At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins, one with radius 3 inches and the other with radius 10 inches. Compute the surface area and the volume for each pumpkin. Then find the surface-area-to-volume ratio for both pumpkins. Which pumpkin has the larger ratio? (Do not round until the final answer. Then round to nearest tenth as needed.)
Find the angular size of a circular object with a 2-inch diameter viewed from a distance of 5 yards. (Do not round until the final answer. Then round to nearest tenth as needed.)
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of 64 squares of a chess board. On the second square the King would place two grains of wheat on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed in square 15? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
The initial population of a town is 3400, and it grows with a doubling time of 10 years. What will the population be in 12 years? (Round to the nearest whole number as needed.)
An economic indicator is increasing at the rate of 7% per year. What is its doubling time? By what factor will the indicator increase in 2 years? (Type an integer or decimal rounded to the nearest tenth as needed.)
The half-life of the radioactive element unobtanium-41 is 10 seconds. If 48 grams of unobtanium-41 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?
Urban encroachment is causing the area of a forest to decline at the rate of 9% per year. What is the half-life of the forest? What fraction of the forest will remain in 20 years? (Type an integer of decimal rounded to the nearest hundredth as needed.)
Use a growth rate of 0.6% to predict the population in 2038 of a country that in the year 2006 has a population of 400 million. Use the approximate doubling time formula. (Round the final answer to the nearest whole number as needed. Round the doubling time to the nearest year as needed.)
How many times greater is the intensityof sound from a concert speaker at a distant of 1 meter than the intensity at a distance of 14 meters?
The intensity of sound is times as strong at 1 m as at 14 m. (Simplify your answer.)
The concentration of hydroen ions in a liquid laboratory sample is 0.001 moles/liter. Find the pH of the sample. ph= (Simplify your answer.)
You drive along the highway at a constant speed of 60 miles per hour. How far do you travel in 4.7 hours? in 6.5 hours? (Type a integer or decimal.)
The price of a particular model car is $60,000 today and rises with time at a constant rate of $1,700 per year. How much will a new car cost in 5 years? Identify the independent and dependent variables. Write an equation for the linear function and use it to answer the given questions. The independent variable is ??
A $1350 washing machine in a laundromat is depreciated for tax purposes at a rate of $90 per year. Find a function for the depreciated value of the wasing machine as it varies with time. When does the depreciated value reach $0? The equation of the line in slope-intercept form is V= (Type your answer in slope-intercept form. Type an expression using t as the variable. Do not include the $ symbol in your answer.)
Find the slope and the y-intercept. Then graph the equation. y=-7x-9. What is the slope? (Type in integer or a fraction.)
Find the slope and the y-intercept. Then graph the equation. y=-2x-9. What is the slope? (Type in integer or a fraction.)
Kara’s Custom Tees experienced fixed costs of $500 and variable cost of $5 per shirt. Write and equation that can be used to determine the total expenses, find the cost, C, of Producing 20 shirts, and graph the equations. Let the x equal the total number of shirts.
Answer the questions for the problem give. The average price of a home in a town was $179,000 in 2007 but home prices are rising by 5% per year. a. Find an exponential function of the form Q=Qox(1+r)t (where r>0) for growth to model the situation described. Q=$ x (1+ )t (type an integer or a decimal.)
The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours. Suppose that a patient receives an initial does of 25 milligrams of Valium at midnight. a: How much Valium is in the patient’s blood at noon on the first day? b. Estimate when the Valium concentration will reach 25% of its initial level.
A toxic radioactive substance with a density of 2 milligrams per square centimeter is detected in the ventilating ducts of a nuclear porcessing building that was used 45 years ago. If the half-life of the substance is 20 years, what was the density of the substance when it was deposited 45 years ago? The density of the radioactive substnace when it was depositied 45 years ago was approximately mg/cm2? (Round to the nearest tenth as needed.)
5x=53 x=? (Round to the nearest hundredth as needed.)