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Oksana_A [137]
4 years ago
14

In a survey of 480 students, 253 indicated that play the piano, 268 indicated that they play the harp and 73 indicated they play

the piano and the harp. How many students surveyed play at least one of these instruments mentioned here?
Mathematics
1 answer:
Bond [772]4 years ago
5 0

Answer:

The no. of students that play at least one instrument = 448

Step-by-step explanation:

Total number of students surveyed = 480

Students play piano =  253

Students play harp   =  268

Students play both harp & Piano = 73

Thus number of student surveyed that they play at least one of the instrument  = (Students play piano) + (Students play harp) - (Students play both devices)

= 253 + 268 - 73

= 448

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3 years ago
Suppose an unknown radioactive substance produces 8000 counts per minute on a Geiger counter at a certain time, and only 500 cou
mariarad [96]

Answer:

The half-life of the radioactive substance is of 3.25 days.

Step-by-step explanation:

The amount of radioactive substance is proportional to the number of counts per minute:

This means that the amount is given by the following differential equation:

\frac{dQ}{dt} = -kQ

In which k is the decay rate.

The solution is:

Q(t) = Q(0)e^{-kt}

In which Q(0) is the initial amount:

8000 counts per minute on a Geiger counter at a certain time

This means that Q(0) = 8000

500 counts per minute 13 days later.

This means that Q(13) = 500. We use this to find k.

Q(t) = Q(0)e^{-kt}

500 = 8000e^{-13k}

e^{-13k} = \frac{500}{8000}

\ln{e^{-13k}} = \ln{\frac{500}{8000}}

-13k = \ln{\frac{500}{8000}}

k = -\frac{\ln{\frac{500}{8000}}}{13}

k = 0.2133

So

Q(t) = Q(0)e^{-0.2133t}

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

Q(t) = Q(0)e^{-0.2133t}

0.5Q(0) = Q(0)e^{-0.2133t}

e^{-0.2133t} = 0.5

\ln{e^{-0.2133t}} = \ln{0.5}

-0.2133t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.2133}

t = 3.25

The half-life of the radioactive substance is of 3.25 days.

7 0
3 years ago
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sashaice [31]

#5: estimate: 180

answer: 170

#8: estimate: 360

answer: 354

#6: estimate: 320

answer: 296

4 0
3 years ago
If f(x) = 8^x , find the value of f(2/3).
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Answer:

4

Step-by-step explanation:

This is a substitution question

So we will have to substitute the value of x given into the given question

f(x)=8^x

And x is given as 2/3

So let's get to work

8^2/3 which means that cube root of 8 then square the answer

(3√8)^2

Cube root of 8 is 2

So we will have to square 2 to get 4

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