9x^2+12x=4 solve by completing the square

Evaluate: 20 Σ 4(8/9)^n-1 = [?] 1 Round to the nearest hundredth.

lianna [129]

Answer:

32.59 (nearest hundredth)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: $a_n=ar^{n-1}$

(where a is the first term and r is the common ratio)

Given:

$\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}$

Therefore:

a = 4
r = 8/9

Sum of the first n terms of a geometric series:

$S_n=\dfrac{a(1-r^n)}{1-r}$

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

$\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}$

$\implies S_{20}=32.58609013...$

$\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)$

7 0

2 years ago

Read 2 more answers

Try to solve (-78)+43 #

Valentin [98]

Answer:

-35

Step-by-step explanation:

you put -78 on top and take put 43 the put the negative back on

4 0

3 years ago

Read 2 more answers

What is the measure of the missing angle in this triangle Yes

sladkih [1.3K]

Answer:

The measure of the missing angle is 25 degrees.

8 0

3 years ago

Read 2 more answers

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op

Anika [276]

Answer:

The probability that the maximum speed is at most 49 km/h is 0.8340.

Step-by-step explanation:

Let the random variable X be defined as the maximum speed of a moped.

The random variable X is Normally distributed with mean, μ = 46.8 km/h and standard deviation, σ = 1.75 km/h.

To compute the probability of a Normally distributed random variable we first need to convert the raw score of the random variable to a standardized or z-score.

The formula to convert X into z-score is:

$z=\frac{X-\mu}{\sigma}$

Compute the probability that the maximum speed is at most 49 km/h as follows:

Apply continuity correction:

P (X ≤ 49) = P (X < 49 - 0.50)

= P (X < 48.50)

$=P(\frac{X-\mu}{\sigma}$

*Use a z-table for the probability.

Thus, the probability that the maximum speed is at most 49 km/h is 0.8340.

8 0

4 years ago

An individual who has automobile insurance from a certain company is randomly selected. Let X be the number of moving violations

grin007 [14]

Answer:

(X) 0 1 2 3 4

P(X) 0.17 0.23 0.27 0.24 0.09

F(x) 0.17 0.04 0.65 0.91 1

Step-by-step explanation:

Given that;

(X) 0 1 2 3 4

P(X) 0.17 0.23 0.27 0.24 0.09

cumulative distribution function can be calculated by; be cumulatively up the value of p(x) with the values before it;

so

x F(x)

0 P(X = 0) = 0.17

1 P(X = 0) + P(X = 1) = 0.17 + 0.23 = 0.4

2 P(X = 0) + P(X = 1) + P(X = 2) = 0.17 + 0.23 + 0.27 = 0.65

3 P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.17 + 0.23 + 0.27 + 0.24 = 0.91

4 P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.17 + 0.23 + 0.27 + 0.24 + 0.09 = 1

Therefore, cumulative distribution function f(x) is;

(X) 0 1 2 3 4

P(X) 0.17 0.23 0.27 0.24 0.09

F(x) 0.17 0.04 0.65 0.91 1

8 0

3 years ago