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tatyana61 [14]
3 years ago
10

Can someone give me the answers and step by step instructions please??

Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

-1,4,-7,10,...  neither

192,24,3,\frac{3}{8},...  geometric progression

-25,-18,-11,-4,...  arithmetic progression

Step-by-step explanation:

Given:

sequences: -1,4,-7,10,...

192,24,3,\frac{3}{8},...

-25,-18,-11,-4,...

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For -1,4,-7,10,...:

4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)

Hence,the given sequence does not form an arithmetic progression.

\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}

Hence,the given sequence does not form a geometric progression.

So, -1,4,-7,10,... is neither an arithmetic progression nor a geometric progression.

For  192,24,3,\frac{3}{8},... :

\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For -25,-18,-11,-4,... :

-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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Answer:

(a)   Dahl Motors = 8 Cars

       Farthington Auto Sales = 7 Cars

(b)   Roger will purchase from Farthington Auto Sales with higher weekly profit

Step-by-step explanation:

Dahl Motors / Week      

(1)          Car Sold             5         6        7       8         9        10         11          12

(2)          Probability         5%      9%     14%   24%    18%     14%     11%        5%

(3)             (2 x 3 )               0.25   0.54   0.98  1.92     1.62    1.40     1.21     0.60

(4)       Average sales = 0.25  + 0.54  + 0.98  + 1.92 + 1.62 +  1.40  +  1.21+0.60

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Profit/ Car =    $544

Total weekly profit =  544 x 8

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Farthington Auto Sales/ Week    

(1)           Car Sold             5         6        7       8         9        10      

(2)          Probability         8%      21%    31%   24%    10%     6%    

(3)          (2 x 3 )               0.40   1.26   2.17     1.92     0.9     0.6    

(4)       Average sales = 0.40  + 1.26  + 2.17  + 1.92 + 0.90 + 0.60  

                                   =   7.25‬ cars/ week

                                  = 7 cars/week

Profit/ Car =    $651

Total weekly profit =  651 x 7

                               =  $4,557‬

From the calculations above , Roger will purchase from Farthington Auto Sales

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