The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams

Answers

Answer 1

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]

Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.

Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:

[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:

[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]

Divide both sides by 9:

[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]

By logarithm properties:

[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]

Solve for t:

[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.


Related Questions

I’m new to this app and I need help with those two questions please help!!

Answers

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

f(x) = (2x – 1)(3x + 5)(x + 1) has zeros at I = -
1
cole
2= -1, and x =
What is the sign of f on the interval
5
<<
3
เล
?
Choose 1 answer:
А
f is always positive on the interval.
B
f is always negative on the interval.
f is sometimes positive and sometimes negative on the interval.

Answers

Interval of function f(x) is sometimes negative and sometimes positive.

What is interval of function?

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.

Given function,

f(x) = (2x – 1)(3x + 5)(x + 1),

Zeros of function,

x = 1/2 = 0.5

x = -5/3 = - 1.6667

x = -1

From the graph

Interval of function is negative between -∞ < x < -1.6667

Interval of graph is positive between -5/3 < x < -1

Interval of function is negative between -1 < x < 0.5

Interval of graph is positive 0.5 < x < ∞

Hence, f(x) has sometimes positive interval and sometimes negative interval.

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Solve for x in the diagram

Answers

Answer:

x = 20°

Step-by-step explanation:

x + 2x + (x+10) =90° {being a right angle triangle}

3x + x + 10 = 90°

or, 4x = 90° - 10°

or, 4x = 80°

or, x = 80°/4

so, x = 20°

A perfect correlation is denoted by:

A. +1.0 and -1.0

B. +1.00

C. -1.00

D. .50

Answers

A perfect correlation is denoted by:

A. +1.0 and -1.0

Transposition
make (m) the subject.
E = mc²

Answers

Answer:

m = [tex]\frac{E}{c^2}[/tex]

Step-by-step explanation:

Given

E = mc² ( isolate m by dividing both sides by c² )

[tex]\frac{E}{c^2}[/tex] = m

Answer:

m=E over c2

Step-by-step explanation:

u divide both sides by c2.then on the right side the c2 cancel each other .

then u will m=E over c2

Graph the function f(x) = 1/2(2)^x

Answers

Answer; Down

Step-by-step explanation:The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0). The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).

Biểu diễn 1 ràng buộc trên mặt phẳng tọa độ Oxy là

Answers

Step-by-step explanation:

yah kaun se language mein likha hai aapane

What is the perimeter of the octagon below!!

Answers

Answer:

C) sixty five units

Step-by-step explanation:

have a great day

If a state issued license plates using the scheme of 3 letters followed by 3 digits, how many plates could it issue?

Answers

Answer:

17,576,000

Step-by-step explanation:

there are 26 english letters (A-Z) and 10 digits(0-9).

there are 3 spaces for letters. therefore Any of the 26 letters can be combined with any 26 other letters and any of those can be combined with any of another 26 letters.

26*26*26= 17576

similarly 10 digits can combined in 1000 ways

10*10*10=1000

17576 letter combination can combine with 1000 digits combination.

so  17,576 x 1000 = 17,576,000 different plates could issue.

I need help with ged

Answers

Answer:

General Educational Development (GED) tests

What do subject do you need help?

Step-by-step explanation:

The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.

I need help! I will give brainliest, if correct!

For a certain value of $k$, the system

x + y + 3z = 10,

-4x + 3y + 5z = 7,

kx + z = 3

has no solutions. What is this value of k?

Answers

kx + z = 3 means z = 3 - kx. Substitute this into the first two equations:

x + y + 3 (3 - kx) = 10   ==>   (1 - 3k) x + y = 1

-4x + 3y + 5 (3 - kx) = 7   ==>   (-4 - 5k) x + 3y = -8

Multiply through the first equation by -3 :

-3 ((1 - 3k) x + y) = -3 (1)   ==>   (-3 + 9k) x - 3y = -3

Add this to the second equation to eliminate y :

((-3 + 9k) x - 3y) + ((-4 - 5k) x + 3y) = -3 + (-8)

(-7 + 4k) x = -11

Normally, you would solve for x by dividing both sides by -7 + 4k. But you can't do that if this turns out to be equal to 0, which happens for

-7 + 4k = 0   ==>   k = 7/4

Answer:

k = 7/4

Step-by-step explanation:

Find the mean 9,1,8,3,2,1 graphically.

Answers

10+11+3
21+3
24
24/6
The mean is 4

Help me please and thank you

Answers

Answer:

Option C is correct

Step-by-step explanation:

[tex]log( {10}^{3} )[/tex]

Use logarithm rules to move 3 out of the exponent.

[tex]3 \: log \: (10)[/tex]

Logarithm base 10 of 10 is 1.

[tex]3×1[/tex]

Multiply 3 by 1.

[tex]3[/tex]

Hope it is helpful....
C is the correct answer

The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.

Answers

Answer:

0.9332

Step-by-step explanation:

We are given that

Mean diameter, [tex]\mu=73[/tex]

Variance, [tex]\sigma^2=4[/tex]

We have to find the probability that the diameter of a selected bearing is less than 76.

Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]

[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]

[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]

Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]P(x<76)=P(Z<1.5)[/tex]

[tex]P(x<76)=0.9332[/tex]

Hence, the probability that the diameter of a selected bearing is less than 76=0.9332

If 6x + 5y = 10, what is y in terms of x?
Please include an explanation!

Answers

what you're trying to do is form an equation for y

6x + 5y = 10    

5y = -6x + 10         we need y to be singular so divide by numeral before y

y = - 6x/5 + 10/5

y = - 6x/5 + 2

The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities

a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?

Answers

Solution :

a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.

P (correct in the 4th attempt)

= [tex]$(1-0.75)^3 \times 0.75$[/tex]

= 0.01171875

b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.

P( X = 3) for X = B in (n = 10, p = 0.75)

= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]

= 0.0031

c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :

There are = 6 success, p = 0.75.

Therefore, this is a case of a negative binomial distribution.

[tex]$E(X)=\frac{k}{p}$[/tex]

         [tex]$=\frac{6}{0.75}$[/tex]

         = 8

So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]

     [tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]

        = 1.6330

Please due in 1 hour

Answers

I hope that helped you

9514 1404 393

Answer:

d + q = 440.10d +0.25q = 8.30

Step-by-step explanation:

The first equation describes the total number of coins. It says the sum of the numbers of dimes and quarters is 44, the total number of coins.

__

The second equation describes the total value of the coins. It will say that 0.10 times the number of dimes plus 0.25 times the number of quarters is 8.30, the total dollar value of the coins.

The two equations are ...

  d + q = 44

  0.10d +0.25q = 8.30

__

Additional comment

The solution can be found by substituting for d:

  0.10(44 -q) +0.25q = 8.30

  0.15q = 3.90

  q = 26

  d = 44 -26 = 18

Vinnie has 18 dimes and 26 quarters in his bag.

How many composite number between 1 and 50

Answers

Step-by-step explanation:

There are 34 composite numbers between 1 to 50 which are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50.

Can someone help me with this plz

Answers

Answer:

170.7

Step-by-step explanation:

We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7

Answer:

171

Step by step explanation:

Volume = lwh/3
= 8 x 8 x 8
≈171 km^3

A rectangle is 19 inches long and 6 inches wide find it’s area

Answers

Step-by-step explanation:

how to find the area

multiply the length times the width

19 × 6 = 114 inches squared

The area of the rectangle is 114 square inches if the length and breadth of the rectangle are 19 inches and 6 inches.

A rectangle is one of the elementary geometric figures. It is a quadrilateral with a pair of equal and parallel sides. All angles of a rectangle are right angles.

The length of the rectangle is given as 19 inches.

The breadth of the rectangle is given as 6 inches.

The area of the given rectangle is given as:

Area = length × breadth

Area = 19 × 6

Area = 114 square inches

Thus, the area of the given rectangle is 114 square inches.

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−12x+y=10 in slope-intercept form

Answers

Answer:

y=12x+10

Step-by-step explanation:

Slope-intercept form is y=mx+b

1. Add -12x to both sides of the equation

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Chapter 11 part 2:

What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.

Answers

The three main log rules you'll encounter are

log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)

The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.

Here are examples of each rule being used (in the exact order they were given earlier).

log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)

----------------

Here's a slightly more complicated example where the log rules are used.

log(x^2y/z)

log(x^2y) - log(z)

log(x^2) + log(y) - log(z)

2*log(x) + log(y) - log(z)

Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.

The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is:
A. 3
B. 0
C. not enough information
D. infinitely many

Answers

Answer:

D. infinitely many

Step-by-step explanation:

Perpendicular lines can be drawn everywhere on the lone in infinitely different places, making the answer infinite.

The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.

The correct answer is an option (D)

What is perpendicular to line?"It is a straight line that makes an angle of 90° with another line. "

For given question,

Lines are perpendicular to each other if their intersection with one another forms a right angle. Through any given line, there are an infinite number of perpendicular lines.Through a specific point on a line, there exists only one perpendicular line. Similarly, for a line and a point not on that line, there is only one perpendicular line through the point.              

We can draw infinite perpendicular lines to a

Therefore, the number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.

The correct answer is an option (D)

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What is the equation of a circle with a center at (4, -9) and a radius of 5?

Answers

Answer:

(x - 4)² + (y + 9)² = 25

Step-by-step explanation:

The equation of a circle is written as seen below.

(x – h)² + (y – k)² = r²

Where (h,k) represents the center of the circle and r represents the radius

We want to find the equation of a circle that has a center at (4,-9) and a radius of 5.

We know that (h,k) represents the center so h = 4 and k = -9

We also know that r represents the radius so r = 5

Now to find the equation of this specific circle we simply plug in these values into the equation of a circle formula

Equation: (x – h)² + (y – k)² = r²

h = 4, k = -9 and r = 5

Plug in values

(x - 4)² + (y - (-9))² = 5²

5² = 25

The two negative signs in front of the 9 cancel out and it changes to + 9

The equation of a circle with a center at (4,-9) and a radius of 5 is

(x - 4)² + (y + 9)² = 25

What is the mean of 86, 80, and 95

Answers

87 is the mean.

To find the mean, you must

- add all of the numbers

- divide by the amount of numbers given

In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.

87 is the answer.
Mean is the same thing as average so you just all the given numbers and divide by the number of terms given (in this case 3 were given)

if a point is chosen inside the large circle what is the probability that it will also be inside the small circle?

Answers

Answer:

1/4

Step-by-step explanation:

The probability will be equal to 1 - (probability that it will not be inside the small circle) = 1 - (pi*4-pi)/(pi*4)=1/4

one-sixteenths are there in 3 wholeshow many 1/16 are in 3 wholes

Answers

Answer:

48

Step-by-step explanation:

3 divided by 1/16 = 48/16 divided by 1/16

                            = 48 1/16 in 3 wholes

A cylinder Container must
hold al or 2,000 cm3 of
liquid, which of the following
is the optimazation equation
in terms of the radius r.
if the anaunt of material
used to make the container
is to be minimized?

Answers

its 300cm from the square root

0.6 reoccurring decimal as a fraction in the simplest term​

Answers

Answer:

3/5

Step-by-step explanation:

here,

0.6

in fraction = 6/10

in simplest form 6/ 10 both term can be divided by 2 so,

6/10 ÷2

= 3/5

A grocery store buys cereal using the cost function
c(n) = { 2n when n < 100 1.9n when 100
Sn = 500 1.8n when n > 500 where n is
the number of boxes of cereal the grocery store
buys and c(n) is the cost of the cereal. The grocery
store then sells the cereal using the sales function
s(c) = 1.3c. What is the cost of the cereal if the
grocery store buys 250 boxes?

Answers

The cost of the cereal if the grocery store buys 250 boxes is $475

We know that:

The cost function is:

c(n) = 2*n              if n < 100

c(n) = 1.9*n            if  100 ≤ n ≤ 500

c(n) = 1.8*n            if   n > 500.

(we can assume that the cost function is in dollars)

This is a piecewise function, this means that we need to see in which interval we have the number n, and then select the correct function to use.

Now, we want to find the cost of the cereal if the store buys 250 boxes.

Then we have n = 250.

We can see that n = 250 is in the second interval,  100 ≤ n ≤ 500, then we will use the second function to find the cost.

We will get:

c(250) = 1.9*(250) = $475

We can conclude that the cost if the store buys 250 boxes is 475

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