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Step-by-step explanation:c
Answer:
11 positive integers can be expressed.
Step-by-step explanation:
Consider the provided information.
The number of possible prime numbers are 5,7,11,and 13.
There are 4 possible prime numbers.
How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.
The formula to calculate combinations is: ![^nC_r=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
The number of ways are:
![^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}](https://tex.z-dn.net/?f=%5E4C_2%2B%5E4C_3%2B%5E4C_4%3D%5Cfrac%7B4%21%7D%7B2%21%284-2%29%21%7D%2B%5Cfrac%7B4%21%7D%7B3%21%284-3%29%21%7D%2B%5Cfrac%7B4%21%7D%7B4%21%7D)
![^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1](https://tex.z-dn.net/?f=%5E4C_2%2B%5E4C_3%2B%5E4C_4%3D%5Cfrac%7B4%21%7D%7B2%212%21%7D%2B%5Cfrac%7B4%21%7D%7B3%21%7D%2B1)
![^4C_2+^4C_3+^4C_4=6+4+1](https://tex.z-dn.net/?f=%5E4C_2%2B%5E4C_3%2B%5E4C_4%3D6%2B4%2B1)
![^4C_2+^4C_3+^4C_4=11](https://tex.z-dn.net/?f=%5E4C_2%2B%5E4C_3%2B%5E4C_4%3D11)
Hence, 11 positive integers can be expressed.
Answer:
10 customers
Step-by-step explanation:
16x+4y=360
x=20
16(20)=320
320+4y=360
4y=40
y=10
16 ounces = 1 pound so 16 x 8 = 128 so 128 ounces is your answer
Answer:
∠GEF = 25
Step-by-step explanation:
Here, we want to find the value of the marked angle
Please check the attachment for the diagrammatic representation of the triangle
Mathematically, the sum of opposite interior angles equals the exterior angle
We can have this sum as follows;
∠EFG + ∠GEF = ∠FGH
Thus;
2x + 1 + x + 19 = 6x + 2
3x + 20 = 6x + 2
6x-3x = 20-2
3x = 18
x = 18/3
x = 6
Now , substitute x into the ∠GEF
That will be;
6 + 19 = 25