carolyn makes and sells necklaces. the material to make each neckalce costs $3.20. she has 12 necklaces to sell and wants to make a total profit of $54. the following equation describes the situation. 12 (x minus 3.20) = 54
carolyn found that x = 7.7 and determined that she will make a profit of $7.70 on each necklace . which error did carolyn make?

Complete the equation of the line through (−10,3) and (−8,−8). use exact numbers.

Daniel expanded the expression as shown below -2(-8x-4y+3/4)=-10x-8y-11/4 what errors did he make? check all that apply

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).