(1 point) Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in South Africa along with the remains of a campfire. Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire. Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.
Answers
Answer:
The estimated age of the skull is 39118 years.
Step-by-step explanation:
The amount of the substance after t years is given by:
\(A(t) = A(0)(1-r)^t\)
In which A(0) is the initial amount, and r is the decay rate.
The half-life of carbon-14 is about 5600 years.
This means that \(A(5600) = 0.5A(0)\). We use this to find r, or 1 - r, to replace in the equation. So
\(A(t) = A(0)(1-r)^t\)
\(0.5A(0) = A(0)(1-r)^{5600}\)
\((1-r)^{5600} = 0.5\)
\(\sqrt[5600]{(1-r)^{5600}} = \sqrt[5600]{0.5}\)
\(1 - r = (0.5)^{\frac{1}{5600}}\)
\(1 - r = 0.9999\)
So
\(A(t) = A(0)(0.9999)^t\)
Only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.
This is t for which \(A(t) = 0.02A(0)\). So
\(A(t) = A(0)(0.9999)^t\)
\(0.02A(0) = A(0)(0.9999)^t\)
\((0.9999)^t = 0.02\)
\(\log{(0.9999)^t} = \log{0.02}\)
\(t\log{0.9999} = \log{0.02}\)
\(t = \frac{\log{0.02}}{\log{0.9999}}\)
\(t = 39118\)
The estimated age of the skull is 39118 years.
Related Questions
If the Federal Reserve decreases the reserve rate from 10% to 8%, how does
this affect the amount of money that would result because of fractional-
reserve banking from an initial deposit into a bank of $40,000?
• A. It decreases the amount by $400,000.
•
B. It increases the amount by $400,000.
• C. It increases the amount by $100,000.
•
D. It decreases the amount by $100,000.
Answers
It increases the amount by $100,000. Therefore, option C is the correct answer.
What is percentage?A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
Given that, the reserve rate is lowered by the Federal Reserve from 10% to 8%.
Reserve=(Initial deposit of one account/Reserve rate)- (Initial deposit of other account/Reserve rate)
Reserve=(40,000/ 0.08)- (400,000/0.10)
Reserve=$500,000-$400,000
Reserve=$100,000 increase
Therefore, option C is the correct answer.
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anyone wanna bang?
Answers
Answer:
me
Step-by-step explanation:
Answer:
Yes pls
Step-by-step explanation:
im thirsty my guy
The population of a village is modeled by the function P(t) = 890e0.024t, where P is the population after t years. What does 890 represent?
Answers
Answer:
Initial Value
Step-by-step explanation:
Trust
Answer:
B
Step-by-step explanation:
Edge2020
Select the correct answer. Which expression is equivalent to the given expression? (6n^-5)(3n^-3)^2
Answers
The equivalenet expression is 54\(n^{-11}\)
What is expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
What is exponent?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.
Starting with:
(\(6n^-5\))(\(3n^-3\))²
We can simplify as follows:
(\(6n^-5\))(\(9n^-6\))
Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.
Therefore:
6 x 9 = 54
\(n^-5 * n^-6 = n^-11\)
So the simplified expression is:
\(54n^-11\)
Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)
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The expression that is equal to (6n-5)(3n-3) option D, 54n11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:
(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)
= 18n² - 18n - 15n + 15
= 18n² - 33n + 15
Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.
So, the answer is option D, 54n11.
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PV = $250,000 / (1+0.065)^1 + $37,500 / (1+0.065)^2 + $180,000 / (1+0.065)^3 + $300,000 / (1+0.065)^4 + $750,000 / (1+0.065)^5 + $725,000 / (1+0.065)^6
Answers
The given expression represents the present value of a series of future cash flows discounted at a rate of 6.5% per year.
Each term in the expression represents a cash flow at a specific time in the future, and the denominator in each term represents the discount factor, which reflects the time value of money.
The first term, $250,000 / (1+0.065)^1, represents a cash flow of $250,000 that will be received in one year.
To determine its present value, we divide it by the discount factor (1+0.065)^1, which reflects the fact that the money will be received one year from now and is, therefore, less valuable than money received today.
Similarly, the second term, $37,500 / (1+0.065)², represents a cash flow of $37,500 that will be received in two years.
To determine its present value, we divide it by the discount factor (1+0.065)²,
which reflects the fact that the money will be received two years from now and is, therefore, less valuable than money received today.
This process is repeated for each term in the expression, representing cash flows that will be received in three, four, five, and six years, respectively.
The sum of these present values represents the total present value of the cash flows or the amount that they are worth today if they are discounted at a rate of 6.5% per year.
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Mrs. Smith left a 15% tip for a dinner that cost $62.40. About how much tip did Mrs. Smith leave?
Answers
Given :-
Mrs. Smith left a 15% tip for a dinner that cost $62.40.To find :-
About how much tip did Mrs. Smith leave?Solution :-
The tip is 15% of $62.40 .
• Calculating 15% of $62.40
$ 62.40 * 15% $ 62.40 * 15/100$ 9.36Answer: $9.36 Tip and In total the cost would be $71.76 including the tip.
What is an equation of the line that passes through the point (2,-5)(2,−5) and is parallel to the line 6x+y=66x+y=6?
Answers
The equation of a line that passes through the point (2,−5) and is parallel to the line 6x + y = 6 is y = -6x + 7.
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard from and general form.
The equation of the line passes through (2,−5) and is parallel to the line 6x + y = 6.
Therefore, using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore, parallel lines have the same slope.
6x + y = 6
y = -6x + 6
The slope of the line is -6.
Let's find the y-intercept of the line using (2, -5).
y = -6x + b
-5 = -6(2) + b
-5 = -12 + b
b = -5 + 12
b = 7
Therefore, the equation of the line is y = -6x + 7.
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URGENT!!! Elementary school students were given a geometry assignment. They were to measure the area of several rectangles and to measure the diagonal of the rectangle as shown in the table.
The equation of the least-squares regression line is
ŷ = 3.6 + 0.113x, where ŷ is the diagonal and x is the area of the rectangle. Which shows the residual plot?
Answers
The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.
Please find attached the graph of the residual plot for the data created with MS Excel
What is a residual plot?A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.
The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158
The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;
Area (in²) \({}\) Residuals
x-value
5 \({}\) -1.0178
10 \({}\) -0.2718
24 \({}\) 0.605
46 \({}\) 0.7874
53 \({}\) 0.7018
78 \({}\) 0.0758
84 \({}\) -0.129
100 \({}\) -0.7538
The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option
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What is the next term in the pattern? 1,1,5,17,71,247
Answers
Answer: 1085
Step-by-step explanation:
A motorcycle can travel 500 miles on 25 gallons of gasoline. How far can it travel on 32 gallons of gasoline.
Answers
For us to be able to determine how far will 32 gallons of gasoline will go, we will be using ratios and proportions.
We get,
Let x = the distance it can travel at 32 gallons
\(\text{ 500 miles : 25 gallons = x : 32 gallons}\)\(\text{ 500 miles : 25 gallons = x : 32 gallons }\rightarrow\text{ }\frac{\text{ 500 miles}}{\text{ 25 (gallons)}}\text{ = }\frac{\text{ x}}{\text{ 32 (gallons)}}\)\(\text{ (500 miles)}(32)\text{ = (}x)(25)\)\(\text{ 16000 miles = 25x}\)\(\text{ }\frac{\text{16000 miles}}{25}\text{ = }\frac{\text{25x}}{25}\)\(\text{ x = }640\text{ miles}\)Therefore, 32 gallons of gasoline can make the motorcycle travel 640 miles.
An account pays 7% per year simple interest. In year 1, the amount in the
account is
$950. How much is in the account in year 6?
Answers
The amount in year 6 is $1282.5.
What is simple interest?
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given,
rate of interest = 7%
time = 1 year
Amount on first year = $950
First we will calculate simple interest for 5 years, because amount is available for 1 year.
SI =PRT
SI = 950(7/100)1
SI = $332.5
Therefore, the amount after 6 years = 950+332.5
=$1282.5
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Ashley completes 3 homework assignments in 50 minutes. At this rate, how many minutes will it take her to complete 9 homework assignments?
Answers
Answer:
144
Step-by-step explanation:
divide 50 by 3 and then multiply by 9
9=150
150=9000 minutes
A prince sent 10 hours riding on a horse at an average speed of 25 mph from his palace to the castle of a prince, a magic flying carpet. Both the Prince and the princess, back to his palace in 2 hours. Whatwas the speed of the of the magic carpet.
Answers
The correct value of speed of the magic carpet is 125 mph.
To determine the speed of the magic carpet, we can use the concept of average speed.
Let's first calculate the distance traveled by the prince on the horse. We can use the formula:
Distance = Speed × Time
The prince rode the horse for 10 hours at an average speed of 25 mph:
Distance = 25 mph × 10 hours = 250 miles
Now, let's calculate the distance traveled by the prince and the princess on the magic carpet. They traveled back to the palace in 2 hours. Since the distance is the same as before (250 miles), we can use the formula:
Speed = Distance / Time
Speed = 250 miles / 2 hours = 125 mph
Therefore, the speed of the magic carpet is 125 mph.
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the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answers
Answer:
To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.
Step-by-step explanation:
particle travels from(-1/3 ,1, -2) to(9,9,6) . Its motion is described by the position function r(t)=(t^3/3, t^2,2t).
a) Find the distance the particle travels along the path, its average speed, and its
displacement [the distance it could have traveled if in a straight line].
b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by
time) including curvature and torsion.
Answers
The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.
To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.
The velocity vector is the derivative of the position function r(t):
\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)
\(= (t^2, 2t, 2)\)
The speed of the particle at any given time t is:
|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)
= √(t^4 + 4t^2 + 4)
= √((t^2 + 2)^2)
To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.
distance = ∫[from -1/3 to 9] |v(t)| dt
= ∫[from -1/3 to 9] |t^2 + 2| dt
= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt
= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)
Evaluating the definite integrals:
distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]
= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]
= [1/27 + 2/3] + [729/3 + 18]
= 1/27 + 2/3 + 729/3 + 18
= 1/27 + 18/27 + 729/3 + 18
= (1 + 18 + 729)/27 + 18
= 748/27 + 18
= 27.63 + 18
= 45.63 units (approximately)
Therefore, the particle travels approximately 45.63 units along the path.
To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.
average speed = distance / time
= 45.63 / (28/3)
= 45.63 * (3/28)
= 4.9179 units per unit time (approximately)
The displacement is the straight-line distance between the initial and final positions of the particle.
displacement = |r(9) - r(-1/3)|
= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|
= |(27, 81, 18) - (-1/27, 1/9, -2/3)|
= |(27 + 1/27, 81
= 2781.
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A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long.If he paints 1/2 of the wall blue, how many square feet will be blue?
Answers
Which expression is equivalent to -2 1/4 divide -2/3?
Answers
Answer:
-9/4 divide (-2/3)
Step-by-step explanation:
When the moon blocks the sun's light ,a _____ eclipse occurs.
solar
lunar
full
partial
Answers
Answer:
solar
Step-by-step explanation:
What is the distance between the points (-2, 1) and(1,3) ?Round your answer to the nearest tenth
Answers
To answer this question we're going to need to use the distance formula, which is
d = √((x2 - x1)2 + (y2 - y1)2)
We are given two points:
(x1, y1) = (-2, 1)
(x2, y2) = (-5, 3)
d = √((-5 - (-2))2 + (3 - 1)2)
= √((-3)2 + (2)2)
= √(9 + 4)
= √(13)
≈ 3.6056
Since it says to round to the nearest tenth, the distance between the 2 points is
3.6 units
d=3.6
1. In this isosceles triangle, all the angles are equal. What is the measure of angle xº?
90
120
We need more information to solve
360
Answers
But I’ll try to help you with this problem. Here are two cases.
One, the problem is actually an equilateral triangle and all sides are indeed equal. The angles in a triangle adds up to 180 degrees. So if all angles are equal, divide 180 by 3 and you get 60. So all angles would be 60 degrees and so should x.
Two, the triangle is isosceles, we will cross out the rest of sentence one after the comma. Since there are no given information about the triangle and I believe the random numbers below the question are the choices, I will teach you how to do this problem. It’s easy. So we already know that a triangle adds up to 180, now we will take 180 and subtract it by the two given and known angles. The remaining number will be what x is.
Hope this helped, good luck!
A recipe for 12 cookies calls for 1 1/3 cups milk, 2 1/2 cups flour, and 1 3/4 cups other ingredients. How many cups of milk, flour, and other ingredients are needed to make 24 cookies?
Answers
i need this with the steps
Answers
3x>24
3/3x>24/3
x>8
i need help my people
Answers
Answer:
no
Step-by-step explanation:
If all of their coresponding angles will have the same measure (AAA Th. of symilarity) then thhey will be symilar
84.6+30.4+66=181 not 180
(-20,13) (16,15)
Can some find the slop for this question
Answers
Slope (m) = (y2 - y1) / (x2 - x1)
Given the points (-20, 13) and (16, 15), we can assign the coordinates as follows:
x1 = -20, y1 = 13
x2 = 16, y2 = 15
Now, we can substitute these values into the slope formula:
Slope (m) = (15 - 13) / (16 - (-20))
= 2 / 36
= 1 / 18
Therefore, the slope of the line passing through the points (-20, 13) and (16, 15) is 1/18.
Sera had the number 548.She adds one to the tens and two to the units. What number would Sera end up with??
Answers
The number she'd have is:
560Explanation:
First, let's see which number is in the tens place and which number is in the ones place (the units place).
In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).
So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :
550
That's not all, since we also add 1 to the tens:
560
Hence, Sera ends up with 560.81% of people surveyed own a smart phone. If 2,500 took the survey, how many of them own a smart phone?
Answers
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
For the polynomial below, 3 is a zero.
g(x)= x³ - 2x² - 5x + 6
Express g (x) as a product of linear factors.
Answers
The complete factorization of the polynomial is:
h(x) = (x - 3)*(x - 1)*(x + 2)
How to factorize the polynomial?Here we have the polynomial:
g(x)= x³ - 2x² - 5x + 6
And we know that x = 3 is a zero, then (x - 3) is a factor.
So if f(x) = a*x² + b*x + c
We can write:
h(x) = (x - 3)*f(x)
Let's find f(x).
Expanding that:
x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)
x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c
x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c
Comparing like terms, we can see that:
a = 1
b - 3 a = -2
c - 3b = -5
-3c = 6
With the first and last equation we can get:
a = 1
c = 6/-3 = -2
Now with one of these values and the second or third equation we can find the value of b.
b - 3 a = -2
b - 3*1 = -2
b - 3 = -2
b = -2 + 3 = 1
Then:
f(x) = x² + x - 2
The zeros of this quadratic function are given by:
\(x = \frac{-1 \pm \sqrt{1^2 - 4*1*-2} }{2} \\\\x = \frac{-1 \pm 3}{2}\)
x = (-1 + 3)/2 = 1
x = (-1 - 3)/2 = -2
Then we can factorize this as:
f(x) = (x - 1)*(x + 2)
And then we can write h(x) as:
h(x) = (x - 3)*(x - 1)*(x + 2)
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a triangular field has boundaries of lengths 170m,195m and 210m,find the size of the largest interior angle of the field
Answers
The size of the largest interior angle of the field is 69.86°
What is cosine law?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given that, a triangular field has boundaries of lengths 170m, 195m and 210m, we need to find the size of the largest interior angle of the field,
We know that, angle opposite to the largest side is largest,
Therefore,
The largest angle is opposite is 210 m side, (say c)
Using the cosine rule,
210² = 170²+195²-2(170)(195)cosC
CosC = 170²+195²-210² / 2(170)(195)
CosC = 22825 / 66300
CosC = 0.344268477
C = 69.86°
Hence, the size of the largest interior angle of the field is 69.86°
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Slope 3/5 yintercept2 write an equation slope-intercept form
Answers
The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.
To write the equation of a line in slope-intercept form, we use the formula:y = mx + b
where:
- y represents the dependent variable (the vertical axis)
- x represents the independent variable (the horizontal axis)
- m represents the slope of the line
- b represents the y-intercept, the point where the line intersects the y-axis.
In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:
y = (3/5)x + 2
This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).
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