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3 years ago

15

What is this simplified?

2 answers:

lisabon 2012 [21]3 years ago

8 0

Answer:

7/4,

Step-by-step explanation:

it cant be simplified

Alex Ar [27]3 years ago

7 0

$\frac{7}{2}$

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Question 21 of 25

Phantasy [73]

It is A hope this helps :)

5 0

3 years ago

The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L

skelet666 [1.2K]

Answer:

The shorter piece x = 8.4 in

The longer one y = 15.6 in

Step-by-step explanation:

If we cut a string length L in to unequal pieces we get two pieces

first one with length x and the other one with length y

Let call x the smaller piece, then y = L - x will be the longer one

If x = 35 % then

x = 0,35* L and

y = L - x = L - 0,35*L ⇒ y = 0,65 L ⇒ y = 0.65*24

Now if L = 24 in

x = 0,35*24 ⇒ x = 8.4 in

and

L - x = 0.65*L ⇒ L - x = 0.65*24 y = L - x = 15.6 in

as way of verification you can add the length of the two pieces and find:

8.4 + 15.6 = 24 in

4 0

3 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

3 years ago

There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees ca

goblinko [34]

Answer: 8008

Step-by-step explanation:

Total entrees = 16

Number of entrees to choose = 6

Since order does not matter , so we combinations .

Number of combinations to choose r things out of n = $C(n,r)=\dfrac{n!}{r!(n-r)!}$

Then, total ways to choose 6 entrees = $C(16,6)=\dfrac{16!}{6!10!}$

$=\dfrac{16\times15\times14\times13\times12\times11\times10!}{(720)10!}\\\\= 8008$

Hence, the required number of ways= 8008

4 0

3 years ago

Please help answer ASAP

Roman55 [17]

I gave it a try, I got c

6 0

4 years ago