Given:
The scale factor between two circles is .
To find:
The ratio of their areas.
Solution:
We know that, all circles are similar.
The ratio of the areas of similar figures is equal to the ratio of squares of their corresponding sides or equal to the square of ratio of their corresponding sides.
The scale factor is the ratio of the corresponding sides.
Ratio of areas of circles = Square of scale factor between two circles
Therefore, the correct option is D.
Answer:
a.
b.
c.
Step-by-step explanation:
Suppose cities represented by C', suburbs represented by S and rural represented by R,
Let x be the total number of bonds issued throughout the US,
According to the question,
n(A) = 70% of x = 0.7x,
n(B) = 10% of x = 0.1x,
n(C) = 20% of x = 0.2x,
n(A∩C') = 50% of n(A) = 0.5 × 0.7x = 0.35x,
n(A∩S) = 20% of n(A) = 0.2 × 0.7x = 0.14x,
n(A∩R) = 30% of n(A) = 0.3 × 0.7x = 0.21x,
n(B∩C') = 40% of n(B) = 0.4 × 0.1x = 0.04x,
n(B∩S) = 30% of n(B) = 0.3 × 0.1x = 0.03x,
n(B∩R) = 30% of n(B) = 0.3 × 0.1x = 0.03x,
n(C∩C') = 60% of n(C) = 0.6 × 0.2x = 0.12x,
n(C∩S) = 15% of n(C) = 0.15 × 0.2x = 0.03x,
n(C∩R) = 25% of n(C) = 0.25 × 0.2x = 0.05x,
n(C') = n(A∩C') + n(B∩C') + n(C∩C') = 0.35x + 0.04x + 0.12x = 0.51x
n(S) = n(A∩S) + n(B∩S) + n(C∩S) = 0.14x + 0.03x + 0.03x = 0.20x
a. The probability that it will receive an A rating, if a new municipal bond is to be issued by a city,
b. The proportion of municipal bonds are issued by cities =
c. The proportion of municipal bonds are issued by suburbs =
is a factor of
because (by the remainder theorem) the remainder upon dividing
by
is
.
There's also the sum of fifth powers formula,