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makkiz [27]
3 years ago
11

Find the sum of the arithmetic series given a1=8,a14=99,n=14.

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
8 0

Answer:

The sum of the series is 749

Step-by-step explanation:

Given

a_1 = 8

a_{14} = 99

n = 14

Required

The sum of the series

This is calculated using:

S_n = \frac{n}{2}[a_1 + a_n]

Substitute 14 for n

S_{14} = \frac{14}{2}[a_1 + a_{14}]

S_{14} = 7[a_1 + a_{14}]

Substitute values for a1 and a14

S_{14} = 7[8 + 99]

S_{14} = 7*107

S_{14} = 749

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5 0
3 years ago
Read 2 more answers
Quadrilateral ABCD is a kite. If AD=AB, find AD<br><br> A. 5/3<br> B. 7<br> C. 5/7<br> D. 22
ICE Princess25 [194]
AD = AB

AD = 2r+8
AB = 5r-13

we need to find the value of r to find the total length

so 2r+8 = 5r-13
subtract 2r from each side:
8 = 3r -13
add 13 to each side:
21 = 3r
divide both sides by 3
r = 21 / 3 = 7
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5 0
3 years ago
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-sevent
Otrada [13]

Answer:

60 ships.

Step-by-step explanation:

Let the total number of ships in the naval fleet be represented by x

One-third of the fleet was captured = 1/3x

One-sixth was sunk = 1/6x

Two ships were destroyed by fire = 2

Let surviving ships be represented by y

One-seventh of the surviving ships were lost in a storm after the battle = 1/7y

Finally, the twenty-four remaining ships sailed home

The 24 remaining ships that sailed home =

y - 1/7y = 6/7y of the surviving fleet sailed home.

Hence

24 = 6/7y

24 = 6y/7

24 × 7/ 6

y = 168/6

y = 28

Therefore, total number of ships that survived is 28.

Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4

Total number of ships in the fleet(x) =

x = 1/3x + 1/6x + 2 + 28

Collect like terms

x - (1/3x + 1/6x) = 30

x - (1/2x) = 30

1/2x = 30

x = 30 ÷ 1/2

x = 30 × 2

x = 60

Therefore, ships that were in the fleet before the engagement were 60 ships.

3 0
3 years ago
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yaroslaw [1]
12/16
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7 0
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nexus9112 [7]

Answer:

87 / 100 I do believe will be your answer.

Step-by-step explanation:

1 is the greatest common divisor of 87 and 100, and therefore the result can't be further reduced. I hope this helps!

5 0
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