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2 years ago

What is the solution to (x + 8) > (2x + 10)? (–∞, –4) (–4, ∞) (–∞, 4) (4, ∞)

Mathematics

1 answer:

Citrus2011 [14]2 years ago

5 0

Answer:

(–∞, -4)

Step-by-step explanation:

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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.

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

$500 = 8000e^{-13k}$

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

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

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

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

$k = 0.2133$

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

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

At the beginning of year 1, Gracie invests $350 at an annual simple interest rate of 4%. She makes no deposits to or withdrawals

scZoUnD [109]

Answer:

Step-by-step explanation:

The answer is A

5 0

3 years ago

Anyone that can help me with this?

mrs_skeptik [129]

If a rational function is not continuous, it'll be due to one of two reasons. Either it has a hole, or it has an asymptote. Plug in -5 for x in the denominator of the rational function. What do you get? You get zero in the denominator, meaning the function is undefined at x=-5.

4 0

4 years ago

What does biased and unbiased mean?

Illusion [34]

Answer: Biased: Opinionated

Unbiased: Actual facts / not opinionated

Step-by-step explanation:

3 0

3 years ago

Change each fraction to a decimal. If the division dosent end round your answer to the nesrest hundreth a.3/4 b.7/16

inysia [295]

Answer:

a. is 0.75 and b. is 0.4375

Step-by-step explanation:

just picture it as a division problem

3 divided by 4 = 0.75

and the other one 0.4375

7 0

3 years ago