Helium expands in a nozzle from $0.8\ \mathrm{MPa}, 500 \mathrm{~K}$, and negligible velocity to $0.1\ \mathrm{MPa}$. Find the throat and exit areas for a mass flow rate of $0.34 \mathrm{~kg} / \mathrm{s}$, assuming the nozzle is isentropic. Why must this nozzle be convergingdiverging?

Evaluate expression $2^{\left(\log _2 3+\log _2 5\right)}$.

Find the image of A(3,-2) under the given composition of transformations.

$$T_{-1.4} \circ r_{y=x}$$

Write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.

If f is a function defined by y=f(x), then x is called the _____ variable, and y is the ______ variable.

Decide whether the following statement is true or false:
The least hostile and aggressive children who play violent video games get into more fights than the most hostile and aggressive children who don’t.$\underline{\phantom{blanks}}$

Given the circle with center $O$ and rectangle $ABCO$, find the diameter of the circle.

A material that has a fracture toughness of $33 \mathrm{~MPa}-\mathrm{m}^{0.5}$ is to be made into a large panel that is $2000 \mathrm{~mm}$ long by $250 \mathrm{~mm}$ wide and $4 \mathrm{~mm}$ thick. If the minimum allowable total crack length is $4 \mathrm{~mm}$, what is the maximum tensile load in the long direction that can be applied without catastrophic failure with a safety factor of $2.5$ ?

Write an if statement that assigns 20 to the variable y and assigns 40 to the variable z if the variable x is greater than 100.

Copy and complete: In the equation y=x+5, x is the _ variable and y is the ? variable.

The children's choice experiment has 210 subjects. Explain how you would assign labels to the 210 children in the actual experiment. Then use Table B at line 125 to choose only the first 5 children assigned to the first treatment.

For the bicycle pedal arm assembly in the figure with a rider-applied force of $1500 \mathrm{~N}$ at the pedal, Find the von Mises stress in the $15-\mathrm{mm}-\mathrm{dia}$ pedal arm. The pedal attaches to the arm with a $12-\mathrm{mm}$ thread. Find the von Mises stress in the screw. Find the safety factor against static failure if the material has $S_{y}=350 \mathrm{~MPa}$.

Work each problem.

Match each probability in parts (a) with one of the statements in A-F.

(a) $P(E)=-0.1$

A. The event is certain to occur. B. The event is impossible. C. The event is very likely to occur. D. The event is very unlikely to occur. E. The event is just as likely to occur as not occur. F. This probability cannot occur.

Write an equation of the conic section. Circle with center $(1,3)$ and radius 3