This phenomenon is modeled with a differential equation,

and that equation may be solved to give

T(t) = TA + [To-TA]b¹

where T(t) is the varying temperature of the object at a given time, t, TA is the surrounding ambient temperature, To is the initial temperature of the object, and b is a constant that depends on the material the object is composed of and how fast it heats or cools.

Suppose you decided to make a cup of hot tea heated to 220 °F in the kitchen that is at 70 °F.

1.Solve the above equation for the constant b.

2. If the cup of hot tea cooled to 170 °F in 10 minutes, find the value of the constant b in the above equation. Express your answer to 5 decimal places.

3.Solve the above equation for t.

The equation |pl = 2 represents the total number of points that can be earned or lost during one turn of a game. which best describes how many points can be earned or lost during one turn? o o -2 2 oor 2 -2 or 2 o

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

21 type the correct answer in each box. if necessary, round your answers to the nearest hundredth the vertices of abc are a(2,8), b(16, 2), and c(6,2). the perimeter of abc is units, and its area is square units