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bonufazy [111]
2 years ago
15

What is the sum of a 6-term geometric sequined if the first term is 22 and the last term is 1299078

Mathematics
1 answer:
stira [4]2 years ago
8 0

Answer:

1461460

Step-by-step explanation:

From the question given, we obtained the following data:

a = 22

Last term = T6 = 1299078

Let us find the common ratio(r)

Tn = ar^(n-1)

T6 = ar^5

1299078 = 22r^5

Divide both side by 22

r^5 = 1299078/22

r^5 = 59049

Take the fifth root of both side

r = 5√ 59049

r = 9

Now we can find the sum of the 6th term as follows

Sn = a[(r^n) — 1] / (r —1)

S6 = 22[(9^6) — 1] / 9—1

S6 = 22[(9^6) — 1] / 9—1

S6 = 22[531441 — 1] / 8

S6 = 22[531440] /8

S6 = 22 x 66430

S6 = 1461460

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What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?
Anestetic [448]

Answer:

-12

Step-by-step explanation:

Let b = -1 and a = -3

The average rate of change = \frac{f(b) - f(a)}{b - a}

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

\frac{f(b) - f(a)}{b - a} = -24/2 = -12

4 0
2 years ago
suppose that the lifetime of a transistor is a gamma random variable x with mean of 24 weeks and standard deviation of 12 weeks.
emmainna [20.7K]

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma(\alpha ,\beta)

E(X)= \alpha \beta                 \beta= 12^{2}/24=6 weeks

V(x)= \alpha \beta ^{2}                \alpha=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

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P(12\leq X\leq 24)

P(12/6\leq G\leq 24/6)

P(2\leq G\leq 4)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

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Use binomial theorem.
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n = 11
k = 10,11
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