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Solve for N in the expression (23 x 52) − sqrt(144) + N = 240.

Mathematics

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Answer

52\text{52}

Step-by-step solution

4 steps
  1. Evaluate the terms in the expression.

    First, calculate 232^3 and 525^2.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8 52=5×5=255^2 = 5 \times 5 = 25

    Next, calculate their product.

    23×52=8×25=2002^3 \times 5^2 = 8 \times 25 = 200

    Then, find the square root of 144.

    144=12\sqrt{144} = 12
  2. Substitute the calculated values into the given expression.

    The expression is (23×52)−144+N=240(2^3 \times 5^2) - \sqrt{144} + N = 240.
    Substitute the values:

    200−12+N=240200 - 12 + N = 240
  3. Simplify the left side of the equation.

    188+N=240188 + N = 240
  4. Solve for NN.

    Subtract 188 from both sides of the equation.

    N=240−188N = 240 - 188 N=52N = 52

    The value of NN is 52\boxed{\text{52}}.

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