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allsm [11]
3 years ago
5

The population of a local species of beetle can be found using an infinite geometric series a1=960 and the common ratio is .25 w

rite the sum in sigma notation and calculate the sum of possible that will be the upper limit of this population
Sigma 960 (1/4)^i-1 ; the sum is 1280
Signa 960 (1/4)^-1 the sun is divergent
Sigma 960 (1/4)^i sum is 1280
Sigma (1/4)^i sum is divergent

I=1 for them all
Mathematics
2 answers:
inysia [295]3 years ago
7 0
Sigma 960(1/4)^(i-1)

Since r^2<1, the sum is convergent and has a value of

960/(1-1/4)

960/(3/4)

4(960)/3

1280
user100 [1]3 years ago
3 0
<h2>Answer:</h2>

         The answer is:

Sigma 960 (1/4)^i-1 ;    the sum is 1280

<h2>Step-by-step explanation:</h2>

We are given the first term of the geometric sequence as:

a_1=960

Also, the common ratio of the terms in geometric sequence is: \dfrac{1}{4}

We know that if the series is a geometric series than the sum of the terms is given by:

a+ar+ar^2+.....\\\\=a(1+r+r^2+....)\\\\=\sum ar^{n-1}

where a is the first term of the series and r is the common difference.

Here a=960

and r=1/4

Hence,

The sum of the series is:

=\sum 960(\dfrac{1}{4})^{i-1}

Now we know that the sum of the infinite geometric series is given by:

S=\dfrac{a}{1-r}

where S is the sum of the series.

Hence, here the sum of the series is calculated by:

S=\dfrac{960}{1-\dfrac{1}{4}}\\\\\\S=\dfrac{960}{\dfrac{3}{4}}\\\\\\S=\dfrac{960\times 4}{3}\\\\\\S=1280

Hence, the sum is:   1280

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2 years ago
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djyliett [7]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
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Enter the missing numbers in the boxes to complete the table of equivalent ratios of time to distance.
andre [41]
Answer:  Here is the complete table, with the filled in values:
______________________________________________________________
Time (h)    Distance (mi)
    3                2 
    9                6
   12                8
   18               12
___________________________________________________

Explanation:
___________________________________________________
Let us begin by obtaining the "?" value; that is, the "distance" (in "mi.") ;
         when the time (in "h") is "18" ; 
___________________________________________________

12/8 = 18/?  

Note: "12/8 = (12÷4) / (8÷4) = 3/2 ;

Rewrite:  3/2 = 18/? ;  cross-multiply:  3*? = 2 * 18 ; 
                                                                        3*? = 36 ;

                                                                      Divide each side by "3" ;
                                                                            The "?" = 36/3 = 12 ;

So, 12/8 = 18/12 ;

The value: "12" takes the place for the "?" in the table for "distance (in "mi.);
                              when the "time" (in "h") is "18".
__________________________________________________________
Now, let us obtain the "? " value for the "distance" (in "mi.");
                when the "time" (in "h") is:  "9" .

12/8 = 9/? ;  Solve for "?" ;

We know (see aforementioned) that "12/8 = 3/2" ; 

So, we can rewrite:  3/2 = 9/? ;  Solve for "?" ; 

Cross-multiply:  3* ? = 2* 9 ;    3* ? = 18 ;  
                                                           Divide each side by "3" ;
                                                    to  get:  "6" for the "?" value.

When the time (in "h") is "9", the distance (in "mi.") is "6" .
____________________________________________________
Now, to solve the final "?" value in the table given.

9/6 = ?/2 ;  Note:  We get the "6" from our "calculated value" (see above problem). 

9/6 = (9÷3) / (6÷3) = 3/2 ;  

So, we know that the "?" value is:  "3" .

Alternately:   9/6 = ?/2 ; 

Cross-multiply:  6*? = 2*9 ;   6 * ? = 18 ;  Divide each side by "6" ;
                                                               to find the value for the "?" ; 
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When the "distance" (in "mi.") is:  "2" ;  the time (in "h") is:  "3" .
____________________________________________________
Here is the complete table—with all the values filled in:
____________________________________________________

<span>Time (h)    Distance (mi)
____________________________________________________
    3                2 
    9                6
   12                8
   18               12
____________________________________________________
</span>
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Scilla [17]

Answer:

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2 years ago
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Drupady [299]
Becca: in 1 hour; 

(3(3/4) miles in 1/2 hour)2 
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Alice: in 1 hour; 

(5(1/4) miles in 3/4 hours)
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Travels 1.75x4 = 7 miles in 1 hour 

As seen, Becca runs faster, 0.5 miles per hour faster. 

Hope I helped :) 
6 0
3 years ago
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