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ohaa [14]
2 years ago
11

Find the sum of the first six terms of the sequence. S6 = ⇒ 84

Mathematics
1 answer:
k0ka [10]2 years ago
7 0

Answer:

Explained below.

Step-by-step explanation:

Consider the series is a set of first 6 natural numbers.

Sum of first <em>n</em> terms is:

\text{Sum of n terms}=\frac{n(n+1)}{2}

\text{Sum of first 6 terms}=\frac{6(6+1)}{2}

                               =3\times7\\=21

Consider the series is an arithmetic sequence.

Sum of first <em>n</em> terms is:

S_{n}=\frac{n}{2} [2a+(n-1)d]

Here<em>,</em>

<em>a</em> = first term

<em>d</em> = common difference

Consider the series is an geometric sequence.

Sum of first <em>n</em> terms is:

S_{n}=\frac{a_{1}\cdot(1-r^{n})}{(1-r)}

Here<em>,</em>

<em>a₁</em> = first term

<em>r</em> = common ratio

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I calculated and got 314.16
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3 years ago
Are the following two binomials
Rainbow [258]

Answer: x = 2/3

Step-by-step explanation:

7 0
2 years ago
If 2x + 5 = 8x, then 12x = ?A.5B.10C.15D.20
butalik [34]
<h2>Answer:</h2>10.\text{ Option B is correct}

<h2>Explanation:</h2>

Given the equation expressed as:

2x+5=8x

First, we need to calculate the value of "x" from the given expression.

Step 1: Given the equation 2x + 5 = 8x

Step 2: Subtract 5 from both sides:

\begin{gathered} 2x+5-5=8x-5 \\ 2x+\cancel{5}-\cancel{5}=8x-5 \\ 2x=8x-5 \end{gathered}

Step 3: Subtract 8x from both sides

\begin{gathered} 2x-8x=8x-8x-5 \\ -6x=\cancel{8x}-\cancel{8x}-5 \\ -6x=-5 \end{gathered}

Step 4: Divide both sides by -6

\begin{gathered} \frac{-6x}{-6}=\frac{-5}{-6} \\ x=\frac{5}{6} \end{gathered}

Step 5: Get the value of 12x. Substitute x = 5/6 into the expression to have:

\begin{gathered} 12x=12(\frac{5}{6}) \\ 12x=\cancel{12}^2(\frac{5}{\cancel{6}^1}) \\ 12x=2\times5 \\ 12x=10 \end{gathered}

Therefore the value of 12x is 10

3 0
11 months ago
What is the probability that more than twelve loads occur during a 4-year period? (Round your answer to three decimal places.)
Nataly_w [17]

Answer:

Given that an article suggests

that a Poisson process can be used to represent the occurrence of

structural loads over time. Suppose the mean time between occurrences of

loads is 0.4 year. a). How many loads can be expected to occur during a 4-year period? b). What is the probability that more than 11 loads occur during a

4-year period? c). How long must a time period be so that the probability of no loads

occurring during that period is at most 0.3?Part A:The number of loads that can be expected to occur during a 4-year period is given by:Part B:The expected value of the number of loads to occur during the 4-year period is 10 loads.This means that the mean is 10.The probability of a poisson distribution is given by where: k = 0, 1, 2, . . ., 11 and λ = 10.The probability that more than 11 loads occur during a

4-year period is given by:1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]= 1 - [0.000045 + 0.000454 + 0.002270 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.125110+ 0.125110 + 0.113736]= 1 - 0.571665 = 0.428335 Therefore, the probability that more than eleven loads occur during a 4-year period is 0.4283Part C:The time period that must be so that the probability of no loads occurring during that period is at most 0.3 is obtained from the equation:Therefore, the time period that must be so that the probability of no loads

occurring during that period is at most 0.3 is given by: 3.3 years

Step-by-step explanation:

8 0
3 years ago
Isabella earns $48.75 for 5 hours of babysitting. At this rate, how much more would she earn for 11 hours of babysitting?
MAVERICK [17]
She would earn $107.25
4 0
3 years ago
Read 2 more answers
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