Alice made 48 cupcakes. she froasted 1/2 of the cupcakes. she put sprinkles on 1/3 of the frosted cupcakes. she ate 1/4 of the frosted cupcakes that had sprinkles. what is the total number of cupcakes that alice ate?

Fa bus driver leaves her first stop by 7: 00 a.m., her route will take less than 37 minutes. if she leaves after 7: 00 a.m., she estimates that the same route will take no less than 42 minutes. which inequality represents the time it takes to drive the route, r?

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).

Given the quadratic function f(x)=3x^2-24x+49 a. use “completing the squares” to convert the quadratic function into vertex form b. state the vertex c. find the x and y intercepts d. graph the function