4 lines extend from point E. A horizontal line extends to the left to point A and a vertical line extends up to point C. Another
2 answers:
You might be interested in
So what will it be a percentage of? it will be the percentage of the original recruits, of the original 150.
for this, we need to divide the number of recruits that left over all recruits, and multiply by 100%:
so the number of trainees decreased by 20 %
for this, we need to divide the number of recruits that left over all recruits, and multiply by 100%:
so the number of trainees decreased by 20 %
Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a = a + (n - 1)d
- a is the first term
- d is the common difference between each 2 consecutive terms
- n is the position of the term
The formula of the sum of nth terms is S =
[2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S = 185
→ Substitute the value of S and d in the 2nd rule above
∵ 185 = [ 2a + (n - 1)3]
∴ 185 = [2a + 3(n) - 3(1)]
∴ 185 = [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10