Find two positive numbers such that the sum of the first and twice the second is 100

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1982, the hay in that

galina1969 [7]

Answer:

25.48 days

Step-by-step explanation:

For a radioactive substance, the Amount of the substance remaining A(t) is modeled by the equation

$A(t)=A_0(\dfrac{1}{2})^{\dfrac{t}{t_{1/2}} }$

where

$A_0 =$Initial Amount$\\t_{1/2}=$Half-Life of the Substance$\\t=$Time elapsed$$

In the given problem:

Half Life of the Radioactive Isotope = 8

Initial Amount, $A_0$ =100%=1

A(t)=11% =0.11

Therefore substituting in the model above:

$0.11=1(\dfrac{1}{2})^{\dfrac{t}{8} }\\0.11=0.5^{t/8}\\$Change to Logarithm form$\\Log_{0.5}0.11=\frac{t}{8}\\\frac{Log 0.11}{Log 0.5} =\frac{t}{8}\\3.1844=\frac{t}{8}\\t=8X3.1844=25.4752$

The farmer need to wait for 25.48 days

4 0

3 years ago

Help me please The question is in this photo

Tju [1.3M]

Answer:

x² + x - 12 = 0

Step-by-step explanation:

Given the solutions are x = - 4 and x = 3, then the factors are

(x + 4) and (x - 3) and the equation is the product of the factors, that is

(x + 4)(x - 3) = 0 ← expand factors using FOIL

x² + x - 12 = 0 ← in standard form

3 0

3 years ago

The director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal t

denpristay [2]

Answer:

The value of t test statistics is 4.518.

Step-by-step explanation:

We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.

He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.

Let $\mu$ = mean length of commercials on his station.