Aresearcher is using a chi-square test to determine whether people have any preferences among three brands of televisions. the null hypothesis for this test would state that
answer
a. in the population, one brand is preferred over the other two
b. one-third of the population prefers each brand
c. there are real preferences in the population
d. one-third of the sample prefers each brand

G(x) = 2 sin(2x - π) + 4. using complete sentences, explain how to find the minimum value for the function.

Ijust need to see how to do this. so you don’t have to answer all of them just a step by step explanation of one.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.