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Anna11 [10]
3 years ago
10

Erica and John are making brackets.Erica makes 25 bracelets John makes m More bracelets than Erica which expression represents t

he total number of bracelets Erica and John made
Mathematics
1 answer:
pantera1 [17]3 years ago
4 0

Answer: 50 + m

Step-by-step explanation:

From the question, Erica and John are making brackets and Erica makes 25 bracelets while John makes m more bracelets than Erica. The total number of bracelets made will be:

Erica bracelet = 25

John bracelet = 25 + m

Total bracelet = 25 + 25 + m

= 50 + m

The expression that represents the total number of bracelets Erica and John made is 50 + m

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Determine if the series is convergent or divergent 20-15+10-5....
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Answer:

Option b is correct.

The series 20-15+10-5....is Divergent

Step-by-step explanation:

Alternating series Test:

\sum_{n=1}^{\infty} (-1)^{n-1} (b_n) =b_1-b_2+b_3-........

b_n>0 satisfies:

  • b_{n+1} \leq b_n   for all n
  • \lim_{n\rightarrow \infty} b_n = 0

Then the series converges,

otherwise diverges.

Given the series: 20-15+10-5....

This is a alternating series:

\sum_{n=1}^{\infty} (-1)^{n-1} (20-5(n-1))

b_n = (20-5(n-1))

b_{n+1} = (20-5(n+1-1)) = (20-5n)

using the alternating series test;

b_{n+1} \leq b_n  for all n

\lim_{n\rightarrow \infty} b_n = \lim_{n\rightarrow \infty} (20-5(n-1)) = -\infty

⇒ the series diverges.

therefore, the given series i,e 20-15+10-5.... is divergent.

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Given that t<span>he total weight w in pounds of a tractor trailer capable of carrying 8 cars depends on the number of cars c on the trailer and that the situation is represented by the function rule w = 37,000 + 4,200c

To graph the function, we draw the coordinate axis with the number of cars in the horizontal (x) axis and the weight of the truck (in thousands) in the vertical (y) axis.

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From the given function rule, when c = 0 (i.e. when the truck is carrying no car) the weight of the truck is given by w = 37,000 + 4,200(0) = 37,000

Thus, the graph will start at point (0, 37).

Also when the truck is carrying 8 cars, the weight of the truck is given by w = 37,000 + 4,200(8) = 70,600

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