Please solve and explain.

1. A telephone pole 35ft. tall has a guy wire attached to it 5 ft. from the top and tied to a ring on the ground 15 feet from the base of the pole. Assume that an extra 2 feet of wire are needed the wire to the ring and the pole. What length of wire is needed for the job? Give an answer to the nearest tenth of a foot.

Real-life examples of parabolic shapes : Select and discuss two examples of real life objects that incorporate the parabolic shape. Explain why the parabolic shape was used for the objects. |

Ending inventory levels : Financial Statements of ABC Corp. indicates that ending inventory levels in 2010 and 2011 were $200,000 and $350,000 respectively. Net Sales for 2010 and 2011 were $5,000,000 and $5,500,000 respectively. Cost of Goods sold for 2010 and 2011 were $.. |

Compute cohen-s d to measure effect size for both test : Compute Cohen's d to measure effect size for both test ( standard deviation 20 and 10) If the population standard deviation is 10. |

Geometrical constructions-tangents to circle : Let C be a circle with center P and X a point in the exterior of C. Construct the two tangent lines to the circle that pass through X. |

Length of hypotenuse : A telephone pole 35ft. tall has a guy wire attached to it 5 ft. from the top and tied to a ring on the ground 15 feet from the base of the pole. |

Employer payroll tax expense : The company is subject to state unemployment taxes at the rate of 2% and federal unemployment taxes at the rate of 0.8%. By May 15, some employees had earned over $7,000, so only $9,000 of the $20,000 weekly gross pay was subject to unemployment t.. |

Describe statistical experiment to test the belief : Salaries upon graduating than are graduates of other programs. Describe a statistical experiment that could help test your belief. |

Determine the total dividends paid to each class : Wade's outstanding stock consists of 40,000 shares of noncumulative 7.5% preferred stock with a $10 par value and also 100,000 shares of common stock with a $1 par value. |

Area of triangular sail : A triangular sail has an area of x^2 + 5x + 6 square meters and a height of x + 3 meters. Find the length of the sail's base. |

## Determine location in the planeFormulate a mathematical program that can be used to determine where the "hub" should be located in the plane. Clearly define your decision variables, objective and constraints |

## Fourier series-expansions and differentiationLet f (x) = |x| for x greater or equal to -1, less than or equal to +1. Write the Fourier series for f (x) on [-1,1]. Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1] |

## Describe the shape of the histogramDescribe the shape of the histogram. The probability that there are five first-shift workers. The probability that there are four second-shift workers. |

## Minimum sample size analysisOne researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.25 hour is desired. Past studies suggest that a population standard deviation of 1.7 hours is reasonable. |

## Determining semidirect productIf H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H. |

## Symbolic logic problem-proofConstruct a formal proof which shows that the sentence below is a theorem of predicate logic. *the E's are existential quantifiers (usually designated by backwards E's). the & are "and". Do not use quantifier negation rules. |

## Factor the polynomial and state the multiplicityFactor the polynomial and state the multiplicity of each zero and zeroes of a real polynomial |

## Triangle inequality theoremWrite a compound inequality to describe tha range of possible measures for side c in terms of a and b. |

## Probability of a singled parent in us military from the armyProbability of a singled parent in US military from the army. This table shows the breakdown of 89 thousand single parents in the us military in a certain year. All numbers are in thousands and rounded to the nearest thousand |

## Subtracting, adding and multiplying two complex numbersSubtracting, Adding and multiplying two complex numbers |

## Determining partial ordering relationLet A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff m|n. Show that this relation is a partial ordering relation. Draw its Hasse diagram. |

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