How to solve this math problem, and teach me it too.?
1) let R = the rate of the river in mph Upriver, the overall rate is (8 - R) (the canoe is slowed by the river) Downriver, the overall rate is (8 + R) Distance = Rate * Time so Time = Distance/Rate Upriver time = 60/(8-R) Downriver time = 60/(8+R) Overall time is 16 hours, so... 16 = 60/(8-R) + 60/(8+R) Multiply through by (8-R)(8+R) (8-R)(8+R)16 = 60(8+R) + 60(8-R) (64 - R^2)16 = 480 + 60R + 480 - 60R (64 - R^2)16 = 960 64 - R^2 = 60 4 = R^2 R = +- 2 Based on the problem, R can't be negative, so... The rate of the river is 2 mph --------------------------------------... 2) Let C be the price of cashews per pound Let P be the price of peanuts per pound. 4C + 3P = 10.54 5C + 2P = 11.11 Two equations, two unknowns.... Multiply the first equation through by 2 and the second equation through by 3 8C + 6P = 21.08 15C + 6P = 33.33 Now subtract the first equation from the second... 7C + 0P = 12.25 C = 1.75 The cashews cost $1.75/pound --------------------------------------... let B = the width of the border. Since the border is along all 4 sides, the new length will be 11 - 2B and the new width will be 8 - 2B Area = L*W or (11 - 2B)(8 - 2B) = 54 Use foil... 11*8 + (-2B)*8 + 11*(-2B) + (-2B)*(-2B) = 54 88 - 16B - 22B + 4B^2 = 54 34 - 38B + 4B^2 = 0 2B^2 - 19B + 17 = 0 Factor (2B - 17)(B - 1) = 0 By the zero property, either (2B - 17) = 0 OR (B - 1) = 0 so... 2B = 17, B = 17/2 = 8.5 or B - 1 = 0, B = 1 The first root (B = 8.5) does not make sense, as the border can't be wider than the paper. So the answer is... The border is 1 inch wide -------------------------------------- 4) since the vat fills in 40 minutes, the fill rate is (1/40) vats/minute since the vat drains in 120 minutes, the drain rate is (1/120) vats/minute. (1/40) vats/minute - (1/120) vats/minute = 1 vat 3/120 vats/minute - 1/120 vats/minute = 1 vat 2/120 vats/minute = 1 vat 1/60 vats/minute = 1 vat 1 vat = 60 minutes. So.... The vat takes 1 hour to fill.
What are the things that need to be considered when starting new business?
When starting a business you need to know the following:A business starts with a need - identify a need that is shared by many people, who are willing to pay for a solution. Identifying a need is as simple as asking them.Forget about changing the world - your first concern is creating cash flow, so focus on products or services that are easy to sell and is something people would need to keep on buying.Don’t start a business to earn money for living costs - that is why you need a job. Businesses are investments that take time to mature. As my one mentor always said: bread and butte money comes first, and then you can play.Keep track of everything - the value of your business depends on how well you keep and use records. Write invoices and receipts, track emails, copy and store administrative documents and contracts. Make sure that you know precisely how much money is coming in and going out at any given time.Be ready to fail - success isn’t getting lucky at your first try. You are going to live an exciting adventure and you will probably fail many times before you get it just right.Sell your product or service before it exists - it may seem contrary, but we call this validation. If people are excited enough about your offering to hand you a deposit or sign an order before you are there, you have proof that your business can work.Don’t make debt - if you absolutely have to get money, rather get investors. Debt is an evil pit of slavery that will steal your personal money and leave you a poor man.Have fun - don’t get too caught up in chasing money. Money is worth nothing - it is the experiences, friendships and knowledge we gain that has true value. No amount of money is worth a sleepless night.
How do I calculate my hourly rate as a consultant?
There are 2 ways to do calculate the consulting rate per hour. In most cases, the results are about the same.1. Simplified formula:Take your annual salary, divide it by 2,000 hours and multiply it by 2Take your annual salary, divide it by 2,000 hours and multiply it by 3The above responses will give you the range to charge per hour.For example:Annual salary $100,000, divided by 2,000= $50multiplied by 2= $100.multiplied by 3= $150.Based on these results, you should charge $100 to $150 per hour.To simplify the formula, we are dividing by 2,000. Most people work fewer hours per year, some more (see below).2. Detailed formula:Salary $100,000Bonus (25%) $25,000Medical care $16,000401K contribution (6%) $ 6,000Paid vacation + paid public holidays $7,692Corporate discounts, Thanksgiving turkey $900Employer taxes* $ 12,500Total compensation $ 168,092Hours worked 1,681Rate per hour $100*Employer taxes include: Social Security Taxes, Medicare Taxes, Federal Unemployment Taxes (FUTA Tax), State Unemployment Taxes (SUTA Tax), Disability Taxes, Work Force Development Taxes, Family Leave Insurance, Worker Compensation Tax, Health Care Tax (MA).**Corporate discounts include: Gym subsidized fee, Day Care, Hotel & Car discounts, the turkey you get at Thanksgiving etc.About the rangeThe best way to calculate a consulting rate is not based on how much money one was making before, but rather on how much an employer would pay to hire a new employee.In 2019, the national range in the US for a Corporate Controller is $100,000 to $150,000 (40% more in NYC). Therefore, the range of the rate to charge should be $100 (assuming a $100,000 salary) to $150 (assuming a $150,000 salary).GeorgeLinkedin Twitter