answer:The archer shoots 200 arrows 4 days a week, so he shoots a total of 200 x 4 = 800 arrows per week. He is able to recover 20% of his arrows, so he can reuse 800 x 20% = 160 arrows per week. This means he needs to buy 800 - 160 = 640 new arrows per week. Each arrow costs 5.5, so the total cost of the arrows is 640 x 5.5 = 3520. His team agrees to pay for 70% of the cost, so he needs to pay 30% of the cost himself. 30% of 3520 is 0.30 x 3520 = 1056. Therefore, he needs to spend 1056 for arrows each week. 1056 The answer is: 1056

answer:We are given that the vector begin{pmatrix} 1 2 X end{pmatrix} is rotated 90^circ about the origin and passes through the x-axis. To find the resulting vector, we can use the concept of rotation matrices. A 90^circ rotation about the origin in three dimensions can be represented by the following rotation matrix: begin{pmatrix} 1 & 0 & 0 0 & 0 & -1 0 & 1 & 0 end{pmatrix} To find the resulting vector, we can multiply this rotation matrix by the original vector: begin{pmatrix} 1 & 0 & 0 0 & 0 & -1 0 & 1 & 0 end{pmatrix} begin{pmatrix} 1 2 X end{pmatrix} Multiplying the matrices, we get: begin{pmatrix} 1 cdot 1 + 0 cdot 2 + 0 cdot X 0 cdot 1 + 0 cdot 2 + -1 cdot X 0 cdot 1 + 1 cdot 2 + 0 cdot X end{pmatrix} Simplifying, we have: begin{pmatrix} 1 -X 2 end{pmatrix} Given that the resulting vector is begin{pmatrix}2sqrt{2} -frac{1}{sqrt{2}} -frac{1}{sqrt{2}}end{pmatrix}, we can equate the corresponding components: 2sqrt{2} = 1 -frac{1}{sqrt{2}} = -X -frac{1}{sqrt{2}} = 2 Solving for X, we find: X = frac{1}{sqrt{2}} The value of X is frac{1}{sqrt{2}}. The answer is: 2

answer:Mrs. Taylor bought x smart televisions that cost 650 each. The total cost of the televisions before the discount is x * 650. The total sales price after the 25% discount is (1 - 0.25) * (x * 650) = 0.75 * x * 650 = 0.75x * 650. We are given that Mrs. Taylor paid 975 for the two televisions, so we can write: 0.75x * 650 = 975. Dividing both sides by 0.75 * 650, we get: x = 975 / (0.75 * 650). Simplifying the right side, we get: x = 975 / 487.50. Dividing 975 by 487.50, we get: x = 2. The value of x is 2. 2 The answer is: 2

answer:The cost of the two cassette tapes is 9 x 2 = 18. The total cost of the two cassette tapes and the headphone set is 18 + 25 = 43. Therefore, Amanda will have 50 - 43 = 7 left. 7 The answer is: 7