Carry out the algorithm presented to get the minimal DFA equivalent to the twelve-state DFA drawn below. This DFA has alphabet {0, 1} and determines whether a string represents a number in binary that is divisible by twelve. The state set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. On input 0, the machine goes from state i to state 2i. On input 1, the machine goes from state i to state (2i 1). Give each of the equivalence relations produced by the algorithm and demonstrate that your last one is really the last one. Draw the resulting minimal DFA.

Write a program that uses a widgetviewer object to do the following: generate two random integers between 1 and 9 (inclusive). name one of them x, the other y. display them to the user using jlabel objects. create a jlabel object displaying the text "enter an operation number." create a jtextfield for the user's input. create a jbutton displaying the text "press here when you've entered your operation." use addandwait to add it to the widgetviewer object. when the user clicks the jbutton, evaluate operation in the following order to determine the one and only mathematical operation to perform on x and y. use a jlabel to display the result. if operation is between 1 and 10 inclusive, add x and y. if operation is evenly divisible by 4, subtract y from x. if operation is evenly divisible by 5, use integer division to divide y into x. if operation is an even number, use floating point division to divide y into x. if none of the other tests on operation apply, multiply x and y. note: operation can be negative or zero.

The following is an excerpt from a slide presentation. today we will inverse operations solving equations using inverse operations solving inequalities using inverse operations from which part of the presentation does the slide most likely come from? a. introduction b. outline c. body d. conclusion

What are some ways to use a range name in a formula? check all that apply. in the defined names group, click use in formula, and then select the desired name. begin typing the name in the formula, select a name from the autocomplete list, and use the arrow keys and tab key to enter the name in the formula. begin typing the formula, and then click and drag with the mouse to select the cells to include in the formula. right-click one of the cells in the range. click formula options, and use the dialog box to add the name.