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densk [106]
3 years ago
5

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
Elina [12.6K]3 years ago
5 0

Answer:

Slope: 2/3

Y-intercept: 6

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Billy is monitoring the exponential decay of a radioactive compound. He has a sample of the compound in a test tube in his lab.
Over [174]

Solution:

Formula for radioactive Decay is given by

R_{0}= R(1-\frac{S}{100})^t

R_{0}= Initial Population

R = Remaining population after time in hours

Rate of Decay = S % per hour

Initial Population = 72 grams

Final population = 15 grams

Rate of Decay = 35 % per hour

Substituting the values to get value of t in hours

72=15(1-\frac{35}{100})^t\\\\ 4.8= (0.65)^t\\\\ t= -3.64→→1 St expression

But taking positive value of t , that is after 3.64 hours the sample of 72 grams decays to 15 grams at the rate of 35 % per hour.

Now , it is also given that, Once the sample reaches a mass of 15 grams, Billy will continually add more of the compound to keep the sample size at a minimum of 15 grams.

Substituting these in Decay Formula

Final Sample = 15 gm

Starting Sample = 15 +k, where k is amount of sample added each time to keep the final sample to 15 grams.

Time is over 3.64 hours i.e new time = 3.64 + t

Rate will remain same i.e 35 % per hour.

15=(15+k)(1-\frac{35}{100})^{3.64+t}→→→  Final expression (Second) , that is inequalities can be used to determine the possible mass of the radioactive sample over time.







5 0
3 years ago
Read 2 more answers
2y2(35 – 4y) in standard form
Alex73 [517]

Step-by-step explanation:

2 {y}^{2} (35 - 4y) \\  = 2 {y}^{2}  \times 35 - 2 {y}^{2}  \times 4y \\  = 70 {y}^{2}  - 8 {y}^{3}  \\  = \red { \bold{ - 8 {y}^{3} + 70 {y}^{2} }} \\ is \: in \: the \: standard \: form.

8 0
3 years ago
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Suppose that y is directly proportional to x, and y = 150 when x = 15. What is the constant of proportionality?
galina1969 [7]

Answer:  The required constant of proportionality is 10.

Step-by-step explanation:  Given that y is directly proportional to x, and y = 150 when x = 15.

We are to find the constant of proportionality.

According to the given information, we can write

y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~[\textup{where k is the constsnt of propotionality}].

When y = 150 and x = 15, we get from the above equation that

y=kx\\\\\Rightarrow 150=k\times15\\\\\Rightarrow k=\dfrac{150}{15}\\\\\Rightarrow k=10.

Thus, the required constant of proportionality is 10.

3 0
3 years ago
It is possible to represent most data in both qualitative and quantitative forms.<br> true or false
Eva8 [605]

The answer is True......

6 0
3 years ago
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(2,?) is on the line 4x – 5y = -7. Find the other half of the coordinate.
Cerrena [4.2K]
(x,y)=(2,?) \\ x=2 \\ y=? \\ \\&#10;4x-5y=-7 \\&#10;4 \times 2-5y=-7 \\&#10;8-5y=-7 \\&#10;-5y=-7-8 \\&#10;-5y=-15 \\&#10;y=\frac{-15}{-5} \\&#10;y=3

The coordinate is (2,3).
4 0
3 years ago
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