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In 1991, the moose population in a park was measured to be 4,360. By 1999, the population was measured again to be 5,880. Assume the population continues to change linearly.

  1. Find a formula for the moose population, P since 1990.
  2. What does your model predict the moose population to be in 2003?
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In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. Let the input be years since 1990.

  1. Find a formula for the owl population, P . Let the input be years since 2003.
  2. What does your model predict the owl population to be in 2012?
  1. Ordered pairs are  ( 0 , 340 )  and  ( 4 , 285 ) m = 285 340 4 0 = 13.75  and  ( 0 , 340 ) y = m x + b y = −13.75 x + 340  or  P ( t ) = −13.75 t + 340
  2. The year 2012 corresponds to t = 9 P ( 9 ) = −13.75 ( 9 ) + 340 = 216.25  or 216 owls
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The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year.

  1. Give a linear equation for the remaining federal helium reserves, R , in terms of t , the number of years since 2010.
  2. In 2015, what will the helium reserves be?
  3. If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?
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Suppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year:

  1. Give a linear equation for the remaining oil reserves, R , in terms of t , the number of years since now.
  2. Seven years from now, what will the oil reserves be?
  3. If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?
  1. The year 2014 corresponds to t = 0 . We have  m = −25  and  ( 0 , 1820 ) y = m x + b y = 25 x + 1820  or  R ( t ) = −25 t + 1820
  2. R ( 7 ) = −25 ( 7 ) + 1820 = 645 billion cubic feet
  3. 0 = −25 t + 1820 −1820 = −25 t 72.8 = t  2014 + 72 .8 = 2086 .8 . So, in the year 2086
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You are choosing between two different prepaid cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

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You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window. How many windows would you need to have for the second company to be preferable?

Plan 1:  y = 5 x  where x is number of windows Plan 2:  y = 3 x + 40  where x is number of windows 3 x + 40 5 x 40 2 x 20 x So, more than 20 windows
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When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $17,000 a year with a commission of 12% of your sales

Option B: Base salary of $20,000 a year with a commission of 5% of your sales

How much jewelry would you need to sell for option A to produce a larger income?

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When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $14,000 a year with a commission of 10% of your sales

Option B: Base salary of $19,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Option A:  y = 0.10 x  + 14,000 where  x  is dollars of sales . Option B:  y = 0.04 x + 19 , 000  where  x  is dollars of sales 0 .10 x + 14 , 000 0.04 x + 19 , 000 0.06 x + 14 , 000 19 , 000 0.06 x 5 , 000 x 83 , 333.33 So, more than $83,333 .33 in sales
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When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $20,000 a year with a commission of 12% of your sales

Option B: Base salary of $26,000 a year with a commission of 3% of your sales

How much electronics would you need to sell for option A to produce a larger income?

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When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $10,000 a year with a commission of 9% of your sales

Option B: Base salary of $20,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Option A:  y = 0.09 x  + 10,000 where x is dollars of sales Option B:  y = 0.04 x + 20 , 000  where x is dollars of sales 0.09 x + 10 , 000 0.04 x + 20 , 000 0.05 x + 10 , 000 20 , 000 0.05 x 10 , 000 x 200 , 000 So, more than $200,000 in sales .
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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is the dimension formula of energy?
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what is viscosity?
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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what are the types of wave
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answer
Magreth
progressive wave
Magreth
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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