Ask question

Ask question

All categories

3 years ago

6

A mutual fund manager must decide how much money to invest in Atlantic Oil (A) and how much to invest in Pacific Oil (P). At lea

st 60% of the money invested in the two oil companies must be in Pacific Oil. A correct modeling of this constraint is

1 answer:

xenn [34]3 years ago

5 0

Answer:

$\frac{P}{A+P}\geqslant 0.6$

Step-by-step explanation:

Amount of money to invest in Atlantic Oil= A

Amount of money to invest in Pacific Oil = P

Total money invested in the two oil companies = A+P

Since at least 60% of the money invested in the two oil companies must be in Pacific Oil

$\frac{P}{A+P} \times 100\geqslant 60$

$\Rightarrow \frac{P}{A+P} \geqslant \frac{60}{100}$

$\Rightarrow$ $\frac{P}{A+P}\geqslant 0.6$

Hence the required model is $\frac{P}{A+P}\geqslant 0.6$

You might be interested in

A baker makes 84 loaves of bread, she burns 4. What fraction of the loaves does the burn? Simplify your answer.

svetoff [14.1K]

Answer:

1/21

Step-by-step explanation:

The baker makes 84 loaves of bread,

Out of the 84 bread, 4 of them got burn.

Fraction that the loaves does the burn will be expressed in 4/84 = 1/21.

3 0

3 years ago

Each month for 7 months, Samuel mows 3 lawns . How many more lawns does he need to mow before he has mowed 29 lawns

Nimfa-mama [501]

The answer is 8 : ) hope this helped

8 0

3 years ago

collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and

saw5 [17]

Answer:

21 windows

Step-by-step explanation:

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y

Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).

Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7

Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows

5 0

3 years ago

Are step functions one to one?

dlinn [17]

Answer: the function as they change value from one interval to the next

6 0

3 years ago

Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

we have

$a=32\ units$

$b=27\ units$

$B=37\°$

step 1

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}$

substitute the values

$\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}$

$sin(A)=(32)Sin(37\°)/27=0.71326$

$A=arcsin(0.71326)=45.5\°$

The measure of angle A could have two measures

the first measure-------> $A=45.5\°$

the second measure -----> $A=180\°-45.5\°=134.5\°$

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=45.5\°$

$B=37\°$

$45.5\°+37\°+C=180\°$

$C=180\°-(45.5\°+37\°)=97.5\°$

step 3

Find the first length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}$

$c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units$

therefore

the measures for the first solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=97.5\°$ , $b=52.7\ units$

step 4

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=134.5\°$

$B=37\°$

$134.5\°+37\°+C=180\°$

$C=180\°-(134.5\°+37\°)=8.5\°$

step 5

Find the second length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}$

$c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units$

therefore

the measures for the second solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

6 0

3 years ago