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frutty [35]
3 years ago
10

John gets 76% of the questions correct in a trivia game. He misses 4 questions. What is the change in his score in percentage po

ints for each question he gets
incorrect?
Mathematics
1 answer:
VMariaS [17]3 years ago
8 0

Answer:

-6%

Step-by-step explanation:

Here's why: The total he could have gotten was 100%. He got a 76%, which is 24% less. If you do 24 divided by 4, the answer will tell us how many points is for each question. The answer is 6. To double check, you can do this, if each question is worth 6 points, and he misses 4 questions, that means that he loses 24% worth of points, 100 minus 24 equals 76%. I did my answer negative, because the question wants to know his change in score for each question he gets incorrect, that means his score is going down which is negative...

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10. (a) Consider the following matrices: A = ( 2 ) B = (3) and C = (-3) w = Find the det(A). [1] (ii) Is the matrix A singular?
Viefleur [7K]

i) We have to find the determinant of A.

We can do this as:

\det(A)=|\begin{bmatrix}{3} & {6} \\ {1} & {-2}\end{bmatrix}|=3*(-2)-6*1=-6-6=-12

ii) We have to find if the matrix A is singular.

Singular matrix have determinant equal to 0.

This is not the case for A, as its determinant is -12. Then, A is not a singular matrix.

iii) We have to find the values of x and y so that AB = C.

We have to write the matrix multiplication and we will obtain a system of linear equations:

We can now solve the system of equations by adding 3 times the second equation to the first equation:

\begin{gathered} 3(x-2y)+(3x+6y)=3(-3)+(-3) \\ 3x-6y+3x+6y=-9-3 \\ 6x+0y=-12 \\ x=\frac{-12}{6} \\ x=-2 \end{gathered}

We can now use the second equation to find the value of y:

\begin{gathered} x-2y=-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{-2+3}{2} \\ y=\frac{1}{2} \end{gathered}

The values are x = -2 and y = 1/2.

iv) When we want to multiply two matrices, the required condition is that the number of columns of the matrix on the left is equal the number of rows of the matrix on the right.

In the case of A(2x2) and B(2x1), when we do A*B this condition is satisfied.

But when we try to multiply BA, the number of columns of B is not equal to the number of rows of A, so the matrix mulitplication is not possible.

Answer:

i) det(A) = -12

ii) A is not singular because singular matrices have determinant equal to zero.

iii) x = -2 and y = 1/2.

iv) Is not possible because the number of columns of the first matrix has to be equal to the number of rows of the second matrix.

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