Define a class for complex numbers. A complex number is a number of the form a + b*i where for our purposes, a and b are numbers of type double, and i is a number that represents the quantity sqrt(-1). Represent a complex number as two values of type double. Name the member variables real and imaginary. (The variable for the number that is multiplied by i is the one called imaginary.) Call the class Complex. Include a constructor with two parameters of type double that can be used to set the member variables of an object to any values. Include a constructor that has only a single parameter of type double; call this parameter realPart and define the constructor so that the object will be initialized to realPart + 0*i. Include a default constructor that initializes an object to 0(that is, to 0 + 0*i). Overload all the following operators so that they correctly apply to the type Complex: ==, +, -, *, >>, and <<. You should also write a test program to test your class. In the interface file, you should define a constant i as follows: const Complex i(0,1);

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Researchers measured the data speeds for a particular smartphone carrier at 50 airports. the highest speed measured was 78.1 mbps. the complete list of 50 data speeds has a mean of x overbarequals16.11 mbps and a standard deviation of sequals18.65 mbps. a. what is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. how many standard deviations is that [the difference found in part (a)]? c. convert the carrier's highest data speed to a z score. d. if we consider data speeds that convert to z scores between minus2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant? a. the difference is nothing mbps.

Read this excerpt from helen keller’s autobiography, the story of my life. have you ever been at sea in a dense fog, when it seemed as if a tangible white darkness shut you in, and the great ship, tense and anxious, groped her way toward the shore with plummet and sounding-line, and you waited with beating heart for something to happen? i was like that ship before my education began, only i was without compass or sounding-line, and had no way of knowing how near the harbour was. "light! give me light! " was the wordless cry of my soul, and the light of love shone on me in that very hour. . the morning after my teacher came she led me into her room and gave me a doll. the little blind children at the perkins institution had sent it and laura bridgman had dressed it; but i did not know this until afterward. when i had played with it a little while, miss sullivan slowly spelled into my hand the word "d-o-l-l." i was at once interested in this finger play and tried to imitate it. when i finally succeeded in making the letters correctly i was flushed with childish pleasure and pride. running downstairs to my mother i held up my hand and made the letters for doll. i did not know that i was spelling a word or even that words existed; i was simply making my fingers go in monkey-like imitation. in the days that followed i learned to spell in this uncomprehending way a great many words, among them pin, hat, cup and a few verbs like sit, stand and walk. based on this excerpt, which words best describe helen keller?