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 2004 and 2007 using the equation y = -1777x + 27,152, we need to substitute the appropriate values of x into the equation.
For 2004 (x = 4), we have:
y = -1777(4) + 27,152
y = -7108 + 27,152
y = 19,044
Therefore, the predicted number of gun deaths in 2004 is 19,044.
For 2007 (x = 7), we have:
y = -1777(7) + 27,152
y = -12,439 + 27,152
y = 14,713
So, the predicted number of gun deaths in 2007 is 14,713.
To find the year when the number of gun deaths will be 12,937, we can rearrange the equation and solve for x.
12,937 = -1777x + 27,152
Subtract 27,152 from both sides:
-14,215 = -1777x
Divide both sides by -1777 to solve for x:
x = -14,215 / -1777
x ≈ 7.999
Since x represents the number of years after 2000, we can round 7.999 to 8. Therefore, the number of gun deaths will be 12,937 approximately 8 years after 2000.
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To graph the equation y = 5/3x + 7, we can use the slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.
In this equation, the slope is 5/3, which means for every unit increase in x, y will increase by 5/3 units. The y-intercept is 7, which is the value of y when x is 0.
To graph this equation, start by plotting the y-intercept point (0, 7). Then, use the slope to determine other points on the line. For example, if x increases by 3, y will increase by 5/3 * 3 = 5 units. So, you can plot the point (3, 7 + 5) = (3, 12).
Continue this process to find more points, and then connect them to create a straight line. The graph of the equation y = 5/3x + 7 will look like a diagonal line with a positive slope.
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To represent life expectancy in year t since 1994, we can use the equation E = 65.7 + (69.0 - 65.7)t.
Here, E represents the life expectancy, and t represents the number of years since 1994. The equation takes the initial life expectancy in 1994 (65.7) and adds the annual increase (69.0 - 65.7) multiplied by the number of years since 1994 (t).
For example, in 1998 (4 years since 1994), we have:
E = 65.7 + (69.0 - 65.7)(4)
E = 65.7 + 3.3(4)
E = 65.7 + 13.2
E = 78.9
Therefore, the life expectancy in 1998 is 78.9 years.
You can use the same equation for any year t since 1994 by plugging in the appropriate value for t.
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To determine the time when Train B catches up with Train A, we need to find the time difference between when Train A passed the station and when Train B passed the station.
Given that Train A passed at 6:10 A.M. and Train B passed at 6:40 A.M., the time difference is 30 minutes.
Since Train B travels at a faster speed, it will catch up with Train A after the same amount of time it took for the time difference to occur.
Therefore, Train B will catch up with Train A 30 minutes after they both passed the station at 6:40 A.M. This means they will meet at 7:10 A.M.