The area of a rectangular barnyard is given by the trinomial 6x^2 + 7x -20. What are the possible dimensions of the barnyard? Use factoring.

Sarah is collecting recyclables for a science project. on the first day she collected 35 recyclable objects. on the second day she had a total of 52 recyclables. on the third day she had a total of 69 recyclables. determine if the scenario describes an arithmetic or a geometric sequence. then, write the recursive formula for the sequence described.

The thickness of photoresist applied to wafers in semiconductor manufacturing at a particular location on the wafer is uniformly distributed between 0.2070 and 0.2171 micrometers.(a) determine the proportion of wafers that exceeds 0.2125 micrometers of photoresist thickness. (round your answer to 3 decimal places.)enter your answer in accordance to the item a) of the question statement(b) determine the mean of x. (round your answer to 4 decimal places.)enter your answer in accordance to the item b) of the question statement micrometers(c) determine the variance of x. (round your answer to 8 decimal places.)enter your answer in accordance to the item c) of the question statement micrometers2

Suppose a batch of steel rods produced at a steel plant have a mean length of 150 millimeters, and a standard deviation of 12. if 100 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.5 millimeters?