Answer:
Part 1: 114,570,685 people
Part 2: The population grew by 2.5% (1,722,862 people)
Step-by-step explanation: For part 1 you would multiply 100,236,820 by 1.143 because of the fact that your percentage is increasing. so the 1 before the decimal point stands for 100% of the starting number and the .143 stands for the 14.3% that the population is increasing by.
Part 2 you would divide 53,594,378 by 55,317,240 to get approximately .975. .975 shows that 53,594,378 is about 97.5% of 55,317,240. You then subtract the numbers 100 and 97.5 to get 2.5. 2.5 is the percentage that the population is increasing by. So, then you could just subtract 55,317,240 and 53,594,378 to get 1,722,862. This is the amount of people the population increased by. Then you just put your answer that the population increased. That it increased by 2.5% and 2.5%= 1,722,862 people
I hope this helps you :)
Answer:
It will take Tara 3 hours to get to Nashville. If they meet, it would take them 1 hour and 46 minutes or 1.766 hours.
Step-by-step explanation:
Divide 212 miles by 65 mph: 212÷65=3.2 and 3.2 rounded is 3. They will each drive half the way if they meet in the middle, so 212 miles divided by 2 is 106. Divide that by 60: 106/60=1.766. That is equivalent to 1 hour and 46 minutes.
Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.
<h3>
Answer: 25</h3>
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Explanation:
Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).
Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.
As a way to check the answer, we can say
g(x) = 2x^2 + 6x + 5
g(-5) = 2(-5)^2 + 6(-5) + 5
g(-5) = 25
So the answer is confirmed.