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2 years ago

Emanuel read 150 pages in 5 hours. Find his average reading rate.

Mathematics

1 answer:

Zina [86]2 years ago

7 0

Answer:

30 pages per hour

Step-by-step explanation:

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An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let

Advocard [28]

Answer:

$P(t)=3,000,000-3,000,000e^{0.0138t}$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The <em>integrating factor </em>is

$e^{Kt}$

Multiplying both sides of the equation by the integrating factor

$e^{Kt}P'(t)+e^{Kt}KP(t)= e^{Kt}3,000,000*K$

Hence

$(e^{Kt}P(t))'=3,000,000Ke^{Kt}$

Integrating both sides

$e^{Kt}P(t)=3,000,000K \int e^{Kt}dt +C$

$e^{Kt}P(t)=3,000,000K(\frac{e^{Kt}}{K})+C$

$P(t)=3,000,000+Ce^{-Kt}$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^{-50K}=\frac{1}{2}\Rightarrow K=-\frac{log(0.5)}{50}=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^{0.0138t}$

5 0

2 years ago

Which inequality represents the problem? A duck can dive below sea level at a rate of 5 feet per second. How many seconds will i

jok3333 [9.3K]

it will take the duck 5.8 seconds to reach 29 feet of depth.

7 0

2 years ago

Holly has a budget of $40 per month to spend on movies. She made a table showing the total amount of movie money she will have l

sammy [17]

The slope intercept equation is y=mx + b

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2 years ago

Type the correct answer in each box. If necessary, use / for the fraction bar. A bag contains 5 blue marbles, 2 black marbles, a

serg [7]

Answer:

P (not drawing a black marble) = 4/5

P (red marble) = 3/10

Step-by-step explanation:

The total number of marbles is

5 blue marbles +2 black marbles+ 3 red marbles = 10 marbles

P (not drawing a black marble) =

The marbles that are not black/ total marbles

(blue + red)/ total

(5+3)/10

8/10

4/5

P (red marble) = red marble/ total

= 3/10

7 0

2 years ago

the amount of gasoline at a gas station changes from 58,432.4 gallon to 56,475.2 gallon from 2:00 pm to 4:00 pm. what rational n

jarptica [38.1K]

Answer:

I take it you mean the average gallons lost an hour, in which case you would do 58,432.4 - 56,475.2 to get 1,597.2 to which you divide by 2 getting your final answer of 978.6

4 0

2 years ago