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DerKrebs [107]
3 years ago
13

In four years, 40% of a radioactive element decays. Find its half-life. Round to one decimal place.

Mathematics
2 answers:
Misha Larkins [42]3 years ago
7 0

Answer:

T(Half Life) = 5.42 s

Step-by-step explanation:

Given :

t = 4years

[R]₀(Initial Concentration) = 100(say)

[R](Concentration Left after time t=4yrs) = 100 - 40 = 60

We know that,

k = 2.303 / t (log{[R]₀/[R]})

where k = rate constant

k = 2.303 / t (log[100/60])

k = 2.303 / 4 (log[10] - log[6])

k = 2.303 / 4 (1 - 0.7781)

k = 2.303 / 4 (0.2219)

k = 0.5110 / 4

k = 0.1277          --------(i)

Now, to find its half life,

We know that,

T(Half Life) = 0.693 / k

T = 0.693 / 0.1277

T = 5.42 years

White raven [17]3 years ago
5 0

To find the answer, use k = \frac{2.303 }{ 4} (log\frac {100 }{ 40}) , and then use the equation t=\frac{.693}{k} To find it's half life.

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A storage tank has A circumference Of 200 meters what is the area of the base of the tank
lorasvet [3.4K]

Circumference = 2 pi r

2 pi r = 200

r = 100 / pi

Area of base = pi r r

Area of base = 100*100 / pi

Area of base = 3183.1 sq. m.

6 0
3 years ago
3/4, 4/5, 7/8, 9/11, 5/6<br>can they be simplified? give your reasons below.​
Bad White [126]
They cannot be simplified
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3 years ago
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The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,
strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=400 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=80 represent the population standard deviation

n=15 represent the sample size  

2) Part a

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

400-2.58\frac{80}{\sqrt{15}}=346.708    

400+2.58\frac{80}{\sqrt{15}}=453.292

So on this case the 99% confidence interval would be given by (346.708;453.292)    

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that t_{\alpha/2}=2.98

Now we have everything in order to replace into formula (1):

400-2.98\frac{80}{\sqrt{15}}=338.445    

400+2.98\frac{80}{\sqrt{15}}=461.555

So on this case the 99% confidence interval would be given by (338.445;461.555)    

4 0
3 years ago
Help me I give you a cookie:)
olga55 [171]

Answer:

x=11

Step-by-step explanation:

complimentary means the two angles add to 90. Since we already know one angle equals 68, subtract 68 from 90= 22. 2x=22. divide 22 by 2 to isolate the variable. Boom, the answer is x=11

7 0
2 years ago
Read 2 more answers
Select the correct answer.
stich3 [128]

The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³

<h3>Calculating Volume </h3>

From the question, we are to determine the volume of the container

Volume of the container = Volume of the cone - Volume of the small cone

The volume of a cone is given by the formula,

V = 1/3πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

For the small cone,

Diameter = 10 cm

∴ Radius, r = 10cm/ 2 = 5 cm

h = 6 cm

For the big cone

diameter = diameter of the container = 30 cm

∴ Radius = 30cm/ 2

Radius = 15cm

h = height of small cone + height of container

h = 6 cm + 20 cm

h = 26 cm

Putting the parameters into

Volume of the container = Volume of the cone - Volume of the small cone

We get,

Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6

Volume of the container = 1/3π (15² ×26 -  5² × 6)

Volume of the container = 1/3π (5850 -  150)

Volume of the container = 1/3π (5700)

Volume of the container = 1/3 × π × 5700

Volume of the container = 5969.026 cm³

Volume of the container ≈ 5969 cm³

Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³

Learn more on Calculating volume here: brainly.com/question/12004994

#SPJ1

8 0
2 years ago
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