Twenty-six students in a college algebra class took a final exam on which the passing score was 70. The mean score of those who passed was 78, and the mean score of those who failed was 26. The mean of all scores was 72. How many students failed the exam?

A back-to-back stemplot is particularly useful for (A) identifying outliers. (B) comparing two data distributions. (C) merging two sets of data. (D) graphing home runs. (E) distinguishing stems from leaves.

Find the x-and y-intercepts of the graph of the equation algebraically.
${\displaystyle y=3x-1}$

I understand the process for how Eigenvalues are involved in Differential Equations. If you have Differential System of Equations like this
${\overrightarrow{x}}^{\prime }=\left(\begin{array}{cc}2& 1\\ 0& 1\end{array}\right)\overrightarrow{x}$
The solution to that System of Differential Equations is a Linear Combination of e to the power of the eigenvalues times the corresponding eigenvectors.
$\overrightarrow{x}=C_1{e}^{2t}\left(\begin{array}{c}1\\ 0\end{array}\right)+C_2{e}^t\left(\begin{array}{c}-1\\ 1\end{array}\right)$
However, what I am struggling with figuring out how Generalized Eigenvalues translate to the solutions in Differential Equations. If you take this System of Differential Equations
${\overrightarrow{x}}^{\prime }=\left(\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 6& 3& 1\end{array}\right)\overrightarrow{x}$
The solution to this Differential Equations is
$\overrightarrow{x}=C_1{e}^t\left(\begin{array}{c}1\\ 3t\\ 6t+\frac{9}{2}{t}^2\end{array}\right)+C_2{e}^t\left(\begin{array}{c}0\\ 1\\ 3t\end{array}\right)+C_3{e}^t\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)$
But the eigenvectors of this matrix (including the generalized eigenvectors) are
${\overrightarrow{v}}_1=\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right),{\overrightarrow{w}}_1=\left(\begin{array}{c}0\\ 1\\ 3\end{array}\right),{\overrightarrow{w}}_2=\left(\begin{array}{c}1\\ 1\\ 3\end{array}\right)$
These eigenvectors do share some similarities to the solution to the System of Equations. However, the
$6t+\frac{9}{2}{t}^2$
term in the solution is one I have no idea how generalized eigenvectors relate. May someone please explain how these eigenvectors translate into Differential Equations?

What is the Z-score for a 10% confidence level (i.e. 0.1 pvalue)?
I want the standard answer used for including in my thesis write up. I googled and used excel to calculate as well but they are all slightly different.
Thanks.

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramers

Saving for college in 20 years, a father wants to accumulate $40,000 to pay for his daughters

Qualitatively (or mathematically "light"), could someone describe the difference between a matrix and a tensor? I have only seen them used in the context of an undergraduate, upper level classical mechanics course, and within that context, I never understood the need to distinguish between matrices and tensors. They seemed like identical mathematical entities to me.
Just as an aside, my math background is roughly the one of a typical undergraduate physics major (minus the linear algebra).