By the binomial theorem, the 
term in the expansion of 
is
which suggests that the contribution of the binomial coefficient should make up the remaining factor of 21. That is,
Answer: the sum invested = $600
<u>Step-by-step explanation:</u>
Interest (I) = Principal (P) × rate (r) × time (t)
Original amount: I = P × r × 3
Increased by 1%: I + 18 = P × (1+ .01)r × 3
Substitute I with Prt and set the equations equal to each other to find r:
3Pr + 18 = 3.03Pr
Solve for Pr:
18 = 0.03Pr
<u> ÷0.03</u> <u>÷ 0.03 </u>
600 = Pr
Since the p-value of the test is of 0.00001 < 0.01, these results have statistical significance.
<h3>What is the relation between the p-value and the conclusion of the test hypothesis?</h3>
Depends on if the p-value is less or more than the significance level:
- If it is more, the null hypothesis is not rejected, which means that the results do not have statistical significance.
- If it is less, it is rejected, which means that the results have statistical significance.
In this problem, the probability is the p-value, hence since the p-value of the test is of 0.00001 < 0.01, these results have statistical significance.
More can be learned about p-values at brainly.com/question/13873630
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First we find the slope between the two given points.
m = (y2 - y1)/(x2 - x1) = (-5 - 2)/(7 - 6) = -7/1 = -7
Now we use the slope-intercept equation of a line.
y = mx + b
We use one point as x and y, and we solve for b.
2 = -7(6) + b
2 = -42 + b
b = 44
The equation is
y = -7x + 44
Answer: f(x) = -7x + 44
The answer to the selected math problem is 10
