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3 years ago

What word phrase can you use to represent the following algebraic expression: 4(x-7)?

Mathematics

1 answer:

snow_tiger [21]3 years ago

8 0

Bob bought 4 shirts that are 7$ off each.

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If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

3 years ago

Is the following relation a function?

abruzzese [7]

Answer:

Yes bc the x is not repeating

Step-by-step explanation: Remember if the domain(x) is repeating like (4,4) (4,3) it is not a function because of the x and don't worrying about the y (range) and if the domain is not repeating like (2,3)(3,8) it is a function bc of the domain (x) hope this help:)

7 0

3 years ago

Mr. Simpson spent five hours working on his lawn if you spent 25% of the time edging the flowerbeds how much time did he spend e

cricket20 [7]

He spend one hour and twenty five minutes (1:25)

5 0

3 years ago

The sum of four times a number and 18 is the same as the difference of fourteen and twice a number

Citrus2011 [14]

$4x+18=14-2x \\ 4x=-4-2x \\ 6x=-4 \\ x= \frac{2}{3}$

4 0

3 years ago

I really need on these cause I really don't know this and I need to understand. please help me please.

lawyer [7]

Answer:

-6m^4-m^3

Step-by-step explanation:

First you move the parenthesis then you group the like terms after you group the like terms you get $m^4-7m^4-m^3$ which is adding the similar elements and after you add similar elements you get -6m^4-m^3. Srry if this makes no sense

8 0

3 years ago

Read 2 more answers