Kate and Nate play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Kate makes 6 goals and 3 penalties, ending the game with 6 points. Nate earns 8 goals and 9 penalties and ends the game with -22. Write a system of equations that describe Kate and Nate's outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty

One integer is 5 more than another. their product is 104. find the integers

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).

Two triangles can be formed with the given information. use the law of sines to solve the triangles. b = 49°, a = 16, b = 14