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Kisachek [45]
3 years ago
5

Find the sum of first seventeen numbers of an ap whose 4th and 9th tearm are -15 and -30

Mathematics
1 answer:
Radda [10]3 years ago
4 0

Answer:

The sum of first seventeen terms is - 510

Step-by-step explanation:

Given as :

The 4th term of an A.P =  t_4 =  - 15

The 9th term of an A.P =  t_9 =  - 30

For an arithmetic progression

The nth term is given as t_n = a + ( n - 1)×d

Where a is the first term and d is the common difference between numbers

<u>So, For 4th term </u>

t_n = a + ( n - 1)×d

Or, t_4 = a + ( n - 1)×d

- 15 = a + ( 4 - 1)×d

Or, - 15 = a + 3 d            .........1

<u>So, For 9th term </u>

t_n = a + ( n - 1)×d

t_9 = a + ( n - 1)×d

- 30 = a + ( 9 - 1)×d

Or, - 30 = a + 8 d            .........2

Solve eq 1 and 2

( a + 8 d ) - ( a + 3 d ) = - 30 - ( - 15)

or, ( a - a ) + ( 8 d - 3 d ) = - 30 + 15

or, 0 + 5 d = - 15

∴ d = - \frac{15}{5} = - 3

Now, put the value of d in eq 1

I.e - 15 = a + 3 × ( - 3)  

Or. - 15 = a - 9

∴ a = -15 + 9 = - 6

Now The sum of nth term is written as :

s_n = \frac{n}{2} × [ 2 × a + ( n - 1 )×d ]

Where n is the nth term

a is the first term

d is the common difference

So<u> For n = 17th term </u>

s_17 = \frac{17}{2} × [ 2 × ( - 6) + ( 17 - 1 )×( - 3) ]

Or, s_17 = \frac{17}{2} × [ - 12 - 48 ]

Or, s_17 = \frac{17}{2} × ( - 60 )

Or, s_17 = 17 × ( - 30)

∴  s_17 = - 510

Hence The sum of first seventeen terms is - 510  Answer

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Scrat [10]

Answer:

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{17.4}{\sqrt{73}} = 3.99

The lower end of the interval is the sample mean subtracted by M. So it is 230 - 3.99 = 226.01

The upper end of the interval is the sample mean added to M. So it is 230 + 3.99 = 233.99.

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

4 0
3 years ago
A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successi
My name is Ann [436]

Answer:

option C

c. least: $101

greatest: $1001

Step-by-step explanation:

A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successive prize.

Sum of 10 prizes = 5510

100 is the difference. there is a common difference d=100

So its a arithmetic sequence

the sum formula for arithmetic sequence is

S_n = \frac{n}{2}(2a_1 +(n-1)d)

Sn = 5510, n=10 n d= 100 we need to find out first term a1

5510 = \frac{10}{2}(2a_1 +(10-1)100)

5510 = 5 (2a1 + 900)

5510 = 10a1 + 4500

Subtract 4500 on both sides

1010= 10a1

divide by 10 on both sides

a1 = 101

so first term that is least term is 101

To find out greatest term we use formula

a_n = a_1 + (n-1) d

a(10) = 101 + (10-1)100

= 101 + 900= 1001

greatest is 1001

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Answer:foot

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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