Here we work in the system of integer polynomials. Those are polynomials of the Form f(x)=rnxn+···+r1x+r0 where every coefficient is an integer. General question: When does some combination of the polynomials ax + b and cx + d equal 1 ? That is, when do there exist integer polynomials P(x) and Q(x) with P(x)·(ax + b) + Q(x)·(cx + d) = 1 ? We concentrate here on cases when c = 0. (a) Prove: No combination of 2x + 5 and 3 can equal 1. That is, no integer polynomials P (x), Q(x) can satisfy: P (x)·2x + 5 + Q(x)·3 = 1. (b) Find a combination of 2x + 5 and 4 that equals 1. (c) Does some combination of 15x+9 and 25 equal 1? How about 15x+9 and 20? Explain your reasoning. (d) Investigate further examples of ax + b and d, deciding in each case whether 1 is a combination. What patterns do you detect? Can you prove that some of your observed patterns always hold true?

Arianna is buying plants for her garden. she buys 15 flowering plants for $96. pink flowering plants sell for $8, and purple flowering plants sell for $5. how many pink flowering plants did arianna buy? i figured out the answer! the answer is 7. 8x +5y = 96 plug in 7 for x 8 (7) + 5y = 96 56 + 5y = 96 subtract 56 from both sides 5y/y = 40/5 y = 8 she bought 7 pink and 8 purple plants

Identify all the cases where non-probability sampling is used when attempting to study the characteristics of a large city. studies on every subject in the population divide a population in groups and obtain a sample studies with a limited amount of time demonstrate existing traits in a population studies with the nth person selected

Overproduction of uric acid in the body can be an indication of cell breakdown. this may be an advance indication of illness such as gout, leukemia, or lymphoma.† over a period of months, an adult male patient has taken nine blood tests for uric acid. the mean concentration was x = 5.35 mg/dl. the distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl. (a) find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. what is the margin of error? (round your answers to two decimal places.) lower limit upper limit margin of error (b) what conditions are necessary for your calculations? (select all that apply.) σ is unknown n is large σ is known normal distribution of uric acid uniform distribution of uric acid (c) interpret your results in the context of this problem. there is not enough information to make an interpretation. the probability that this interval contains the true average uric acid level for this patient is 0.05. the probability that this interval contains the true average uric acid level for this patient is 0.95. there is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. there is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. (d) find the sample size necessary for a 95% confidence level with maximal margin of error e = 1.10 for the mean concentration of uric acid in this patient's blood. (round your answer up to the nearest whole number.) blood tests