Which of the following are exact numbers? $\pi=3.1415927$

Major League Bat Company manufactures baseball bats. In addition to its work in process inventories, the company maintains inventories of raw materials and finished goods. It uses raw materials as direct materials in production and as indirect materials. Its factory payroll costs include direct labor for production and indirect labor. All materials are added at the beginning of the process, and conversion costs are applied uniformly throughout the production process. You are to maintain records and produce measures of inventories to reflect the July events of this company. Set up the following general ledger accounts and enter the June 30 balances: Raw Materials Inventory, $25,000; Work in Process Inventory,$8,135 ($2,660 of direct materials and$5,475 of conversion); Finished Goods Inventory, $110,000; Sales,$0; Cost of Goods Sold, $0; Factory Wages Payable,$0; and Factory Overhead, $0. 1. Prepare journal entries to record the following July transactions and events. a. Purchased raw materials for$125,000 cash (the company uses a perpetual inventory system). b. Used raw materials as follows: direct materials, $52,440; and indirect materials,$10,000. c. Recorded factory wages payable costs as follows: direct labor, $202,250; and indirect labor,$25,000. d. Paid factory payroll cost of $227,250 with cash (ignore taxes). e. Incurred additional factory overhead costs of$80,000 paid in cash. f. Allocated factory overhead to production at 50% of direct labor costs. 2. Information about the July inventories follows. Use this information with that from part 1 to prepare a process cost summary, assuming the weighted-average method is used. $$ \begin{matrix} \text{Units}\\ \text{Beginning inventory}\ldots\ldots\ldots & \text{5,000 units}\\ \text{Started} \ldots\ldots\ldots & \text{14,000 units}\\ \text{Ending inventory} \ldots\ldots\ldots & \text{8,000 units}\\ \text{Beginning inventory}\\ \text{Materials—Percent complete} \ldots\ldots\ldots & \text{100\\%}\\ \text{Conversion—Percent complete}\ldots\ldots\ldots & \text{75\\%}\\ \text{Ending inventory}\\ \text{Materials—Percent complete} \ldots\ldots\ldots & \text{100\\%}\\ \text{Conversion—Percent complete} \ldots\ldots\ldots & \text{40\\%}\\ \end{matrix} $$ 3. Using the results from part 2 and the available information, make computations and prepare journal entries to record the following: g. Total costs transferred to finished goods for July (label this entry g). h. Sale of finished goods costing $265,700 for$625,000 in cash (label this entry h). 4. Post entries from parts 1 and 3 to the ledger accounts set up at the beginning of the problem. 5. Compute the amount of gross profit from the sales in July. (Note: Add any underapplied overhead to, or deduct any overapplied overhead from, the cost of goods sold. Ignore the corresponding journal entry.)

Find the derivative of f(x) and the indefinite integral of g(x). $f(x)=e^{4 x} ; g(x)=\frac{1}{x}$

Specify which of the following equations represent oxidation–reduction reactions, and indicate the oxidizing agent, the reducing agent, the species being oxidized, and the species being reduced. $2 \mathrm{H}^{+}(a q)+2 \mathrm{CrO}_{4}^{2-}(a q) \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$

Find each of the indefinite integrals $\int \sin x \cos x \, d x$.

A rectangular block has dimensions $2.9\ \mathrm{cm} \times 3.5\ \mathrm{cm} \times 10.0\ \mathrm{cm}.$ The mass of the block is 615.0 g. What are the volume and density of the block?

Give a pair of limit expressions that describe the end behavior of the function. $f(x)=\frac{9 x^{2}+6 x+1}{4 x^{2}+4 x+1}$

A parallel-plate capacitor consists of two square plates, size $L \times L$, separated by distance d. The plates are given charge $\pm Q$. What is the ratio $E_{\mathrm{f}} / E_{\mathrm{i}}$ of the final to initial electric field strengths if (a) Q is doubled, (b) L is doubled, and (c) d is doubled? Each part changes only one quantity; the other quantities have their initial values.

Use vectors, and also the dot and cross product, to prove the following theorems from geometry. In a kite (four-sided figure made up of two pairs of equal adjacent sides), the diagonals are perpendicular.

Find each derivative and simplify. $\frac{d}{d x}\left[3 x\left(x^{2}+1\right)^{3}\right]$

Prepare a proper title for the annual schedule of cost of goods manufactured of Google. Does the date match the balance sheet or income statement? Why?

The values of the following integrals are known and can be found in integral tables or by computer. Your goal in evaluating them is to learn about contour integration by applying the methods discussed in the examples above. Then check your answers by computer. $\int_{0}^{\infty} \frac{\cos 2 x d x}{\left(4 x^{2}+9\right)^{2}}$

Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the plane. Complete the following steps for each vector field F. a. Calculate the two-dimensional curl of F. b. Calculate the two-dimensional divergence of F. c. Is F irrotational on R? d. Is F source free on R? F = (y, -3x)

The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent. $\int 3 x^{2}\left(x^{3}+1\right) d x$