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AleksandrR [38]
3 years ago
8

Help with question 5a

Mathematics
1 answer:
Llana [10]3 years ago
5 0
This is a refreshing question!

We are given that
f(r)=ar+b, and
Sum f(r) =125 for r=1 to 5
Sum f(r) = 475 for r=1 to 10.

and we know, using Gauss's method, that
G(n)=sum (1,2,3.....n) = n(n+1)/2 or
G(n)=n(n+1)/2

Sum f(r) =125 for r=1 to 5
=>
sum=a(sum of 1 to 5) + 5b => G(5)a+5b=125   [G(5)=15]
15a+5b=125 ...................................................(1)

Similarly, Sum f(r) =  475 for r=1 to 10 => G(10)a+5b=475  [G(10)=55]
=>
55a+10b=475.................................................(2)

Solve system of equations (1) and (2)
(2)-2(1)
55-2(15)a=475-2(125) => 25a=225 =>
a=9

Substitute a=9 in 1 => 15(9)+5b=125 => 5b=-10
b=-2

Substitute a and b into f(r), 
f(r)=9r-2
check: sum f(r), r=1,5 = (9-2)+(18-2)+(27-2)+(36-2)+(45-2)=135-10=125 [good]

We define the sum of f(r) for r=1 to n as
S(n)=sum f(r) for r=1 to n = 9(sum 1,2,3....n)-2n = 9n(n+1)/2-2n = 9G(n)-2n
S(n)=9n(n+1)/2-2n
checks:
S(5)=9(15)-2(5)=135-10=125  [good]
S(10)=9(55)-2(10)=495-20=475 [good]

Hence 
(a)
S(n)=sum f(r) for r=1,n
= 9(sum i=1,n)+n(-2)
= 9(n(n+1)/2 -2n
=(9(n^2+n)/2) -2n

(b) sum f(r) for i=8,18
=sum f(r) for i=1,18  -  sum f(r) for i=1,7
=S(18)-S(7)
=(9(18^2-18)/2-2(18))-(9(7^2-7)/2-2(7))
=1503-238
=1265
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Answer:

a. Convex solutions ,GO Methods

b. market efficiency

Explanation :

Step-by-step explanation:

A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions "in the vicinity" with better objective function values. You can picture this as a point at the top of a "peak" or at the bottom of a "valley" which may be formed by the objective function and/or the constraints -- but there may be a higher peak or a deeper valley far away from the current point.

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GO Methods

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5 0
3 years ago
Can you guy's help me quick!
nadya68 [22]

Answer:

480,700 sets (first choice)

Step-by-step explanation:

If all 25 questions are different,

When order of selection counts:

P(25,7)

= 25!/(25-7)!

= 15511210043330985984000000/6402373705728000

= 2422728000

When order of selection does not count count:

C(25,7)

=25!/(7!*(25-7)!)

=15511210043330985984000000/(6402373705728000*5040)

= 480,700

Hope this helps, have a nice day.

6 0
3 years ago
A garden is shaped like a rectangle whose perimeter is 150 ft. The length is 2 times as long as the width. Find the length and t
vlabodo [156]

Answer:

Step-by-step explanation:

L=2W

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6 0
3 years ago
Robert went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 300 mg of sodium and each f
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There are 9 cans of soup and 5 cans of frozen dinner.

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Step-by-step explanation:

Let,

Soup = x

Frozen Dinner = y

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300x + 500y = 5200 eqn 1

And,

x + y = 14 eqn 2

Multiplying\ equation\ 2\ with\ 300\\300(x+y=14)\\300x+300y=4200\ Eqn 3\\

Subtracting Eqn 3 from Eqn 1;

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Putting value of y in Eqn 1;

300x+500(5)=5200\\300x+2500=5200\\\\Subtracting\ 2500\ from\ both\ sides\ \\300x+2500-2500=5200-2500\\300x=2700\\x=\frac{2700}{300} \\x=9

There are 9 cans of soup and 5 cans of frozen dinner.

The variables used for soup and frozen dinner are x and y respectively.

Keywords: Variables, linear equations, subtraction.

Learn more about linear equations at;

  • brainly.com/question/5047646
  • brainly.com/question/5048216

#LearnwithBrainly

5 0
3 years ago
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Ber [7]

Answer:

False

Step-by-step explanation:

The triangles are similar because the angles are the same

We know nothing about the side lengths, so we can say nothing about concurrency.  They may or may not be congruent.  

4 0
3 years ago
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