g Define Wi to be the subset of Mn consisting of all invertible n × n matrices. Determine whether Wi is a subspace of Mn.

The initial amount of cupcakes = 48

If they sold each cupcake for $2.75, they would make $132 which is more than the required $100 to go on band field trip to New York.

The excess money available for spending is thus $32

Step-by-step explanation:

The complete question is presented in the attached image to this answer.

They need to make $100

Let x be the initial amount of cupcakes

During the first hour, Brady sold (1/3) of the cupcakes and Jaquan sold (3/8)

Total amount of cupcakes sold in the first hour = [(1/3) × x] + [(3/8) × x] = (17x/24)

Amount of cupcakes remaining after the first hour = x - (17x/24) = (7x/24)

After the first hour, they sold 2 cupcakes

Amount of cupcakes left after the first hour = (7x/24) - 2 = (0.292x - 2)

During the second hour, they sold 75% of the remaining cupcakes, meaning they had 25% of the remaining cupcakes left.

Amount of cupcakes left = 25% × (0.292x - 2)

= (0.07292x - 0.5)

During the third hour, they sold the remaining 3 cupcakes

Meaning that the amount of cupcakes left from the second hour = 3

(0.07292x - 0.5) = 3

0.07292x = 3.5

x = (3.5/0.07292) = 47.998 = 48 cupcakes.

Hence, the initial amount of cupcakes = 48.

If they sold each cupcake for $2.75, they would make 2.75 × 48 = $132

Which is more than the required $100 to go on band field trip to New York.

The excess money available for spending is thus $132 - $100 = $32.

Hope this Helps!!!