Q and A for the topic: General

A summer camp has 672 campers who will be going on an outing. Estimate the number of vans needed to accommodate the entire camp if each van can comfortably hold 12 passengers. Then calculate the actual number of vans that will be needed.

80,829−77,931⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ Step 2 of 2 : Find the actual difference.

Round the following whole number to the nearest ten thousand. 50,705

The Gorno-Altai Autonomous Soviet Socialist Republic, whose residents mainly spoke Altai,was one of many nominally autonomous Soviet___ by giving these restive republics the right to assert their prerogatives，President Mikhail Gorbachev likely hastened the Soviet Union's breakup. Which choice completes the text so that it conforms to the conventions of Standard English? A republics; established along ethnolinguistic lines B republics established along ethnolinguistic lines, C republics. Established, along ethnolinguistic lines, D republics established along ethnolinguistic lines;

A system is in………………….. equilibrium if the temperature is the same throughout the entire system.

A system is in…………………..equilibrium if there is no change in pressure at any point of the system with time.

Express in polar form z=-4-3i

Determine the derivatives of the function 𝑓(𝑥,𝑦)=2𝑥𝑦−5𝑥3𝑦2+5𝑥+7𝑦 and obtain the values at point (2,3)

Elon has misplaced the sales contract for his and cannot remember the amount he originally financed. He know that the add-on interest rate was 5.2% and the loan required a total of 36 monthly payments of $314.53 each. How much did Elon borrow?

Elsies Limited is a nationally recognised supplier of catering equipment. It offers safe and secure shopping via its online store and its state-of-the-art premises in each of the provinces of South Africa. The company offers a wide selection of catering equipment and supplies at competitive prices. The target market includes restaurants, hotels, hostels and spaza shops. Their products carry an industry-leading warranty that is backed by good after-sales service and availability of spares. The company was established in 2015 with an authorised share capital of 1 500 000 ordinary shares of which 900 000 were issued at R2 each at the initial public offering in 2015. The financial manager and her team were in the process of forecasting the financial performance for 2024 and financial position of the company as of 31 December 2024. The starting point was the following figures that were obtained from the financial statements for the year ended 31 December 2023: The sales amounted to R9 600 000, and the cost price of the goods sold was R7 200 000. Operating expenses totaled R1 200 000 whilst the company tax amounted to R336 000. The carrying value of the fixed assets was R4 200 000 whilst the inventories, trade debtors and cash reflected values of R1 200 000, R1 800 000 and R600 000 respectively. The ordinary share capital balance remained unchanged since the establishment of the company in 2015 whilst the undistributed profits of the company accumulated to R2 100 000. An amount of R2 400 000 was owed to Jip Bank for a long-term loan. The amount owed to trade creditors was R1 467 000 and the company tax payable to SARS was R33 000. The following predictions were made for the financial year ended 31 December 2024: Sales are expected to increase by 25%. Seventy-five percent (75%) of the total sales is estimated to be on credit. Company tax will be calculated at 27% of the pre-tax profit and 10% of this amount is expected to be unpaid on 31 December 2024. A final dividend of R400 000 is expected to be declared on 31 December 2024, and is payable during 2025. The unsold shares are expected to be issued on 31 March 2024 at R3 each. The amount owed by trade debtors will be based on a collection period of 54.75 days. The company’s closing inventory and the amount owed to trade creditors are expected to change directly with the change in sales in 2024. A new machine with a cost price of R700 000 will be purchased during January 2024. Depreciation for 2024 (included in the operating expenses) is expected to amount to R300 000. R760 000 will be paid to Jip Bank during 2024 and this amount includes R360 000 for interest. The cash balance must be calculated (balancing figure). Elsies Limited is considering the purchase of a machine to manufacture some of the spare parts for the catering equipment during 2025. The company desires a minimum required rate of return of 12%. The machine will cost R2 000 000 plus R400 000 for installation and is predicted to have a useful life of five years. A salvage value of R100 000 is estimated. The machine is expected to generate cash inflows of R800 000 per year but will require the employment of two new machine operators at R100 000 per year for each operator, and it will require maintenance and repairs averaging R40 000 per year. Depreciation will be calculated using the straight-line method. Refer to the investment opportunity for 2025 and calculate the following. (Ignore taxes.) Where discount factors are required, use the four decimals present value tables that appear in the module guide. 2.1 Accounting Rate of Return on average investment (expressed to two decimal places). (3) 2.2 Benefit Cost Ratio (expressed to two decimal places). (4) 2.3 Internal Rate of Return (expressed to two decimal places). Your answer must reflect two NPV calculations (using consecutive rates/percentages) and interpolation.

Find the numerical value if x=5 and y=3 4(x+7y)=

Obtain the gradient vector for the function 𝑓(𝑥,𝑦)=5𝑥²𝑦³, at the point (𝑥,𝑦)=(3,2)

approximate value of the area of the region y=4x^(2),y=e^(x)

The quality manager at Bestiful Company is certifying a new process that must produce 95% (or better) good product before the process is considered proven. A sample of 40 containers from the process line are tested, and 93% are found to be good. (a) Formulate the appropriate hypotheses and test them using an α = 0.01 significance level. (b) Explain your results.

3 divided by 135

Calculate the derivatives of the functions: 𝑦 = 6𝑥5− 8𝑥4 + 3𝑥3 + 𝑥 − 15

Watch or read an interview—it can be focused on a person that you are interested in (such as a celebrity discussing their life) or a cause you are interested in (such as someone describing the impact that a charity has had on their life). The interview can be accessed via a YouTube video, a documentary, or an article from a magazine or newspaper (e-versions of these publications are entirely acceptable).

Jack purchased a new stereo that sells for $1200 including tax and delivery. He paid $750 down and the remaining cost in five equal monthly payments. What were his monthly payments?

log5 1 25 = −2,

A secretary is making an inventory of office supplies. She finds 12 full boxes of blue pens which have 15 pens in each box. How many pens will she indicate on the inventory?