Mrs. barkley is teaching a class in which the students are decorating gift boxes. she wants the students to decorate gift boxes using a ratio of 4 gems for every 3 ribbon flowers. dan used 20 gems for every 15 ribbon flowers. mary used 22 gems for every 18 ribbon flowers. nancy used 18 gems for every 24 ribbon flowers. jason used 26 gems for every 20 ribbon flowers.

Find the gradient of f(x, y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Complete the solution of the equation. find the value of y when x equals to 1 9x-5y=29

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.