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aniked [119]
2 years ago
12

What is the sum of the first 4 terms of the arithmetic sequence in which the 8th term is 10 and the 14th term is 29.5?

Mathematics
1 answer:
Sholpan [36]2 years ago
8 0

Answer:

Sum of the first 4 terms is

14.50

Explanation:

In an arithmetic sequence, whose first term is

a

and difference between a term and its preceding term is

d

,

the

n

t

h

term is

a

+

(

n

−

1

)

d

and sum of first

n

terms is

n

2

(

2

a

+

(

n

−

1

)

d

)

Hence

6

t

h

term will be

a

+

5

d

=

8

and

10

t

h

term will be

a

+

9

d

=

13

Subtracting first from second,

4

d

=

5

or

d

=

1.25

and

a

=

8

−

5

⋅

1.25

=

8

−

6.25

=

1.75

Hence sum of first four terms is

4

2

⋅

(

2

⋅

1.75

+

3

⋅

1.25

)

=

2

⋅

(

3.5

+

3.75

)

=

2

⋅

7.25

=

14.50

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Step-by-step explanation:

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3 years ago
B2-4b+4=0 using quadratic forumla
Ivan

Trying to factor by splitting the middle term   

Factoring <span> b2-4b+4</span> 
The first term is, <span> <span>b2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span>  1 • 4 = 4</span> 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is  <span> -4 </span>.
<span><span>     </span></span>

<span><span>-4   +   -1   =   -5</span><span>     -2   +   -2   =   -4   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  -2 
                     <span>b2 - 2b</span> - 2b - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
                    b • (b-2)
              Add up the last 2 terms, pulling out common factors :
                    2 • (b-2)
Step-5 : Add up the four terms of step 4 :
                    (b-2)  •  (b-2)
             Which is the desired factorization

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3 years ago
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A Freight train is traveling 30 miles per hour. An automobile starts out from the same place 1 hour later and overtakes the trai
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3 years ago
Select the correct answer,
ivanzaharov [21]

Answer:

D. 81

Step-by-step explanation:

Raise  

3

to the power of  

4

.

81

=

x

Rewrite the equation as  

x

=

81

.

x

=

81

7 0
2 years ago
In a recent contest, the mean score was 210 and the standard deviation was 25. a) Find the z-score of John who scored 190 b) Fin
denpristay [2]

Answer:

a) Z = -0.8

b) Z = 2.4

c) Mary's score was 241.25.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 210, \sigma = 25

a) Find the z-score of John who scored 190

Z = \frac{X - \mu}{\sigma}

Z = \frac{190 - 210}{25}

Z = -0.8

b) Find the z-score of Bill who scored 270

Z = \frac{X - \mu}{\sigma}

Z = \frac{270 - 210}{25}

Z = 2.4

c) If Mary had a score of 1.25, what was Mary’s score?

Z = \frac{X - \mu}{\sigma}

1.25 = \frac{X - 210}{25}

X - 210 = 25*1.25

X = 241.25

Mary's score was 241.25.

3 0
3 years ago
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