Master Algebra with our Comprehensive Practice Problems

Consider the non-triangle below. Suppose that ${\displaystyle \mathrm{\angle }ACB={103}^{\circ }}$ and ${\displaystyle m\mathrm{\angle }BAC={44}^{\circ }}$, and that $y=50.5cm$. What of the value of X?

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.  ${\displaystyle \sqrt{x^5}{x}^5}$

Consider that math modeling following initial valu problem
${\displaystyle \frac{dy}{dt}=3-2t-0.5y,y\left(0\right)=1}$
We would liketo find an approximation solution with the step size $h=0.05$
What is the approximation of $y(0.1)?$

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $\left[\begin{array}{ccccc}1& 0& -1& 3& 9\\ 0& 1& 2& -5& 8\\ 0& 0& 0& 0& 0\end{array}\right]$

Does the series (showing the picture) converge or diverge?
Choose the correct answer below.
1) The integral test shows that the series converges
2) The nth-term test shows that the series converges
3) The series diverges because the series is a geometric series with $|r|>=1$
4) The nth-term test shows that the series diverges
$\sum _{n=1}^{\mathrm{\infty }}\frac{4^n}{n+1}$

Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.

$\begin{array}{|cccc|}\hline & \text{Yes}& \text{No}& \text{Total}\\ \text{Group 1}& 56& 42& 98\\ \text{Group 2}& 135& 67& 202\\ \text{Group 3}& 66& 23& 89\\ \text{Total}& 257& 132& 389\\ \hline\end{array}$
Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Expected count =?
contribution to the chi-square statistic = ?