a) Let M>0, and let f:[a,b]-->R be a function which is continuous on [a,b] and differentiable on (a,b), and such that |f'(x)| <= M for all x belonging to (a,b) (derivative of f is bounded). Show that for any x,y belonging to [a,b] we have the inequality |f(x)-f(y)| <= M|x-y|. *apply mean value theorem.

b) Let f:R-->R be a differentiable function such that f' is bounded. Show that f is uniformly continuous. Use part a from above.

What volume (in ml) of this solution would be used : An aqueous solution that contains 329 ppm of KNO3 is being used to feed plants in a graden. What volume (in mL) of this solution is need to prepare 9 L of a solution that is 23 ppm in KNO3? |

Find seasonally adjusted sales for second quarter : The same for each of the four quarters next year. The seasonal factor for the second quarter is 145. Determine the seasonally adjusted sales for the second quarter of next year. |

Proof by using intermediate value theorem : Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x). |

Using periodic system cost of goods purchased : Sampson Company's accounting records show the following for the year ending on December 31, 2010. Using the periodic system, the cost of goods purchased is? |

Proof lipschitz continuous : Let M>0, and let f:[a,b]-->R be a function which is continuous on [a,b] and differentiable on (a,b), and such that |f'(x)| |

How many ml ethanol solution would you need : How many mL of a 22.5% (v/v) ethanol solution would you need to measure out in order to have 12.5 mL of ethanol? The Molar Mass of ethanol is 46.07g/mol. |

Proportion of americans drink more than eight servings : Servings of water is approximately normally distributed with a standard deviation of 1.4 serving, what proportion of americans drink a. more than the recommended 8 servings. |

Apply the theory of constraints to your own working : Apply the Theory of Constraints to your own working environment (past or present). Explain why your organization doesn't have unlimited resources (space, inventory, product line, etc) |

Are rental payments for a business tax deductible : Why do you think that mortgage interest and real estate taxes for a personal residence are tax deductible, but rent payments are not? Are rental payments for a business tax deductible? |

## Production lot size-waiting line problemKellam Images prints snack food bags on long rolls of plastic film. The plant operates 250 days a year. The daily production rate is 6000 bags, and the daily demand is 3500 bags. The cost to set up the design for printing is $300. The holding cost.. |

## Highlighting the part indicated by given intervalFind a definite integral that represents the arc length of the curve over the indicated interval and observe that the length cannot be evaluated with the techniques studied so far |

## Revenue function and graphingA small gift shop is trying to determine the number of gift items it can sell to maintain a monthly revenue greater than $10,000. The revenue function for this business is R = -0.10N2 +70N, where R=monthly revenue and N=number of gift items sold p.. |

## Interpreting graphs and charts in mathIn a percent change graph of an average teachers annual salary the bars representing successive years are either unchanged or decreasing in size. |

## Calculate the expected rate of returnGiven the following probability distribution for asset Y, compute the expected rate of return, variance, standard deviation, and coefficient of variation for the assets. |

## Calculating probabilitiesWhat is the total defect rate? I came up with 6%. A randomly selected product was defective. What is the probability that it came from Plant A? |

## Solve the system with any methodSolve the system with any method - Find which of the given two pairs are solutions for the following system |

## Expected value indifference probabilities expected utilityExpected value, indifference probabilities, expected utility, For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35. |

## A coin is flipped eight times where each flip comes upA coin is flipped eight times where each flip comes up with either heads or tails how many possible outcomes?a) contain exactly 3 heads |

## Biologists stocked a lake with 400 fishBiologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 7000 |

## Solving the word problem using the properties of similar triSolving the word problem using the properties of similar triangles |

## Evaluate the sequence generated by generating functionsEvaluate the sequence generated by generating functions |

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