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3 years ago

Need an answer thanks in advance!

Mathematics

1 answer:

slamgirl [31]3 years ago

6 0

Answer:

1806 seats.

Step-by-step explanation:

From the question given above, the following data were obtained:

Row 1 = 24 seats

Row 2 = 27 seats

Row 3 = 30 seats

Total roll = 28

Total number of seat =?

From the above data, we can liken the roll to be in arithmetic progress.

Also, we are asked to determine the total number of seats in the theater.

Thus the sum of the sequence can be written as:

Roll 1 + Roll 2 + Roll 3 +... + Roll 28 i.e

24 + 27 + 30 +...

Thus, we can obtain obtained the total number of seats in the theater by applying the sum of arithmetic progress formula. This can be obtained as follow:

First term (a) = 24

Common difference (d) = 2nd term – 1st term

Common difference (d) = 27 – 24 = 3

Number of term (n) = 28

Sum of the 28th term (S₂₈) =?

Sₙ = n/2 [2a + (n –1)d]

S₂₈ = 28/2 [2×24 + (28 –1)3]

S₂₈ = 14 [48 + 27×3]

S₂₈ = 14 [48 + 81]

S₂₈ = 14 [129]

S₂₈ = 1806

Thus, the number of seats in the theater is 1806.

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Heather has divided $5400 between two investments, one paying 8%, the other paying 5%. if the return on her investment is $

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Answer:

$2500 at 8%.

$2900 st 5%.

Step-by-step explanation:

Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.

We have been given that Heather has divided $5400 between two investments. We can represent this information as:

$x+y=5400...(1)$

The return on her investment is $345.

Earnings from the investment at 8% will be 8% of x.

Earnings from the investment at 5% will be 5% of y.

$(\frac{8}{100})x+(\frac{5}{100})y=345...(2)$

$0.08x+0.05y=345...(2)$

We will use substitution method to solve our system of equations. From equation (1) we will get,

$x=5400-y$

Substituting this value in equation (2) we will get,

$0.08(5400-y)+0.05y=345$

$432-0.08y+0.05y=345$

$-0.08y+0.05y=345-432$

$-0.03y=-87$

$\frac{-0.03y}{-0.03}=\frac{-87}{-0.03}$

$y=2900$

Therefore, Heather has invested an amount of $2900 at 5%.

Let us substitute y=2900 in equation (1) to solve for x.

$x+2900=5400$

$x+2900-2900=5400-2900$

$x=2500$

Therefore, Heather has invested an amount of $2500 at 8%.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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Answer:

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3 years ago

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Korvikt [17]

Answer:

Step-by-step explanation:

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3 years ago

Need an answer thanks in advance​!

Need an answer thanks in advance!