I think you mean "if the points <span>(2,5), (3,2) and (4,5) satisfy an unknown 3rd degree polynomial, what is the polynomial?"
Since 3 roots {2, 3, 4} are known, we might begin by assuming that this poly would have the form y = ax^3 + bx^2 + cx + d (which has three factors). Unfortunately, three roots are not enough to determine all four constants {a, b, c, d}.
So, let's assume, instead, that the poly would have the form y = ax^2 + bx + c. Three given points should make it possible to determine {a, b, c}.
(2,5): 5 = a(2)^2 + b(2) + c => 5 = 4a + 2b + c
(3,2): 2 = a(3)^2 + b(3) + c => 2 = 9a + 3b + 5 - 4a - 2b
(4,5): 5 = a(4)^2 + b(4) + c => 5 = 16a + 4b + 5 - 4a - 2b
Now we have two equations in a and b alone, which enables us to solve for a and b:
</span>2 = 9a + 3b + 5 - 4a - 2b becomes -3 = 5a + b
<span>and
</span>5 = 16a + 4b + 5 - 4a - 2b becomes 0 = 12a + 2b, or 0 = 6a + b, or 0=-6a-b
<span>
Adding this result to -3 = 5a + b, we get -3 = -a, so a =3.
Thus, since -3 = 5a + b, -3 = 5(3) + b, so b = -18
All we have to do now is to find c. Let's do this using </span>5 = 4a + 2b + c.
We know that a = 3 and b = -18, so this becomes 5 = 4(3) + 2(-18) + c.
Thus, 5 = 12 - 36 + c, or c = 29.
With a, b and c now known, we can write the poly as y = 3x^2 - 18x + 29.
Now the only thing to do remaining is to verify that each of the three given points satsifies y = 3x^2 - 18x + 29. Try this, please.
24 square feet + 12 square feet = total square feet?
I'm not sure. I think I can solve it if this question is more simplified. Contact me if you need help!
A binomial distribution has the following properties;
1. There is a fixed number of trials.
2. Each trial is independent of the others.
3.Each trial has a constant probability of success.
4. There are only two possible outcomes, 'success' and 'failure'.
Statements B and D meet the requirements for the variable X to have a binomial distribution.
Answer:
About 4 times the MAD
Step-by-step explanation:
If you go in from right to left moving you finger one dot at a time then the center of the Data Set A is 42.5 beacuse you add the two numbers together (this is because you have an even number of dots) and the center of Data Set B is 20. The MAD for set A is about 5.83 the MAD for set B is about 5.83 also. Now you have to figure out the means. The mean of data set A is 42.5, the mean for data set B is 20. The difference in the means is 22.5 and if you divide the difference of the means by the MAD you will get 3.859348199, or ≈4 times the MAD
Answer:
35.325 in³
Step-by-step explanation:
Since the base of a cylinder is a circle,
area of cylinder= πr²h
Radius, r
= diameter ÷2
= 3 ÷2
= 1.5 inches
Volume of can
= 3.14(1.5)²(5)
= 35.325 in³
