Answer:
D. 10,699
Step-by-step explanation:
The given data for the Population Count Per Year is presented as follows;
Number of Years (x); 1, 2, 3, 4, 5, 6, 7, 8
The data regression equation is y = 1,200·(1.2)ˣ
Based on the regression equation for the data, the predicted value of the town's population after 12 years is given by substituting x = 12 as follows;
After 12 years, y = 1,200 × (1.2)¹² ≈ 10,699.32
Therefore, the option which is the best prediction is 10,699.
<h3>
Answer: Choice C</h3>
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Explanation:
For choice C, the x values are out of order, so it might be tricky at first. I recommend sorting the x values from smallest to largest to get -2, -1, 0, 1, 2. Do the same for the y values as well. Make sure the correct y values stay with their x value pairs. You should get the list of y values to be 4, 2, 1, 1/2, 1/4
Check out the attached image below for the sorted table I'm referring to
We can see the list of y values is going down as x increases. This is a good sign we have decay. Further proof is that we multiply each term by 1/2 to get the next one
4 times 1/2 = 2
2 times 1/2 = 1
1 times 1/2 = 1/2
1/2 times 1/2 = 1/4
and so on. Effectively we can say the decay rate is 50%
Answer:
Each pitcher has the same fraction of the other drink.
Step-by-step explanation:
After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).
The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.
_____
You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.
Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:
tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2
It could possibly be the first on but I’m not completely sure
g(x) = 2x-6
f(x) = -4x +7
(g•f)(x) = g(f(x))
= 2(f(x)) - 6
= 2 ( -4x+7) -6
= -8x + 14 -6
= -8x +8
now
(g•f)(1) = -8(1) + 8= -8+8
= 0
so option a is answer
