Design a deterministic finite automaton that accepts all binary strings that correspond to a value divisible by 3. For example, it should accept 110 (since 6 is divisible by 3), but not 101 (since 5 is not divisible by 3).

Show by example that these three statements are generally false:(a) A and AT have the same nullspace.(b) A and AT have the same free variables.(c) If R is the reduced form rref(A) then RT is rref(AT ).

You are given the following information about a new binary operator valid for a,b,c E R+, known as smiley-face: I. In order of operations, it takes precedence over Multiplicaiton/Divison. That is, the order of operations is now: P,E,Ⓒ,MD,AS II. aa = a III. aⒸ (boc) √(ab).c Note that THIS smiley-face operator is actuall self consistent. To wit: Using the definition: a (aa) √(aa).a √a·a Evaluating the parentheses first: a (aⒸa) = a Ⓒa = a That is to say: I BELIEVE it is self-consistent! Let me know if I've messed up again!!! = = = Here is the question. Solve for x ER: 2023 Ⓒ (170x) = 357 = √a² = a

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Identify the main operator of the sentence: P → ((~P V Q) & ~R) O P>((~P v Q) & ~R) O P → MP V Q) & ~R) O P → ((~PVQ) & ~R) OP → ((~PV Q) & R) O P → ((~PV Q) & MR)

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.

Just choose one (1) from the given formula for each no.