Answer:
a) there is s such that <u>r>s</u> and s is <u>positive</u>
b) For any <u>r>0</u> , <u>there exists s>0</u> such that s<r
Step-by-step explanation:
a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.
b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.
Answer: The total number of different types of labels will the manufacturers have to produce = 24.
Step-by-step explanation:
Given: Choices for flavours = 4
Choices for sugar = 2 {either sugar or sugar free}
Choices for the qunatity = 3
By Fundamental counting principle,
Total number of different types of labels will have to produce = (Choices for flavors) x (Choices for sugar)x (Choices for the quantity )
= 4 x 2x 3
=24
Hence, the total number of different types of labels will the manufacturers have to produce = 24.
Answer:
13
Step-by-step explanation:
Given number = -48
Listing out the possible factors of -48 in pairs along with their difference:
Factors () Difference () Difference ()
-26 26
26 -26
-19 19
19 -19
-16 16
16 -16
-14 14
14 -14
On listing out the factors we find out that two of the pairs have difference = 19
The pairs are and
It is given that the factor with greater absolute value is positive. This means 16 would be positive while 3 would be negative.
So, our factors are
The sum of the factors is = (Answer)
For any arbitrary 2x2 matrices
and
, only one choice of
exists to satisfy
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on
. One such restriction would be to ensure that
is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking
we'd get equality.