28 teachers prefer mint.
Step-by-step explanation:
Given,
Total number of teachers = 98
Ratio of teacher that prefer rocky road to mint = 5:2
Let,
x be the original number.
Teachers who like rocky road = 5x
Teachers who like mint = 2x
![5x+2x=98\\7x=98](https://tex.z-dn.net/?f=5x%2B2x%3D98%5C%5C7x%3D98)
Dividing both sides by 7
![\frac{7x}{7}=\frac{98}{7}\\x=14](https://tex.z-dn.net/?f=%5Cfrac%7B7x%7D%7B7%7D%3D%5Cfrac%7B98%7D%7B7%7D%5C%5Cx%3D14)
Teachers who prefer mint = 2x = 2(14) = 28
28 teachers prefer mint.
Keywords: ratio, division
Learn more about division at:
#LearnwithBrainly
Answer:
600
Step-by-step explanation:
So final step to do is you square root the x^2 and square root the 4000 which will get you answer of x = 63.2455532034 which can be 63.2. Hope this help!!
If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are
![\dbinom52=\dfrac{5!}{2!(5-2)!}=10](https://tex.z-dn.net/?f=%5Cdbinom52%3D%5Cdfrac%7B5%21%7D%7B2%21%285-2%29%21%7D%3D10)
ways of picking the vowels, and
![\dbinom{20}2=\dfrac{20!}{2!(20-2)!}=190](https://tex.z-dn.net/?f=%5Cdbinom%7B20%7D2%3D%5Cdfrac%7B20%21%7D%7B2%21%2820-2%29%21%7D%3D190)
ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is
![4!\dbinom52\dbinom{20}2=\boxed{45,600}](https://tex.z-dn.net/?f=4%21%5Cdbinom52%5Cdbinom%7B20%7D2%3D%5Cboxed%7B45%2C600%7D)
Keep in mind that this means words like TRIES and TIRES are treated as different.