The only way 3 digits can have product 24 is
1 x 3 x 8 = 241 x 4 x 6 = 242 x 2 x 6 = 242 x 3 x 4 = 24
So the digits comprises of 1,3,8 or 1,4,6, or 2,2,6, or 2,3,4
To be divisible by 3 the sum of the digits must be divisible by 3.
1+ 3+ 8=12, 1+ 4+ 6= 11, 2 +2 + 6=10, 2 +3 + 4=9Of those sums of digits, only 12 and 9 are divisible by 3.
So we have ruled out all but integers whose digits consist of1,3,8, and 2,3,4.
Meanwhile they must be odd they either must end in 1 or 3.
The only ones which can end in 1 are 381 and 831.
The others must end in 3.
They must be greater than 152 which is 225. So the
First digit cannot be 1. So the only way its digits can contain of1,3,8 and close in 3 is to be 813.
The rest must contain of the digits 2,3,4, and the only way they can end in 3 is to be 243 or 423.
So there are precisely five such three-digit integers: 381, 831, 813, 243, and 423.
Answer: C
Step-by-step explanation:
For this problem, we need to know the standard form of a sine function and the meaning of each part.
Standard form: ![y=asin[b(x-h)]+k](https://tex.z-dn.net/?f=y%3Dasin%5Bb%28x-h%29%5D%2Bk)
a=amplitude
b=period
h=phase shift
k=vertical replacement/shifting
Now that we know the standard form and the components, we know that we can forget about k and plug in 0 for h. This would leave us with ![y=asin[b(x)]](https://tex.z-dn.net/?f=y%3Dasin%5Bb%28x%29%5D)
. We know that the amplitude is 2, therefore, a=2. To find the period, you divide 2π by the given period. 
, therefore, b=1/2.
[plug in a=2]
![y=2sin[b(x)]](https://tex.z-dn.net/?f=y%3D2sin%5Bb%28x%29%5D)
[plug in b=1/2]
Therefore, C is the correct answer.
Answer:
12
Step-by-step explanation:
The number of combinations for 2 shirts 3 pants and 2 shoes can be counted from the tree.
Count the different items at the end of the tree
There are 12 different combinations
Answer:
2
Step-by-step explanation:
The 2 integers are 103 and 104
