Question

1. find the mean of the integers: 5, -7, 12, -10, 15
2. evaluate the expression: |-16|+(-2)^2 - 4^2
3. 6 - 12+(-3)
4. \frac{-10+(-2)}{-3}
5. -96, 48, -24, 12,... find the next two numbers in the pattern.
6. 12500, -2500, 500, -100,...
7. a skateboarder descends on a ramp from 172 feet to 67 feet in 15 seconds. what is the mean change in height per second?
8. the velocity (in feet per second) of a bouncing ball was recorded every second. the table shows the velocity for each second.

time (sec)	velocity (ft/sec)
2	-6
3	2
4	10
5	-11

Explanation:

1. First, find the sum of the integers: \(5+( - 7)+12+( - 10)+15 = 5 - 7+12 - 10+15=15\). There are 5 integers. The mean is \(\frac{15}{5}=3\).
2. \(| - 16|+( - 2)^2-4^2=16 + 4-16 = 4\).
3. \(6-12-3=-9\).
4. The sequence \(-96,48,-24,12,\cdots\) is a geometric - sequence with a common ratio \(r=-\frac{1}{2}\). The next two numbers are \(12\times(-\frac{1}{2})=-6\) and \(-6\times(-\frac{1}{2}) = 3\).
5. The sequence \(12500,-2500,500,-100,\cdots\) is a geometric - sequence with a common ratio \(r =-\frac{1}{5}\).
6. The mean change in height is \(\frac{67 - 172}{15}=\frac{- 105}{15}=-7\) feet per second.
7. To find the mean change in velocity, first find the differences in velocity for each time - interval:

• From \(t = 1\) to \(t = 2\): \(-6-( - 15)=9\).
• From \(t = 2\) to \(t = 3\): \(2-( - 6)=8\).
• From \(t = 3\) to \(t = 4\): \(10 - 2 = 8\).
• From \(t = 4\) to \(t = 5\): \(-11 - 10=-21\).
• The sum of the differences is \(9 + 8+8+( - 21)=4\). There are 4 intervals. The mean change in velocity is \(\frac{4}{4}=1\) ft/sec.

Answer:

(14) 3
(15) 4
(16) -9
(19) -6, 3
(20) Geometric sequence with \(r =-\frac{1}{5}\)
(21) -7 feet per second
(22) 1 ft/sec