right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.

Q.1 dr. frank needs to choose 3 students from her advanced biology course to attend a conference in hawaii. the course has 40 students. which of the following methods could dr. frank use to choose a simple, random sample of 3 students? select all that apply. 1 dr. frank could have the students line up from shortest to tallest, then use her birthdate, 2/5/39, to select 3 students from the line (the 2nd student, the 5th student, and the 39th student). 2. dr. frank could upload her class roster into a spreadsheet and use a ranom-number generating function to produce 3 random numbers. the students whose names are located in the rows with these 3 numbers on the spreadsheet would be chosen. 3. dr. frank could choose the students with the 3 highest grades in the class. 4. dr. frank could count to three, then the first students to come to the front of the classroom and grab a golden ticket from her hand would be selected. 5. dr. frank could ask all students to write their name on a card, place all of the cards in a hat, shake the hat, and then pull 3 cards out from the hat. the students whose names appear on those 3 cards will be selected. 6. dr. frank could ask for volunteers to go to the conference, then choose the first 3 students who raise their hands. q2. now, choose one of the methods that you did not select and explain why this method would not result in a simple, random sample:

The height of a certain banner is equal to one third of its length. if the banner is 5 feet tall, write an equation that can be used to find the banner's length,l, in feet

The perimeter of a rectangle is 40 inches. the table shows some of the possible dimensions for the length and area of the rectangle. length (inches) area (square inches) 2 36 7.5 93.75 10 100 12.5 93.75 18 36 given that the area of the rectangle is dependent on the length of its sides, which graph could best be used to display the relationship shown in the table?