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question:Calculate the product of the following numbers, expressing your answer as a decimal: dfrac{3}{4} times -dfrac{2}{5} times 2.5
answer:First convert the fractions to decimals: dfrac{3}{4} = 0.75 -dfrac{2}{5} = -0.4 Now we have: 0.75 times -0.4 times 2.5 = {?} phantom{0.75 times -0.4 times 2.5} = -0.75
question:Evaluate the function ( f(x) = tan left(frac{11x^2}{2} + 3right) - cos left(frac{15x}{2} + frac{17}{2}right) ) at the point ( x = -15 ).
answer:To evaluate the function at ( x = -15 ), we substitute ( -15 ) for ( x ) in the function: [ f(-15) = tan left(frac{11(-15)^2}{2} + 3right) - cos left(frac{15(-15)}{2} + frac{17}{2}right) ] Now, let's compute the individual terms: [ tan left(frac{11(-15)^2}{2} + 3right) = tan left(frac{11(225)}{2} + 3right) = tan left(frac{2475}{2} + 3right) = tan left(frac{2475 + 6}{2}right) = tan left(frac{2481}{2}right) ] [ -cos left(frac{15(-15)}{2} + frac{17}{2}right) = -cos left(frac{-225}{2} + frac{17}{2}right) = -cos left(-frac{208}{2}right) = -cos (-104) ] Now, we calculate these values: [ tan left(frac{2481}{2}right) approx -1.160 ] [ -cos (-104) = -cos (104) approx 0.489 ] So, ( f(-15) approx -1.160 + 0.489 approx -0.671 ). Hence, the function evaluated at ( x = -15 ) is approximately ( -0.671 ).
question:How do you account for repeated elements in a permutation problem?
answer:To account for repeated elements in a permutation problem, divide the total number of permutations by the factorial of the number of repetitions for each repeated element.
question:What is the area of an office with dimensions 13 units by 9 units?
answer:To find the area of a rectangle, we use the formula Area = Length × Width. In this case, the length of the office is 13 units and the width is 9 units. Let's calculate the area: Area = 13 units × 9 units = 117 square units So, the office has an area of 117 square units. The answer is expressed in square units because area is measured in units squared.