Answer:
P(A)=0.55
P(A and B)=P(A∩B)=0.1265
P(A or B)=P(A∪B)=0.7635
P(A|B)=0.3721
Step-by-step explanation:
P(A')=0.45
P(A)=1-0.45=0.55
P(B∩A)=?
P(B|A)=0.23
P(B|A)=(P(A∩B))/P(A)
0.23=(P(A∩B))/0.55
P(A∩B)=0.23×0.55=0.1265
P(A∪B)=P(A)+P(B)-P(A∩B)
=0.55+0.34-0.1265
=0.7635
P(A|B)=[P(A∩B)]/P(B)=0.1265/0.34 ≈0.3721
Answer
Find out the ratio of price to pound for each bag.
To prove
As given
A store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for $27.93 .
7 pound = $27.93
Now find out the cost for the 1 pound.

1 pound cost = $3.99
As given large bags cost $66.98.
Now find out pounds in the large bags.
Let us assume that the number of pounds in the large bags be x.
Than
3.99 × x = 66.98

x = 16.8 pounds (approx)
Now find out the ratio of price to pound for each bag.
As small bags weight = 7 pounds
Cost of the small bags = $27.93

As large bags weight = 16.8 pounds
Cost of the large bags = $66.98

Hence proved
Step-by-step explanation:
The value of k in the equation g(x) = f(x) + k comes out to be 8.
How the vertical shifting of a graph takes place?
If the graph of a function f(x) is shifted vertically by k units, f(x) becomes f(x)+k.
From the diagram, we can say that graph of f(x) has been shifted vertically by 8 units
If we shift f(x) vertically by 8 units f(x) becomes f(x)+8 and also coincides with the graph of g(x).
So, g(x) = f(x) + 8........(1)
Comparing (1) and g(x) = f(x) + k, we get k=8.
Hence, the value of k in the equation g(x) = f(x) + k comes out to be 8.
Answer:
Two positive zeros, no negative zeros, two complex roots.
Step-by-step explanation:
The given function is 
According to the fundamental theorem of algebra, the function will have 4 roots.
The graph of the function intersects the positive axis at two points.
Hence the function has two positive zeros and no negative zeros.
The two remaining roots are imaginary. The function has two complex zeros.
See graph in attachment