Answer:
120 grams will be left after 180 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
![N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}](https://tex.z-dn.net/?f=N%28t%29%3DN_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%7D)
where,
= quantity of the substance remaining
= initial quantity of the substance
= time elapsed
= half life of the substance
From the information given we know that:
- The initial quantity is 480 g,
- The half-life is 90 years,
- 180 years is the time elapsed.
And we want to find how much will be left. For this we use the above formula.
![N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120](https://tex.z-dn.net/?f=N%28t%29%3D480%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cfrac%7B180%7D%7B90%7D%7D%5C%5C%5C%5CN%28t%29%3D480%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E2%5C%5C%5C%5CN%28t%29%3D480%5Ccdot%20%5Cfrac%7B1%7D%7B2%5E2%7D%3D120)
120 grams will be left after 180 years.
Answer:
D. –X+XY–7y
Step-by-step explanation:
We just have to combine (add) the similar terms... so all terms that have an x in them for example.
–3x + 2xy + 4y – xy + 2x – 11y
Let's first re-write it placing similar terms next to each other
(-3x + 2x) + (2xy - xy) + (4y - 11y)
Then we sum them up, for each similar terms
1x + 1xy -7y
so, x + xy -7y
Answer D.
ANSWER
36√3 square units.
EXPLANATION
The area of a parallelogram is obtained by multiplying the base by the height.
We use the sine ratio to obtain the height.
![\sin(60 \degree) = \frac{h}{6}](https://tex.z-dn.net/?f=%20%5Csin%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Bh%7D%7B6%7D%20)
![h = 6 \sin(60 \degree)](https://tex.z-dn.net/?f=h%20%3D%206%20%5Csin%2860%20%5Cdegree%29%20)
![h = 3 \sqrt{3}](https://tex.z-dn.net/?f=h%20%3D%203%20%5Csqrt%7B3%7D%20)
The area becomes:
![12 \times 3 \sqrt{3} = 36 \sqrt{3} {units}^{2}](https://tex.z-dn.net/?f=12%20%5Ctimes%203%20%5Csqrt%7B3%7D%20%20%3D%2036%20%5Csqrt%7B3%7D%20%7Bunits%7D%5E%7B2%7D%20%20)
If you are solving for x than the answer would be x=4.
Answer:
hmmm 38
Step-by-step explanation:
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