In a necklace there is one blue bead for every four

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alexis3567

26.01.2022

Mathematics

I would say 3 blue 12 yellow in my opinion. Have a great day

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sana20

19.02.2022

Mathematics

The half-life of carbon-14 is 5730 years.decay equation: for initial value $a_0$ , the amount of carbon-14 left after $t$ years is $a = a_0\left(\dfrac{1}{2}\right)^{t/5730}$ we are given that $a = 0.27a_0$ (final amount is 27%, which is 0.27, of the intial)so $\begin{aligned} 0.27a_0 & = a_0\left(\dfrac{1}{2}\right)^{t/5730} \end{aligned}$ divide both sides by $a_0$ $\begin{aligned} 0.27 & = \left(\dfrac{1}{2}\right)^{t/5730} \end{aligned}$ take log base 10 of both sides $\begin{aligned} \log(0.27) & = \log\left[\left(\dfrac{1}{2}\right)^{t/5730} \right] \end{aligned}$ use logarithm property $\log m^n = n \log m$ $\begin{aligned} \log(0.27) & = \log\left[\left(\dfrac{1}{2}\right)^{t/5730} \right] \\ \log(0.27) & = \frac{t}{5730} \log(0.5) \\ \log(0.27) & = t \cdot \frac{\log(0.5)}{5730} \\ t & = \frac{5730 \log(0.27)}{\log(0.5)} \\ t & \approx 10823.79\text{ years} \end{aligned}$ so approximately 10824 years old.

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In a necklace there is one blue bead for every four yellow beads there are 15 beads altogether. a) how many blue beads are there? b) how many yellow beads are there? c) how can you check your answer..

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