Solve for x. help please

Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.

Korolek [52]

Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t

7 0

3 years ago

Help Thrhfjfhfhhfhfhfjf

12345 [234]

Answer: 5

Step-by-step explanation:

a^2 + b^2 = c^2

12^2 + x^2 = 13^2

144 + x^2 = 169

x^2 = 25

square root both sides

x = 5

to check, do 12^2 + 5^2 =169

sqrt of 169 is 13

hope this helps

4 0

3 years ago

Can someone please help me?

storchak [24]

5lbs=8.25
/5 /5
1lbs=1.65

6 0

3 years ago

For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each. How much did the school sp

NNADVOKAT [17]

Answer: $\$264.95$

Step-by-step explanation:

You know that 1 sandwich costs $4.60 and the school bought 47 sandwiches.

Therefore, in order to calculate the total cost of 47 sandwiches, you need to multiply this number of sandwiches bought by the schoole, by the cost of 1 sandwich. Then:

$sandwiches=(47)(\$4.60)\\\\sandwiches=\$216.2$

You know that 1 bag of chip costs $1.25 and the school bought 39 bags of chips.

So, in order to calculate the total cost of 39 bags of chips, you must multiply the total number of them bought by the school, by the cost of 1 bag of chips.

Then:

$bag\ of\ chips=(39)(\$1.25)\\\\bag\ of\ chips=\$48.75$

Therefore, the total amount school spent was:

$Total\ spent=\$216.2+\$48.75\\\\Total\ spent=\$264.95$

8 0

3 years ago

Read 2 more answers

Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.

Vitek1552 [10]

The answer is 3/4 ft² = 0.75 ft²

The area (A) of the parallelogram with altitude a and base b is:
A = a * b

We have:
A = ?
a = 6 in
Since 1 inch is 0.083 feett, then 6 inches is
a = 6 * 0.083 ft = 0.498 ft ≈ 0.5 ft = 1/2 ft
b = 1 1/2 ft = 1 + 1/2 ft = 2/2 + 1/2 ft = 3/2 ft
_______
A = a * b
a = 1/2 ft
b = 3/2 ft
A = 1/2 * 3/2 = 3/4 ft² = 0.75 ft²

4 0

3 years ago