Asecurity alarm requires a four digit code the code can use the digits 0-9 and the digits cannot be repeated what is the approximate probability that the code contains only odd numbers

Probability = 0.2381

Step-by-step explanation:

A security alarm requires a four digit code by using 0 - 9 and the digits cannot be repeated.

First we calculate how many codes can be made.

Combination =

Where n = 10 and r = 4

=

         =

         = 10 × 9 × 8 × 7

        = 5,040 combinations.

Now we have to find the probability that the code contains only odd numbers. So in 0-9 the odd numbers are = 1, 3, 5, 7, 9

There are 5 odd numbers and we have to make a code of 4 numbers.

Therefore, On first place there are 5 options and in second place 4 options, in third place there are 3 options and in fourth place we have only 2 options.

5 × 4 × 3 × 2  = 120 combinations.

Total combinations of odd numbers are 120.

Then the probability that the code contains only odd numbers is

= 0.0238095 ≈  0.02381

Probability = 0.2381

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)

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.