white : milk : dark
w : m : d
The ratio of white to not white is 3:4
w : (m+d) = 3:4
The ratio of not dark to dark is 17:4.
(w+m) : d = 17:4
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We treat the colons as fraction bars and cross multiply.
4w = 3(m+d) = 3m + 3d
4w + 4m = 17 d
Subtracting,
4m = 17d - (3m+3d) = 14d - 3m
7m = 14 d
m/d = 14/7
m:d = 2:1
Since w:(m+d)=3:4 let's make m+d a multiple of 4.
m:d = 8:4
w : (m+d) = 3:4 = 9:12
w:m:d = 9:8:4
Answer: 9:8:4
Check:
white to non white 9 to 8+4=12 = 3:4, good
non dark to dark (9+8):4=17:4, good
i think you multiply 4*80=320
Answer:
True
True
False
Step-by-step explanation:
TRUE
If the equation Ax = 0 has only the trivial solution, then A is row equivalent to the n × n identity matrix
Here's why
If the equation Ax = 0 has only the trivial solution the determinant of the matrix is NOT 0 and the matrix is invertible therefore it is row equivalent to the nxn identity matrix.
TRUE
If the columns of A span ℝ^n , then the columns are linearly independent
Here's why
Remember that the rank nullity theorem states that
According to the information given we know that
Therefore you have
and
Which is equivalent to the problem we just solved.
FALSE
If A is an n × n matrix, then the equation Ax = b has at least one solution for each b in ℝ^n
Here's why
Take b as a non null vector and A=0, then Ax = 0 and Ax=b will have no solution.
The temperature at noon was 6 °F.