MIT

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question:f Mrs. Snyder used to spend 40% of her monthly income on rent and utilities, and her salary was recently increased by 600, making her rent and utilities only 25% of her monthly income, what was her previous monthly income?

answer:Let x be Mrs. Snyder's previous monthly income. 40% of her previous monthly income is 0.40x. Her rent and utilities used to be 40% of her monthly income, so 0.40x = rent + utilities. Her salary was recently increased by 600, so her new monthly income is x + 600. 25% of her new monthly income is 0.25(x + 600). Her new rent and utilities is 25% of her monthly income, so 0.25(x + 600) = rent + utilities. Since her rent and utilities are the same both before and after the salary increase, we can set the two equations equal to each other: 0.40x = 0.25(x + 600) 0.40x = 0.25x + 150 0.15x = 150 x = 150 / 0.15 x = 1000 Mrs. Snyder's previous monthly income was 1000. 1000 The answer is: 1000

question:Compute sin 150^circ.

answer:We can use the angle addition formula for sine to write sin 150^circ = sin (90^circ + 60^circ). Using the formula sin (A + B) = sin A cos B + cos A sin B, we have sin (90^circ + 60^circ) = sin 90^circ cos 60^circ + cos 90^circ sin 60^circ. Since sin 90^circ = 1 and cos 90^circ = 0, this simplifies to sin 150^circ = 1 cdot frac{1}{2} + 0 cdot frac{sqrt{3}}{2} = boxed{frac{1}{2}}. The answer is: frac{1}{2}

question:Bubba bought a new two-story warehouse. When empty, the first floor of the building contains twice as much floor space for storage as the second floor. The first items he brought into his empty building were several thousand boxes; and he put them all on the second floor, which filled one-quarter of the second floor storage space. If the boxes used up 5,000 square feet of storage space, how many square feet of storage space is still available in the building?

answer:If the boxes used up 5,000 square feet of storage space and that represents one-quarter of the second floor storage space, then the total storage space on the second floor is 5,000 * 4 = 20,000 square feet. Since the first floor contains twice as much floor space for storage as the second floor, then the total storage space on the first floor is 20,000 * 2 = 40,000 square feet. The total storage space in the building is the sum of the storage space on the first and second floors, which is 40,000 + 20,000 = 60,000 square feet. Therefore, there are 60,000 - 5,000 = 55,000 square feet of storage space still available in the building. 55000 The answer is: 55000

question:f James can make 4 hats out of one yard of velvet and he needs three yards of velvet to make a cloak, how much velvet does he need to make 6 cloaks and 12 hats in total?

answer:To make one cloak, James needs 3 yards of velvet. To make 6 cloaks, he will need 3 yards x 6 = 18 yards of velvet. To make one hat, James needs 1/4 yard of velvet. To make 12 hats, he will need (1/4) yard x 12 = 3 yards of velvet. Therefore, in total, James needs 18 yards + 3 yards = 21 yards of velvet. 21 The answer is: 21