A 41 gram sample of a substance that's used to detect explosives has a k-value of 0.1392. Find the substance's half life, in days.

Answers

Answer 1

Answer:

The substance half-life is of 4.98 days.

Step-by-step explanation:

Equation for an amount of a decaying substance:

The equation for the amount of a substance that decay exponentially has the following format:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which k is the decay rate, as a decimal.

k-value of 0.1392.

This means that:

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

Find the substance's half life, in days.

This is t for which [tex]A(t) = 0.5A(0)[/tex]. So

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

[tex]0.5A(0) = A(0)e^{-0.1392t}[/tex]

[tex]e^{-0.1392t} = 0.5[/tex]

[tex]\ln{e^{-0.1392t}} = \ln{0.5}[/tex]

[tex]-0.1392t = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.1392}[/tex]

[tex]t = 4.98[/tex]

The substance half-life is of 4.98 days.


Related Questions

4x+2=-13 solve for x

Answers

Answer:

Solution given

4x+2=-13

subtract each term by 2

4x+2-2=-13-2

divide both side by 4

4x/4=-15/4

we get

x=-15/4

is a required answer.

Let's solve:

[tex]4x+2=−13[/tex]

Step 1: Subtract 2 from both sides.

[tex]4x+2−2=−13−2 \\ 4x = - 15[/tex]

Step 2: Divide both sides by 4.

[tex] \frac{4x}{4} = \frac{ - 15}{4} [/tex]

Answer:

[tex] \frac{ - 15}{4} [/tex]

The amount of rona cases in Gotham city is 540 people for the first ½ of 2020. In July, a rona spike at the rate of 5.2 people for each day in the month hits. Additionally, the joker has infected all of Arkham Asylum’s 225 patients with the virus. What month will you hit 1,000 cases of rona in Gotham?

Answers

Answer:

Imma but it in the comments because i can't put it on here plus i can't put the thing on here either that's why i didn't do it yesterday

Step-by-step explanation:

4. Explain what an imaginary number is and its relationship to complex numbers. Then give
an example of where complex numbers occur naturally in mathematics.

Answers

Answer:

564643

Step-by-step explanation:

Answer:

In the real number system, there is no solution to the equation x^2=-1x

2

=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.

The backbone of this new number system is the number iii, also known as the imaginary unit.

i^2=-1i

2

=−1i, squared, equals, minus, 1

\sqrt{-1}=i

−1

=isquare root of, minus, 1, end square root, equals, i

By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i

5

i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.

However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−

2

i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.

Defining complex numbers

A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.

\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}

a

Real

part

 

+

 

bi

↑i

Imaginary

part

\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.

The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.

Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts

7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.

4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd

9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd

-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd

Step-by-step explanation:

plz brian list and allways happy to help.

Look at the picture

Answers

Its d because 16/12=1.33 same with 20/15 and 40/30 so its 24x1.33 which is 32 there for d is correct

A Dilation has a center (0,0). Find the image of this point for the given scale factor: P (2-4); D 0.5 (P)

Answers

Answer:

(1, -2)

Step-by-step explanation:

The dilation that has a center of (0, 0) means that you would multiply each number in your coordinate point by your given scale factor.

For your given point (2, -4) with a scale factor of 0.5:

2 times 0.5 = 1

-4 times 0.5 = -2

Therefore your new point will be (1, -2).

Ken recorded the weights (in pounds) of 78 boxes. He created a box plot of his data. What is the interquartile range of Ken’s data?

A) 8

B) 10

C) 17

D) 48

Answers

The answer is d 48 I just took the test

The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.

What is the interquartile range of a data?

The interquartile range(IQR) = third quartile(Q3) - first quartile(Q1)

The third quartile of in the box plot given is : 56 pounds

The third quartile of the data as represented in the box plot given :

39 pounds

The interquartile range(IQR) of ken's data = 56 - 39

= 17 pounds

Hence, The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.

Find more information about the interquartile range here

https://brainly.com/question/4102829

#SPJ2

Which is not a solution of 5g - 6 => 24?
A. g=6
B. g=10
C. g. 20
D. g=-8

Answers

Answer:

A. g=6

Step-by-step explanation:

5g-6=24

5g=30

g=30/5

g=6

Answer:

D, g = -8

Step-by-step explanation:

5 (-8) - 6 => 24

-40 - 6 => 24

-46 is NOT greater than or equal to 24.

The number of patients treated at Dr. Frank's dentist office each day was recorded for nine days: 18,
19, 19, 4, 14, 8, 22, 3, 1. Using the given data, find the mean for this sample.

A. 12

B.19

C. 29

D. 14

Answers

Answer: 12

Step-by-step explanation: The mean is basically the average. So, start by lining up the numbers from smallest to largest. 1, 3, 4, 8, 14, 18, 19, 19, 22. Then, add them all together. You get 108. Then, divide 108 by the number or numbers in the data set, which in this case is 9. So 108 divided by 9 = 12. Your answer is A. --> 12

Hope that helped!!

pls answer thank you

Answers

435.6

mark me brainliestt pls :)))

SA = 411.4 cm2

Explanation:

Area of square = s x s = 11 x 11 = 121 cm2

Area of triangle = 1/2 x b x h = 1/2 x 11 x 13.2 = 72.6 cm2

Area of 4 triangles = 72.6 x 4 = 290.4 cm2

Total surface area = 121 + 290.4 = 411.4 cm2

There are 29 students in Mrs. Dixon's science class. On the last test, only 1 student earned the median score of 84.
How many students scored an 84 or lower?

A - 15
b - 14
C - 13
D - 12

Answers

Answer:

A

Step-by-step explanation:

Median can be described as the number that occurs at the middle of a set of observations.

for example, in the set of numbers, 1 2 3 4 5, the median is 3

median = (first number + last number) / 2

If there are 29 students,

median = (1 + 29) / 2 = 30/2 = 15

the 15th students scored 84

and students between 1 - 14 scored lower than 84

so, 15 students scored an 84 or lower


[tex]find \: the \: volume \: of \: cube \: \\ \\ side = 5m[/tex]

Answers

Volume of Cube = a³

side a = 5 Cm

Volume = 5³ = 125 Cm³

Answer:

125m³

Step-by-step explanation:

GIVEN :-

Length of a side of a cube = 5m

TO FIND :-

Volume of cube

GENERAL FORMULAE TO BE USED IN THIS QUESTION :-

Volume of a cube = (where a = length of each side of a cube)

SOLUTION :-

Volume of the cube = 5³ = 125 m³

Select the values that make the inequality n > -8 true.
(Numbers written in order from least to greatest going across.)

Answers

Answer:

9

Step-by-step explanation:

I'm somewhat confused I think you're forgot to put so more information

The value that makes the inequality n > -8 true will be -2. Thus, the correct option is A.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below:

n > -8

The value of n is greater than -9. Then the value that makes the inequality n > -8 true will be -2.

Thus, the correct option is A.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

The missing options are given below.

a) - 2

b) - 9

c) - 10

d) - 20

What is the definition of mean?

Answers

Answer:

D. It is the sum of the data divided by the number of pieces of data

Step-by-step explanation:

It's also known as the average of the numbers in a data set.

What is the definition of mean?

[tex]{\boxed{\mathcal{\red{Answer.}}}}[/tex]

[tex]D.\:It \: is \: the \: sum \: of \: the \: data \: divided \: by \: the \: number \: of \: pieces \: of \: data.[/tex]

The mean is the average of the numbers.To find the mean, we add up all the numbers, then divide by how many numbers there are.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Find the volume of a pyramid with a square base, where the area of the base is 19 cm^2 and the height of the pyramid is 23.8 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answers

Answer:

150.7

Step-by-step explanation:

Formula to the find volume of a pyramid:

V=1/3 (B)(h)

V=1/3 (19) (23.8)


Imani is a scientist working with a cylindrical beaker. The base of the right cylinder has a diameter of 19 cm. She fills the
beaker with 2256.254 Cms of an acid. Approximately how high did the acid fill up the beaker?

Answers

Answer:

7.96 cm

Step-by-step explanation:

radius of bottom: 19/2 = 9.5

area of bottom = pi * r^2 = 283.53

height * base area = volume

What is the measure of the reference angle for a 112 degrees angle?

Answers

Answer:

68

Step-by-step explanation:

A P E X

please help :),))))

Answers

Answer:

option 1

Step-by-step explanation:

The rate of increasing is the fastest in exponential functions.

Then comes powers and last logarithmic functions.

The order it increases at the fastest rate.

[tex]log < powers < exponential[/tex]

I need help with this one thank you.

What is the length of the missing leg?

Answers

Answer:

Hello! answer: 6

Step-by-step explanation:

8 × 8 = 64

6 × 6 = 36

64 + 36 = 100

√100 = 10 so therefore a = 6 Hope that helps!

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.

[tex]y=15x+1[/tex]
[tex]y=15x+2[/tex]

Answers

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

First equation :

[tex]y = 15x + 1[/tex]

[tex]y - 15x - 1 = 0[/tex]

Second equation :

[tex]y = 15x + 2[/tex]

[tex]y - 15x - 2 = 0[/tex]

Now, the equations are in the form of

[tex]a_1x {}^{2} + b_1x + c_1 = 0[/tex]

[tex]a_2x {}^{2} + b_2x + c_2 = 0[/tex]

where,

[tex] \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} [/tex]

therefore the equations would have no solution .

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Kelly is making a rectangular garden that has a width of (2x + 3) and length of (2x - 4)
How much fertilizer would she need to lay down before she starts to
plant her flowers (area)?

Answers

Answer 2x^2 -12

Explanation

On a​ map, 1 inch equals miles. Two houses are inches apart on the map. What is the actual distance between the​ houses? Use pencil and paper. Show how you can represent the scale with two different ratios.

Answers

Answer:

The actual distance between the houses is 18.9 miles.

Step-by-step explanation:

The exact question is as follows :

Given - On a​ map, 1 inch equals 5.4 miles. Two houses are 3.5 inches apart on the map.

To find - What is the actual distance between the​ houses?

Solution -

Given that,

1 inch = 5.4 miles

⇒3.5 inches = 3.5 × 5.4 miles

                 = 18.9 miles

∴ we get

The actual distance between the houses is 18.9 miles.

NEED HELP HERE PLEASE!! π∆π

Give the value of the six trigonometric ratios in the figure.​

Answers

Answer:

Step-by-step explanation:

take theta as reference angle

using sin rule

sin theta=opposite/hypotenuse

sin theta=3/5

sin theta=0.60

theta=sin 37 degree

therefore the value of theta is 37 degree.

Help me with this please

Answers

Answer:

F'

Your answer is correct

Step-by-step explanation:

The image most of the time we will put ' prime on it to let the other know that this is the image

Find the vertex of the graph of the equation $y = -2x^2 + 8x - 15.$

Answers

Answer:

(2,-7)

Step-by-step explanation:

The number of hours that each of 6 students spent reading last week is shown in the bar graph below. For the data in the bar graph, which measure is the LEAST? *
1 point
Captionless Image

Answers

There is no photo sorry

the radius of a circle is 14.2 m. Find the circumference to the nearest tenth.​

Answers

Answer:

C=89.2

Step-by-step explanation:

The formula of the circumference of a circle is C=2piR (or C=piD). Now, when calculating, plug in the numbers, giving you C=2pi14.2. Multiply everything, you get a super long irrational number; just round. You will get 89.2.

what is the smallest angle of this triangle

17,26,29

Answers

The answer is 17 is the smallest angle
The awnswr is 17……….

Jina has scored 79, 85, 89 and 68 on her previous four tests. What score does she need on her next test so that her mean is 80?

Answers

Answer:

79

Step-by-step explanation:

79, 85, 89, 68 have a mean of 80.25 according to calculator.net. the number itself Is close to the number you want, in this case 80, i input 80, but it gave me a score of 80.2, so i tried again with 81, it gave me a score of 80.4, so the third attempt was successful with 79 being the input and 80 the output

calculator.net is approved on my school computer so there is a chance it is on yours as well.

A coffee roaster is designing a coffee can that can be modeled with a right cylinder for its new Breakfast Blend . Breakfast Blend costs the roaster $0.03 per cubic inch to produce. The roaster wants the can to contain an amount of coffee that will cost him no more than $7.50 to produce. Given that the height of the can is to be equal to its diameter, what is the maximum height allowable for the can? Round to the nearest tenth of an inch.

Answers

Answer: 6.8 inches

Step-by-step explanation:

30 POINTS I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade

Answers

Answer:

[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]

Step-by-step explanation:

[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]

[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]

3. This problem incorporates an exponent property.

Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]

[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]

Answer:

1. 6

2. 8/25

3. 5

4. 4/5

Step-by-step explanation:

Other Questions
A letter is randomly chosen from the word CANDLESTICK. Find the probability thatyou chose an Nor S. 5N5 N19 N19 NPls help look at the pic In this lab, you complete a C++ program that uses an array to store data for the village of Marengo.The program is described in Chapter 8, Exercise 5, in Programming Logic and Design. The program should allow the user to enter each household size and determine the mean and median household size in Marengo. The program should output the mean and median household size in Marengo. The file provided for this lab contains the necessary variable declarations and input statements. You need to write the code that sorts the household sizes in ascending order using a bubble sort and then prints the mean and median household size in Marengo. Comments in the code tell you where to write your statements.InstructionsMake sure that the file HouseholdSize.cpp is selected and open.Write the bubble sort.Output the mean and median household size in Marengo.Execute the program by clicking the Run button and the bottom of the screen.Enter the following input, and ensure the output is correct. Household sizes: 4, 1, 2, 4, 3, 3, 2, 2, 2, 4, 5, 6 followed by 999 to exit the program.Here is my code so far. I need help finishing it (printing the mean & median, etc). Thanks so much:// HouseholdSize.cpp - This program uses a bubble sort to arrange up to 300 household sizes in// descending order and then prints the mean and median household size.// Input: Interactive.// Output: Mean and median household size.#include #include using namespace std;int main(){ // Declare variables. const int SIZE = 300; // Number of household sizes int householdSizes[SIZE]; // Array used to store 300 household sizes int x; int limit = SIZE; int householdSize = 0; int pairsToCompare; bool switchOccurred; int temp; double sum = 0; double mean = 0; double median = 0; // Input household size cout > householdSize; // This is the work done in the fillArray() function x = 0; while(x < limit && householdSize != 999) { // Place value in array. householdSizes[x] = householdSize; // Calculate total of household sizessum+= householdSizes[x]; x++; // Get ready for next input item. cout > householdSize; } // End of input loop.limit = x;// Find the mean// This is the work done in the sortArray() functionpairsToCompare = limit - 1;switchOccured = true;while(switchOccured == true){ x = 0; switchOccured == false; while (x < pairsToCompare) { if(householdSizes[x]) > householdSizes[x+1]) { //perform switch } x++; } pairsToCompare--;}// This is the work done in the displayArray() function//Print the mean// Find the medianmedian = (limit-1) / 2;if (limit % 2 ==0){ cout You want to produce a magnetic field of magnitude 5.50 x 10 T at a distance of 0.0 6 m from a long, straight wire's center. (a) What current is required to produce this field? (b) With the current found in part (a), how strong is the magnetic field 8.00 cm from the wire's center? Benjamin was a lanky kid. He was the tallest kid in the class, and he was not a big kid. His mom packed him a huge lunch in the hopes he would get some more muscle on his bony arms and legs.What does the word lanky suggest about Benjamin in the sentence above?A.He looked healthy.B.He looked like a kid.C.He looked like a twig.D.He looked smart. NEED ASAP URGENTWhich similarity statement expresses the relationship between the two triangles?triagleZYX- triangleCABtriangleZYX-triangleACBtriangleZYX-triangleCBAtriangleZYX - triangleABC How do you solve the equation 3 1/5 +n=9? Which of the following is Abraham Lincoln best known for? PLZZZZZZZZZZZZZ HELPPPPPPPPP Jason and Beth each have a bank account. Jason starts with $1.65 in his account and puts in $0.20 each week. Beth starts with $2.95 in her account and also puts in $0.20 each week. Complete the table to show how much money each has saved after five weeks. Need the answer ASAP!! 20 points What is the length of the hypotenuse? HELLLLPPPPPPP PLEASEEEEEE BEGGGGI G SOMEONE PLEASEEEEEEEEE PLEASE ANSWER URGENT easy points easy question just put down a songs lyrics find its theme and what verse best describes it. 3x 3 y 4 3x 3 y 3 Which option is the clearest example of internal conflict? your parents have just organised a birthday party for you.write diary entries for two days.The first entry must be the day before the party and the second one the day of the party compare the time period of two pendulums of length 4m and 9m what is the answer? please helppp