The probability that she makes an A in neither is 0.10
Answer:
![A)\ \ \ \ \left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=A%29%5C%20%5C%20%5C%20%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given the matrix: ![\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D)
, it's inverse is calculated using the formula:
![\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]^{-1}=\frac{1}{det\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] }\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
#Therefore, we calculate as;
![\frac{1}{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] }\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\\#det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] =1\\\\\\\\=\frac{1}{1}\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\=\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%5C%23det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D1%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Hence, the inverse of the matrix is ![\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
57.3
Step-by-step explanation:
just rounded up one
Answer:
2 hours * (47 miles / hour) = 94 miles
multiply the value in miles per hour by the conversion factor '1.609344'.
So, 2.2 miles per hour = 2.2 × 1.609344 = 3.5405568 kilometers per hour.
Step-by-step explanation:
Answer:
807.8 in^2
Step-by-step explanation:
The total area of the box is the sum of the areas of all faces of the box. The top, bottom, front, and back faces are rectangles 18 in long. The end faces each consist of a rectangle and a triangle. We can compute the sum of these like this:
The areas of top, bottom, front, and back add up to be 18 inches wide by the length that is the perimeter of the end: 2·5in +2·8 in + 9.6 in = 35.8 in. That lateral area is ...
(18 in)(35.6 in) = 640.8 in^2
The area of the triangle on each end is equivalent to the area of a rectangle half as high, so we can compute the area of each end as ...
(9.6 in)(8.7 in) = 83.52 in^2
Then the total area is the lateral area plus the area of the two ends:
640.8 in^2 + 2·83.52 in^2 = 807.84 in^2 ≈ 807.8 in^2
