Paula's bank statement showed the following transactions for last month. The beginning balance was $138.24. There was a withdrawal of$46.59, then a deposit of $29.83, plus$1.87 in interest added. What was the balance after these transactions?

A motorboat starts from rest (initial velocity $v(0) = v_0 = 0$). Its motor provides a constant acceleration of $4 \text { ft } / \mathrm { s } ^ { 2 }$, but water resistance causes a deceleration of $v ^ { 2 } / 400 \text { ft } / \mathrm { s } ^ { 2 }$. Find $v$ when $t = 10 \text{ s,}$ and also find the limiting velocity as $t \rightarrow + \infty$(that is, the maximum possible speed of the boat).

A car travels along a road, which for a short distance is defined by $r=(200 / \theta) \mathrm{ft}$, where $\theta$ is in radians. If it maintains a constant speed of $v=35 \mathrm{ft} / \mathrm{s}$, determine the radial and transverse components of its velocity when $\theta=\pi / 3 \mathrm{rad}$.

An electric motor at steady state draws a current of $10\ \mathrm{amp}$ with a voltage of $110 \mathrm{~V}$. The output shaft develops a torque of $10.2 \mathrm{~N} \cdot \mathrm{m}$ and a rotational speed of $1000\ \mathrm{RPM}$. (a) If the outer surface of the motor is at $42^{\circ} \mathrm{C}$. determine the rate of entropy production within the motor, in $\text{kW}/ \mathbf{K}$. (b) Evaluate the rate of entropy production, in $\mathrm{kW} / \mathrm{K}$, for an enlarged system that includes the motor and enough of the nearby surroundings that heat transfer occurs at the ambient temperature, $22^{\circ} \mathrm{C}$.

Which of the following steps is optional during the closing process?

a. Adjusting entries are journalized and posted to the ledger.
b. An end-of-period spreadsheet is prepared.
c. An unadjusted trial balance is prepared.
d. A post-closing trial balance is prepared.

Let S be the hemisphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = a ^ { 2 }$, for $z \geq 0$, and let T be the paraboloid $z=a-\left( x ^ { 2 } + y ^ { 2 } \right) / a$, for $z \geq 0$, where $a>0$. Assume the surfaces have outward normal vectors.

Show that the flux of the radial field $F=\langle x , y , z \rangle$ across S is $2 \pi a ^ { 3 }$.

Consider the following preference schedule for four candidates.

Suppose the winner is decided by the plurality method. Analyze whether this choice satisfies the four fairness criteria.

In a news article, it is stated that a recently devel­oped geared turbofan engine produces 15,000 pounds of thrust to propel the aircraft forward. Is “pound” mentioned here lbm or lbf? Explain.

Herbert's checking account balance was $233. His account has overdraft protection if he withdraws more than his balance, but the bank charges$12 for covering the overdraft. Herbert made 4 withdrawals of $70 each. Does Herbert's account require overdraft protection? Why or why not? What is his final balance?

List (a) through (j) in the order they would be performed in preparing and completing and end-of-period spreadsheet. j. Extend the adjusted trial balance amounts to the Income Statement columns and the Balance Sheet columns.

On the line provided, write the plural form or forms of the noun below. Example 1. appendix $\underline{\text{\color{#c34632}appendixes or appendices}}$

and ________________

The current density inside a long, solid, cylindrical wire of radius $a$ is in the direction of the axis and varies linearly with radial distance $r$ from the axis according to $j=j_0 r / a$. Find the magnetic field inside the wire. Express your answer in terms of the total current $i$ carried by thz wire.

Which of the forms of psychotherapy discussed so far would probably work best for a client who has commitment issues in relationships? Why?

Consider an in-control process with mean $\mu=25$ and $\sigma=1.0.$ Suppose that subgroups of size 5 are used with control limits $\mu \pm 3 \sigma / \sqrt{n},$ and centerline at $\mu.$ Suppose that a shift occurs in the mean, and the new mean is $\mu=26.5$ (a) What is the average number of samples required (following the shift) to detect the out-of-control situation? (b) What is the standard deviation of the number of runs required?