cost of the item. explain whether her expression is correct based on the situation.

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?