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3 years ago

a machine can reduce 21 inches of ribbon every 3 minutes. How many feet of ribbon can the machine make in one hour?

1 answer:

3 0

Okay. Let's make a proportion for this. So we can do 21/3=x/60. Let's multiply cross way. So 21 x 60 is 1260. We multiply 3 by x to get 3x. So our equation will be 3x=1260. We can isolate the equation by 3, and 1260 divided by 3 is 420. So x=420. We then have to convert into feet. So 420 divided by 12 is 35. So it would be 35 feet. Therefore, the machine can make 35feet of ribbon in a hour.

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Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14

PilotLPTM [1.2K]

Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

$N(t)=N_{0}e^{-\lambda t}$

Where:

No = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

$\lambda$ = The decay constant.

One important parameter related to radioactive decay is the half-life:

$\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }$

If we know the value of the half-life, we can calculate the decay constant:

$\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}$

Carbon-14 has a half-life of 5,730 years, thus:

$\displaystyle \lambda=\frac {\ln(2)}{ 5,730}$

$\lambda=0.00012097$

The equation of the remaining quantity of Carbon-14 is:

$N(t)=N_{0}e^{-0.00012097\cdot t}$

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

$0.10N_o=N_{0}e^{-0.00012097\cdot t}$

Simplifying:

$0.10=e^{-0.00012097\cdot t}$

Taking logarithms:

$ln 0.10=-0.00012097\cdot t$

Solving for t:

$\displaystyle t=\frac{log 0.10}{-0.00012097}$

$t\approx 19,035\ years$

Carbon-14 will take 19,035 years to decay to 10 percent.

6 0

3 years ago

Read 2 more answers

Triangles A B C and X Y Z are shown. Which would prove that ΔABC ~ ΔXYZ? Select two options. StartFraction B A Over Y X = StartF

sergejj [24]

Answer: Answer is 3

BC 6

------ = ------

XY 3

Step-by-step explanation:

The statements below can be used to prove that the triangles are similar.

On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.

A B Over X Y = 4 Over 2

A C Over X Z = 52 Over 13

△ABC ~ △XYZ by the SSS similarity theorem.

Which mathematical statement is missing?

1. Y Z Over B C = 6 Over 3

2. ∠B ≅ ∠Y

3. B C Over Y Z = 6 Over 3

4. ∠B ≅ ∠Z

5 0

3 years ago

Read 2 more answers

Find the radius of a circle using the Pythagorean theorem, given that the center is at (1, 5) and the point (5, 1) lies on the c

Assoli18 [71]

Given :

Center of circle, C = ( 1 , 5 )

Point on circle, P = ( 5 , 1 )

To Find :

The radius of a circle.

Solution :

We know, radius of circle is the distance between center and point of circle.

Distance between two points A(p,q) and B(r,s) is given by :

$D = \sqrt{(p-r)^2+(q-s)^2}$

So, distance between the points (1, 5) and (5, 1) is :

$D = \sqrt{(1-5)^2+(5-1)^2}\\\\D = 5.66 \ units$

Therefore, radius of circle is 5.66 units.

Hence, this is the required solution.

4 0

3 years ago

I don't know how to do this

Gre4nikov [31]

Answer:

x = -11/5 and y = 24/5

Step-by-step explanation:

Use elimination.

First, we need to multiply so that at least one variable can cancel out.

We can multiply the top equation by 2.

So we get

4x + 6y = 20

Then, we can use elimination.

The x's cancel out.

So we get 5y = 24

Or y = 24/5

Then, we can plug in this y value back into the first equation to find x.

2x + 3(24/5) = 10

2x + 72/5 = 50/5

2x = -22/5

x = -11/5

So x = -11/5 and y = 24/5

5 0

3 years ago

there are 14 girls trying out for volleyball. Each team will have six players. How many four teams will be made?

nikdorinn [45]

Answer:

Step-by-step explanation:

14 divided by 6 = 2.33333333

only 6 in a group so you round it

and you get 2

3 0

3 years ago