Nick and Nora are married and have three children in college. They have an adjusted gross income of $47,400. If their standard d
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Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like:
where is the population at time "t",
is the initial (starting) population
is the common ratio,
and is the rate of growth
Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:
This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155
We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:
So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %
Answer:
Step-by-step explanation:
Given: The radius of circle O is r, and the radius of circle X is r'.
To prove: Circle O is similar to circle X.
Proof: Move the center of the smaller circle onto the center of the largest circle. Translate the circle X by the vector XA onto circle O. The circles now have the same center.
A dilation is needed to increase the size of circle X to coincide with the circle O. A value which when multiplied by r' will create r.
The scale factor x to increase X:
⇒
A translation followed by a dilation with scale factor will map one circle to the other, thus proving the given both circles similar.
Therefore, circle O is similar to circle X.
Step-by-step explanation:
Answer:
Step-by-step explanation:
