1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alecsey [184]
3 years ago
11

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determi

ned using the equation f(t)=100(1/2)^t/10. After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is f(t)=100(1/2)^t-3/10. After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?
A.78.1%
B.81.2%
C.123.1%
D.128.0%
Mathematics
1 answer:
grandymaker [24]3 years ago
4 0
The mass of the first shipment at time t is
m_{1}=100( \frac{1}{2} )^{ \frac{t}{10}}

The mass of the second shipment at time t is
m_{2}=100( \frac{1}{2} )^{ \frac{t-3}{10} }

At time t, the ratio of m₁ to m₂ is
\frac{m_{1}}{m_{2}} = \frac{100}{100}. \frac{(1/2)^{t/10}}{(1/2)^{(t-3)/10}} \\ =  \frac{(1/2)^{t/10}}{(1/2)^{t/10}}. \frac{1}{(1/2)^{-3/10}} \\ = (1/2)^{3/10} \\ = 0.8123

Therefore as a percentage,
\frac{m_{1}}{m_{2}} =100*0.8123 = 81.23 \%

Answer: B. 81.2%

You might be interested in
Determine the inverse of the function. (show work please)
uysha [10]

Answer:

This is easy -- it's just a list of steps.  At this level, the problems are pretty simple.

Let's just do one, then I'll write out the list of steps for you.

Find the inverse of f( x ) = -( 1 / 3 )x + 1

STEP 1:  Stick a "y" in for the "f(x)" guy:

y = -( 1 / 3 )x + 1

STEP 2:  Switch the x and y

                   ( because every (x, y) has a (y, x) partner! ):

x = -( 1 / 3 )y + 1

STEP 3:  Solve for y:

x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3

STEP 4:  Stick in the inverse notation, f^( -1 )( x )

f^( -1 )( x ) = -3x + 3

Step-by-step explanation:

5 0
3 years ago
Write a numerical expression that represents the number of increments it will take to reach -60 feet.
Marizza181 [45]

Answer:

Step-by-step explanation:

Write a numerical expression that represents the number of increments it will take to reach -60 feet

4 0
3 years ago
A cost of 90 dvds cost rupees 17910 what will be the cost of 32 such dvds​
Juliette [100K]
It would be 27 DVD’s. :]
8 0
2 years ago
Read 2 more answers
A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to the nearest tenth.
Marizza181 [45]

Answer:

754.0 inches cubed

Step-by-step explanation:

The volume of a cylinder is denoted by: V=\pi r^2h, where r is the radius and h is the height.

Here, the radius is r = 4 and the height is h = 15. So plug these in:

V=\pi *4^2*15=754.0

The volume is 754.0 inches cubed.

Hope this helps!

5 0
2 years ago
Read 2 more answers
What is the slope of the line that passes through the points (8, 2) and (9, 3)? Write
Burka [1]

Answer:

The slope of the line is 1

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Given the function. f(x)= x-2+3, choose the correct transformation
    15·1 answer
  • 18.4x-3.1=12.4x-16.9
    10·1 answer
  • at the bake sale,jonah sold 4 cakes for 8 dollars each and 36 muffins for 2 dollars each.what was the total amount in dollars,th
    14·2 answers
  • What two numbers multiply to get 54 and add to get 36?
    6·1 answer
  • How do you graph Y=-5x+15
    10·1 answer
  • The Pave the Way Company is installing a new walkway. The installer uses 13 paving stones for every foot of walkway. He needs 11
    8·1 answer
  • A company has a profit of$1750 this week. This profit is $900 more than profit p last week. What equals p
    5·1 answer
  • An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 5 small chandelie
    10·1 answer
  • 20 people show up to the party and they will get the same amount of pizza. There are 11 pizzas. How much pizza does each person
    5·1 answer
  • Hello! Does anyone know how to do this I already tried some but I got them wrong. Giving brainliest!!
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!