Billy drove 3.75 miles. You find the answer by dividing 7.5 by 2
Step-by-step explanation:
![A=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%267%5Cend%7Barray%7D%5Cright%5D)
![B=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%5C%5C6%260%5Cend%7Barray%7D%5Cright%5D)
![C=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]](https://tex.z-dn.net/?f=C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D)
![D=\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]](https://tex.z-dn.net/?f=D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%264%5C%5C0%26-2%261%5C%5C3%264%26-1%5Cend%7Barray%7D%5Cright%5D)
![1.\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]+\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]=\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&2\\11&7\end{array}\right]](https://tex.z-dn.net/?f=1.%5C%5CA%2BB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%267%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%5C%5C6%260%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%2B4%261%2B1%5C%5C5%2B6%267%2B0%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%262%5C%5C11%267%5Cend%7Barray%7D%5Cright%5D)
![2.\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right]](https://tex.z-dn.net/?f=2.%5C%5CB-A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%5C%5C6%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-3%261-1%5C%5C6-5%260-7%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%26-7%5Cend%7Barray%7D%5Cright%5D)
![3.\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right]](https://tex.z-dn.net/?f=3.%5C%5C3C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%283%29%28-2%29%26%283%29%283%29%26%283%29%281%29%5C%5C%283%29%28-1%29%26%283%29%280%29%26%283%29%284%29%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%269%263%5C%5C-3%260%2612%5Cend%7Barray%7D%5Cright%5D)
![4.\\C\cdot D=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\cdot\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\=\left[\begin{array}{ccc}7&-8&-6\\14&13&-8\end{array}\right]](https://tex.z-dn.net/?f=4.%5C%5CC%5Ccdot%20D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%264%5C%5C0%26-2%261%5C%5C3%264%26-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28-2%29%28-2%29%2B%283%29%280%29%2B%281%29%283%29%26%28-2%29%283%29%2B%283%29%28-2%29%2B%281%29%284%29%26%28-2%29%284%29%2B%283%29%281%29%2B%281%29%28-1%29%5C%5C%28-1%29%28-2%29%2B%280%29%280%29%2B%284%29%283%29%26%28-1%29%283%29%2B%280%29%28-2%29%2B%284%29%284%29%26%28-1%29%284%29%2B%280%29%281%29%2B%284%29%28-1%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26-8%26-6%5C%5C14%2613%26-8%5Cend%7Barray%7D%5Cright%5D)
The diameter of the new rubber ball, to the nearest foot, must be D = 4.0 ft (in the case of the maximum cost).
<h3>
How to find the diameter of the ball?</h3>
Remember that for a sphere of diameter D, the surface area is:
A = 4*pi*(D/2)^2
In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:
$0.02*A = $1
A = $1/$0.02 = 50
So the surface of the ball must be 50 square feet.
Then we solve:
50ft^2 = 4*3.14*(D/2)^2
D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft
If you want to learn more about spheres, you can read:
brainly.com/question/10171109
20,000 • 26 = 520,000 miles.
In scientific notation, 520,000 becomes
5.20 x 10^5
Answer is 11
all you have to do is 55 divided by 5
