When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of Np-240, a radioactive isotope of Neptunium, initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answers
The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
What is radioactive decay?The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.Alpha, beta, and gamma decay are three of the most prevalent types of decay, and they all entail the emission of one or more particles.The formula so used: A = [tex]\frac{-dN}{dt}[/tex]
=> N = A ([tex]e^{-kt}[/tex]), where:
N = amount left after the decay.A = initial amountk = constantt = time taken by the decayNow,
AS shown in the table (refer to the image attached), for k:
=> 322 = 1284[tex]e^{-2k}[/tex]
=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]
=> 0.25 = [tex]e^{-2k}[/tex]
Taking natural logarithm on both sides.
=> ln(0.25) = ln([tex]e^{-2k}[/tex])
=> ln(0.25) = (-2k) ln(e)
As ln (e) = 1,
=> ln (0.25) = -2k
=> -1.386 = -2k
=> k = 0.693
Now, for t = 1 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(1)}[/tex])
=> N = 1284 (0.5)
=> N = 642
For t = 3 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(3)}[/tex])
=> N = 1284 (0.125)
=> N = 160.6g
For t = 4 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(4)}[/tex])
=> N = 1284(0.0625)
=> N = 80.3g
Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
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Related Questions
D bisects AB. If AD = 2² - x and DB= 2x - 2, find the value(s) of x, AB, DB, and
AD.
Answers
The required values are x = 2 , AB = 4 , DB = 2 and AD = 2 .
Since D bisects AB , therefore AD = DB
hence , ( 2 ^ 2 ) - x = 2 x - 2
Solving linear equation ,
4 - x = 2 x - 2
3 x = 6
x = 2
AD = 4 - 2 = 2 .
DB = AD = 2 .
AB = AD + DB = 2 + 2 = 4 .
Hence , x = 2 , AB = 4 , DB = 2 and AD = 2 .
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Several friends buy jeans for $20.00 a price. What type of relation exists between the amount of money spent and the number of jeans purchased
Answers
The amount of money spent and the number of jeans purchased have a direct relationship.
What do we mean by direct relationship?A direct relationship exists when both variables increase or decrease together. In a direct relationship, Y rises as X rises. A direct relationship always has a positive slope on a graph. A positive relationship is another term for a direct relationship. The relationship between the height from which a ball bounces and the height from which it bounces back is an example of a direct relationship. The higher the ball is bounced (variable x), the higher it will rebound (y).So, in the given situation where several friends buy jeans for $20.00 a price.
The amount of money spent and the number of jeans purchased have a direct relationship.Therefore, a direct relationship exists between the amount of money spent and the number of jeans purchased.
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Solve each equation. Check each solution. 3/x =5
Answers
The solution of the given equation 3/x = 5 is at x = 3/5.
According to the given question.
We have an equation 3/x = 5.
As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Here, we have to find the solution of the equation 3/x = 5 is given by
3/x = 5
⇒ 3 = 5x (multiplying x both the sides)
⇒ 3/5 = x (dividing both the sides by 5)
⇒ x = 3/5
Hence, the solution of the given equation 3/x = 5 is at x = 3/5.
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Find the arithmetic mean a n of the given terms. a n₋₁ =100, an ₋₁ =140
Answers
The arithmetic mean a n of the given terms a n₋₁ =100, an ₋₁ =140 is
a (n) = 20.
What is arithmetic mean?a n₋₁ =100, an ₋₁ =140
a (n) = (140-100)/2
a (n) = 20
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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writ all the factors other than 1 and the number itself
for 5th grade
Answers
Answer:
A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13
if this is what you are looking for..
find the area of the shaded section ABC
Answers
Answer:
The shaded area is 66.40 cm²============================
The shaded section is the difference of sector OAB and triangle OAC.
Area of sectorFind the measure of angle Ocos ∠O = OC/OAcos ∠O = 5/13m∠O = arccos (5/12)m∠O = 65.4° (rounded)Find the area of sector OABA = πr²θ/360A = 3.14*13²*65.4/360A = 96.40 cm²Area of triangleFind the height of triangleUse Pythagorean
OA² = OC² + AC²13² = 5² + AC²AC² = 169 - 25AC² = 144AC = √144AC = 12Find area of triangleA = bh/2A = 5*12/2A = 30 cm²Shaded areaFind shaded areaA = 96.40 - 30A = 66.40 cm²6.8 divided by 34 HELP PLSSSSSS i also need it in step by step because i have to show my work ;) RIGHT ANSWER GETS MARKED BRAINLIST
Answers
Answer:
[tex]\mathrm {\dfrac{1}{5} \; or\; 0.2 \; in \; decimal}[/tex]
Step-by-step explanation:
We are asked to find [tex]\dfrac{6.4}{34}[/tex]
Multiply numerator and denominator by 10 to convert them to whole numbers
[tex]\dfrac{6.8}{34} = \dfrac{6.8 \times 10}{34 \times 10} = \dfrac{68}{34 \times 10}\\\\= \dfrac{68}{34} \times \dfrac{1}{10}\\\\= 2 \times \dfrac{1}{10}\\\\= \dfrac{2}{10}\\\\= \dfrac{1}{5}\\\\= 0.2[/tex]
. If BD 1 AC, m/DBE = (2x - 1)°, and
m/CBE = (5x - 42), find the value of x.
Answers
Step-by-step explanation:
well, because the 2 lines are intersecting each other at a right angle (90°), the complete angle CBD is 90°.
that means the sum of the sub-angles must be 90° :
DBE + CBE = 90
2x - 1 + 5x - 42 = 90
7x = 133
x = 19
what is the probability that the customer is either older than 50 or younger than 30 ?
Answers
Answer: 0.71
Step-by-step explanation:
Older than 50: 50-60 and >=60
50-60 : 90 customers
>=60 : 52 customers
90+52=142 customers
Younger than 30: <20 and 20-30
<20 : 67 customers
20-30: 100 customers
67+100=167 customers
142+167=309 customers are either older than 50 or younger than 30
Total customers:
67+100+55+72+90+52=
167+127+142=
294+142=434 customers
309/434=0.71
HELP ASAP PLEASE
13. <1 and < 2 are supplementary. If <1 = 2y = 9 and m<2 = 3y-4, what is the measure of <1?
*
m<1 = 35
m<1 = 101
m<1 = 13
m<1 = 79
Answers
Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.
Hence, option D)79° is the correct answer.
What is the measure of ∠1?Supplementary angles refer to the pair of angles that sum up to 180 degree.
Given the data in the question;
∠1 and ∠2 are supplementary∠1 = 2y + 9∠2 = 3y - 4Measure of ∠1 = ?Since ∠1 and ∠2 supplementary angles, they will sum up to 180 degree.
∠1 + ∠2 = 180°
(2y + 9) + (3y - 4) = 180
Solve for y
2y + 9 + 3y - 4 = 180
5y + 5 = 180
5y = 180 - 5
5y = 175
y = 175/5
y = 35
Hence, the measure of ∠1 will be;
∠1 = 2y + 9
∠1 = 2(35) + 9
∠1 = 70 + 9
∠1 = 79°
Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.
Hence, option D)79° is the correct answer.
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Ayúdame, es para mañana
Answers
Answer: 1) x=20° 2) x=50°
Step-by-step explanation:
1)
[tex]x+20+x+30=90\\2x+50=90\\2x+50-50=90-0\\2x=40\\Divide\ both\ parts\ of \ the\ equation\ by\ 2:\\x=20^0[/tex]
2)
The sum of adjacent angles is always 180 degrees.
[tex]x+80+x=180\\2x+80=180\\2x+80-80=180-80\\2x=100\\Divide\ both \ parts\ of\ the\ equation\ by\ 2:\\x=50^0[/tex]
Anyone know how to do this?
Answers
Answer:
The square root of 48 to the nearest tenth is 6.9
Rotate the figure 90° clockwise. Then rotate the figure 180°
Answers
Answer:
this is super easy...
u first rotate it 90° until the BC is downwards.
then rotate it one round until it comes to the way it was..that means once again BC down...hope it is clear...
Rebecca used 3/15 of string on Monday and 5/15 on Tuesday. How much string does she have left?
answer choices
7/15
8/15
6/15
Answers
Answer: 7/15
Step-by-step explanation:
Choose the vocabulary term that correctly completes each sentence.
There is a constant ________ between consecutive terms in a geometric sequence.
Answers
There is a Constant Ratio between consecutive terms in a geometric sequence.
The consecutive terms in a Geometric Progression or Sequence are separated by a Constant Ratio which remains constant for the whole sequence and all of the terms in that sequence are separated by that Ratio. Generally, the Constant Ratio is denoted by 'r'. The next term of the sequence can be determined by using this Ratio.
To determine the next term or [tex]n^{th}[/tex] term, we need to multiply the previous term with the Ratio. There is a specific formula to determine the [tex]n^{th}[/tex] term in a geometric sequence. The formula for determining the next term or [tex]n^{th}[/tex] term is: => [tex]a_{n} = ar^{(n-1)}[/tex]
Here, [tex]n = n^{th}[/tex] term, [tex]a =[/tex] First term, and [tex]r =[/tex] Constant Ratio
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Two cars start at the same time from two towns 792 kilometers apart and meet in 9
hours. One car can travel 8 km faster than the other car. How far did each car Travel
before they meet?
Answers
The distance the slower and faster car travelled are 360 km and 432 km respectively.
How to find the distance travelled by each car?Two cars start at the same time from two towns 792 kilometres apart and meet in 9 hours.
One car can travel 8 km faster than the other car.
let
x = speed of the slower car
x + 8 = speed of the faster car
The cars meet in 9 hours and both cover a distance of 792 km.
Therefore,
speed = distance / time
distance = time × speed
Hence,
9x + 9(x + 8) = 792
9x + 9x + 72 = 792
18x = 792 - 72
18x = 720
divide both sides by 18
x = 720 / 18
x = 40
Therefore,
speed of the slower car = 40 km per hour
speed of the faster car = 48 km per hour
Hence,
how far the slower car go(distance) = 40 × 9 = 360 km
how far the faster car go(distance) = 48 × 9 = 432 km
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URGENT: DUE TODAY
In the picture, k || p, m 21 = 2x + 24, and mz3 = 10x. Find m<2.
Answers
Answer:
C
Step-by-step explanation:
Jessica wants to attach ribbon around her wardrobe.
1 3/4 m, 2/3 m
She has 4 metres of ribbon.
How much more does she need?
Give your answer as a fraction.
Answers
Based on the fact that Jessica wants to attach ribbons around her wardrobe, the amount more of ribbons that she needs is 5/6 meters of ribbons
How much ribbons does Jessica need?Find out the distance wound Jessica's wardrobe:
= 1¹/₃ + ²/₃ + 1¹/₃ + ²/₃
= 58 / 12
= 4 ⁵/₆ meters
The amount more that Jessica needs is therefore:
= 4 ⁵/₆ - 4
= 5/6 meters of ribbons
In conclusion, Jessica needs 5/6 meters of ribbons
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If X+y=x, show that (a+b)²= a²+2ab+b²
Answers
Answer:
a^2+2ab+b^2
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
a(a+b)+b(a+b)
(a^2+ab)+(ab+b^2)
a^2+2ab+b^2
Pls pls pls help with the math quetion!
Answers
Answer:
Answer no. 4
Step-by-step explanation:
1.67 x 10^3 = 1670
16.7 x 10^3 = 16700
those number are clearly the biggest in their categories, so answers 1 and 2 are not worth further consideration. Also note that all the numbers are the same in every answer except 1.67 x 10^3 or 16.7 x 10^3, so the 16.7 might be an error. Fortunately it does not change the answer.
Let's choose between answers 3 and 4. We start with easy numbers:
4^2 = 16
50/3 = 16.6666...
So 50/3 must come after 4^2.
We're left with answer 4.
We can also convert everything to decimal:
[tex]15.75\\\sqrt{250} = 15.8113883...\\4^2 = 16\\50/3 = 16.666666....\\16.7 \cdot 10^3 = 16700\\1.67 \cdot 10^3 = 1670[/tex]
from which we can order conventionally
How am I supposed to do this? I know that the x = 11, but I have no clue on what to do from there
Find m∠CED.
Answers
Answer: 140°
Step-by-step explanation:
x = 11
5 x 11 = 55
55 - 15 = 40
The 5x-15 = 40°
tHe 3x+7 is opposite, so it also equals 40°
40 + 40 = 80°
360° - 80° = 280
280 divided by 2 = 140°
in his garden Tim plants the seed 4 3/4 below the ground. after one month the tomato plant has grown a total of 8 1/2. How many inches is the plant above the ground
Answers
Answer: 3 3/4
Step-by-step explanation:
The plant is 4 3/4 below ground, but then it grows 8 1/2.
Use subtraction to find the difference.
8 1/2 - 4 3/4 = 3 3/4
Answer:the answer would be 3 3/4
Step-by-step explanation:
To steer an airboat, rudders sit behind the fan. When the air
passes through the turned rudders, it turns the boat. Use Newton's third
law to construct an explanation on how the rudders turn the boat.
Answers
The fluid is redirected by the rudders, which then produce an opposing force that helps the boat move in the desired direction.
Describe Newton's third law of motion?According to Isaac Newton's law, whenever an object X applies a force on another object Y, object Y must respond by applying a force that is equal in magnitude but directed in the opposite direction.
In the case of the rudder, it causes the fluid to flow in a different direction while still exerting an equivalent force of the same size. Consequently, this causes the boat to move, making it the best option.
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Write a flow proof of the Exterior Angle Theorem.
Given: ΔXYZ
Prove: m ∠ X + m ∠ Z = m ∠ 1
Answers
Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.
What is meant by angle sum property?
Triangle angle sum property states that the sum of a triangle's interior angles is 180°. parallel to the given triangle's side BC. As a result, the sum of a triangle's interior angles is 180°.
The Triangle Angle-Sum Theorem and the Definition of a Linear Pair serve as the foundation for this proof. Create two equations based on the diagram, one for each of these relationships. When two angles form a linear pair, we know they are supplementary and add up to 180 degrees. At this point in the proof, you can set the two equations equal to each other and simplify to obtain the proof's final conclusion.
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A bag contains 180 cars. Some are red and the rest are blue. There are 14
red cars for every blue car.
How many red cars are in the bag?
012
O 114
06
O 168
Answers
Answer:
114
Step-by-step explanation:
If you use the probability of statistics equation ax+bx+cx=x^3 and plugin the numbers you will get 114 as your answer.
Can yall help me on this please please Ill give brainlist and 100 points
Answers
Answer:
d) (-2)⁶/(-2)⁴
Step-by-step explanation:
Given that,
→ (-2)⁴/(-2)²
→ 16/4 = 4
Then the equivalent expression is,
→ (-2)⁶/(-2)⁴
→ 64/16 = 4
Hence, option (d) is correct.
An unbiased statistic is one in which the average value of the statistic is ____________ the population parameter.
a. less than
b. greater than
c. either greater than or less than
d. equal to
Answers
An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.
Unbiased Statistic/estimator is defined as the accurate statistic that is used in approximation a population parameter.
In the above statement the word "accurate" means that it should be neither greater than nor less than the population parameter.
If the average value is less than the population parameter or greater than the population parameter then the statistic will be termed as "biased".
Therefore , An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.
The correct option is (d) equal to.
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Determine a base and a height for each shape.
Answers
Answer:
base :6 units
height:4units
area of a triangle: 1/2 ×b×h
1/2× 6×4=12
12sqaure units should be the area
Let f(x) = x²+1 and g(x)=3 x . Evaluate each expression. (g ₀ f) (1/2)
Answers
The value of the expression (g ₀ f) (1/2) is 15/4
In this question, we have been given two functions f(x) = x² + 1 and g(x) = 3x.
We need to evaluate an expression. (g ₀ f) (1/2)
We know that the composite function is a function where the output of one function becomes the input of another function.
First we find the composite function (g ₀ f) (x)
(g ₀ f) (x)
= g(f(x))
= 3(f(x))
= 3 (x² + 1 )
= 3x² + 3
So, (g ₀ f) (x) = 3x² + 3
Now, we find the value (g ₀ f) (1/2)
(g ₀ f) (1/2)
= 3(1/2)² + 3
= 3(1/4) + 3
= 3/4 + 3
= 15/4
Therefore, the value of the expression (g ₀ f) (1/2) is 15/4
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Solve the system of equations. 4x – y = 4 2x2 – y = 4 (0, 4) and (0, –4) (1, 0) and (1, –6) (2, 4) and (0, –4) (3, 8) and (0, –4)
Answers
Answer: Choice C
(2, 4) and (0, -4)
========================================================
Explanation:
Let's solve the first equation for y
4x - y = 4
-y = -4x+4
y = 4x-4
Now plug this into the other equation and solve for x.
2x^2 - y = 4
2x^2 - ( y ) = 4
2x^2 - ( 4x-4 ) = 4
2x^2 - 4x+4 = 4
2x^2 - 4x+4-4 = 0
2x^2 - 4x = 0
2x(x - 2) = 0
2x = 0 or x-2 = 0
x = 0 or x = 2
-----------------
If x = 0, then,
y = 4x-4
y = 4(0)-4
y = -4
This gives one solution as (0, -4)
-----------------
If x = 2, then,
y = 4x-4
y = 4(2)-4
y = 4
The other solution is (2, 4)
-----------------
To check the answers, plug the x and y coordinates into each equation. You should get the same thing on both sides.
Below is verification using a graph. The points of intersection are the solutions.
