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Sunny_sXe [5.5K]
2 years ago
8

James has a piece of construction paper with a length of 9/10 feet and a width of 2/3 feet.

Mathematics
2 answers:
creativ13 [48]2 years ago
7 0

Area = length x width

When you multiply fractions, multiply top number by top number and bottom number by bottom number:

9/10 x 2/3 = (9 x 2) / (10 x 3) = 18/30 this can be reduced by dividing both numbers by 6:

18/30 reduces to 3/5

Answer: 3/5 square feet

Anuta_ua [19.1K]2 years ago
5 0

Answer:

3/5

Step-by-step explanation:

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When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance
bekas [8.4K]

a) v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}

The average speed is equal to the ratio between the total distance (d_{tot} and the total time taken (t_{tot}):

v=\frac{d_{tot}}{t_{tot}}

the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:

d_1 = (3 h)(60 mph)=180 mi

So the total distance is

d_{tot}=d_1 +d_2 = 180 mi+20 mi=200 mi

The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:

t_{tot}=3 h +t_2

So, the equation can be rewritten as:

v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}


b) 0.50 h (half a hour)

Since we know the value of the average speed, v=57.14 mph, we can substitute it into the previous equation to find the value of t_2, the time the trucker drove in the city:

v=\frac{200 mi}{3h +t_2}\\3h+t_2 = \frac{200 mi}{v}\\t_2 = \frac{200 mi}{v}-3h=\frac{200 mi}{57.14 mph}-3 h=0.50 h


3 0
3 years ago
Give an example of a rule for a pattern. List a set of numbers that fit the pattern.
Jlenok [28]
In this pattern , the numbers are doubling..
2,4,6,8,10...
7 0
3 years ago
What is the slope of the line that passes through the points (2, 8) and (6, 12)?
zubka84 [21]
Yeah, where I live, to find the slope (or as we call it, the gradient), you just have to do the two y values subtracted from each other, over the two x values subtracted from each other. The important thing is to remember that if you subtract the first y value from the second (so, 12 - 8), you have to do the same thing for the x (6 - 2)

\frac{12-8}{6-2} = \frac{4}{4} = 1.

The slope is 1. 
5 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
Find cos(β) in the triangle.
svetlana [45]

90°+b+b =180

90°+ 2b=180

2b=180-90

2b= 90

<u>2</u><u>b</u><u>=</u><u>9</u><u>0</u>

<u>2</u> = 2

b=45°

ave tried I don't know if its correct

8 0
2 years ago
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