Answer:
Step-by-step explanation:
Answer:
63
Step-by-step explanation:
Answer: I am not so sure but I think it’s asking for the median so that would be ANSWER 9.2
Step-by-step explanation:
Answer:
12 teeth
Step-by-step explanation:
<em>The attachment of this question is missing; however, the question can be solved without the attachment</em>
Given:
Larger Gear = 6
Smaller Gear = 1
Required
Number of Smaller Gear if there are 72 larger gears
When the number of larger gear is 6, smaller gears is 1;
<em>This can be represented using the following ratio;</em>
![6 : 1](https://tex.z-dn.net/?f=6%20%3A%201)
Let x represent the number of smaller gear, when there are 72 larger gears;
<em>This can also be represented using the following ratio;</em>
![72 : x](https://tex.z-dn.net/?f=72%20%3A%20x)
Equate both ratios
![6 : 1 = 72 : x](https://tex.z-dn.net/?f=6%20%3A%201%20%3D%2072%20%3A%20x)
Convert the ratios to fraction
![\frac{6}{1} = \frac{72}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B1%7D%20%3D%20%5Cfrac%7B72%7D%7Bx%7D)
Multiply both sides by x
![x * \frac{6}{1} = \frac{72}{x} * x](https://tex.z-dn.net/?f=x%20%2A%20%5Cfrac%7B6%7D%7B1%7D%20%3D%20%5Cfrac%7B72%7D%7Bx%7D%20%2A%20x)
![x * 6 = 72](https://tex.z-dn.net/?f=x%20%2A%206%20%3D%2072)
Divide both sides by 6.
![\frac{x * 6}{6} = \frac{72}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2A%206%7D%7B6%7D%20%3D%20%5Cfrac%7B72%7D%7B6%7D)
![x = \frac{72}{6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B72%7D%7B6%7D)
![x = 12](https://tex.z-dn.net/?f=x%20%3D%2012)
<em>This implies that there are 12 teeth on the smaller gear</em>
Answer:
A polynomial is prime if it can not be factored into polynomials of lower degree also with integer coefficients.
For example, the first option:
x^3 + b*x^2 can be rewritten as:
(x - 0)*(x^2 + b*x)
So it is not prime.
The second option:
x^2 -4x - 12
Because here we can factor this into:
(x + 2)*(x - 6) = x^2 - 6x + 2*x - 12 = x^2 - 4x - 12
Now, the third option is a two variable polynomial, here the degree is equal to the sum of the degrees of both variables.
x^4 + 8*x*y^3
(x - 0)*(x^3 + 8*y^3)
So each side has a lower degree than the original polynomial, then it is not prime.
4th option:
x^2 - b^3
This can be written as:
(x + b^(3/2))*(x - b^(3/2))
Now, here we have a problem.
If for example, b = 1, this would not be a prime.
because 1^(3/2) = 1.
But if b^(3/2) is not an integer, then we can not factorize the initial polynomial into lower degree polynomials with only integer coefficients, then we can not be 100% sure that this is not a prime polynomial, then this is the correct option.