Step-by-step explanation:
the lowest common denominator (LCD) is the lowest common multiple (LCM) of the denominator numbers (the ones at the bottom of the fractions).
finding the LCM of 9 and 12 using the prime factor method :
9 = 3×3
12 = 2×2×3
the LCM is the combination of the longest chains per prime factor. which means we have 2×2 and 3×3 as longest chains for 2 and 3.
LCD = LCM = 2×2×3×3 = 36
2/9 turns into x/36 by multiplying by 4/4 :
2/9 × 4/4 = 8/36
5/12 turns into x/36 by multiplying by 3/3 :
5/12 × 3/3 = 15/36
so, the third answer option is correct.
First, it would be helpful to find out how many teachers there are at the school.
2470 students x (1 teacher/26 students)=95 teachers
To find the number of teachers needed, just use the ideal ratio:
2470 students x (1 teacher/19 students)=130 teachers
So to reduce this ratio to 19:1, the school needs 130 teachers. To know how many new teachers the school needs, just subtract the ideal from the current amount.
130-95=35 new teachers needed
Answer:
0.339
Step-by-step explanation:
Given that :
Total number of songs = 12
Number of songs to choose = 8
Total number of draws = 8
Selecting 2 of the 4 songs with syprano solos : 4C2
The 6 remaining songs from. The rest:
12-4C8-2 = 8C6
Total possible selections = 12C8
Hence,
probability that the set s/he chooses contains two of the four songs that have soprano solos will be :
(4C2 * 8C6) / 12C8
(6 * 28) / 495
168 / 495
= 0.339
Replace x with 3 and solve for y to equal 12:
y = 4(3) = 12
the answer is y = 4x
