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USPshnik [31]
2 years ago
3

The half-life of rubidium-89 is 15 minutes. If the initial mass of the isotope is 250 grams, how many grams will be left after 1

00 minutes?
Mathematics
Mathematics
1 answer:
Sidana [21]2 years ago
6 0
Exponential decay can be expressed as:

f=ir^t, f=final value, i=initial value, r=common ratio or "rate" and t=times ratio is applied or "time"

We are told that the half life is 15 minutes and that means that i=2f at that point

1=2r^15

1/2=r^15  if we raise each side to the power of 1/15 we have:

(1/2)^(1/15)=r  now that we know the rate and the initial value, 250g we have:

f=250(1/2)^(1/15)^t which is equal to:

f=250(1/2)^(t/15)  so when t=100 minutes...

f=250(1/2)^(100/15) g

f≈2.46 g  (to nearest hundredth of a gram)
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Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that
Nadusha1986 [10]

Answer: Our required probability would be 0.70.

Step-by-step explanation:

Since we have given that

Number of players = 14

Number of players have recently taken a performance enhancing drug = 3

Number of players have not recently taken a performance enhancing drug = 14-3=11

Number of members chosen randomly = 5

We need to find the probability that at least one of the tested players is found to have taken a performance enhancing drug.

P(Atleast 1) = 1 - P(none is found to have taken a performance enhancing drug)

So, P(X≥1)=1-P(X=0)

P(X\geq 1)=1-^5C_0(\dfrac{11}{14})^5\\\\P(X\geq 1)=1-(0.786)^5\\\\P(X\geq 1)=0.70

Hence, our required probability would be 0.70.

7 0
2 years ago
During his last 5 jobs, an electrician used the following amounts of cable:
ella [17]

The total amount of cable used is 47.4m

<u>Explanation:</u>

Given:

Amounts of cable used that has to be rounded off to 1 decimal place:

12.995 m  ≈ 13.0 m

7.505 m  ≈ 7.5m

10.08 m  ≈ 10.1 m

6.95 m  ≈ 7.0 m

9.75 m ≈ 9.8 m

Total amount of cable used = 13m + 7.5m + 10.1m + 7m + 9.8m

                                              = 47.4m

Therefore, total amount of cable used is 47.4m

7 0
2 years ago
Zane and Matt are both keen runners. Zane takes 4 minutes to jog around a running track and Matt takes 5 minutes. They start at
Sergio [31]
I believe that the correct answer to this question is B. because matt took more than 5 minutes .
3 0
2 years ago
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc
Mademuasel [1]
Let X is the random number Erik thinks of, and Y is the random number Nita thinks of.
Both X and Y are in the range from 0 to 20.
<span>X<=20
Y<=20
If the difference between their two numbers is less than 10, then Erik wins.
The difference between the two numbers can be written X-Y, or Y-X depending on which number (X or Y) is greater. But we do not know that. In order not to get negative value, we calculate absolute value of X-Y,  written |X-Y| which will give positive value whether X is greater than Y or not.
If |X-Y|<10 Erik wins.
</span><span>If the difference between their two numbers is greater than 10, then Nita wins. 
</span><span>If |X-Y|>10 Nita Wins

</span>
6 0
2 years ago
A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each m
kykrilka [37]

Answer:

Family will save 3600 gallons of water by replacing the shower-heads.

Step-by-step explanation:

Number of family members in a family = 5

Each member of the family averages shower per day = 8 minutes

Total time for shower = 5×8 = 40 minutes

With a 5 gallon shower-heads each member will use water in a day = 5×40 = 200 gallons

Water consumption in 30 days = 200×30 = 6000 gallons per month

After replacing the shower-heads with 2 gallons per minute shower-heads family will use the amount of water = 40×2= 80 gallons per day

Water used in one month = 80×30 = 2400 gallons

Now water save by the family in 30-day period = 6000 - 2400 = 3600 gallons

Therefore, family will use 3600 gallons less water by replacing the water saving water heads.

8 0
2 years ago
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