The equation y=-1777x+27,152 can be used to predict the number of y of gun deaths in the U.S. x years after 2000, that is x=0 corresponds to 2000, x=3 corresponds to 2003, x=4 corresponds to 2004 and so on. Predict the number of gun deaths in 2004 and 2007. In what year will the number of gun deaths be 12,937?
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graph the equation using the slope and the y-intercept. Y=5/3x+7
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In 1994, the life expectancy of males in a certain country was 65.7 years. In 2000, it was 69.0 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994.
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Trains A and B are traveling the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling 110 mph. Train A passes a station at 6:10 A.M. If train B passes the same station at 6:40 A.M. at what time will train B catch up with Train A?
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To predict the number of gun deaths in a specific year using the equation y = -1777x + 27,152, where x represents the number of years after 2000:
1. To find the number of gun deaths in 2004 (x = 4), substitute x = 4 into the equation:
y = -1777(4) + 27,152
y = -7108 + 27,152
y = 20,044
Therefore, the predicted number of gun deaths in 2004 is 20,044.
2. To find the number of gun deaths in 2007 (x = 7), substitute x = 7 into the equation:
y = -1777(7) + 27,152
y = -12,439 + 27,152
y = 14,713
Therefore, the predicted number of gun deaths in 2007 is 14,713.
To find the year when the number of gun deaths is 12,937, we need to set the equation equal to that value and solve for x:
12,937 = -1777x + 27,152
Rearranging the equation to solve for x:
-1777x = 12,937 - 27,152
-1777x = -14,215
Dividing both sides by -1777:
x = 8
Since x represents the number of years after 2000, we add 8 years to 2000 to find the year:
2000 + 8 = 2008
Therefore, the number of gun deaths is predicted to be 12,937 in 2008.
For the equation y = 5/3x + 7:
The slope of the line is 5/3, which means that for every 3 units increase in x, y will increase by 5 units. The y-intercept is 7, which is the point where the line crosses the y-axis.
To graph the equation:
1. Start by plotting the y-intercept, which is the point (0, 7). This is where the line intersects the y-axis.
2. From the y-intercept, use the slope of 5/3 to find additional points on the line. For example, if we increase x by 3, y should increase by 5:
(0 + 3, 7 + 5) = (3, 12)
Plot the point (3, 12).
3. Connect the plotted points with a straight line.
To find when Train B catches up with Train A:
1. Determine the time difference when Train B passes the station (6:40 A.M.) and when Train A passes the station (6:10 A.M.):
Train B takes 30 minutes (6:40 - 6:10)
Train A takes 0 minutes
2. Train B catches up to Train A at a rate of 10 mph (110 mph - 100 mph).
3. Since Train B is 30 minutes ahead at the start, it needs to cover the distance Train A travels in that time plus the additional distance to catch up.
4. The distance Train A travels in 30 minutes at 100 mph is:
Distance = speed * time
Distance = 100 mph * (30 minutes / 60 minutes per hour)
Distance = 100 mph * 0.5 hours
Distance = 50 miles
5. Train B needs to cover the initial 50 miles and the additional distance to catch up, which is equal to the distance Train A travels in time t.
6. Set up an equation to find the time t:
Distance covered by Train B = Distance covered by Train A
50 miles + 10 mph * t = 100 mph * t
7. Solve for t:
50 miles + 10t = 100t
50 miles = 90t
t = 50 miles / 90 = 5/9 hours
8. Convert the time to minutes:
5/9 hours * 60 minutes per hour = 33.33 minutes
9. Add the time difference to the starting time of Train B:
6:40 A.M. + 33.33 minutes ≈ 7:13 A.M.
Therefore, Train B will catch up with Train A at approximately 7:13 A.M.