Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 900 cm3 , the pressure is 160 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

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Step 1: Write all the rates in the problem (including the one you are trying to find) as
derivatives.

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Step 2: Identify the dependent variables in the derivatives. Find an equation relating
the dependent variables in the derivatives. You will often need a formula from
geometry for this.

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Step 3: Differentiate both sides of the equation from Step 2 with respect to the
independent variable time. The result will be an equation relating the rates (relating the
derivatives).

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Step 4: Substitute the values that you are given in the problem for the derivatives and
the variables and solve for the derivative for which the question is asking.

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Thanks for any help!!!

A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.

With a significance level of 1%, can the statement made by the company be accepted? What is the P-Value?

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 100 cm³, the pressure is 160 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

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Illustrate by noting relevant details on the normal curve below (label the x axis!), and shading the appropriate region. You may use your calculator to determine the probability, and you must show the syntax of your calculator inputs. Round final result to 4 decimals.

A report states that the total cholesterol level of children between the ages of 2 and 6 years is approximately normally distributed with a mean of 192 mg/dL (milligrams per deciliter) and a standard deviation of 27 mg/dL. Please answer all the questions.

a) What is the probability that one randomly selected child between the ages of 2 and 6 years has a total cholesterol level between 150 mg/dL and 200 mg/dL?

b) What is the probability that of 7 children between the ages of 2 and 6 years, exactly 4 have total cholesterol levels between 150 mg/dL and 200 mg/dL? Hint: Think of the binomial distribution!

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