A 45-g piece of ice at 0 degree C is added to a sample of water at 8 degrees C. All of the ice melts and the temperature of the water decreases to 0 degree C. How many grams of water were there in the sample?

Derivatives of products and quotients Find the derivative of the following functions by first expanding or simplifying the expression.
${\displaystyle f\left(w\right)=\frac{w^3-w}{w}}$

When establishing the differences between histogram and polygon: a) Which of the two diagrams is drawn with the help of class marks of a frequency distribution? b) Which of the two diagrams is drawn at the class boundaries of a frequency distribution? c) Which of the two diagrams contains a series of vertical rectangular bars? d) Which diagram is produced by connecting a set of consecutive points? e) Which of the two diagrams can be used to compare two or more data sets that are plotted according to the corresponding frequency distributions?

Finding inverse matrix $A^{-1}$ and I was given hint that I could firstly find inverse matrix to matrix B which is transformed from A.
$A=\left(\begin{array}{cccc}1& 3& 9& 27\\ 3& 3& 9& 27\\ 9& 9& 9& 27\\ 27& 27& 27& 27\end{array}\right)$
$B=\left(\begin{array}{cccc}1& 3& 9& 27\\ 1& 1& 3& 9\\ 1& 1& 1& 3\\ 1& 1& 1& 1\end{array}\right)$
I found that that $B^{-1}$ is
$B^{-1}=\left(\begin{array}{cccc}-\frac{1}{2}& \frac{3}{2}& 0& 0\\ \frac{1}{2}& -2& \frac{3}{2}& 0\\ 0& \frac{1}{2}& -2& \frac{3}{2}\\ 0& 0& \frac{1}{2}& -\frac{1}{2}\end{array}\right)$
I don't know how to continue. What rule do I use to find $A^{-1}$?

Determine the inverse Laplace transform of the function below.
${\displaystyle \frac{3}{{(2s+7)}^4}}$
${\displaystyle L^{-1}\left\{\frac{3}{{(2s+7)}^4}\right\}=}$???

The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (Water Research, $1984: 1169-1174$ ) suggests the uniform distribution on the interval (7.5,20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.
What are the mean and variance of depth?
b. What is the cdf of depth?
What is the probability that observed depth is at most 10? Between 10 and $15 ?$
What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

Find the derivatives of the functions defined as ${\displaystyle y=2x{\sec }^{4}x}$