Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion.

2 answers:

8 0

<span>The hypothesis is : If Robbie wants to save money to buy a car. Conclusion : he must get a part-time job.

Robbie already started the new job yesteday. So, that makes the hypothesis true.

So, the conclusion would be : Robbie will save money to buy a car/ Robbie will buy a car.</span>

Leokris [45]3 years ago

4 0

The answer is, "Therefore, Robbie is saving money to buy a car."

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From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2

Kruka [31]

Assume that a certain population is P. If the population has decreased 2.8% at the end of one year, this means that the population now is

100%P-2.8%P=97.2%P. Thus a decrease of 2.8% can means a multiplication by 97.2%, which is 97.2/100=0.972.

So, assume the population in 2006 was P. Then the population in 2007 was

0.972P. Similarly, we can see that the population in 2008 was 0.972(0.972P).

The population in 2009 the population was 0.972(0.972(0.972P)), which is $(0.972)^3P$ .

Finally, in the end of 2010 the population was $(0.972)^4P$ .

The decline of the population from 2006 to 2010 was 22,000. This means that

$P-(0.972)^4P=22,000$ . Factorizing P we have:

$P(1-(0.972)^4)=22,000$ . We can calculate $(0.972)^4=0.8926$ , thus

$P= \frac{22,000}{1-0.8926}= \frac{22.000}{0.1074}= 204,842$ .

We saw that the population after the n'th year after 2006 was $(0.972)^4P$ .

2040 is the (2040-2006)=34th year after 2006, so the population in 2040 will be
$(0.972)^{34}P=(0.972)^34\cdot204,842$ .

$(0.972)^{34}=(((((0.972)^2)^2)^2)^2)^2\cdot(0.972)^2=0.4\cdot0.9448\approx0.378$

(to calculate $((((0.972)^2)^2)^2)^2)^2$ : 0.972_*_=*_=*_=*_=*_=, one *_= for each 2)

Thus, the population in 2040 was 0.378*204,842=77,430.

3 0

4 years ago

Read 2 more answers

Please help me to understand how to simplify this. Thanks

Solnce55 [7]

The power of a power rule: