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Lunna [17]
3 years ago
6

An element with mass 310 grams decays by 5.7% per minute. How much of the element is remaining after 9 minutes, to the nearest 1

0th of a gram?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
8 0
1st
I need to find out what percentage is left after 1 minute
100 - 5.7 = 94.3% (0.943)

2nd plug into the formula A =  A_{0}  r^{t}

A0 = 310
r = 0.943
t = 9

A = 310(0.943)^{9} \\ A = 310(0.58966) \\ A = 182.8 g
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Answer: (72.535, 76.665)

Step-by-step explanation:

The confidence interval for population mean is given by :-

\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}

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n= Sample size

\overline{x} = sample mean.

z^* = Critical z-value (two-tailed)

Given : \sigma=11.3

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The critical values for 90% confidence interval : z^*=\pm1.645

Now, the confidence interval for population mean would be :

74.6\pm (1.645)\dfrac{11.3}{\sqrt{81}}\\\\=74.6\pm(1.645)(\dfrac{11.3}{9})\approx74.6\pm2.065\\\\=(74.6-2.065,\ 74.6+2.065)\\\\=(72.535,\ 76.665)

Hence, a 90 percent confidence interval estimatefor the average score of all students. : (72.535, 76.665)

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