Quadratic
The quadratic mean of 3, 5, 6, and 10 is
Find the quadratic mean of 8, 6, 3, 5, and 4.
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ELEMENTARY STATISTICS W/CONNECT >IP<
- Keplers Third Law According to Keplers third law of planetary motion, the mean distance D, in millions of miles, from a planet in our solar system to the sun is related to the time P, in years, that it takes for the planet to complete a revolution around the sun, and the relationship is D=93P2/3. It takes the planet Pluto 249 years to complete a revolution around the sun. What is the mean distance from Pluto to the sun? What is the mean distance from Earth to the sun? Give your answers to the nearest million miles.arrow_forwardEXERCISES Net Profit Margin The net profit margin tells how much profit a company makes for every dollar it generates in revenue. If N is the net income the income after tax have been paid and R is the total revenue, then the net profit margin M is given by, M(N,R)=NR A certain company pays a tax rate of 20 on its income. a. Use I for the income before taxes, and express the net income N in terms of I. Be careful: N is the part of I that is left after taxes-not the part you pay in taxes.. b. Use a formula to express the net profit margin in terms of the variables I and R.arrow_forwardFlesch Reading Ease The Flesch Reading Ease Test is a test that ranks the reading level of passages.2 Let W be the total number of words in the passage, S the number of sentences, and L the number of syllables. Then the Flesch test calculates the score F of the passage using the formula F=206.8351.015WS84.6LW. a. Calculate F for the paragraph above the one that describes the Flesch Reading Ease Test. Omit the formula itself. Round your answer to the nearest whole number. We count 3 sentences, 51 words, and 71 syllables. b. For the rest of this exercise, we consider passages that have 10 sentences and 350 syllables. Find a formula expressing F as a function of W for such passages. c. A passage is thought to be easily understandable by 13- to 15-year-old students if the Flesch scour, rounded to one decimal place, is 60 or higher. For the passages considered is part b, how many words should be in the passage to make it easily understood Suggestion: First use a table increment of 20 to get an estimate of the answer. Then change to table increment of 1. d. What is the maximum number of words in the passages considered in part b? Can there be more words than syllables? e. Bear in mind your answer from part d, and determine the maximum possible Flesch score for the passages considered in part b. Round your answer to the nearest whole number.arrow_forward
- Renting Motel Rooms You own a motel with 30 rooms, and you have a pricing structure that encourages rentals of rooms in groups. One room rents for 85, two rent for 83 each, and in general the group rate per room is found by taking 2 off the base of 85 for each extra room rented. a. How much money do you take in if a family rents two rooms? b. Use a formula to give the rate you charge for each room if you rent n rooms to an organization. c. Find a formula for a function R=R(n) that gives the revenue from renting n rooms to a convention hose. d. What is the most money you can make from rental to a single group? How many rooms do you rent?arrow_forwardAerobic Power Aerobic power can be thought of as the maximum oxygen consumption attainable per kilogram of body mass. There are a number of ways in which physical educators estimate this. One method uses the Queens College Step Test. In this test, males step up and down a 16-inch bleacher step 24 times per minute for 3 minutes, and females do 22 steps per minute for 3 minutes. Five seconds after the exercise is complete, a 15-second pulse count P is taken. Maximum oxygen consumption M, in milliliters per kilogram, for males is approximated by M=111.3-1.68P. For females, the recommended formula is F=65.81-0.74P. a. Calculate the maximum oxygen consumption for both a male and a female who show a 15-second pulse count of 40. b. What 15-second pulse count for a male will indicate a maximum oxygen consumption of 35.7 milliliters per kilogram? c. What 15-second pulse count will indicate the same maximum oxygen consumption for a male as for a female? d. What maximum oxygen consumption is associated with your answer in part c?arrow_forwardpH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?arrow_forward
- Stock is removed from a block in two operations. The original thickness of the block is represented by n. The thickness removed by the milling operation is represented by p and the thickness removed by the grinding operation is represented by t. What is the final thickness of the block?arrow_forwardCutting up a Wire A piece of wire is bent as shown in the figure. You can see that one cut through the wire produces four pieces and two parallel cuts produce seven pieces. How many pieces will be produced by 142 parallel cuts? Write a formula for the number of pieces produced by n parallel cuts.arrow_forwardHarvard Step Test The Harvard Step Test was developed4 in 1943 as physical fitness test, and modifications of it remain in use today. The candidate steps up and down on a bench 20 inches high 30 times per minute for 5 minutes. The pulse is counted three separate times for 30 seconds each: at 1 minute, 2 minutes, and 3 minutes after the exercise is completed. If P is the sum of the three pulse counts, then the physical efficiency index E is calculated using E=15,000P. The following table shows how to interpret the results of the test. Efficiency Index Interpretation Below 55 Poor condition 55 to 64 Low average 65 to 79 High average 80 to 89 Good 90 & above Excellent a. Does the physical efficiency index increase or decrease with increasing values of P? Explain in practical terms what this means. b. Express using functional notation the physical efficiency index of someone whose total pulse count is 200, and then calculate that value. c. What is the physical condition of someone whose total pulse cont is 200? d. What pulse counts will result in an excellent rating?arrow_forward
- Framing a Painting Ali paints with watercolors on a sheet of paper 20 in. wide by 15 in. high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 in. How wide is the strip of the mat showing around the picture?arrow_forwardAlexanders Formula One interesting problem in the study of dinosaurs is to determine from their tracks how fast they ran. The scientist R. McNeil Alexander developed a formula giving the velocity of any running animal in terms of its stride length and the height of its hip above the ground. The stride length of dinosaur can be measured from successive prints of the same foot, and the hip height roughly the leg length can be estimated on the basis of the size of a footprint, so Alexanders formula gives a way of estimating from dinosaur tracks how fast the dinosaur was running. See Figure 2.45. If the velocity v is measured in meters per second, and the stride length s and hip height h are measured in meters, then Alexanders formula is v=0.78s1.67h1.17. For comparison, a length of 1 meter is 39.37inches, and a velocity of 1 meter per second is about 2.2milesperhour. First, we study animals with varying stride lengths, but all with a hip height of 2meters so h=2 i. Find the formula for the velocity v as a function of the stride length s. ii. Make a graph of v versus s. Include stride lengths from 2to10meters. iii. What happens to the velocity as the stride length increases? Explain your answer in practical terms. iv. Some dinosaur tracks show a stride length of 3meters, and a scientist estimates that the hip height of the dinosaur was 2meters. How fast was the dinosaur running?arrow_forwardAPPLICATIONS 61-74 CombinationsThese exercises involve counting combinations. Jogging RoutesA jogger jogs every morning to his health club, which is eight blocks east and five blocks north of his home. He always takes a route that is as short as possible, but he likes to vary it see figure. How many different routes can he take ? Hint: The route shown can be thought of as ENNEEENENEENE, where E is East and N is North.arrow_forward
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