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tresset_1 [31]
4 years ago
11

a 40 gram sample of a substance that's used for drug research has a k-value of 0.1446. find the substance's half life in days

Mathematics
2 answers:
Dovator [93]4 years ago
4 0

Answer:

4.7935 days

Step-by-step explanation:

The expression that describes exponential decay is the following:

N(t) = No * e^{-kt}

Where N(t) is the mass of the substance after a period t of time.

No is the original amount of substance

k is the relative decay rate and t is the period of time elapsed.

The half life is the period of time after which the amount of substance has decreased by half.

We can issolate t in the expression, using the properties of logarithms:

\frac{N(t)}{No}=e^{-kt}

ln(\frac{N(t)}{No}) = -k*t

t = - ln(\frac{N(t)}{No})/k = - ln(\frac{1}{2})/0.1446 = 4.7935 days.

Novay_Z [31]4 years ago
3 0

The applicable decay formula is:N = No*e^(-kt)WhereN = Mass left after time tNo = Original massk = constantt = half lifeUsing the values given,N/No = e^(-0.1446t) = 1/2ln (1/2) = -0.1446 t *ln e^1-0.6931 = -0.1446 tt = 0.6331/0.1446 = 4.79 daysTherefore, half-life is 4.8 days.

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3 0
3 years ago
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If Judy completes a puzzle by herself, it takes her 3 hours. working with sal, it only takes them 2 hours.
timurjin [86]

Answer:

C. \frac{1}{3}

Step-by-step explanation:

We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.

We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.

Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be \frac{1}{3}, therefore, correct choice is option C.

6 0
3 years ago
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Find the value of x (rounded to the nearest tenth as needed).
mars1129 [50]

Answer:

x = 367.1m

Step-by-step explanation:

Use the SohCahToa trigonometry ratios because this is a right triangle.

First, we need an interior angle of reference for the triangle. Because you know that angle labelled 37°, we can use <u>alternating angles</u> to find an interior angle. Alternating angles create a "Z" pattern where the two angles are equal. In this triangle, the missing angle on the left is 37° also.

According to SohCahToa, we will use the sinθ ratio (opposite/hypotenuse).

sinθ = opposite/hypotenuse       Substitute values from the diagram

sin37° = x/610yd        Isolate 'x'. Multiply both sides by 610 yd

x = (610yd)(sin37°)      Multiply

x = 367.107...m      Unrounded answer

x ≈ 367.1m      Answer rounded to the nearest tenth

Therefore x is 367.1 meters.

7 0
4 years ago
Please answer the question and leave an explanation on how to solve each part. Thank you in advance!
horsena [70]

The solutions are

  • it is going to take 15.9 months to raise 10000 dollars
  • You will have $37.31 after you have bought the car
  • The money deficit would be $37.31

<h3>How to solve the question</h3>

a. 10000 = 9359.08e(0.05)

e⁰⁰⁵ = 10000/9359.08

= 0.05 = ln(10000/9359.08)

= 1.325 years

convert to months = 15.9 months

Hence it is going to take 15.9 months to raise 10000 dollars

b. 9359.08 x e^(0.05 x1.25)

= 9962.69

10000 - 9962.69

= $37.31

You will have $37.31 after you have bought the car

c. The money loss and the deficit would be same as above $37.31

d. ln(e^a) = a

We can clearly see that the money cannot be raised in the 15 months from $ 9359.08. there is a deficit amount of $37.31

Read more on compound interest here: brainly.com/question/24924853

#SPJ1

3 0
2 years ago
Carl ordered 2 pants at $22.54 each and 2 shirts at $19.89 each. With sales tax of 6% and shipping below, what was his total ord
lubasha [3.4K]

Answer:

Total order cost = $98.90

Step-by-step explanation:

Cost of 1 pair of pants = $22.54

Cost of 2 pairs of pants = 2*22.54 = 45.08


And

Cost of 1 shirt = $ 19.89

Cost of 2 shirts = 2 * 19.89 = 39.78



Now total cost of all 4 items = $45.08 + $39.78 = $84.86


Now 6% sales tax is to be added so

Total cost = 84.86 + (0.06 * 84.86) = 89.9516

= $89.9516


Now from the table we can see that $8.95 shipping charges are to be added.


So total order cost = $89.9516 + $8.95 = $98.9016

= $98.90

8 0
4 years ago
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