Question: Let E be the splitting field of X4+1 over Q. How many intermediate fields are normal extensions of Q? Show your work and explain your answer.

Linear programming model to maximize the profit : Formulate a linear programming model for this problem. |

Determining odds student gets questions correct : Determine odds student gets more than 14 questions correct? Determine the odds student gets exactly 12 questions correct? |

Find optimum level of production and maximize profit : Bavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets-What is the optimal level of production of wine decanters? |

Compilation of performa balance sheet : Compilation of Performa Balance Sheet - Find the specific option available to the company for meeting its resource needs, if the bank declined the loan request and Please quantify and compile an appropriate proforma balance sheet for the situation. |

The number of intermediate fields : The number of intermediate fields which are normal extensions. |

Hypothesis testing by chi-square distribution : Advertisers need to know which age groups are likely to see their ads. Purchasers of 120 copies of Cosmopolitan are shown by age group Perform the chi-square test for a uniform distribution at α = .01 |

Computation of implicit interest of the bond : Computation of implicit interest of the bond and Suppose your company needs to raise $10 million by issuing 10-year zero coupon bonds |

What the market price is given the price leaders output : Compute the profit-maximizing output for the price leader. Illustrate what the market price is given the price leader's output in (c). Elucidate how much does each competitive firm produce. |

Find the specific option available to the company : Preparation of Performa Balance Sheet from the given ratios and other information - Find the specific option available to the company for meeting its resource needs if the bank provided a loan of $200,000 as sought by the company? |

## Find the sum or difference as a product of sines or cosinesFind the sum or difference as a product of sines or cosines. |

## Cyclic groupA cyclic group is a special kind of group that has many similarities with modular arithmetic. |

## Factoring a problem of computing on input a positive intgerFactoring is the problem of computing, on input a positive integer n, a factorization of n in terms of prime powers |

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

## Prepare a research paper on two independent variablesPrepare a research paper on two independent variables |

## Chart of the topological manifoldDe?nition of smoothness of functions on a smooth manifold is chart independent and hence geometric. |

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