Mathematics: The probability of a thunderstorm is 80%. what are the odds that there will be a thunderstorm?

A. $25.36, $75.99Step-by-step explanation:Given recursive formula: Also, Put n=6 in the above formula , we getSimilarly, for n=5 in the above formula , we getfor n=4 in the above formula , we getfor n=3 in the above formula , we getfor n=2 in the above formula , we getHence, the first two numbers in the sequence are $25.36 and $75.99....

The probability of a thunderstorm is 80%. what are

Ответ:

pkcfox

15.08.2022

Mathematics

A. $25.36, $75.99

Step-by-step explanation:

Given recursive formula: $a_n=1.025(a_{n-1})+50$

Also, a_6=291.51

Put n=6 in the above formula , we get

$a_6=1.025(a_{6-1})+50\\\Rightarrow291.51=1.025(a_5)+50\\\Rightarrow1.025(a_5)=291.51-50\\\Rightarrow1.025(a_5)=241.51\\\Rightarrow(a_5)=235.619512195$

Similarly, for n=5 in the above formula , we get

$a_5=1.025(a_{5-1})+50\\\Rightarrow235.619512195=1.025(a_4)+50\\\Rightarrow1.025(a_4)=235.619512195-50\\\Rightarrow1.025(a_4)=185.619512195\\\Rightarrow(a_4)=181.09220702$

for n=4 in the above formula , we get

$a_4=1.025(a_{4-1})+50\\\Rightarrow181.09220702=1.025(a_3)+50\\\Rightarrow1.025(a_3)=181.09220702-50\\\Rightarrow1.025(a_3)=131.09220702\\\Rightarrow(a_3)=127.894836117$

for n=3 in the above formula , we get

$a_3=1.025(a_{3-1})+50\\\Rightarrow127.894836117=1.025(a_2)+50\\\Rightarrow1.025(a_2)=127.894836117-50\\\Rightarrow1.025(a_2)=77.894836117\\\Rightarrow(a_2)=75.9949620654\approx75.99$

for n=2 in the above formula , we get

$a_2=1.025(a_{2-1})+50\\\Rightarrow75.99=1.025(a_1)+50\\\Rightarrow1.025(a_1)=75.99-50\\\Rightarrow1.025(a_1)=25.99\\\Rightarrow(a_1)=25.356097561\approx25.36$

Hence, the first two numbers in the sequence are $25.36 and $75.99.

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