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sammy [17]
3 years ago
12

"Which number can be inserted in the parentheses so the numbers are ordered from least to greatest?" -3,(),-1 1/8 A. -3 1/2 B. 0

C. -2 1/4 D 1 1/2
Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0

Answer:

Option C

Step-by-step explanation:

The first number is - 3, then we have a blank and the third number is - 1 1/8

In order for the numbers to be arranged from least to greatest, the number in the center should be greater than -3, and lesser than -1 1/8

Note that for negative numbers, the larger the constant, the smaller the number. i.e. -5 is smaller than -4.

So from the given options, the only number that is greater than -3 and lesser than -1 1/8 is - 2 1/4

So, option C gives us the correct answer to have the numbers ordered from least to greatest.

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A sample of a radioactive isotope had an initial mass of 360 mg in the year 1998 and
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Answer:

193 mg

Step-by-step explanation:

Exponential decay formula:

  • A_t = A_0e^r^t
  • where Aₜ = mass at time t, A₀ = mass at time 0,  r = decay constant (rate), t = time  

Our known variables are:

  • 1998 to the year 2004 is a total of t = 6 years.
  • The sample of radioactive isotope has an initial mass of A₀ = 360 mg at time 0 and a mass of Aₜ = 270 mg at time t.

Let's solve for the decay constant of this sample.

  • 270=360e^-^r^(^6^)
  • 270=360e^-^6^r
  • \frac{3}{4} =e^-^6^r
  • \text{ln} (\frac{3}{4} )= \text{ln}(e^-^6^r)
  • \text{ln} (\frac{3}{4} )=-6r
  • r=-\frac{\text{ln}\frac{3}{4} }{6}
  • r=0.04794701

Using our new variables, we can now solve for Aₜ at t = 7 years, since we go from 2004 to 2011.

Our new initial mass is A₀ = 270 mg. We solved for the decay constant, r = 0.04794701.

  • A_t=270e^-^(^0^.^0^4^7^9^4^8^0^1^)^(^7^)
  • A_t=270e^-^0^.^3^3^5^6^2^9^0^7
  • A_t=193.01982213

The expected mass of the sample in the year 2011 would be 193 mg.

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3 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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