Вариант 1 1. Является ли поле а соленоидальным \( \quad \boldsymbol{a}=x\left(z^{2}-y^{2}\right) \boldsymbol{i}+y\left(x^{2}-z^{2}\right) \boldsymbol{j}+z\left(y^{2}+x^{2}\right) \boldsymbol{k} \) 2. Найти циркуляцию вектора F вдоль ориентированного контура L \[ \boldsymbol{F}=z^{3} \boldsymbol{i}+x^{3} \boldsymbol{j}+y^{3} \boldsymbol{k} \] \( \quad L=\left\{(x, y): 2 x^{2}+z^{2}-y^{2}=a^{2}, \quad x+y=0\right\} \) 3. Применяя дифференцирование по параметру вычислить интеграл \[ \int_{0}^{a} \frac{\ln (1+a x)}{1+x^{2}} d x \]

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 16 years with a variance of 16. If the claim is true, in a sample of 48 wall clocks, what is the probability that the mean clock life would be greater than 15.3 years? Round your answer to four decimal places.

Resuelva la fracción mixta \( \frac{9}{4}=\square \)

The Booster Club is having a bake sale. The members place 25 baked goods in each bag. There are 630 baked goods donated. About how many bags will the club have for sale?

sample of size 110 will be drawn from a population with mean 36 and standard deviation 14 . Use the \( O \) cumulative Normal Distribution Table if needed. Part: \( 0 / 2 \) Part 1 of 2 (a) Find the probability that \( \bar{x} \) will be between 33 and 38 . Round the final answer to at least four decimal places. The probability that \( \bar{x} \) will be between 33 and 38 is

Solve the following system of equations. \[ \begin{array}{l}4 x-8 z=32 \\ 6 x-y+3 z=-5 \\ 2 x+y=-45\end{array} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is ( (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is \( \{(x, y, z) \mid 2 x+y=-45\} \). The solution set is \( \varnothing \).