8. A substance has a half life of 2.347 minutes.
a. If the initial amount of the substance was 110.4 grams, how many half-lives will have passed
before the substance decays to 6.9 grams.
b. What is the total time of the decay?

Answers

Answer 1

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

[tex]A=A_0b^{\frac{t}{c}}[/tex]

Where [tex]A[/tex] is the final population

[tex]A_0[/tex] is the initial population

[tex]b[/tex] is the growth factor

[tex]c[/tex] is the time taken for the growth 'b'

[tex]t[/tex] is the amount of time

Here, we are given that:

[tex]A[/tex] = 6. 9 grams

[tex]A_0[/tex] = 110.4 grams

[tex]b = \dfrac{1}{2}[/tex]

[tex]c = 2.347[/tex] min

To find:

a.) Number of half lives taken for the decay.

b.) Total time in the decay.

Solution:

a.) Number of half lives taken for the decay is nothing but equal to [tex]\frac{t}{c}[/tex].

Putting the values in the formula, we get:

[tex]6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4[/tex]

Therefore, the answer is:

4 half lives have passed.

b.) Total time of decay. We have to find the value of [tex]t[/tex] here.

From answer of part a.):

[tex]\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}[/tex]


Related Questions


PLEAS HELP FAST!!!!!!!!!!!!!!

Answers

Answer: Point D

Step-by-step explanation: Point D is at 3 and 3/4.

I think the answer is point D

300/12.500000000000000000​

Answers

Answer: 24

Step-by-step explanation: Hope this helps.

Raul Del Valle's gross weekly salary is S615. His weekly federal withholding is S55. The Social Security tax is
6,2% of the first $97.500 he earns. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay.
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Answer:

Step-by-step explanationjiuijkk8

u:

Find the length x of QR

Answers

Answer:

4.5

Step-by-step explanation:

If they are symilar their sides are in proportion so write the proportion

[tex]\frac{x}{5} =\frac{2.7}{3}[/tex]   you can pick any other 2 sides as long as you take them in the same order

x= 5*2.7/3=4.5

What is the perimeter of the figure?

A. 22.0 yd2
B. 21.1 yd
C. 22.0 yd
D. 21.1 yd2

Answers

Answer:

B. 21.1 yd

Step-by-step explanation:

The perimeter of the figure is the sum of all its three sides.

Take note that the dotted line is not a side length of the figure.

The side lengths are 9 yd, 5 yd, and 7.1 yd.

Therefore, the perimeter of the figure = 9 + 5 + 7.1

Perimeter = 21.1 yd.

Also, take note of the unit of the perimeter. Unit of the perimeter would not be squared. Only area has a unit that is squarred.

8 more than the quotient of a number and 2 is 14. find the number

Answers

Answer:

x = 12

Step-by-step explanation:

x/2 + 8 = 14Subtract 8 from both sides because it is the inverse operation of addition. x/2 = 6Multiply both sides by 12 because it is the inverse operation of division. x = 12

(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Answers

Answer:

See below

Step-by-step explanation:

[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]

Thus proved

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)f(x) = 3 â 48x + 4x2, [5, 7]

Answers

Answer:

Step-by-step explanation:

The given equation is:

f(x) = 3 - 48x + 4x²      [5,7]

where; f(x) is continous and derivable in [5,7]

f'(x) = -48x + 8x

f(5) = 3 - 48(5) + 4(5)² = -137

f(7) = 3 - 48(7) + 4(7)² = -137

Thus, it satisfies the hypotheses of Rolle's Theorem

f'(x) = f'(c) = 0

-48 + 8c = 0

c =48/8

c = 6

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answers

Answer:

The dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

Step-by-step explanation:

Let 'l' be the length and 'w' be the width of the rectangle

The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

[tex]l=2w-3[/tex]

Also, the area of the rectangle is 27ft^2.

[tex]A=27\:ft^2[/tex]

As the area of the rectangle has the formula:

[tex]\:A\:=\:l\times w[/tex]

so

[tex]27=\:l\times w[/tex]

so the equation becomes

[tex]27=\left(2w-3\right)\times \:w[/tex]

[tex]27=2w^2-3w[/tex]

[tex]2w^2-3w-27=0[/tex]

[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]

if   [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]

[tex]w=-3,\:w=\frac{9}{2}[/tex]

as the width can not be negative, so

[tex]w=\frac{9}{2}=4.5[/tex] ft

As

[tex]l=2w-3[/tex]

[tex]l=2\left(4.5\right)-3[/tex]

[tex]l=9-3[/tex]

[tex]l=6[/tex]

So the dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

A die is rolled twice. Find the chance that the ace (single dot) comes up on one of the two rolls, but not both. Record your answer as a percentage rounded to the nearest tenth of a percent.

Answers

Answer:

13.9%

Step-by-step explanation:

In order to calculate the probability of this happening, we would need to multiply the probability of one of the rolles being an ace with the probability of one of the roles NOT being an ace. Since the probability of rolling an ace is 1/6 (since there is only one ace in a six-sided die) then the probability of NOT rolling an ace is 5/6

[tex]\frac{1}{6} * \frac{5}{6} = \frac{5}{36}[/tex] or 0.1388     multiply by 100 to get percentage value

0.1388 * 100 = 13.9%

Therefore, the probability of getting one ace and one non-ace roll is 13.9%

Solve for www. -4(w+1) = -24

Answers

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-4w-4=-24

-4w=-24+4

-4w=-20 to find w divide both side by -4

-4w/-4 =-20/-4

w=5

Choose the point-slope form of the equation below that represents the line that
passes through the points (-6,4) and (2,0). (2 points)

Answers

Answer:

y - 4 = -0.5(x + 6)

Step-by-step explanation:

Answer:(4-,6)

Step-by-step explanation:hope this helps  u i do my best to helps ever one

Can sumone please help me w this question? It math. 10 points. What is the value of r in the equation 3r − 6 = 18?

Answers

In this problem r=4 !!!
the answer is r=8

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(HELP 50 POINTS)
A beach lifeguard wants to create the largest triangular area he can with three lengths of rope to provide beach goers with maximum amount of space to play and swim in the water. Multiple buoys are attached to each rope in order to identify the designated swimming area. The first rope is 42 feet long, the second is 50 feet long, and then the third is 107 feet long. The lifeguard can only cut one of the ropes in order to create a triangle with the largest possible perimeter. How much rope, in feet, will be remaining after the lifeguard creates the designated swimming triangle? (Note: answer should be a whole number.)

Answers

Answer:

16

Step-by-step explanation:

I am doing Prepworks Basic triangles as well :D

How many different four digit alarm codes can be form for a house alarm be 2,4 or 9 and all the other digits can be any number and numbers can be repeated

Answers

Answer:

Bro, are you trying to break into someone's house of somethin?

Step-by-step explanation:

If triangle ABC is equilateral, and side AC is 7m long, how long is side BC?

Answers

Answer:

7m

Step-by-step explanation:

In an equilateral triangle all the sides and angles are the same

I believe the answer is 8m

Please help me due today by 3:00pm please help me

Answers

-3n+9 = 3n + 9
9 = 0n + 9
n = 0

Answer

n= 0

Explanation

- 3 (n - 3) = 3n + 9−3(−3)=3+9

−3+9=3+9

−3=3

-3n=3n−3n=3n

−3−3=3−3

−6=0

4:9 is an equivalent ratio to 36:__

Answers

Answer:

36:81

Step-by-step explanation:

4 to 36 is times 9, so you have to multiply 9 by 9 to complete the ratio which is how you get 81.

I NEED HELP WITH B AND E​

Answers

B is 100 but I’m not that sure of what e is sorry!

(04.04 LC)
On a coordinate grid, point T is at (2,-4) and point Sis at (2,6). The distance (in units) between points T and Sis
numbers, such as 2.) (5 points)
(Input only whole

Answers

Answer:

The distance 'd' between T and S:

[tex]d=10[/tex]

Step-by-step explanation:

As the point 'T' is located at (2, -4)

So, the point 'T' has the coordinates (2, -4)

And the point 'S' is located at (2, 6)

So, the point 'T' has the coordinates (2, 6)

The distance 'd' between T and S can be computed using the formula:

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]

[tex]=\sqrt{0+10^2}[/tex]

[tex]=\sqrt{10^2}[/tex]

[tex]d=10[/tex]

Therefore, the distance 'd' between T and S:

[tex]d=10[/tex]

Answer:

t and s

Step-by-step explanation:

can someone help me with this?

Answers

Answer:haha no

Step-by-step explanation:

PLEASE HELP!!!!
The state of Texas did a random sample of the weight of 15 year old boys. The 10 boys they sampled had a total weight of 1250 pounds. What is the best guess (point estimate ) for the average weight of 15 yearold boys in Texas?

Answers

1250/10=125

Hope this helps and have and AWESOME night!!! :)

Find the area A of the polygon with the given vertices. A(−6, 1), B(4, 1), C(4,−8), D(−6,−8)

A= __ square units

Answers

u must use the formula

so, the answer is 10 units²

Nick volunteers at the library shelving books.
The graph shows how many books Nick shelves one Saturday.

Graph of a diagonal line on a coordinate plane with ALTDCTime in hoursALTDC on x-axis and ALTDCNumber of BooksALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 60) and (4, 120).

Part A
How many books does Nick shelve in 2 hours? Enter your answer in the box.

books


Part B
What does the point (3, 90) represent on the graph?
A.


Nick volunteers 90 hours in 3 weeks.
B.


Nick earns $90 in 3 weeks.
C.


Nick shelves 90 books in 3 hours.
D.


Nick shelves 90 books on 3 Saturdays.

Answers

Answer:

B: A

He earns $90 in 3 weeks.

C

He shelves 90 books in 3 hours.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sum of two numbers is -14. If the smaller number is subtracted from the larger number, the result is 10. Find the number

Answers

Answer:

The sum of two numbers is 78. If four times the smaller number is subtracted from the larger number, the result is 13. What are the two numbers?

Step-by-step explanation:

EQUATION:

x+ y = 78

x-4y = 13

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

solve by any method to get:

x = 65

y = 13

Answer this please thanks

Answers

Answer:

The answer is yes, since the graph is an equal line throughout.

Step-by-step explanation:

9
Use the graph to answer the following questions.
D
175
150
(4.150)
125
Total Cost
100+
(2.100)
75
50 10.50
25
Days
Part C: Write the equation for the line if x = the number of days and y = the total cost.
So
IM 2020
10
Use the graph to answer the following questions.
a

Answers

Your equation for the first point will be y=x+50

Explanation...

The x is zero so we just only put x. The y is 50 so we input a 50 giving us y=x+50.

Your equation for the second point will be y=2x+100.

Explanation...

Your slope is 2 so we input that and the y intercept is 100 giving us the equation y=2x+100.

Your equation for the third point will be y=4x+150

Explanation...

Your slope is 4 so we input that. Your y intercept is 150 so we input that. It gives us the equation y=4x+150.

There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of acorns to squirrels? Enter your answer in reduced form.

Answers

Answer: 1:6

Step-by-step explanation:

Reduce each side of the ratio

Answer:

For every 1 squirrel there are 6 acorns

Step-by-step explanation:

u just divide 18 by 3

There are 40 students in a class.
Each student walks to school or cycles to school or gets the bus to school
There are 22 girls in the class.
9 of the girls walk to school.
7 of the boys cycle to school.
6 of the 10 students who get the bus to school are boys.
Find the number of these students who walk to school.

Answers

Step-by-step explanation:

Total no. of students = 40

Total no. of girls = 22

Total no. of boys = 40 - 22 = 18

No. of girls walking to school = 9

No. of girls who cycle to school = 22 - 9

No. of boys who cycle to school = 7

No. of students who take the bus = 10

(6 boys and 4 girls)

No. of boys who walk to school = 18 - (7 + 6) = 5

Total no. of students who walk to school = 9 + 5 = 14

The number of students who walked to school was 14 students

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equations will be ,

Let the total number of students in the class be A = 40 students

The number of girls in the class = 22 students

The number of boys in class = total number of students - number of girls

                                                = 40 - 22

                                                = 18 students

Now ,

The number of girls who walked to school = 9 students

The number of boys who cycled to school = 7

So , remaining boys = 18 - 7

                                 = 11 students

The number of boys who take bus to school = 6 students

So , remaining boys = 11 - 6

                                 = 5 students

Therefore , the remaining boys in the class walks to school = 5 students

So , the equation will be

And , the total number of students who walked to school =
number of boys in the class that walks to school + number of girls who walked to school

Total number of students who walked to school = 9 + 5

                                                                                = 14 students

Hence , The number of students who walked to school was 14 students

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

Please help me with this

Answers

Answer:

$62.50

Step-by-step explanation: 250 divided by 4 equals $62.10

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