Answer:
18 small dogs
Step-by-step explanation:
Given the ratio of small dogs to all dogs was 3:7
Total dogs that are there = 42 dogs
Number of small dogs there = ratio of small/ratio of all dogs * Total dogs
Number of small dogs there = 3/7 * 42
Number of small dogs there = 3 * 6
Number of small dogs there = 18
Hence there are 18 small dogs there
From the information obtained from the question, two equations can be created:
Let x and z be the two numbers (parts)
![\frac{1}{z} + \frac{1}{x} = \frac{3}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bz%7D%20%20%20%2B%20%20%20%5Cfrac%7B1%7D%7Bx%7D%20%20%3D%20%20%20%5Cfrac%7B3%7D%7B10%7D%20%20)
. . . . (1)
![z + x = 15](https://tex.z-dn.net/?f=z%20%20%2B%20%20%20x%20%20%3D%20%2015)
. . . . (2)
By transposing (2), make 'z' the subject of the equation
![z = 15 - x](https://tex.z-dn.net/?f=z%20%3D%2015%20-%20x)
. . . . (3)
By substituting (3) into equation (1) to find a value for x
![\frac{1}{(15 - x)} + \frac{1}{x} = \frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%2815%20-%20x%29%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D)
![\frac{15}{( 15 - x ) ( x )} = \frac{3}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B15%7D%7B%28%2015%20-%20x%20%29%20%28%20x%20%29%7D%20%20%3D%20%20%20%5Cfrac%7B3%7D%7B10%7D%20)
![3 ( - x^{2} + 15 x ) = 150](https://tex.z-dn.net/?f=3%20%28%20-%20x%5E%7B2%7D%20%20%2B%2015%20x%20%29%20%20%3D%20%20150)
![3 x^{2} - 45x + 150 = 0](https://tex.z-dn.net/?f=3%20x%5E%7B2%7D%20%20-%2045x%20%2B%20150%20%3D%200)
⇒
![( x - 5 ) ( x - 10 ) = 0](https://tex.z-dn.net/?f=%28%20x%20-%205%20%29%20%20%28%20x%20-%2010%20%29%20%20%3D%200)
∴ either
![( x - 5) = 0](https://tex.z-dn.net/?f=%28%20x%20-%205%29%20%3D%200)
OR
![( x - 10 ) = 0](https://tex.z-dn.net/?f=%28%20x%20-%2010%20%29%20%3D%200)
Thus x = 5 or x = 10
By substituting the values of x into (2) to find z
z + (5) = 15 OR z + (10) = 15
⇒ z = 10 OR z = 5
So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.
Answer: 3/8
Step-by-step explanation: Divide 3 ft by 8
Answer:
120 degrees the sum of all angle is 720 degrees In the above
Hello! quartiles divide data into fourths, and percentiles divide data into hundredths! hope this helps! ;)