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New questions in Mathematics
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
By differentiating the function f(x)=(x³−6x)⁷ we will obtain
Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.
All the liquid contained in a barrel is distributed into 96 equal glasses up to its maximum capacity. We want to pour the same amount of liquid from another barrel identical to the previous one into glasses identical to those used, but only up to 3/4 of its capacity. How many more glasses will be needed for this?
2.3/-71.32
-4y-6(2z-4y)-6
In a order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with Sample 1 the results found in the table to the right. Complete parts a through e below. X1 = 5,319 S1= 143 a. Use a 95% confidence interval to estimate the difference between the population means (H - H2) Interpret the contidence interval. The contidence interval IS (Round to one decimal place as needed.) Sample 2 X2 = 5,285 S2 = 198 Aa. Use a 95% confidence interval to estimate the difference between the population means (A1 - M2) Interpret the contidence interval. The contidence interval Is (Round to one decimal place as needed.) b. Test the null hypothesis Ho versus alternative hypothesis Ha (H What is the test statistic? H2) + Give the significance level of the test, and interpret the result. Use a = 0.05. Z=
Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?
Which of the methods below can be used to workout 95% of an amount? a. Dividing the amount 100 and multiply by 95 b. Working out 5% of the amount and taking it away from the full amount c. Dividing 95 by 100 and multiplying the answer by the amount d. Dividing the amount by 95 and then multiply by 100
392929-9
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
A buyer purchased a North Carolina home for $475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of $110,000. How much is the excise tax paid in the transaction? $951 $729.50 $950.50 $221 none of the above
Calculate the pH of a solution obtained by mixing 100ml of 0.2M HCl with 100ml of 0.1M NaOH
A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
The slope of the tangent line to the curve f(x)=4tan x at the point (π/4,4)
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a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?
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You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations): Overheads R 176,200 Cost of capital (% of purchase price per annum) 11.25% Annual License Fees—Truck R 16,100 Driver Monthly cost R 18,700 Assistant Monthly cost R 10,500 Purchase price: - Truck R 1,130,000 Depreciation: straight line method Truck residual value 25% Truck economic life (years) 5 Purchase price: Trailer R 370,000 Tyre usage and cost (c/km) 127 Trailer residual value 0% Trailer economic life (years) 10 Annual License Fees—Trailer R 7,700 Fuel consumption (liters/100km) 22 Fuel price (c/liter) 2053 Insurance (% of cost price) 7.5% Maintenance cost (c/km) 105 Distance travelled per year (km) 48000 Truck (tyres) 6 Trailer (tyres) 8 New tyre price (each) R 13,400 Lubricants (% of fuel cost) 2.5% Working weeks 50 Working days 5 days / week Profit margin 25% VAT 15% Q1. Calculate the annual total vehicle costs (TVC)
A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)
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We have received our p&l statement back from accounts. The board has asked for an innovation hub. What items should we prioritise reviewing to decide if we can afford an innovation hub?
2X+2=8
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25) Paulo saves R$250.00 per month and keeps the money in a safe in his own home. At the end of 12 months, deposit the total saved into the savings account. Consider that, each year, deposits are always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account after 3 years, from the moment you started saving part of your money monthly, it will be A) R$6,644.70. B) R$ 9,210.00. C) R$ 9,644.70. D) R$ 10,319.83. E) R$ 13,319.83
A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
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