Your answer will be 2.6 pounds of apples, 1.2 pounds of bananas.
(a) is false. Consider the identity matrix, . Then
bu
(b) is false. Since is invertible, we have
but in general, matrix multiplication is non-commutative.
(c) is true. Let ; then
and so on, down to
which is to say .
(d) is false. Consider , so that
which is singular (i.e. determinant is zero), and thus not invertible.
(e) is true. It follows from the distributivity of matrix multiplication:
(f) is false for the same reason as (b). Expanding the product gives
but in general, .
Answer:
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
The questions asks about Combinations of Pizza toppings, so by employing the Combination Formula:
We are given:
p = probability = 0.12<span>
n = total students = 39 </span>
x = left handers = 5<span>
u = mean = p* n = 4.68
σ = standard dev = √ ( n*p*(1-p)) = √ ( 39 * 0.12 * 0.88 ) =
2.03</span>
Calculating for the z score:
z = (x – u) / σ<span>
z = (5 – 4.68) / 2.03</span>
<span>z
= 0.1576 = 0.16
</span>
Using the standard tables for z, the p value is:
p value = 0.5636 = 56.36%
Hence there is a 56.36% chance.
<span> </span>