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uysha [10]
3 years ago
6

Which of the following choices is the simple formula for the nth term of the following arithmetic sequence?

Mathematics
1 answer:
kkurt [141]3 years ago
8 0
\bf 7~~,~~\stackrel{7-4}{3}~~,~~\stackrel{3-4}{-1}~~,~~\stackrel{-1-4}{-5}~~,~~\stackrel{-5-4}{-9}~~,~~...

so namely, the "common difference" d = -4, and the first term a₁ = 7.

\bf n^{th}\textit{ term of an arithmetic sequence}
\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
d=-4\\
a_1=7
\end{cases}
\\\\\\
a_n=7+(n-1)(-4)\implies a_n=7+(4-4n)
\\\\\\
a_n=11-4n\implies a_n=-4n+11
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second table

Step-by-step explanation:

Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.

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3 years ago
The length of a side of a triangle is 26 in. A line, parallel to the given side ,divides the triangle into 2 parts of equal area
lubasha [3.4K]

Answer:

13√2

Step-by-step explanation:

The areas of the larger triangle, and the smaller triangle (formed when the larger triangle was cut by the parallel line) are similar. Therefore we can compare their areas:

Area1/Area2 =  (Length1)^2/(Length2)^2,

x/2x = (Length1)^2/(26)^2,

1/2 = (Length1)^2/676,

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6 0
3 years ago
In 2020, dawn earned $248,000. social security tax is 6.2% to a maximum income of $137,700. what was your monthly gross pay? in
Dovator [93]

Monthly gross pay is $20,666.67; Dawn reached the maximum taxable social security income in July; the amount of social security tax Dawn paid in February, July and November are $1,281.33, $849.42, and $0 respectively.

<h3>How do we calculate Social Security Tax?</h3>

Annual gross pay = $248,000

Monthly gross pay = $248,000 / 12 = $20,666.67

Maximum taxable social security income = $137,700

Social Security Tax Rate = 6.2%

Total Social Security Tax = Maximum social security income * Social Security Tax Rate = $137,700 * 6.2% = $8,537.40

Monthly Social Security Tax = Monthly gross earnings * Social Security Tax Rate = $20,667 * 6.2% = $1,281.33

Number of months Don reached the maximum taxable social security income = Maximum social security income / Monthly gross pay = $137,700 / $20,666.67 = 6.66 months

Since 6.66 months is greater than 6 but less than 7, this implies that the month Don reached the maximum taxable social security income is the 7th month which is July 2020.

Also, the 6.66 months imply that Dawn will fully pay his Total Social Security Tax in July.

Social security tax Dawn paid in February = Monthly Social Security Tax = $1,281.33

Social security tax Dawn paid in July = Total Social Security Tax - (Monthly Social Security Tax * 6) = $8,537.40 - ($1,281.33 * 6) = $849.42

Social security tax Dawn paid in November = $0

Note that $0 was paid in November because Dawn had already paid fully his Total Social Security Tax in July.

Learn more about Total Social Security Tax here: brainly.com/question/18268724.

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3 0
1 year ago
Lela and Pepe are playing a video game. The ratio of Lela’s game score to Pepe's score is 2 : 5. Then Lela completes a quest and
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Answer:        Lela's original score was 16.

Step-by-step explanation:

Alright lets get started.

Suppose Lela score was L.

Suppose Pepe score was  P.

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So the equation will be

\frac{L}{P} = \frac{2}{5}

Cross multiplying

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Cross multiplying

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15L=240

L=16

Hence the score of Leela originally was 16.                Answer

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