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线性建模・解释与预测进阶
Scientists collected fallen acorns that each housed a colony of the ant species P . ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has x worker ants, the equation \( y=0.67x+2.6 \), where \( 20\le x\le110 \), gives the predicted number of larvae, y, in the colony. If one of these colonies has 53 worker ants, which of the following is closest to the predicted number of larvae in the colony?
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线性建模・解释与预测挑战
To purchase a used car at a total price of 11,000 dollars, a onetime down payment is required, and then fixed monthly payments are made for the remaining amount owed for the car. The equation \( 11,000=2,200+200t \) represents this situation, where t is the number of fixed monthly payments that are made. Which of the following is the best interpretation of 200 in this context?
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线性建模・解释与预测进阶
\( w\left(t\right)=600-3t \)
The function w models the volume of water, in milliliters, in a container t seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?
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线性建模・解释与预测进阶
\( W\left(x\right)=4x+80 \)
The function W gives the total time, in minutes, it takes for a gardener to water x plants and mow the grass. According to the function, how many minutes does it take the gardener to mow the grass?
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线性建模・解释与预测进阶
A bank account was opened with an initial deposit. Over the next several months, regular deposits were made into this account, and there were no withdrawals made during this time. The graph of the function \( f \) shown, where \( y=f\left(x\right) \), estimates the account balance, in dollars, in this bank account x months since the initial deposit. To the nearest whole dollar, what is the amount of the initial deposit estimated by the graph?
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线性建模・解释与预测进阶
The function \( F\left(m\right)=7m \), models the force, in newtons, acting on each object in a certain field as a function of the object's mass m, in kilograms. Which statement is the best interpretation of \( F\left(4\right)=28 \) in this context?
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线性建模・解释与预测进阶
A school swim team sold shirts to raise money. The team raised $13 from each short-sleeved shirt sold and raised $14 from each long-sleeved shirt sold. The team raised a total of $423 from the sale of these shirts. The equation \( 13x+14y=423 \) represents this situation. Which of the following is the best interpretation of y in this context?
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线性建模・解释与预测进阶
A linear model estimates the population of a city from 1995 to 2019. The model estimates the population was 55 thousand in 1995, 217 thousand in 2015, and x thousand in 2019. To the nearest whole number, what is the value of x?
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线性建模・解释与预测进阶
A family has money in an account for renting movies online. Each time the family rents a movie, the cost of the rental is withdrawn from the account, and each rental costs the same amount of money. The function \( f\left(m\right)=21-3m \) gives the amount of money, in dollars, in the account after the family has rented m movies. Which of the following represents the amount of money, in dollars, withdrawn from the account each time the family rents a movie?
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线性建模・解释与预测进阶
The graph models the number of active projects a company was working on x months after the end of November 2011, where \( 0\le x\le6 \). According to the model, what is the predicted number of active projects the company was working on at the end of November 2011?
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线性建模・解释与预测进阶
\( d=15t \)
The given equation relates the distance d, in inches, of an object from its starting position to the time t, in seconds, since the object started moving. What is the rate of change of the object's distance from its starting position over time?
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线性建模・解释与预测进阶
A company that manufactures staplers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The equation \( 11,000=2.00x-6,500 \) represents this situation for a month where x staplers are manufactured and sold. Which statement is the best interpretation of \( 2.00x \) in this context?
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