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algol [13]
3 years ago
15

A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the

automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.
Mathematics
1 answer:
andriy [413]3 years ago
7 0

Answer:

P=0.54.

Step-by-step explanation:

We know that in a sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans.

We calculate the number of  sedans that are not black:

3120-1170=1950

We calculate the number of black cars  that are not sedans:

1560-1170=390

The number of automobiles  which are black or a sedan is

1950+390+1170=3510.

The probability that  the automobile is black or a sedan is:

P=3510/6500

P=0.54.

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3 years ago
Suppose a population of honey bees in Ephraim, UT has an initial population of 2300 and 12 years later the population reaches 13
Rama09 [41]

Answer:

common ratio: 1.155

rate of growth: 15.5 %

Step-by-step explanation:

The model for exponential growth of population P looks like: P(t)=P_i(1+r)^t

where P(t) is the population at time "t",

P_i is the initial (starting) population

(1+r) is the common ratio,

and r 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:

P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\

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:

1+r=1.155273\\r=1.155273-1=0.155273

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

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3 years ago
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