ANSWER
99.83 grams
EXPLANATION
The function that describes the amount of sample (in grams) after t years of decomposition is:
![C(t)=100\cdot(\frac{1}{2})^{\frac{t}{5730}}](https://tex.z-dn.net/?f=C%28t%29%3D100%5Ccdot%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B5730%7D%7D)
To get the amount of carbon 14 after 14 years, we calculate <em>C(14)</em> as following:
![\begin{gathered} C(14)=100\cdot(\frac{1}{2})^{\frac{14}{5730}} \\ \\ \Rightarrow C(14)=99.83 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20C%2814%29%3D100%5Ccdot%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7B14%7D%7B5730%7D%7D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20C%2814%29%3D99.83%20%5Cend%7Bgathered%7D)
This way, we'll have 99.83 grams left.
Answer:
Eh you got 3 wrong
Step-by-step explanation:
!! You got wrong !! First picture the answer is A b/c a function is when the X value only has 1 Y value assigned to it.
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!! You got wrong !! The second picture, the answer is 35 T-Shirts
12T + 25S = 795
T - 20 = S
12T + 25(T - 20) = 795
12T + 25T - 500 = 795
37T = 1295
T = 35
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!! You got wrong too !! First one has a solution of 0. The answer is the last answer choice.
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You got this one correct, it is (2,3)
Answer:
0.12
Step-by-step explanation:
Total number of questions in the book = 10
Number of questions answered correctly by Alice = 6
Number of questions answered correctly by Bob = 8
Probability of Alice answering a question correctly = 0.6
Probability of Alice answering a question incorrectly = 1- 0.6 = 0.4
Probability of Bob answering a question correctly = 0.8
Probability of Bob answering a question incorrectly = 1- 0.8 = 0.2
Probability that there exists at least one question on the test which is answered correctly by Alice but not by Bob = 0.6 *0.2 = 0.12
Machine can make 114 copies in 4 minutes and 45 seconds. So first convert 45 seconds into minutes. We will use ratio and proportion for that using 1 minute = 60 seconds. So let say X minutes = 45 seconds.
![\frac{1 minute}{60 seconds} = \frac{X minutes}{45 seconds}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20minute%7D%7B60%20seconds%7D%20%3D%20%5Cfrac%7BX%20minutes%7D%7B45%20seconds%7D%20)
solve for X as shown
![\frac{1}{60} \times 45 = \frac{X}{45} \times 45](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B60%7D%20%5Ctimes%2045%20%3D%20%5Cfrac%7BX%7D%7B45%7D%20%5Ctimes%2045%20)
= X
0.75 = X
So 45 seconds =0.75 minutes
So it takes 4 minutes +0.75 minutes = 4.75 minutes for machine to make 114 copies. We have to find copies made in 1 minute. So lets say it makes C copies in 1 minute. Again we will use ratio and proportion
= ![\frac{C copies}{1 minute}](https://tex.z-dn.net/?f=%20%5Cfrac%7BC%20copies%7D%7B1%20minute%7D%20%20)
Now solve for C as shown
= ![\frac{C}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7BC%7D%7B1%7D%20%20)
24 = C
So machine can make 24 copies in 1 minute. So thats the final answer.