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3 years ago

10

A bag contains two red marbles and three blue marbles. You randomly pick a marble.

1 answer:

Mice21 [21]3 years ago

3 0

Uh yeah I agree. Mhmm. Absolutely.

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1. What is 12/3 as an improper fraction?

LiRa [457]

ans would be this 4 0/4

8 0

4 years ago

A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio

GaryK [48]

Answer:

a) $N=N_0e^{-0.069t}$

b) $N=696.9$ grams

c) $t=10$ days

Step-by-step explanation:

a)

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

$\frac{dN}{dt}=-0.069N$

Multiply both sides by $dt$ :

$dN=-0.069N dt$

Divided both sides by $N$ :

$\frac{dN}{N}=-0.069 dt$

Integrate both sides:

$\ln|N|=-0.069t+C$

The equivalent exponential form is:

$e^{-0.069t+C}=N$

Using law of exponents you can write this as:

$e^{-0.069t}e^C=N$

$e^C$ is just a positive constant that I'm going to replace with K:

$e^{-0.069t}K=N$

Applying the symmetric property of equality:

$N=e^{-0.069t}K$

Applying the commutative property of multiplication:

$N=Ke^{-0.069t}$

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

$N=Ke^{-0.069 \cdot 0}$

$N=Ke^{0}$

$N=K(1)$

$N=K$

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with $N_0$ instead. So the exponential equation is:

$N=N_0e^{-0.069t}$

b)

We are given $N_0=800$ at $t=0$ .

We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in $N=800e^{-0.069t}$ :

$N=800e^{-0.069 \cdot 2}$

Put into calculator:

$N=696.9$ (this was rounded to the nearest tenths)

c)

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

$\frac{1}{2}(800)=800e^{-0.069t}$

$400=800e^{-0.069t}$

Divide both sides by 800:

$\frac{400}{800}=e^{-0.069t}$

Reduce the fraction:

$\frac{1}{2}=e^{-0.069t}$

Convert to logarithmic form:

$\ln(\frac{1}{2})=-0.069t$

Divide both sides by -0.069:

$\frac{\ln(\frac{1}{2})}{-0.069}=t$

Input into calculator:

$10.0=t$

$t=10.0$

$t=10$

6 0

4 years ago

The sum of the interior angle measures in a regular polygon is 1260° . What is the measure of one of the interior angles of the

LUCKY_DIMON [66]

Answer:

140°

Step-by-step explanation:

5 0

3 years ago

Caroline won $250,000 in a lottery. After paying $96,000 in taxes, she placed the remaining amount in a savings account at a 2%

Serjik [45]

Answer:

18,480

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, first, you would fine how much she put in the bank in the first place!

250,000-96,000=154,000

Then you would do 154,000*0.02 to find how much interest is charged per month.

154,000*0.02=3080

Finally, you would multiply 3080 by 6 {because you need to account for all of the months}.

3080*6=18,480

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

5 0

4 years ago

The slope in the linear equation y=12x+5 is _[blank]_.

Kazeer [188]

The slope is 12x, remember the slope is the number value before the variable!

7 0

3 years ago