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skad [1K]
2 years ago
8

HELPPPPPO

Mathematics
1 answer:
Rina8888 [55]2 years ago
6 0

Answer:

150

Step-by-step explanation:

'x' = number of students out of 500 who selected math

18/60 = x/500

cross-multiply:

60x = 9000

x = 150

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Determine whether the sequence converges or diverges. If it converges, give the limit.
vaieri [72.5K]

Answer:

The given series converges and \lim_{n \to \infty} a_n =0

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

<u>Since each next term is less than its preceding term, so it is decreasing.</u>

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>

Hence, the given series converges.

Now limit will be: \lim_{n \to \infty} a_n

\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0

Hence, \lim_{n \to \infty} a_n =0

7 0
3 years ago
Light travels at the speed of approximately 3.0 × 108 meters per second. Find the time in minutes required for light to travel f
expeople1 [14]
Speed = distance / time => time = distance / speed
speed = 3x10^8 x 60 = 180x10^8 m per minute
time = 1.5x10^11/180x10^8 = 150x10^9/180x10^8 = 5/6x10 = 8,3 minutes
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Answer:

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Step-by-step explanation:

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