Answer: 912
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Work Shown:
The starting term is a1 = 3. The common difference is d = 5 (since we add 5 to each term to get the next term). The nth term formula is
an = a1+d(n-1)
an = 3+5(n-1)
an = 3+5n-5
an = 5n-2
Plug n = 19 into the formula to find the 19th term
an = 5n-2
a19 = 5*19-2
a19 = 95-2
a19 = 93
Add the first and nineteenth terms (a1 = 3 and a19 = 93) to get a1+a19 = 3+93 = 96
Multiply this by n/2 = 19/2 = 9.5 to get the final answer
96*9.5 = 912
I used the formula
Sn = (n/2)*(a1 + an)
where you add the first term (a1) to the nth term (an), then multiply by n/2
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As a check, here are the 19 terms listed out and added up. We get 912 like expected.
3+8+13+18 +23+28+33+38 +43+48+53+58 +63+68+73+78 +83+88+93 = 912
There are 19 values being added up in that equation above. I used spaces to help group the values (groups of four; except the last group which is 3 values) so it's a bit more readable.
Then a is Half of 45 wich is 22.5 I believe.
Answer:
no, no, yes, yes
Step-by-step explanation:
If 25% of the people <em>are</em> vaccinated, then 75% of the people are <em>not</em> vaccinated. Of those not vaccinated, each has a 50% chance of contracting the disease. The probability that someone is both not vaccinated and contracts the disease is (0.75)(0.5)=0.375.
The probability that someone is vaccinated and contracts the disease is (0.25)(0.1)=0.025 (it is multiplied by 0.1 because if the vaccine is 90% effective, then there is a 10% chance someone that is vaccinated can contract the disease.
Add these together for the total: 0.375+0.025=0.4
There is a 40% chance that someone chosen at random will contract the disease.
5^(x² - 2x) = 1
5^(x²) - 5^(2x) = 1
5^x² - 5²x = 1
