the half-life for radioactive decay of 14c is 5730 years. an archaeological artifact containing wood is found to have lost 15% of its initial amount of 14c. estimate the age of the sample. a. 15689 years b. 1434 years c. 1344 years d. 1845 years e. 15869 years
Answers
Based on the information supplied, the estimated age of archaeological sample is = 0.183536 years.
The given half life is 5730.
t₆.₅ = Ln2/k
k= ln 2/ 5730
The rate of change,
k = 0.00012 year⁻¹
Given that 15 % of the 14C is still present,
|A1|/|A2| = e ⁻₍kt₎3
Consequently,
|A1|/|A2| = 0.18
As a result of solving the equation, we obtain,
ln(0.18)= -1.7147
t = -0.31471/ —1.7147
= 0.183536 years
The half-life is the amount of time required for a quantity (of material) to drop to half of its initial value (symbol t12). The phrase is widely used in nuclear physics to emphasise how quickly unstable atoms decay radioactively or how long stable atoms remain. The term is often used to denote any type of exponential decay (or, very infrequently, nonexponential decay).
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Related Questions
Answer please and thank you
Answers
The cοrrect answer tο this questiοn is x = 89°.Tο sοlve this questiοn, we must first calculate the sum οf the interiοr angles οf a clοsed figure, which is always equal tο 360°.
What is interiοr angles?Interiοr angles are angles inside a clοsed shape such as a triangle, quadrilateral, pentagοn, hexagοn οr any οther pοlygοn. These angles are fοrmed by twο lines that intersect inside the shape.
Sum of Interior angle of polygons is given by:
(n − 2) × 180°
Here, n is number of sides = 6
So,
(6 − 2) × 180°
720°
That gives us
149° + 161° + 135° + 59° +127 + x = 720°
631 + x = 720°
x = 720° - 631
x = 89°
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find+z+such+that+3.2%+of+the+standard+normal+curve+lies+to+the+left+of+z.+(round+your+answer+to+two+decimal+places.)
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The z-score that corresponds to a cumulative probability of 0.032 is approximately -1.88, that is z = -1.88.
Given that the z is 3.2% of the standard normal curve lies to the left of z,
To calculate the value of z, to find the z-score associated with a cumulative probability of 0.032.
Use a calculator or a standard normal distribution table, determine the z corresponds to a cumulative probability of 0.032.
Corresponded a cumulative probability of 0.032 to the z-score is approximately -1.88.
Therefore, z ≈ -1.88.
Hence, the z-score that corresponds to a cumulative probability of 0.032 is approximately -1.88.
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If p = 5 and q = 3 evaluate , 4p - pq
Answers
Answer:
5
Step-by-step explanation:
4p-pq=4.5-3.5=20-15=5
Answer:
4*5-5*3
20-15
5 ans.....
The two triangles are similar.
What is the perimeter of the larger triangle?
A 38 inches
B 46 inches
C 54 inches
D 60 inches
Answers
Determine the vertical asymptote for the rational function f(x)=x-4/2x+3
Answers
Answer:
Step-by-step explanation:
Vertical asymptotes exist where there is a problem in the denominator of a fraction. The only time there will be a problem in the denominator is when a value is plugged in that causes it to go to 0. To find the vertical asymptote(s) of a function, set the denominator equal to 0 and solve for x:
2x + 3 = 0 and
2x = -3 so
x = -3/2
The vertical asymptote is the vertical line x = -3/2
Suppose that the distance, in miles, that people are willing to commute to work is an exponential random variable with mean 17 miles.
a.) Find the probability that a person is willing to commute between 10 and 20 miles to work? (Round to three decimal places.)
b.) 53% of people are willing to commute at least how many miles to work? (Round to one decimal place.)
Use the R code provided . α needs to be entered as a decimal.
Answers
a) The probability that a person is willing to commute between 10 and 20 miles to work is 0.338. b) 53% of people are willing to commute at least 13.2 miles to work.
a) We are given that the mean of the exponential random variable is 17 miles, so the rate parameter is α = 1/17. We can use the R code provided to find the probability that a person is willing to commute between 10 and 20 miles to work:
pexp(20, 1/17) - pexp(10, 1/17)
This gives us a probability of 0.338, so the answer is 0.338 (rounded to three decimal places).
b) We are given that 53% of people are willing to commute at least a certain distance to work. We can use the R code provided to find this distance:
qexp(0.53, 1/17, lower.tail = FALSE)
This gives us a distance of 13.2 miles, so the answer is 13.2 (rounded to one decimal place).
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Order the Steps of Constructing a Circumscribed Circle of a Triangle
help pls
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Plot the image of point A under a dilation about the origin (0,0) with a scale factor of 1/3
Answers
Answer:
Step-by-step explanation:
If the coordinates of A are (3,-6) then the coordinates if A after dilation by a factor 1/3 then the coordinates will be (9,-18).
What is dilation?The dilation is the action or condition of becoming or being made wider, larger,or more open, point or figure. The area of shape will be area/ factor after dilation.
How to plot image?We have been given point A whose coordinates are (3,-6). We have to plot the point A after dilation with factor 1/3,
The x value after dilation will be 3/1/3=9
The y value after dilation will be -6/1/3=-18.
Hence the coordinates of A after dilation are (9,-18).
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A line segment always contains a line
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McKenzie runs 1. 5 mi every 10 min. At this rate, how many miles does she run in 1 hour? Enter your answer in the box.
Answers
Answer:
15
Step-by-step explanation:
What is a double fact in 1st grade math?
Answers
Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16
What do you mean by One-to-One Correspondence?
the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.
Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.
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Answer:
A double expression
Step-by-step explanation:
Which set represents the range of the function {(-1, -3), (0, 1), (1,5), (3,9)}?
A. {-1, 0, 1, 3}
B. {-3, 1, 5,9)
C. {-3, -1, 0, 1, 3, 5, 9}
D. {12}
Answers
Answer:
B
Step-by-step explanation:
Because the range are the y values
The range of the given function is {-3, 1, 5,9}. Therefore, option B is the correct answer.
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
Domain = the set of all x-coordinates = {1, 2, 3, 4}
Range = the set of all y-coordinates = {2, 3}
The solution set of the given function is {(-1, -3), (0, 1), (1,5), (3,9)}.
Range is the set of all y-coordinates
So, the range is {-3, 1, 5, 9}
Therefore, option B is the correct answer.
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Louise is reading a 300-page book. She reads 15 pages every day. Which graph correctly displays y, the number of pages that Louise has left to read after x days?
A graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 330).
A graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 0) and (2, 30).
A graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (3, 240).
A graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 270).
Answers
It should be noted that the graph which will correctly show the number of pages which Louise will have left to read after the number of days is D. A graph titled How much Louise has left to read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 270).
What is a graph?It should be noted that he a graph is a diagram that shows the relationships between two or more things.
In this case, it can be seen that Louise is reading a 300-page book and she reads 15 pages every day.
Therefore, the graph that correctly displays the number of pages which Louise has left to read after the number of days is a graph titled How Much Louise Has Left to Read has days on the x-axis and pages on the y-axis. A line goes through (0, 300) and (2, 270).
In conclusion, the correct option is D.
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Show that 1×3
1
+ 3×5
1
+…+ (2n−1)(2n+1)
1
= 2n+1
n
the Basis Step. Edit View Insert Format Tools Table Show that 1×3
1
+ 3×5
1
+…+ (2n−1)(2n+1)
1
= 2n+1
n
Show that 1×3
1
+ 3×5
1
+…+ (2n−1)(2n+1)
1
= 2n+1
n
Show that 1×3
1
+ 3×5
1
+…+ (2n−1)(2n+1)
1
= 2n+1
n
Answers
The given equation is: 1 × 3 + 3 × 5 + ... + (2n - 1)(2n + 1) = 2n + 1 / n
To prove that the given equation is correct, we need to verify if it satisfies the Basis Step, Induction Hypothesis and Induction
Step.1. Basis Step:
When n = 1, the left-hand side of the equation is 1 × 3 = 3. Putting n = 1 in the right-hand side of the equation we get:(2 x 1) + 1 / 1 = 3
Hence the Basis Step is verified.
2. Induction Hypothesis:
We assume that the equation holds true for some n = k. That is,1 × 3 + 3 × 5 + ... + (2k - 1)(2k + 1) = 2k + 1 / k3.
Induction Step: We need to prove that the equation holds true for n = k + 1. That is,1 × 3 + 3 × 5 + ... + (2k + 1)(2k + 3) = 2k + 3 / (k + 1)
Now adding (2k + 1)(2k + 3) on both sides of the equation in the Induction Hypothesis, we get:1 × 3 + 3 × 5 + ... + (2k - 1)(2k + 1) + (2k + 1)(2k + 3) = 2k + 1 / k + (2k + 1)(2k + 3) = 2k + 1 + (2k + 1)(2k + 3) / (k + 1)
Factorizing, we get:2k + 1 + (2k + 1)(2k + 3) / (k + 1) = (2k + 3)(k + 1) / (k + 1) = 2k + 3
Thus the Induction Step is verified. Hence proved that the equation1 × 3 + 3 × 5 + ... + (2n - 1)(2n + 1) = 2n + 1 / n is true. Therefore, this is a valid formula for the given equation.
The given formula satisfies the Basis Step, Induction Hypothesis, and Induction Step.
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please answer I need the answer!!
Answers
Answer:
They have different slopes but the same y-intercept, so they have one solution.
Step-by-step explanation:
Both equations are organized in slope-intercept form, y=mx+b. m is the slope and b is the y-intercept.
In the first equation, the slope is 1/2 and the y-intercept is -3.
In the second equation, the slope is -1/2 and the y-intercept is -3.
These two equations have different slopes, in fact, the second equation has the same slope except negative. This means that they travel with the same steepness but one goes up and the other goes down.
However, they have the same y-intercepts. This means that they both intercept the same point on the y axis. Wherever two equations intercept is their solution.
Therefore, these two equations have one solution.
I hope this helps!
As I am completely new to thisPlease, explain thoroughly on how to solve A step by step explanation on how to solve *in the simplest way possible would be amazing, thanks in advance
Answers
ANSWER:
D. 44
STEP-BY-STEP EXPLANATION:
The percentage of a number is calculated by multiplying the percentage number in its decimal form by the number whose percentage is to be calculated.
A percentage number is converted to a decimal by dividing that number by 100, so it would finally look like this:
\(\begin{gathered} p=1100\cdot\frac{4}{100} \\ \\ p=44 \end{gathered}\)So the correct answer is D. 44
Lance bought 15 sets of 3 tennis balls. Some of the tennis balls, t, were lost during each of the 4 matches he played. Now, the are 37 tennis balls left. Which equation represents this situation?
Answers
What operation do you use to solve for sales taxes?
O addition
O subtraction
O multiplication
O division
Answers
Answer:
multiplication
Step-by-step explanation:
Simplify 4^3* 4^5 please help me
Answers
Answer:
C.
Step-by-step explanation:
add the numbers (power numbers)
=4^8
Kala is driving on the highway. She begins the trip with 16 gallons of gas in her car. The car uses up one gallon of gas every 20 miles.
Let G represent the number of gallons of gas she has left in her tank, and let D represent the total distance (in miles) she has traveled. Write an equation relating G to D, and then graph your equation using the axes below.
Answers
Answer: G = 15-D/20
Step-by-step explanation:
Using the variables given,
G = 15 - D/20
A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend
Answers
Answer:
12 diffence
Step-by-step explanation:
Answer: he sold 96 in total
Step-by-step explanation:
The bike store marks up the wholesale cost of all of the bikes they sell by 30%. Andre wants to buy a bike that has a price tag of $125. What was the cost of this bike before the markup?
Answers
Answer:
$96.15
Step-by-step explanation:
Given data
markup = 30%
cost price= $125
let the cost price before markup be x
125-30/100*x= x
125-0.3x= x
125= x+0.3x
125= 1.3x
divide both sides by 1.3
x= 125/1.3
x= $96.15
Hence the price before markup is $96.15
Given P(A)=0.3, P(B)=0.57 and P(A and B)=0.251, find the value of P(B|A):, rounding to the nearest thousandth
Answers
The required value of probability P(B|A) is approximately 0.837.
As mentioned in the question,
P(A)=0.3, P(B)=0.57 and P(A and B)=0.251,
We can use the formula for conditional probability to find P(B|A):
P(B|A) = P(A and B) / P(A)
Substituting the given values, we get:
P(B|A) = 0.251 / 0.3 = 0.83667
Rounding to the nearest thousandth, we get:
P(B|A) ≈ 0.837
Therefore, the value of P(B|A) is approximately 0.837.
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Sue is shopping for a turkey. At Stater Bros., she found an 18 lb turkey for $21.42. At Ralphs, she found a 20 lb turkey for $24.20. At Food for Less, she found a 17 lb turkey for $18.36. Tasks: Find the price per pound of each turkey. Stater Bros.: Ralphs: Food for Less: Which store has the best price? Store name:
Answers
Answer: See explanation
Step-by-step explanation:
At Stater Bros., she found an 18 lb turkey for $21.42. The cost per pound will be:
= $21.42 / 18
= $1.19 / lb
At Ralphs, she found a 20 lb turkey for $24.20. The cost per pound will be:
= $24.20 / 20
= $1.21 / lb
At Food for Less, she found a 17 lb turkey for $18.36. The price per pound will be:
= $18.36 / 17
= $1.08 / lb
Based on the explanation, Food for Less has the best price as it's cheaper than others.
Match a term with its description or what process it describes in a raster data model
A. Groups of raster cells that are clustered to represent an area
B. When data take on values that can't appropriately be added and subtracted, or even ordered
C. When data take on a wide range of possible values which can be ranked or ordered
D. When pixel size is so large that multiple features may occur within one pixel
E. Individual raster cells
F. When a new layer is created with a different pixel size and/or pixel orientation
1. Mixed Pixel Problem
2. Resampling
3. Discrete
4. Continuous
5. Points
6. Polygons
------------------------------------------
Match the data characteristic with its matching definition
A. Resolution set by pixel size
B. Polygon defined by it's boundary lines
C. Data values represent themes or classes
D. Data values don't represent themes or classes
E. High resolution
F. Low resolution
1. Vector data
2. Raster data
3. Continuous entities
4. Discrete entities
5. Large scale
6. Small scale
Answers
Data Characteristics:
A. Resolution set by pixel size - 2. Raster data
B. Polygon defined by its boundary lines - 1. Vector data
C. Data values represent themes or classes - 4. Discrete entities
D. Data values don't represent themes or classes - 3. Continuous entities
E. High resolution - 5. Large scale
F. Low resolution - 6. Small scale
In the Raster Data Model, "Polygons" refer to groups of raster cells that are clustered to represent an area, while the "Mixed Pixel Problem" occurs when data take on values that can't be added, subtracted, or ordered appropriately.
"Continuous" describes data that can take on a wide range of possible values and can be ranked or ordered, whereas "Points" represent individual raster cells. "Resampling" refers to the process of creating a new layer with a different pixel size and/or pixel orientation.
Regarding Data Characteristics, in raster data, the resolution is set by pixel size, making it "Raster data." In contrast, polygons are defined by their boundary lines, representing "Vector data."
"Discrete entities" indicate that data values represent themes or classes, while "Continuous entities" imply that data values don't represent themes or classes. "High resolution" signifies a more detailed or fine-scale representation, while "Low resolution" indicates a less detailed or coarse-scale representation.
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The Rogers family and the Reed family each used their sprinklers last summer. The Rogers family's sprinkler was used for 15 hours. The Reed family's sprinkler was used for 30 hours. There was a combined total output of 1050L of water.
Required:
What was the water output rate for each sprinkler if the sum of the two rates was 45L per hour?
Answers
The water output rate for Reed's sprinkler is 25L/hour. We have to find the water output rate for each sprinkler if the sum of the two rates was 45L per hour. We know that the Rogers family sprinkler was used for 15 hours and the Reed family sprinkler was used for 30 hours.
Therefore the combined time the two sprinklers were used for was:15 + 30 = 45 hours
Therefore, The Rogers family's sprinkler output rate: r₁
The Reed family's sprinkler output rate: r₂
Given that the sum of the two rates was 45L per hour: r₁ + r₂ = 45 -----Equation (1)
Now, let's calculate the water output of each sprinkler using their respective times:
Water output of Rogers' sprinkler = r₁ × 15
Water output of Reed's sprinkler = r₂ × 30
The total output was 1050L:
r₁ × 15 + r₂ × 30 = 1050 -----Equation (2)
We have two equations and two variables. We will solve for r₁ and r₂ :
r₁ + r₂ = 45r₂ = 45 - r₁
Substituting the value of r₂ in equation (2), we get:
r₁ × 15 + (45 - r₁) × 30 = 105015r₁ + 1350 - 30r₁
= 1050-15r₁
= -300r₁
= 20r₂
= 45 - r₁
= 45 - 20 = 25
Therefore, The water output rate for Rogers' sprinkler is 20L/hour.
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Type the correct answer in the box. use numerals instead of words. a right cone is filled with ice cream such that the cone is filled completely but ice cream does not overfill the top. to determine how much ice cream will be in the cone, you approximate the diameter of the cone to be 2.5 inches and the height of the cone to be 5 inches. what is the approximate volume of ice cream in the cone, rounded to two decimal places?
Answers
The approximate volume of ice cream in the cone, rounded to two decimal places, is 16.36 cubic inches.
To calculate the approximate volume of ice cream in the cone, we can use the formula for the volume of a cone, which is given by V = (1/3) * π * r^2 * h, where V is the volume, π is a constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
In this case, we are given that the diameter of the cone is 2.5 inches, so the radius can be calculated as half of the diameter, which is 1.25 inches. The height of the cone is given as 5 inches.
Substituting these values into the formula, we have V = (1/3) * 3.14159 * (1.25)^2 * 5.
Evaluating this expression, we find V ≈ 16.36 cubic inches.
Therefore, the approximate volume of ice cream in the cone, rounded to two decimal places, is 16.36 cubic inches
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If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic ______ follows the t distribution with n-1 degrees of freedom
Answers
In summary, when repeated samples of size n are taken from a normal population with an unknown variance, the statistic t follows the t-distribution with n-1 degrees of freedom.
If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic t follows the t distribution with n-1 degrees of freedom. When a sample of size n is taken from a normal population with a known variance and mean, the sample mean follows a normal distribution with a mean of μ and a variance of σ2/n. This distribution is known as the sampling distribution of the mean.
However, when the variance is unknown, the sampling distribution of the mean can no longer be calculated using the normal distribution. In this scenario, the sample mean is calculated using a t-distribution instead of a standard normal distribution.The t-distribution is similar to the standard normal distribution. However, it is more spread out and flatter than the standard normal distribution. As a result, the t-distribution has thicker tails than the standard normal distribution, which makes it more suitable for analyzing small samples of data.
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In order to prove that a quadrilateral is a square specifically, we must show that it possess the properties of both a ________ and a _________.
triangle; trapezoid
rectangle; trapezoid
rhombus; trapezoid
rectangle; rhombus
Answers
Answer:
rectangle , rhombus
bsj
The difference of half of a number and three is equivalent to negative five? Also im doing some maze thingy, so the answer has to equal x=4, so can someone try and solve this with the answer as 4 please, l really need help.
Answers
Answer:
-4
Step-by-step explanation:
Try writing the question in variable form using x as "a number"
\(\frac{1}{2} x - 3 = -5\)
add 5 to the right side of the equal sign and then do the same thing to the left of the equal sign (do the opposite of the number to both sides)
\(\frac{1}{2} x +2 = 0\)
now we kind of do the same process but with the number 2. Subtract two from the left and right side
\(\frac{1}{2}x = -2\)
now since this equation is saying "multiply one half by x" we can do the OPPOSITE so now divide one half from both sides
\(x= \frac{-2}{.5}\)
NOTICE THAT I CONVERTED 1/2 to .5 they mean the same thing
so now just divide -2 by .5
the answer is -4