The distribution of the possible digits of the numbers are
1.) 9, 9, 9, 9, 3 [Number of arrangements = 5! / 4! = 120 / 24 = 5]
2.) 9, 9, 9, 8, 4 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
3.) 9, 9, 9, 7, 5 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
4.) 9, 9, 9, 6, 6 [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
5.) 9, 9, 8, 8, 5 [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
6.) 9, 9, 8, 7, 6 [Number of arrangements = 5! / 2! = 120 / 2 = 60]
7.) 9, 9, 7, 7, 7 [Number of arrangements = 5! / (3! x 2!) = 120 / 12 = 10]
8.) 9, 8, 8. 8, 6 [Number of arrangements = 5! / 3! = 120 / 6 = 20]
9.) 9, 8, 8, 7, 7 [Number of arrangements = 5! / (2! x 2!) = 120 / 4 = 30]
10.) 8, 8, 8, 8, 7 [Number of arrangements = 5! / 4! = 120 / 24 = 5]
Number of 5 digit numbers whose digit sum up to 39 = 5 + 20 + 20 + 10 + 30 + 60 + 10 + 20 + 30 + 5 = 210
The formula to calculate the sample size is:
n = Z number * standard deviation/ confidence estimate)^2
The z number for 95% confidence is 1.96
The standard deviation is given as 26 minutes.
The confidence estimate is given as 5 minutes.
The sample size is: (1.96 * 26/5)^2 = 103.87 = 104 shoppers.
Answer:
(a) 128 ft
(b) 4 s
(c) Vertex: (1, 144)
Step-by-step explanation:
Given information:
- h(t) = height in feet
- t = time in seconds after the launch
<h3><u>Part (a)</u></h3>
The height of the projectile at launch is the value of h(t) when t = 0 (the y-intercept).
Therefore, from inspection of the graph, the y-intercept is (0, 128).
So the <u>height of the projectile at launch is 128 ft</u>.
<h3><u>Part (b)</u></h3>
The length of time it took for the projectile to land is the time from the beginning (when t = 0) to when the height is 0 (the x-intercept).
From inspection of the graph, the x-intercept is (4, 0)
So the <u>length of time it took for the projectile to land is 4 s</u>.
<h3><u>Part (c)</u></h3>
The vertex is the turning point (minimum/maximum point).
Therefore, from inspection of the graph, the <u>vertex is (1, 144)</u>.
The vertex represents the time and height at which the projectile was at its maximum. So at the time of 1 second, the projectile was at its maximum height of 144 ft.
