Simplify the following.<br> -(3x)2

A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will

QveST [7]

Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

$\frac{dy}{dt} = ky(1-y)$

Solving the differential equation,

$y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}$

The total number of inhabitants of the town = 2000

The number of people that heard the rumor = 160

At 8 AM, let t = 0,

$y(0) = \frac{160}{2000}$

= 0.08

By noon, half of the town as heard the rumor.

Then,

$y(4) = \frac{1}{2}$

Therefore,

$\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}$

$\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}$

$0.08 + 0.92e^{-4k} = 0.16$

$0.92e^{-4k} = 0.16 - 0.08$

$0.92e^{-4k} = 0.08$

$e^{-4k} = \frac {0.08}{0.92}$

$k = - \frac{1}{4} In(\frac {0.08}{0.92})$

k ≈ 0.06106

Calculating time, t when y(t) = 90%

⇒ y(t) = 0.9

$\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9$

$0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}$

$0.08 + 0.92e^{-0.06106t} = 0.089$

$0.92e^{-0.06106t} = 0.089 - 0.08$

$0.92e^{-0.06106t} = 0.0089$

$t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})$

t = 7.59 hours

⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

7 0

3 years ago

Step 1: –10 8x < 6x – 4 step 2: –10 < –2x – 4 step 3: –6 < –2x step 4: ________ what is the final step in solving the i

stiks02 [169]

The final step of the inequality equation –10 + 8x < 6x – 4 is x > 3. Then the correct option is D.

<h3>What is inequality?</h3>

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The inequality equation is given below.

–10 + 8x < 6x – 4

This can be simplified as

–10 + 8x < 6x – 4

–10 < –2x – 4

–6 < –2x

–3 < –x

x > 3

More about the inequality link is given below.

brainly.com/question/19491153

5 0

3 years ago

A donation center has 44 small bins with 24 caned food in them they wanna give each food bank the same amount of food there are

denpristay [2]

Complete question :

A donation center has 44 small bins with 24 caned food in them they wanna give each food bank the same amount of food there are 4 food banks. How many cans should they give to each food bank?

Answer:

264 cans

Step-by-step explanation:

Number of bins = 44

Number of canned food per bin = 24

Total number of canned foods = (number of bins * number of canned food per bin)

Total number of canned foods = 44 * 24 = 1056

Food is to be distributed equally among 4 banks :

Number of food per bank = 1056 / 4 = 264

6 0

3 years ago

Need help with this question please

zubka84 [21]

We can use the two point form to find the answer:
$y1 - y2 = m(x1 - x2)$
Where y1 is the y coordinate(coordinate on the right hand side of (-9)) of the of the first coordinates, and y2 is the y coordinates of the second coordinates given (0).

While x1(-9) and x2(-6) are the x-coordinates(left hand side of the coordinates) of the coordinates given seperately.

m is the slope of the two points, and the formula is:
$\frac{y1 - y2}{x1 - x2}$
In this case:
$\frac{ - 9 - ( 0)}{ - 9 - (-6)} \\ = \frac{ - 9 }{ - 9 + 6 } \\ = \frac{ - 9}{ -3 } \\ = 3$

We can then proceed to find the eqaution by putting *one* of the points into the two-point formula.

Put (-6，0) into the formula:
-0-y = 3(-6-x)
-y = -18 - 3x
y = -(-18 - 3x)
y = 18 + 3x

Therefore the answer is y= 18+3x.

Hope it helps!

8 0

4 years ago

What is the greatest common factor of 88 and 16

tankabanditka [31]

Hey there!

the answer is

The Greates Common Factor (GCF) is: 2 x 2 x 2 = 8

thank you

best regards

OFFICIALLYSAVAGE2003

7 0

4 years ago

Read 2 more answers

Simplify the following. -(3x)2