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Kitty [74]
3 years ago
15

Find the sum of the following series

Mathematics
1 answer:
vazorg [7]3 years ago
8 0

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

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Agri-small business limited expenses on petrol for their fleet is r 4 850.00 at the end of september and they have a balance of
kotykmax [81]

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

Given that the expenses on petrol be R4850.00 at the end of September, balance is R 106360.00, usage on income of salaries be 25%, on electricity,rates and taxes be 11%, 42% of the remaining on insurance and investments.

We are required to find the total income and expenditure in September.

Generally the equation for insurance is mathematically given as :

Insurance=42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Generally the equation for the total after all the other expenditures is mathematically given as:

Total expenditure after all other expenditures=0.64A-0.2688A

Total expenditures after all other expenditures=0.3712A.

Total expenditures after all other expenditures is as 111210 (106360+4850)

Equating both the equation and value:

111210=3712A

A=299596

The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

Learn more about income at brainly.com/question/25745683

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5 0
2 years ago
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If X = 16 feet and Y = 8 feet, what is the area of the figure above ? Use 3.14 for pi .
Setler [38]

Answer:

A

Step-by-step explanation:

You can probably figure out the rectangle of 16 by 8 so no explaining there. 16×8=128. You know that diameter of the cirkel is equal to y so 8. The diameter of a cirkel is two times its radius. so 8=2r. r=4. The area of a cirkel is calculated by the formula \pi×r^2. Fill in r=4 in \pi×r^2 gives us \pi×4^2=16\pi. You only have half of the cirkel so 16\pi/2=8\pi. 128+8\pi=153.12 which is A.

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3 years ago
Please help me, math is so hard
Aneli [31]

Answer:

32 divided by 4 = 8,

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128: 11^2 = 121 close enough, 11 is your answer

We are finding hypotenuse but first we find the length of all sides of the two squares to find the two sides of the triangle then we find hypotenuse.

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B
Gnesinka [82]

Answer:

13

Step-by-step explanation:

We know that a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

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Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 =c

3 0
3 years ago
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