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Likurg_2 [28]
3 years ago
9

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 8, four divided by three, two divided

by nine, ...
Mathematics
2 answers:
Inga [223]3 years ago
7 0

Answer:

Converges, 57.6

Step-by-step explanation:

48, 8, 4/3, 2/9...

ratio = 8/48 = 1/6

A sequence converged if the ratio is between -1 and 1.

So, this sequence converges

Limit = a/(1-r)

Where a is the first term, and r is the common ratio

Limit = 48/[1 - (1/6)]

= 48/[5/6]

= 48 × 6/5

= 57.6

inessss [21]3 years ago
7 0

Answer:

Converges; 0

Step-by-step explanation:

All of the numbers are converging towards 0. Always being divided by 6, each time, getting closer to 0.

48/6 = 8

8/6 = 4/3

4/3/6 = 2/9

etc.

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Peter tracks the goals he scores in 9 soccer games. In two games Peter scored 2 goals each, in one game he scored 0 goals, in tw
Reika [66]

The average number of goals per game Peter scores, rounded to one decimal place is 1.6

<u><em>Explanation</em></u>

In first two games Peter scored 2 goals each. So, total score in two games = (2×2)= 4

In one game he scored 0 goal and in next two games he scored 3 goals each, so the total is (3×2)= 6

In the last four games he scored 1 goal in each, so the total is (1×4)= 4

So, the total score in all 9 games =4+0+6+4=14

Thus, the average number of goals = \frac{14}{9}= 1.5555....

So, the average number of goals per game Peter scores, rounded to one decimal place is 1.6

3 0
3 years ago
Read 2 more answers
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements a
Anni [7]

Answer:

The answer is given below

Step-by-step explanation:

a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.

u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4

u + v < u - v.

b) Let x be a real number and x² be the square of the real number

x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

The statement is true for x is between 0 and ±1

E.g. for x = 1/2, x² = (1/2)² = 1/4

1/4 < 1/2

c) Let n represent all positive integers. n² is the square of n.

n²≥n means that the square of n is greater or equal to n.

We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself

The statement is true.

1² ≥ 1, 2² ≥ 2 e.t.c

d)  Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b

|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.

We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

4 0
3 years ago
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
MA_775_DIABLO [31]

Answer:

Choice A.

y =  -  {2}^{x}  + 4

Step-by-step explanation:

Use graphing calculator

7 0
2 years ago
Someone please help me
Lilit [14]
<h3>Answer:</h3>
  1. C. (9x -1)(x +4) = 9x² +35x -4
  2. B. 480
  3. A. P(t) = 4(1.019)^t

Step-by-step explanation:

1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.

2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...

... (d+43) + d = 1003

... 2d = 960 . . . . . . . subtract 43

... d = 480 . . . . . . . . divide by 2

The second voyage lasted 480 days.

3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.

Since the starting value (in 1975) is 4 (billion), the population t years after that is ...

... P(t) = 4(1.019)^t

7 0
3 years ago
Oil prices are projected to increase by 100% by next June. A quart of oil currently costs $2.45. What is the projected cost of a
lisov135 [29]

Answer:

4.9

Step-by-step explanation:

100% of 2.45 is 2.45.

We add 2.45 + 2.45 which is <u>4.9. </u>

Can I get brainliest?

8 0
3 years ago
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