Consider the network flow studied in Example 2. Determine the possible range of values of x1 and x2.

## What is the volume of grain that can be stored in the siloA grain silo has a cylindrical shape. Its diameter is 19 , and its height is 38 . What is the volume of grain that can be stored in the silo? |

## Eye colour probabilityIn a certain population of people, 20% are blue-eyed and 80% are brown-eyed. Also, 6% of the blue-eyed people are left-handed and 14%of the brown-eyed people are left-handed. |

## Information about rings and idealsLet I be an ideal of R and let S be a subring of R. prove that I(intersection)S is an ideal of S. ALSO, show by some example that not every ideal of a subring S of a ring R |

## Express the hydrostatic force against one sideA trapezoid with bases 4 m and 6 m is partially submerged vertically in water so that the top is 1 m above the surface and the bottom is 1 m below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate.. |

## What is the fastest rate that the secret spreadsWhat is the fastest rate that the secret spreads? Show your justification. Determine the Maximum number of people that will hear the rumor according to this model. |

## Calculate the monthly paymentA loan of $9,800 is to be repaid with monthly payments for 12 years at 3.2% interest compounded monthly. Calculate the monthly payment. |

## Find out the number of bedroom sets and living roomIf a bedroom set sells for $10,000 and a living room set sells for $18,000, determine the number of bedroom sets and living room |

## What is the domain of this modelWrite an equation to represent the volume of an open box constructed by cutting congruent squares from the corners of a 24" by 14" piece of cardboard. |

## Explain variables that would tell how many unitsDefine variables that would tell how many units to purchase from each source. Develop an objective function that would minimize the total cost. |

## What is the probability that the two choose the same numberA student and a professor each choose a number between 1 and 7 (1 and 7 are both possible choices). What is the probability that the two choose the same number? |

## Show that a tree without a vertex of degreeProve Theorem 1.5.1. Theorem 1.5.1. The following assertions are equivalent for a graph T: Show that every tree T has at least ?(T) leaves.Show that a tree without a vertex of degree 2 has more leaves than other vertices. Can you find a very short pr.. |

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