A set of 25 two digit numbers are listed below 10,17,20,23,24,28,32,39,42,25,26,52 ,55,58,61,65,66,72,75,78,79,85,94,9 7,98. What is the probability of the sum of the number's digits is odd?

0.48

Step-by-step explanation:

Given the data:

X:

10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98

Sum of each of the numbers :

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Probability that sum of the number's digit is odd:

Number of odd sum / total numbers

Number of odd sum = 12

Total numbers = 25

12 / 25

= 0.48

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.

a sample of water is taken and kept in a beaker in a freezer at a constant temperature of 0°c. if the system is at dynamic equilibrium, which of these statements is true?