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3 years ago

Amanda reads 300 pages in 10 hours. If each page has 200 words on it, how many words did Amanda read per minute?

Mathematics

2 answers:

puteri [66]3 years ago

7 0

Answer:

100

Step-by-step explanation:

So if there is 200 word per page it will be 200×300, which is 60,000. We are trying to find words per minute, so we do; 10×60 (1 hour=60minutes) which is 600. so to find the words per minute we do:

60,000÷600=100

ICE Princess25 [194]3 years ago

5 0

Answer:

so that means you would divide 300 by 10 and that means she reads 30 pages in 1 hour so if you do 30 divided by 60 or 1 hour you get 0.5 pages so she reads 100 words in 1 minutes

Step-by-step explanation:

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A Hot air balloon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute . The total c

mojhsa [17]

$\bf \stackrel{\textit{cubic feet of air}}{\stackrel{\textit{dependent}}{a(t)}}\qquad \stackrel{\stackrel{\textit{time in minutes}}{independent}}{t}~\hspace{7em}a(t)=6000t$

the "t" variable is independent, namely it can change values "freely", and a(t) is dependent, because it depends on those values on "t" to get its own value.

if we make a table of values for minutes, we know the balloon is inflating at 6000 ft³ each passing minute.

1 minute......................... 6000(1) ft³

2 minutes......................6000(2) ft³

3 minutes......................6000(3) ft³

4 minutes......................6000(4) ft³

t minutes......................6000(t) ft³

before getting in the domain and range, let's find out how much air after 6 minutes.

a(6) = 6000(6)

a(6) = 36000 ft³.

now, what domain, namely values for "t" make sense?

well, we know the balloon can only hold up to 90000 ft³, and on every passing minute is filling up by 6000 ft³, after how many minutes will it be filled up?

90000/6000 = 15, after 15 minutes.

so at 0 minutes, t = 0, the balloon is empty, and 15 minutes later, t = 15, the balloon is filled up, [ 0 , 15 ].

what values for the range, namely a(t), makes sense?

well, we know when the balloon is empty is holding 0 ft³, and when is full it has 90000 ft³, [0 , 90000].

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:

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.

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)

$R=0.06B+0.1S$

$R=0.06(0.3)+0.1(0.7)$