answer:Burt spent 2.00 on a packet of basil seeds and 8.00 on potting soil, so his total cost is 2.00 + 8.00 = 10.00. The packet of seeds yielded x basil plants, and he sells each basil plant for 5.00, so his total revenue is 5.00 * x. The net profit is the total revenue minus the total cost: 5.00 * x - 10.00. We are given that the net profit is 90.00, so we can write: 5.00 * x - 10.00 = 90.00. Adding 10.00 to both sides, we get: 5.00 * x = 100.00. Dividing both sides by 5.00, we get: x = 20. The value of x is 20. 20 The answer is: 20

answer:The cross product of vectors mathbf{a} and mathbf{b} is given by mathbf{a} times mathbf{b} = begin{pmatrix} a_2 b_3 - a_3 b_2 a_3 b_1 - a_1 b_3 a_1 b_2 - a_2 b_1 end{pmatrix}, where mathbf{a} = begin{pmatrix} a_1 a_2 a_3 end{pmatrix} and mathbf{b} = begin{pmatrix} b_1 b_2 b_3 end{pmatrix}. So, if mathbf{a} times mathbf{b} = begin{pmatrix} 5 4 -7 end{pmatrix}, we know that a_2 b_3 - a_3 b_2 = 5, a_3 b_1 - a_1 b_3 = 4, and a_1 b_2 - a_2 b_1 = -7. If we multiply vector mathbf{b} by 3, we get mathbf{c} = begin{pmatrix} 3b_1 3b_2 3b_3 end{pmatrix}. Then, the cross product of vector mathbf{a} and vector mathbf{c} is mathbf{a} times mathbf{c} = begin{pmatrix} a_2 c_3 - a_3 c_2 a_3 c_1 - a_1 c_3 a_1 c_2 - a_2 c_1 end{pmatrix}. Using the values we have, we can simplify this expression to mathbf{a} times mathbf{c} = begin{pmatrix} a_2 (3b_3) - a_3 (3b_2) a_3 (3b_1) - a_1 (3b_3) a_1 (3b_2) - a_2 (3b_1) end{pmatrix} = begin{pmatrix} 3(a_2 b_3 - a_3 b_2) 3(a_3 b_1 - a_1 b_3) 3(a_1 b_2 - a_2 b_1) end{pmatrix} = begin{pmatrix} 3(5) 3(4) 3(-7) end{pmatrix} = begin{pmatrix} 15 12 -21 end{pmatrix}. Therefore, the cross product of vector mathbf{a} and the vector obtained by multiplying vector mathbf{b} by 3 is boxed{begin{pmatrix} 15 12 -21 end{pmatrix}}.The answer is: begin{pmatrix}1512-21end{pmatrix}

answer:Monica made a total of 30 cookies. Her father ate 10 cookies, so there are 30 - 10 = 20 cookies left. Her mother ate half as much as her father, so she ate 10 / 2 = 5 cookies. There are now 20 - 5 = 15 cookies left. Her brother ate 2 more than her mother, so he ate 5 + 2 = 7 cookies. There are now 15 - 7 = 8 cookies left for Monica. 8 The answer is: 8

answer:If there are 12 uniforms in the lab, then there are 6 times as many lab coats, so there are 12 x 6 = 72 lab coats. The number of lab techs is half the number of uniforms, so there are 12 / 2 = 6 lab techs. To share the coats and uniforms equally among the lab techs, each lab tech will get 72 coats / 6 techs = 12 coats. And each lab tech will also get 12 uniforms / 6 techs = 2 uniforms. Therefore, each lab tech will get a total of 12 coats + 2 uniforms = 14 items. 14 The answer is: 14