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Iteru [2.4K]
3 years ago
6

The sum of two numbers is 59 and the difference is 15 . what are the numbers?

Mathematics
1 answer:
UkoKoshka [18]3 years ago
5 0
Write a system of equation based on the number
For an instance, the two numbers are a and b.
"The sum of two numbers is 59" can be written as follows.
⇒ a + b = 59  <em>(first equation)
</em>"The difference is 15" can be written as follows.
⇒ a - b = 15  <em>(second equation)</em>

Solve the system of equation by elimination/substitution method.
First, eliminate b to find the value of a.
a + b = 59
a -  b = 15
--------------- + (add)
2a     = 74
  a     = 74/2
  a     = 37

Second, substitute 37 as a in one of the equations
a + b = 59
37 + b = 59
b = 59 - 37
b = 22

The numbers are 37 and 22
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Answer:

y = 0.80

Step-by-step explanation:

Given:

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- The T-bill rate is r_f = 0.08

Find:

Investing proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.

What is the proportion y?

Solution:

- The proportion y is a fraction of expected risky portfolio and the left-over for the T-bill compliance. Usually we see a major proportion is for risky portfolio as follows:

                                     E(r_c) = y*E(r_p) + (1 - y)*r_f

                                     y*E(r_p) + (1 - y)*r_f = 0.16

- Re-arrange for proportion y:

                                     y = ( 0.16 - r_f ) / (E(r_p) - r_f)

- Plug in values:

                                    y = ( 0.16 - 0.08 ) / (0.18 - 0.08)

                                    y = 0.80

- Hence, we see that 80% of the total investment budget becomes a part of risky portfolio returns.                                    

               

4 0
3 years ago
What is the percent increase 41,700 and 63,00
valentinak56 [21]

Answer:

51.0791%

Step-by-step explanation:

Calculate percentage change

from V1 = 41700 to V2 = 63000

(V2−V1)|V1|×100

=(63000−41700)|41700|×100

=2130041700×100

=0.510791×100

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=51.0791%increase

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Read 2 more answers
11cm by 6 cm rectangle
puteri [66]

Answer:

Question unclear.

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= (11 * 2) + (6 * 2)

= 22 + 12

= 34 cm

If the question was bout Area, the area is:

= Length * width

= 11 * 6

= 66 cm²

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