If the sum of first 7 terms of an A.P is 49 and the sum of first 17 terms is 289 find the sum of first 30 term

Answers

Answer 1
Given:

Sum of first 7 terms of an AP = 49.

Sum of first 17 terms = 289

Find:

the sum of first 30 term

Solution:

We know that,

Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]

Hence,

→ 7/2 * [ 2a + (7 - 1)d ] = 49

→ 2a + 6d = 49 * 2/7

→ 2( a + 3d ) = 14

→ a + 3d = 14/2

→ a + 3d = 7 -- equation (1)

Similarly,

→ 17/2 * [ 2a + 16d ] = 289

→ 17/2 * 2 * (a + 8d) = 289

→ a + 8d = 289 * 2/17 * 1/2

→ a + 8d = 17 -- equation (2)

Subtract equation (1) from (2).

→ a + 8d - (a + 3d) = 17 - 7

→ a + 8d - a - 3d = 10

→ 5d = 10

→ d = 10/5

→ d = 2

Substitute the value of d in equation (1).

→ a + 3 * 2 = 7

→ a = 7 - 6

→ a = 1

Now,

Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]

→ S(30) = 15 (2 + 58)

→ S(30) = 15 * 60

→ S(30) = 900

Therefore, the sum of first 30 terms of the given AP is 900.

I hope it will help you.

Regards.

Answer 2

answer refer in pic siso

If The Sum Of First 7 Terms Of An A.P Is 49 And The Sum Of First 17 Terms Is 289 Find The Sum Of First
If The Sum Of First 7 Terms Of An A.P Is 49 And The Sum Of First 17 Terms Is 289 Find The Sum Of First

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Step-by-step explanation:

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Step-by-step explanation:

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The members of the drama club have 100 tickets to sell

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

The equivalent to three over five (3y + 15) is nine over five y + 9 ⇒ C

Step-by-step explanation:

Let us solve the question

∵ Three over five means [tex]\frac{3}{5}[/tex]

∴ Three over five (3y + 15) = [tex]\frac{3}{5}[/tex] (3y + 15)

→ By using the distributive property, multiply each term inside the

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∴  [tex]\frac{3}{5}[/tex] (3y + 15) =  [tex]\frac{3}{5}[/tex] (3y) + [tex]\frac{3}{5}[/tex] (15)

→ Multiply three over five by 3y

∵  [tex]\frac{3}{5}[/tex] (3y) =  [tex]\frac{3(3)}{5}[/tex] (y) =  [tex]\frac{9}{5}[/tex] y

→ Multiply three over five by 15

∵  [tex]\frac{3}{5}[/tex] (15) =  [tex]\frac{3(15)}{5}[/tex] =  [tex]\frac{45}{5}[/tex] = 9

∴  [tex]\frac{3}{5}[/tex] (3y) + [tex]\frac{3}{5}[/tex] (15) = [tex]\frac{9}{5}[/tex] y + 9

∴ [tex]\frac{3}{5}[/tex] (3y + 15) =   [tex]\frac{9}{5}[/tex] y + 9

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Answers

First you need to know that square means multiplicatin by itself to itself so square of 20 means 20×20=400

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Step-by-step explanation:

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Answer:

26 notches would be made.

Answer:

c) 26

Step-by-step explanation:

If I am understanding the question correctly it's just asking how many notches there will be on a certain length of metal and so in order to find it, you would just divide 6 1/2 by 1/4, also written as 6.5 divided by 0.25, to get 26.

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

6. Miles  [tex]{}[/tex]     cientos       decenas      unidades

  4   [tex]{}[/tex]              9                5               6

7. Catalina podrá hacer un cuadrado con longitud lateral de 4 cartones

8. 45000000 = 4.5 × 10⁶

0.000000000000056 = 5.6 × 10¹⁴

0.000000000034 = 3.4 × 10¹¹

Step-by-step explanation:

6. Los valores posicionales de dígitos son;

Miles  [tex]{}[/tex]     cientos       decenas      unidades

4   [tex]{}[/tex]              9                5                   6

 

7. El número de cuadrados que tiene Fernando = 12

El número de cuadrados que tiene Catalina = 16

El largo y el ancho de un cuadrado son iguales, por lo tanto tenemos;

largo × ancho = Área del cuadrado

largo = ancho = lado del cuadrado

Lado del cuadrado × Lado del cuadrado = Área del cuadrado

(Lado del cuadrado) ² = Área del cuadrado

Lado del cuadrado = √ (Área del cuadrado)

Para Fernando, Área del cuadrado = 12

Lado del cuadrado para Fernando = √12 = 2 · √3 cartones

Para Catalina, Área del cuadrado = 16

Lado del cuadrado para Catalina = √16 = 4 cartones

Por tanto, Catalina podrá realizar un cuadrado con longitud lateral de 4 cartones

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A taxi service charges $1.00 for the first mile then $0.10 for each additional mile after that. How much would you pay for having the taxi drive you 2 MILES?

Answers

$1.10this is because the first mile it’s 1 and every additional mile is .10. So just add 1 + .10

Answer:

$1.10

Step-by-step explanation:

In an equation, this would be written as follows (where y equals the total price and x is the number of miles driven):

[tex]y = 0.10(x-1) + 1.00[/tex]

Therefore:

[tex]y=0.10(2-1)+1.00[/tex]

[tex]y= 0.10(1)+1.00[/tex]

[tex]y=0.10+1.00[/tex]

[tex]y=1.10[/tex]

y = $1.10

Suppose scores on exams in statistics are normally distributed with an unknown population mean. A sample of 26 scores is given below. Use Excel to find a 90% confidence interval for the true mean of statistics exam scores. Round your answers to one decimal place and use increasing order.

Answers

Answer:

Step-by-step explanation:

Using the formula for calculating confidence interval

CI = xbar±z×S/√n

xbar is the mean of the sample

z is the z score at 90% = 1.645

S is the standard deviation of the score

n is the sample size = 26

Since we are not given the scores, we can assume the values of our mean and standard Deviation

Let xbar = 38

S = 3.0

Substitute the given values into the formula

CI = 38±(1.645×3.0/√26)

CI = 38±(1.645×3.0/5.099)

CI = 38±(1.645×0.5884)

CI = 38±0.9678

CI = (38-0.9678, 38+0.9678)

CI = (38.0322, 38.9678)

CI = (38.0, 38.9)

Hence the 90% confidence interval for the true mean of statistics exam scores is 38.0≤p≤38.9

Note that the we will need to generate the mean and standard deviation from the data but since we are not given the required data, we had to assume the value we used in calculation.

Find the area of the rectangle contained within the following four lines

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How do you do this please help with this question pleaseeeeeee if you give good explanation I will make you brain list thing. This is a linear relation ship question. PLEASE HELP WITH THIS QUESTION

Answers

Answer:

should be 15 hope I helped you out.

Step-by-step explanation:

Answer:

15 sq unit

Step-by-step explanation:

Easiest way to understand this question is to plot the lines on the graph which will give you a rectangle with four sides at given points.

the length of the said rectangle will be l = 1 + (-2)

and the breath b = 2 + (-3)

Area= lxb = 15 sq.unit

Which shows a set of three equivalent decimals?
1.9, 1.90, 1.900
1.9, 1.90, 1.090
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O 1.9, 1.09, 1.009

Answers

The best choice is A)

when you add a zero, it does not count on a decimal, so,

1.9, 1.90, 1.900.

Answer:

the answer is a

Step-by-step explanation:

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