The ratio of length to width in a rectangle is if the length is what is the

bacteria). Obligatory anaerobes require absence of oxygen. You are researching how a facultative anaerobe transitions from anaerobic to aerobic respiration along the length of the human intestine (small and large intestine), where oxygen levels – and with them respiration - vary from atmospheric levels of oxygen (aerobic respiration) to no oxygen (anaerobic respiration). You grow cultures of a facultative anaerobic bacteria in flasks with different levels of oxygen that mimic the conditions in the 7.5m long human intestines and collect data on the growth rates of the bacteria (number of bacterial colonies) under the different conditions. Time food spends in the small intestine, 2.5m long, is 4 hrs. The time taken for food to pass through the entire length of the intestine is between 24 and 72 hrs. To determine oxygen levels in your flasks, you use the ratio of oxygen to nitrogen, which you vary between 0 (no oxygen) and 0.25 (atmospheric levels of oxygen). You assume that for conditions where r<0.01 your bacteria will be obligatorily anaerobic, and aerobic respiration will be observed from r=0.05. If the oxygen ratio goes from 0.25 to 0 over 7.5 m, and rO2 = 0.25 – 0.03x (x=distance along the intestine) describes the relationship between oxygen ration and the length of path travelled by the bacteria in the intestine, how long will it take bacteria to pass from the small into the large intestine? Explain how you arrived at your estimate.

ose the breaking point is uniformly distributed on the chalk. Let X denote the length of the shorter piece and R the ratio of the lengths of the shorter to the longer piece. Then X has uniform distribution on [0; 1 2 ]. (a) (6pts) Find the probability density function of R. (b) (8pts) Find the mean and variance of R.

For each piece of glass, Kyle wants the width to length ratio to be 114 inches : 212 inches. Calculate the unit rate of the pieces and use that information to determine which of the following statements are true. Select TWO that apply. Kyle has a piece of glass that has a length of 412 inches. In order to fit in his mosaic, it must have a width of 9 inches. Kyle has a piece of glass with a width of 312 inches. Since it has a length of 6 inches, Kyle did not use it in his mosaic. Kyle wants the total length of his mosaic to be 2 feet. This will make the width of his mosaic 1 foot. Kyle has one piece in the mosaic with the dimensions of 134 inches long by 312 inches wide.

2)(x - 3)(x + 3) d. (x2 - 4)(x2+ 9) Value: 1 The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A? staplergraph.jpg a. $19.95 b. $18.95 c. $16.95 d. $19.25 Value: 1 If equation image indicator then x = a. 7 b. 1/5 c. 5 d. 1/7 Value: 1 A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three? a. 1/3 b. 0 c. 1/2 d. 1/4 Value: 1 If 6m + 4 = 8m, then 4m = a. 6 b. 2 c. 8 d. 4 Value: 1 In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator? a. 2 b. 4 c. 16 d. There is no y-intercept. Value: 1 Which of the following equations has both 2 and −4 as solutions? a. x2 + 6x + 8 = 0 b. x2 - 2x - 8 = 0 c. x2 + 2x - 8 = 0 d. x2 - 2x + 8 = 0 Value: 1 The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure? a. 22 b. 28 c. 35 d. 40 Value: 1 (3x-2y4)-3 = a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown? a. 28 b. 30 c. 32 d. 34 Value: 1 A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening? a. 20 b. 50 c. 70 d. 80 Value: 1 The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank? a. 21 b. 15 c. 19 d. 9 Value: 1 In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P? O and P graph.jpg a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9? a. 54 b. 6 c. 2/3 d. 3/2 Value: 1 A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting? a. 21 b. 11 c. 0 d. 55