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lutik1710 [3]
3 years ago
12

How to get to 12 to 55

Mathematics
1 answer:
leva [86]3 years ago
4 0
Based on your comment about the question, You would have to subtract 55 - 12, to find the remaining amount to get 12 up to 55, which would be 43 ;D
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Benjamin drove 278 miles in 4 hours.
kondor19780726 [428]

Step-by-step explanation:

rate \:of \: driving \\  =  \frac{278}{4}  \\  = 69.5 \: mph

6 0
3 years ago
6. Write an equation of a line that is Parallel to the line: y = 3x -3
jeka94

Answer:

3x - y -6 = 0

Step-by-step explanation:

We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,

\rm\implies y = 3x - 3

<u>Slope </u><u>Intercept</u><u> Form</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = mx + c

where ,

  • m is slope
  • c is y intercept .

Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .

<u>Using</u><u> point</u><u> slope</u><u> form</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y - y_1 = m ( x - x_1)  \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}

3 0
3 years ago
George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his t
nikdorinn [45]

Answer:

a. B+S = 1

0.06B+0.1S \geq 0.075

B \geq 0.3

Objective function:

R=0.06B+0.1S

b) See Attached picture

30% in bonds and 70% in stocks

Step-by-step explanation:

a.

In order to solve the first part of the problem we need to take into account that the problem wants us to determine the percentage that should be allocated to each of the possible investment alternatives. In that case, the sum of the percentages must be equal to 1 (which means that we will have 100 of the trust fund)

so that gives us our first restriction for the problem.

B+S=1

Next, the problem tells us that the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. It also states that he wants to select a mix that will enable him to obtain a total return of at least 7.5%, so we can take this information and get the second restriction from it:

0.06B+0.1S \geq 0.075

Next, the problem tells us that whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund, so that's where the last restriction comes from:

B \geq 0.3

now, the idea is to optimize the investment, this is get the greatest amount of money out of the trust fund, so the objective function is:

R=0.06B+0.1S

which represents the return on the investment.

b)

For part b we can start by graphing each of the restrictions:

B+S = 1

This will be a single line, you can draw the line by setting B=0 first so you get:

0+S=1

S=1

So the first point to plot will be (0,1)

next, we can set s=0 to get:

B+0=1

B=1

so the second point to plot will be (1,0)

so you can plot the two points and connect them with a straight line. This is the green line on the uploaded graph.

Next we can graph the second restriction:

0.06B+0.1S \geq 0.075

we can use the same procedure we used for the previous graph, in this case the points would be:

(0 , 0.75) and (1.25, 0)

and again connect the two points with a straight line. Next we need to decide which region of the graph to shade for which we can pick two arbitrary points on each side of the line, for example we can pick:

(0,0) and (2,2) and see which one makes the inequality true:

for (0,0) we get:

0.06B+0.1S \geq 0.075

0.06(0)+0.1(0) \geq 0.075

0 \geq 0.075

Which is false, therefore we need to shade the other region of the graph:

for (2,2) we get:

0.06B+0.1S \geq 0.075

0.06(2)+0.1(2) \geq 0.075

0.32 \geq 0.075

Which is true, so we shade the region of the graph that contains that point. (see red graph)

now we graph the third restriction:

B \geq 0.3

In order to graph this third restriction we just need to draw a vertical line at B=0.3 and shade everything to the right of that line. (Blue graph)

Now, we can analyze the graph, in this case we need to locate the points where the green line crosses the red and the blue line which gives us the following coordinates:

(0.3, 0.7) and (0.625, 0.375)

these two points can be found by setting the first restriction equal to each of the other two restrictions if you are to do it algebraically. If you are using a graphing device, you can directly read them from the graphs.

So once we got those points, we can see which one gives us the greatest percentage of return.

let's test the first point (0.3, 0.7)

R=0.06B+0.1S

R=0.06(0.3)+0.1(0.7)

R=0.088

so this distribution gives us 8.8% in return, let's test the second point:

(0.625, 0.375)

R=0.06B+0.1S

R=0.06(0.625)+0.1(0.375)

R=0.075

so this distribution gives us 7.5% in return.

In this case the best distribution for us is 30% in bonds and 70% in the stock fund to get a return of 8.8%

6 0
3 years ago
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is th
Naddik [55]

Answer:

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Step-by-step explanation:

The formula for the perimeter of a rectangle is P=2L+2W.

If the width is W=12\:units and the length is L=18\:units, then the perimeter becomes:

 P=2\times 12+2\times 18.

 \implies P=24+36.

 \implies P=60.

Therefore the answer is

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

7 0
3 years ago
Read 2 more answers
-3 + n = 6n + 22 ; Solve for n.
anygoal [31]

Answer:

-3 + n = 6n + 22

-1n on both sides

-3=5n+22

-22 on both sides

-25=5n

divided by 5

-5=n

Step-by-step explanation:

6 0
2 years ago
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