If 150 grams of a radioactive isotope are present at 2:00 PM and 10 grams remain at 6:00 PM (the same day), what is the half-life of the isotope? Round to two decimal places.

Answers

Answer 1

Initial amount, [tex]A_o=150\ g[/tex] .

Final amount, [tex]A =10\ g[/tex] .

Time taken, t = 6:00 - 2:00 = 4 hour.

We know,

[tex]A=A_o(\dfrac{1}{2})^{\dfrac{t}{h}}\\\\10 = 150 \times \dfrac{1}{2}^{\dfrac{4}{h}}\\\\2^{\dfrac{4}{h}}=15\\\\\dfrac{4}{h}= log_215\\\\h = \dfrac{4}{log_215}\\\\h = 1.024 \ hours[/tex]

Therefore, the half-life of the isotope is 1.024 hours.

Hence, this is the required solution.


Related Questions

3x-1/5=x+1/3 solve for x

Answers

Answer:

x = 2

Step-by-step explanation:

First, you cross multiply then that will give you

9x - 3 = 5x + 5

collect like terms

9x - 5x = +5 + 3

= 4x = 8

Divide both sides by the coefficient of x that's 4

= 2

Two helicopters leave a heliport at the same time. The first flies 160km/h in a direction of 290 degrees. The second flies 100km/h in a direction of 250 degrees. After 3 hours, how far apart are the helicopters? Round your answer to the nearest kilometer.

Answers

Answer: 315 km

Step-by-step explanation:

If the angle θ is measured from the x-axis, and we have a magnitude A, we can find the rectangular coordinates as:

Ax = A*cos(θ)

Ay = A*sin(θ)

Then:

The first helicopter has a speed of 160km/h, and it's angle is 290°.

Then the components will be:

Vx = 160km/h*cos(290°) = 54.7 km/h

Vy = 160km/h*sin(290°) = -150.4 km/h

Then the point location as a function of time, can be written as:

(where i assumed that the initial position of both helicopters was (0, 0))

P1(t) = (54.7 km/h*t, -150.4 km/h*t)

where t is time in hours.

We can do the same for the other helicopter:

The speed is 100km/h, and the angle is 250°

Then:

Vx = 100km/h*cos(250°) = -34.2 km/h

Vy = 100km/h*sin(250°) = -94 km/h

Then the point location as a function of time, will be:

P2(t) = (-34.2km/h*t, -94 km/h*t)

After 3 hours, the position of each helicopter will be:

P1(3h) = (54.7 km/h*3h, -150.4 km/h*3h) = (163.1 km, -451.2 km)

P2(3h) = (-34.2km/h*3h, -94 km/h*3h) = (-102.6km, -282km)

Now we can calculate the distance between these two points.

Remember that the distance between the points (a, b) and (c, d) is:

D = √( ( a - c)^2 + (b - d)^2)

In this case the distance will be:

D = √(  (163.1 km - (-102.6km))^2 + (-451.2 km - (-282km))^2)

D = √(  (163.1 km + 102.6km)^2 + (-451.2 km + 282km)^2)

D = 315km

Write each expression in standard form.

6(−5 − 4)− 2( − 7 − 3)

Answers

Answer:

heyyy wassuppp

Step-by-step explanation:

How many sides does a decagon have?

sides

Answers

Answer:

It has 10 sides.

Step-by-step explanation:

Answer:

12 sides.

Step-by-step explanation:

A good way to remember this is "decagon" is called that because it has 12 sides, and the month December is the 12th month of the year.

what is the range of this function (I NEED AN ANSWER RLLY FAST PLSSSS)

Answers

Answer:

d

Step-by-step explanation:

the first oval's domain and the second's range. so you just choose the choice that includes all the values in the ranger.

a line has a slope of -2/3 and passes through the point (-3, 8). what is the equation of the line​

Answers

Answer:

y=-2/3x+6

Step-by-step explanation:

hope this helps

Which of these is equivalent to 1 over x to the power of 5 ? 1 fifth x negative x to the power of 5 x to the power of 5 x to the power of negative 5 end exponent

Answers

Answer:

x^-5 = x to the power of negative 5

Step-by-step explanation:

Which of these is equivalent to 1 over x to the power of 5 ?

Mathematically this is expressed as

(1/x)⁵

We have a rule when it comes to expressing power

(1/a)^b = a^-b

Hence, applying this rule to our question

(1/x)⁵ = (1/x)^5

= x^-5

This is written in words as:

x to the power of negative 5

Given f(x) = -x + 1, solve for x when f(x) = 0.

Answers

Answer:

1

Step-by-step explanation:

0=-x+1

-x=-1

x=1

Can someone help me with this fast please?
Thank You

Answers

Answer:

3/10 is greater

Step-by-step explanation:

2/7 is equal to 0.29... and 3/10 is equal to 0.3

So, 0.3 is bigger than 0.29

There are more boxes shaded in the picture to the right than the picture to the left. 21 > 20

f(x)=3x−5 and g(x)=x2 Find (f°g)(3)

Answers

Answer:

22

Step-by-step explanation:

3!(3)^2-5

3÷9-5

37-5=22

What is the length of the unknown side of the right triangle?

A right triangle with hypotenuse x and legs 21 and 20

21
29
400
441

Answers

According to Pythagoras theorem,

h² = b² + h²

=> x² = 21² + 20²

=> x² = 441 + 400

=> x = √841

=> x = 29

Thus, the length of the unknown side is 29 units.

Solve for X. -15 = 22x + 7

Answers

Answer: x=-1

Step-by-step explanation: Here is one way of answering this question. First you need to subtract 7 from both sides and that will leave you with -22=22x. Then you just divide 22 on both sides. So that will give you an answer of -1=x or x=-1

X=1. Hope this helps you out!!

Hello can someone help me please..?

Answers

Answer:

From 3:23-3:24

Step-by-step explanation:

Increase 2800kg
by 21​

Answers

Answer:

3388 kg

Step-by-step explanation:

If you mean to increase by 21%, then

You may

100% + 21% = 121%

2800 x 121/100

2800 x 1.21

= 3388 kg

2(6-2x)-2x=2(5+x)-4 value of x?

Answers

Answer:

x= 3/4

Step-by-step explanation:

I looked it up. Hope this helps

Answer:

x = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given

2(6 - 2x) - 2x = 2(5 + x) - 4 ← distribute parenthesis on both sides

12 - 4x - 2x = 10 + 2x - 4 ← simplify both sides

12 - 6x = 6 + 2x ( subtract 2x from both sides )

12 - 8x = 6 ( subtract 12 from both sides )

- 8x = - 6 ( divide both sides by - 8 )

x = [tex]\frac{-6}{-8}[/tex] = [tex]\frac{3}{4}[/tex]

Solve for X.

A. 168
B. 180
C. 21
D. 42

Answers

Answer:

Answer = C

Angle x = 21

Property = Angle sum of Triangle

A recipe calls for 3 1/2 cups of milk and makes 10 servings. How many cups of milk are needed for 8 servings? (Hint: Set up a proportion, don’t forget to label!)

Answers

Answer:

2.8 or 2 4/5

Step-by-step explanation:

Here's our proportion of cups of milk to servings

3 1/2:10      For my sake I'm using decimals

3.5:10

Now let's try to get our servings to 1 (a unit rate)

0.35:1         I divided by 10 on each side

We need 8 servings not 1 so let's multiply 8 on each side

2.8:8

In case you want it in fraction form we can do 2 8/10 and simplify it to 4/5 by dividing by 2. Our answer is 2.8 or 2 4/5 cups of milk for 8 servings.

Write an expression that can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound. (Do not enter dollar signs or spaces in your expression.)

Answers

Answer:

3.25g + 0.74f = t

What is the probability of spinning an odd number on the spinner below?

Answers

If the spinner has an odd number of numbers on it, The probability or spinning an odd number will vary

Determine which of following table is NOT a function.

Answers

Answer: C

Step-by-step explanation:

C beacause one X cannot have two different Y values

Please help I have no idea what the answer is

Answers

Answer:

x = 59

Step-by-step explanation:

All the angles in a triangle add up to 180

Add all the known angles

83 + 38 = 121

To find the third angle, subtract the total of all the angles by the total of the known angles

180 - 121 = 59

One gallon of milk has 128 fluid ounces. How much milk is in 6.5 gallons?

Answers

Answer:

832 fluid oz

Step-by-step explanation:

Multiply 128 by 6.5

Answer:

832

Step-by-step explanation:

Multiply 128 by 6.5 gallons

Stacy paid $54 for 6 pizzas, which is a rate of $ ? per pizza.

Answers

Answer: it’s 9

Step-by-step explanation:

54 divined by 6 = 9

C-17 = 19
Hi please help

Answers

Answer:

C=36

Step-by-step explanation:

C-17=19

C=19+17

C=36

PLEASE HELP ME OUT! WIL GIVE BRAINLIEST TO ANYONE WHO ANSWERS BOTH OR ATLEAST ONE AND SHOW WORK!! THANK YOUU

Answers

Answer 1 is the attached pic

Answer:

16

Step-by-step explanation:

(-2i)(8i)

(2(cos(3π/2)+i×sin(3π/2)))×(8(cos(π/2)+i×sin(π/2)))

2×8(cos(3π/2+π/2)+i×sin(3π/2+π/2))

16(cos(2π)+i×sin(2π))

16(cos(0+2π)+i×sin(0+2π))

16(cos(0)+i×sin(0))

16(alternate form)

PLEASE ANSWER I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!

Answers

Answer:

1) third point

2) no is the answer

express 9 3/2 in simplest radical form

Answers

Answer:

Exact Form:

√93

Decimal Form:

27

Step-by-step explanation:

i'll mark you has brainliest​

Answers

Answer:

y= 5 x+ 1

Step-by-step explanation:

Answer:

i think its 21x + 11 = y

Step-by-step explanation:

sorry if this is wrong, if it is someone correct me.

A diver descended 46.36 feet in 12.2 minutes.What was the divers average change in elevation per minute? The average change in elevation per minute was ?Ft per minute

Answers

Answer:

The average change in elevation per minute is 3.8 ft per minute

Step-by-step explanation:

Here. we want to calculate the average change in elevation per minute

To calculate this, we simply need to divide the total descent over the total number of minutes

Mathematically, that would be;

46.36 feet / 12.2 minutes = 3.8 feet per minute

helllppppleaseeeee.

Answers

Answer:c

Step-by-step explanation:

The correct answer would be A
Other Questions
Which of the following statements about anatomical position are true?Anatomical position is different in different hospitals.Anatomical position is not helpful when learning new terms in anatomy.Anatomical position is a standard point of reference for the anatomical planes.Superior and inferior planes describe parts of the body relative to anatomical position. Only the Pro Side will make a Case Outline for the Debate of Fact, the Con Side will create _________ instead.Group of answer choicesRefutation Blocking CardsCross Examination Blocking CardsRebuttal Blocking CardsOnly Evidence Bits What do you like about STEM lessons?What parts of lessons do you feel could be improved? The sun produces 3.3 x 10^ 32 joules of energy per day. A human produces 6.27 10^6 joules per day. How many times more energy does the sun produce than a human per day? To help manage risk, it is essential that you ___________ that can increase levels of risk. Please can you help me, I had to put this question up here twice Read the passage about the life of Jackie Robinson.Jackie Robinson was born on January 31, 1919, in Cairo, Georgia. Growing up, he was very much inspired by his older brother Matthew, who won a silver medal in the 200-meter dash at the 1936 Olympic Games, to pursue his talent and passion for athletics. He attended John Muir High School and then went on to Pasadena Community College, where he played football, basketball, track, and baseball. From there, Jackie went on to the University of California, Los Angeles, where his time was cut short due to financial hardship. After leaving the University of California, Jackie served in the United States Army. Fortunately, Jackie never saw combat; however, other circumstances ultimately led to Jackies honorable discharge from the military. It was shortly thereafter that Jackie began his career in Major League Baseball.During this time, the leagues were still segregated. Jackie was drafted by Branch Rickey to change all of that and integrate baseball. On April 15, 1947, Jackie became the first African-American athlete to play in the major leagues. Despite the ongoing racism that Jackie faced from some teammates, crowds, and players from other teams, he earned the National Leagues Most Valuable Player award in 1949. In his decade-long career with the Dodgers, Jackie helped his team win the National League pennant several times. In 1955, he helped them achieve the greatest victory of all: the World Series.Including which fact would best help nominate Jackie Robinson for the Most Talented category in a yearbook?Jackie earned the National Leagues Most Valuable Player award in 1949.Jackies older brother Matthew inspired him to pursue his athletic talents.Jackie served in the United States Army but was never faced with combat.Jackie pursued different sports while attending Pasadena Community College. The white Dwarfs are a group of stars that are-A)Extremely bright and hotB)Low in brightness but are average to high in temperatureC)Average in brightness but high in temperatureD)Average in brightness and average in temperature A student throws a 0.1 kg dart at an angle of 20 to the horizon. Then the student changes the throwing angle. Which anglewill maximize the distance the dart will travel before it returns to its original height? Which of the following is NOT a part of the listening process? Hearing Understanding Focusing Talking Please answer :D Rearrange the linear equation so that it is in slope-intercept form. Identify the slope (m) and the y-intercept (b). You must show your work for full credit.x - 4 = 2(y - 3) Everytime you swing with the golf club and hit the ball, it is called what? Name 3 different golf clubs. You cannot do what, when someone is about to hit the ball? Explain what PAR means- What do you yell when you hit the ball towards someone? The score of one under PAR on a hole is called what? The score on one over PAR on a hole is called what? How many holes are on a standard golf course? Historians can trace the sport of golf back to what country in the 1400s? Name 3 golf vocabulary terminology (terms) and describe what those 3 vocabulary terms mean. Page 154. How does the author make the eight minutes seem like hours?5. Using context clues, what is meant by lighted rectangles"? Which of the following organisms in the Gulf of Mexico experiences an immediate increase of population due to fertilizer runoff into theMississippi River?bacteriaphytoplanktondolphinsfish Many people living in north and south america tody speak european languages.. Spanish is spoken in places such as mexico , colombia, and venezuela, and portuguese is spoken in brazil. This is an example of how Which correct variables describes the slope?A.X/YB.Y/XC.W/ZD.Z/W It takes a barber 12 minutes to shave a face and 30 minutes to give a haircut. The barber works for 6 hours straight and spends twice as much time shaving faces as he does giving haircuts. If two of his customers get both a haircut and a shave, then how many customers does he see in total? How many molecules of oxygen are in 3.0 moles of oxygen? Please help like please Actual total direct labor $ 655,200 Actual hours worked 37,700 Standard labor-hours allowed for actual output (flexible budget) 36,500 Direct labor price variance $ 23,400 F Actual variable overhead $ 157,120 Standard variable overhead rate per standard direct labor-hour $ 4.20