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2 years ago

What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5? 20 pts.

Mathematics

1 answer:

fgiga [73]2 years ago

6 0

ANSWER

$a_n = 11 - 3n$

EXPLANATION

The explicit rule for an arithmetic sequence is given by:

$a_n = a_1 + d(n - 1)$

It was given that:

$a_1 = 8$

and

$a_2 = 3$

The common difference is

$d = 5 - 8 = - 3$

We plug in the values into the explicit formula to get,

$a_n = 8+ - 3(n - 1)$

Expand to get,

$a_n = 8 - 3n + 3$

The explicit rule is

$a_n = 11 - 3n$

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A teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep

kupik [55]

Answer:

She chose Option 2 which is a linear option, because it offers a smaller lose

in value compared to option 1 which is an exponential option.

The final value for option 2=$32,800

Step-by-step explanation:

Option 1

New Zoomba for 60000 with a depreciation rat of 2%per month for 3 years

Exponential equation;

y=a(1-r)^t

where;

y=future value

a=initial value=60000

r=depreciation rate=2% per month

t=time interval=12×3=36 months

Replacing;

y=60000(1-2/100)^36

y=60000(0.98)^36=28,992.79

The value after 3 years=$28,992.79

Initial value-Final value=(60000-28992.79)=$31007.21

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(31007.21/60000)×100=51.68%

Option 2

New starfish for $40,000 with a depreciation of $200 per month for 3 years

Linear equation;

y=a-bt

where;

y=Future value

a=Initial value=$40,000

b=the depreciation amount per time interval=$200 per month for 3 years

t=time interval=(3×12)=36 months

Replacing;

y=40000-(200×36)

y=32,800

Final value=y=$32,800

Initial value-Final value=(40000-32800)=$7200

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(7200/40000)×100=18%

Option 1(51.68%)>Option 2(18%) therefor Option 1 loses value at a faster rate than Option 2

She chose Option 2 which is a linear option, because it offers a smaller lose

in value compared to option 1 which is an exponential option

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2 years ago

Lesson 3 homework practice mean absolute deviation

Natali5045456 [20]

Assuming that am supposed to calculate the the mean absolute deviation of
1,2,3,4,5,6,7
mean absolute deviation is calculated by first calculating the mean;
(1+2+3+4+5+6+7) =28/7
= 4
Then, find the absolute value (the difference between each value in the data and the mean) (x-μ)
= -3,-2,-1,0,1,2,3
Absolute values= 3,2,1,0,1,2,3
Then we find the mean of the values,
3+2+1+0+1+2+3 = 12
= 12/7
= 1.7143
Therefore, the mean is 4, and the Mean absolute deviation is 1.7143

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2 years ago

The average length of time that three lawn-service mowers operate on a given day is 930 minutes. None of the mowers operates for

Zielflug [23.3K]

Answer:

The answer is <u>A. 990.</u>

Step-by-step explanation:

Now, to find the greatest possible length of time any of the mowers operates.

The 3 lawn-service mowers operate at the average length of time = 930 minutes.

So, the total length of time the 3 lawn mowers take = $930\times 30=2790\ minutes.$

The least length a mowers operates = 900 minutes.

Now, to find the greatest possible length of time any of the mowers operates:

Let $x$ be the greatest possible length of time any of the mowers operates.

<em>As, any one of the mowers operates greatest length.</em>

<em>So, rest of the two mowers be least at length.</em>

According to question:

$x+900+900=2790$

$x+1800=2790$

<em>Subtracting both sides by 1800 we get:</em>

$x=2790-1800$

$x=990.$

<u><em>Thus, the greatest possible length of time any of the mowers operates is 990 minutes.</em></u>

Therefore, the answer is A. 990.

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2 years ago

Which equation could be used to find the length of the hypotenuse?

valina [46]

<h2>=============================</h2><h3>HOPE IT HELPS YOU SEE THE ATTACHMENT FOR FURTHER INFORMATION !!!</h3>

<h2>REGARDS.... ✌✌✌</h2>

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2 years ago

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The Taieri Plain in New Zealand is 6 feet below sea level (or –6 feet). If you are standing 3 feet above sea level, is your elev

Anna11 [10]

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1 year ago