stanley semester 2 final exam\n42. if y is a real number, what is the solution set of the equation…

stanley semester 2 final exam\n42. if y is a real number, what is the solution set of the equation \\(\\sqrt{1 - 5y}=3\\)?\na. \\(\\{-\\frac{8}{5}\\}\\)\nb. \\(\\{\\frac{8}{5}\\}\\)\nc. \\(\\{\\frac{2}{5}\\}\\)\nd. \\(\\{2\\}\\)\n43. consider the following table representing the monthly sales of three products in a store over four months.\n| month | product a | product b | product c |\n| ---- | ---- | ---- | ---- |\n| january | 120 | 80 | 90 |\n| february | 150 | 90 | 110 |\n| march | 140 | 100 | 120 |\n| april | 160 | 85 | 95 |\nif the given data is arranged in a matrix where each column represents the product and row represents the sale in a month, which element represents the data of 2nd column and 3rd row of the matrix?\na. 80\nb. 100\nc. 110\nd. 140\n44. the kinetic energy, e, of an object having mass m and moving with velocity v is given by the formula \\(e = \\frac{1}{2}mv^{2}\\). which expression can be used to find the velocity?\na. \\(\\sqrt{\\frac{2e}{m}}\\)\nb. \\(\\frac{\\sqrt{2e}}{m}\\)\nc. \\(\\frac{4e^{2}}{m}\\)\nd. \\(\\frac{4e^{2}}{m^{2}}\\)

stanley semester 2 final exam\n42. if y is a real number, what is the solution set of the equation \\(\\sqrt{1 - 5y}=3\\)?\na. \\(\\{-\\frac{8}{5}\\}\\)\nb. \\(\\{\\frac{8}{5}\\}\\)\nc. \\(\\{\\frac{2}{5}\\}\\)\nd. \\(\\{2\\}\\)\n43. consider the following table representing the monthly sales of three products in a store over four months.\n| month | product a | product b | product c |\n| ---- | ---- | ---- | ---- |\n| january | 120 | 80 | 90 |\n| february | 150 | 90 | 110 |\n| march | 140 | 100 | 120 |\n| april | 160 | 85 | 95 |\nif the given data is arranged in a matrix where each column represents the product and row represents the sale in a month, which element represents the data of 2nd column and 3rd row of the matrix?\na. 80\nb. 100\nc. 110\nd. 140\n44. the kinetic energy, e, of an object having mass m and moving with velocity v is given by the formula \\(e = \\frac{1}{2}mv^{2}\\). which expression can be used to find the velocity?\na. \\(\\sqrt{\\frac{2e}{m}}\\)\nb. \\(\\frac{\\sqrt{2e}}{m}\\)\nc. \\(\\frac{4e^{2}}{m}\\)\nd. \\(\\frac{4e^{2}}{m^{2}}\\)

Answer

42.

Explanation:

Step1: Square both sides

Square $\sqrt{1 - 5y}=3$ to get $1 - 5y = 9$.

Step2: Solve for y

Subtract 1 from both sides: $-5y=9 - 1=8$. Then $y=-\frac{8}{5}$.

Answer:

There is no option matching $y =-\frac{8}{5}$ in the provided options for this part.

43.

Explanation:

Step1: Identify matrix - row and column

The 2nd column represents Product B and the 3rd row represents March. From the table, the sales of Product B in March is 100.

Answer:

B. 100

44.

Explanation:

Step1: Isolate $v^{2}$

Given $E=\frac{1}{2}mv^{2}$, multiply both sides by 2 to get $2E = mv^{2}$. Then $v^{2}=\frac{2E}{m}$.

Step2: Solve for v

Take the square - root of both sides. Since we are looking for the magnitude of velocity (assuming positive values for the context of the formula manipulation here), $v=\sqrt{\frac{2E}{m}}$.

Answer:

A. $\sqrt{\frac{2E}{m}}$