Answer:
The length of BC = 12
Step-by-step explanation:
c^2 = a^2 + b^2
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
b = 12
The length of BC is 12
A plausible guess might be that the sequence is formed by a degree-4* polynomial,
![x_n = a n^4 + b n^3 + c n^2 + d n + e](https://tex.z-dn.net/?f=x_n%20%3D%20a%20n%5E4%20%2B%20b%20n%5E3%20%2B%20c%20n%5E2%20%2B%20d%20n%20%2B%20e)
From the given known values of the sequence, we have
![\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%2Bb%2Bc%2Bd%2Be%20%3D%20-2%20%5C%5C%2016%20a%20%2B%208%20b%20%2B%204%20c%20%2B%202%20d%20%2B%20e%20%3D%201%20%5C%5C%2081%20a%20%2B%2027%20b%20%2B%209%20c%20%2B%203%20d%20%2B%20e%20%3D%207%20%5C%5C%20256%20a%20%2B%2064%20b%20%2B%2016%20c%20%2B%204%20d%20%2B%20e%20%3D%2025%20%5C%5C%20625%20a%20%2B%20125%20b%20%2B%2025%20c%20%2B%205%20d%20%2B%20e%20%3D%2079%5Cend%7Bcases%7D)
Solving the system yields coefficients
![a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4](https://tex.z-dn.net/?f=a%3D%5Cdfrac58%2C%20b%3D-%5Cdfrac%7B19%7D4%2C%20c%3D%5Cdfrac%7B115%7D8%2C%20d%20%3D%20-%5Cdfrac%7B65%7D4%2C%20e%3D4)
so that the n-th term in the sequence might be
![\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_n%20%3D%20%5Cboxed%7B%5Cfrac%7B5%20n%5E4%7D%7B8%7D-%5Cfrac%7B19%20n%5E3%7D%7B4%7D%2B%5Cfrac%7B115%20n%5E2%7D%7B8%7D-%5Cfrac%7B65%20n%7D%7B4%7D%2B4%7D)
Then the next few terms in the sequence could very well be
![\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}](https://tex.z-dn.net/?f=%5C%7B-2%2C%201%2C%207%2C%2025%2C%2079%2C%20208%2C%20466%2C%20922%2C%201660%2C%202779%2C%20%5Cldots%5C%7D)
It would be much easier to confirm this had the given sequence provided just one more term...
* Why degree-4? This rests on the assumption that the higher-order forward differences of
eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of
by
. Then
• 1st-order differences:
![\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}](https://tex.z-dn.net/?f=%5CDelta%5C%7Bx_n%5C%7D%20%3D%20%5C%7B1-%28-2%29%2C%207-1%2C%2025-7%2C%2079-25%2C%5Cldots%5C%7D%20%3D%20%5C%7B3%2C6%2C18%2C54%2C%5Cldots%5C%7D)
• 2nd-order differences:
![\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}](https://tex.z-dn.net/?f=%5CDelta%5E2%5C%7Bx_n%5C%7D%20%3D%20%5C%7B6-3%2C18-6%2C54-18%2C%5Cldots%5C%7D%20%3D%20%5C%7B3%2C12%2C36%2C%5Cldots%5C%7D)
• 3rd-order differences:
![\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}](https://tex.z-dn.net/?f=%5CDelta%5E3%5C%7Bx_n%5C%7D%20%3D%20%5C%7B12-3%2C%2036-12%2C%5Cldots%5C%7D%20%3D%20%5C%7B9%2C24%2C%5Cldots%5C%7D)
• 4th-order differences:
![\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}](https://tex.z-dn.net/?f=%5CDelta%5E4%5C%7Bx_n%5C%7D%20%3D%20%5C%7B24-9%2C%5Cldots%5C%7D%20%3D%20%5C%7B15%2C%5Cldots%5C%7D)
From here I made the assumption that
is the constant sequence {15, 15, 15, …}. This implies
forms an arithmetic/linear sequence, which implies
forms a quadratic sequence, and so on up
forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.
<span>It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)
</span>
Answer:
C
Step-by-step explanation:
When to use regression test?
- This is done to find the relationship between 2 variables. One dependent and one independent.
When to use Multiple regression test?
- Extension of regression test. It is used to predict value of 1 variable when it depends on 2-3 other variables. Multivariable, basically.
When to use 1-sided t-test?
- We check for possibility of relationship of something from one side. 1 side effect. With a hypothesis and its alternate.
When to use 2-sided t-test?
- This is same as 1-tailed but it looks for possibility from 2sides. A hypothesis and alternate, whether less or more.
Now, Options A and B are not right since we aren't comparing 2 variables here. People believe second born subjects are more intelligent. We have to perform a test to see whether this is true or not. One sided answer. So, we will use One-sided t-test.
For this case we must factor
of the following expression:
![\frac {3} {2} x- \frac {9} {4}y](https://tex.z-dn.net/?f=%5Cfrac%20%7B3%7D%20%7B2%7D%20x-%20%5Cfrac%20%7B9%7D%20%7B4%7Dy)
By law of signs of multiplication it is fulfilled that:
![- * - = +\\- * + = -](https://tex.z-dn.net/?f=-%20%2A%20-%20%3D%20%2B%5C%5C-%20%2A%20%2B%20%3D%20-)
So we have to:
![- \frac {3} {4} * (- 2) = + \frac {6} {4} = + \frac {3} {2}\\- \frac {3} {4} * 3 = - \frac {9} {4}](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B3%7D%20%7B4%7D%20%2A%20%28-%202%29%20%3D%20%2B%20%5Cfrac%20%7B6%7D%20%7B4%7D%20%3D%20%2B%20%5Cfrac%20%7B3%7D%20%7B2%7D%5C%5C-%20%5Cfrac%20%7B3%7D%20%7B4%7D%20%2A%203%20%3D%20-%20%5Cfrac%20%7B9%7D%20%7B4%7D)
Thus, by factoring we have:
![- \frac {3} {4} (- 2x + 3y)](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B3%7D%20%7B4%7D%20%28-%202x%20%2B%203y%29)
Answer:
![- \frac {3} {4} (- 2x + 3y)](https://tex.z-dn.net/?f=-%20%5Cfrac%20%7B3%7D%20%7B4%7D%20%28-%202x%20%2B%203y%29)