The math team sells crunchy and fruity trail mixes to raise money. the ratio of fruit to nuts in each mix and the price they charge for an 8-oz (or 1/2-cup) bag of each mix are given in the table below. [hint: the ratio of fruit to nuts in the crunchy trail mix is 1: 3. so, 1/4 of each bag is fruit and 3/4 of each bag is nuts.] ratio of fruit to nuts price of an 8-oz (or 1/2 cup) bag crunchy trail mix 1: 3 $2.50 fruity trail mix 5: 3 $3.50 they have 30 cups of fruit and 50 cups of nuts to use in their trail mixes. so, they need to know how many bags of each type of mix they should they make. they let c represent the number of bags of crunchy trail mix and f represent the number of bags of fruity trail mix. which set of inequalities below represents the conditions?

a. 1c + 3 f ≤ 30 5c + 3 f ≤ 50 c ≥ 0, f ≥ 0
b. 1c + 5 f ≤ 60 3c + 3 f ≤ 100 c ≥ 0, f ≥ 0
c. 0.25c + 0.625f ≤ 60 0.75c + 0.375f ≤ 100 c ≥ 0, f ≥ 0
d. 0.25c + 0.625f ≤ 30 0.75c + 0.375f ≤ 50 c ≥ 0, f ≥ 0

Negative 5 1/12 + negative 4 1/4 + 6 3/4

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of emdangl be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.