Answer:
The wood was cut approximately 8679 years ago.
Step-by-step explanation:
At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:
[tex]\frac{dm}{dt} = -\frac{m}{\tau}[/tex] (Eq. 1)
Where:
[tex]\frac{dm}{dt}[/tex] - First derivative of mass in time, measured in miligrams per year.
[tex]\tau[/tex] - Time constant, measured in years.
[tex]m[/tex] - Mass of the radioactive isotope, measured in miligrams.
Now we obtain the solution of this differential equation:
[tex]\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt[/tex]
[tex]\ln m = -\frac{1}{\tau} + C[/tex]
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (Eq. 2)
Where:
[tex]m_{o}[/tex] - Initial mass of isotope, measured in miligrams.
[tex]t[/tex] - Time, measured in years.
And time is cleared within the equation:
[tex]t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right][/tex]
Then, time constant can be found as a function of half-life:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (Eq. 3)
If we know that [tex]t_{1/2} = 5730\,yr[/tex] and [tex]\frac{m(t)}{m_{o}} = 0.35[/tex], then:
[tex]\tau = \frac{5730\,yr}{\ln 2}[/tex]
[tex]\tau \approx 8266.643\,yr[/tex]
[tex]t = -(8266.643\,yr)\cdot \ln 0.35[/tex]
[tex]t \approx 8678.505\,yr[/tex]
The wood was cut approximately 8679 years ago.
67
Name
_Michael Goodger Lesson 4 Homework
1.Convert and write an equation with an exponent.
A. 2 meters to centimeters
2m = 200 cm
2 x 10 = 200
B. 108 centimeters to meters 108 cm = 1 m
1.08% 101=108
C. 2.49 meters to centimeters 2.49 m = 249
cm
2.49x 103= 249
D. 50 centimeters to meters 50 cm = 1 m
50x1=50
E 6.3 meters to centimeters 6.3 m = 63 cm
6.3x63=63
F 7 centimeters to meters Icm = _
m
In the space below, list the letters of the problems where smaller units are converted to larger units.
2. Convert using an equation with an exponent. Use your meter strip when it helps you.
a. 4 meters to millimeters
mm
b. 1.7 meters to millimeters
mm
1050 millimetorn
m =
m =
Answer:
Step-by-step explanation:
1)
A. 2 meters to centimeters
1 m = 100 cm
[tex]2 m = 2 \times 100 \\2 m = 200 cm = 2 \times 10^2[/tex]
B)108 centimeters to meters
100 cm =1 m
[tex]1 cm = \frac{1}{100} m \\108 cm = \frac{108}{100}=108 \times 10^{-2} m[/tex]
C)2.49 meters to centimeters
1 m = 100 cm
[tex]2.49 m = 2.49 \times 100 = \frac{249}{100} \times 100 = 249 cm[/tex]
D)50 centimeters to meters
100 cm = 1m
[tex]1 cm = \frac{1}{100} m \\50 cm = \frac{50}{100}= 5 \times 10^{-1} m[/tex]
E)6.3 meters to centimeters
1 m = 100 cm
[tex]6.3 m = 6.3 \times 100=\frac{63}{10} \times 100 = 630 cm[/tex]
F)7 centimeters to meters
100 cm = 1 m
[tex]1 cm = \frac{1}{100} m\\\\7 cm = \frac{7}{100} = 7 \times 10^{-2} m[/tex]
2)
a)4 meters to millimeters
1 m = 1000 mm
[tex]4 m = 4000 = 4 \times 10^3 mm[/tex]
b)1.7 meters to millimeters
1 m = 1000 mm
[tex]1.7 m = 1.7 \times 1000= \frac{17}{10} \times 1000=17 \times 10^2 mm[/tex]
A cash register contains q quarters. Write an algebraic expression that represents the total amount of money (in dollars).
Answer:
0.25q
Step-by-step explanation:
A cash register is a machine used in small business that sums, display and records the total amount made by each sale. A cash register also has a drawer which is used to store money.
A quarter is a coin in the United States which is 25 cents.
Converting 25 cents to dollars:
100 cents = $1
25 cents = 25 cents × $1 / 100 cent = $0.25
The total amount of money registered = number of quarters × $0.25
The total amount of money registered = q × $0.25 = 0.25q
2+2=4 because 2 fingers and then another 2 fingers
Answer:
yes
Step-by-step explanation:
Answer:
yes? That's right. ummmm lol
Help ill give brainliest
Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.
4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?
A. The equation has one solution: x = 0.
B. The equation has one solution: x = 8.
C. The equation has no solution.
D. The equation has infinite solutions.
Answer:
C. no solution
Step-by-step explanation:
3x – 4 = 3x + 4
3x-3x=4+4
0=8
which is not possible.
So, it has no solutions.
You want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does increasing the sample size affect the size of the margin of error?
a. increasing n decreases E.b. increasing n increases E.c. increasing n will cause E to double in value.d. increasing n will not effect E.
Answer:
a. increasing n decreases E
Step-by-step explanation:
The sample size refers to the number (n) of units or observations taken from a population for a study. The results obtained from this sample size can be used to make generalizations about the entire population. The margin of error (E) is a measure of the sampling error or the percentage of the difference between the results obtained from the study and the true population value. The relationship between the sample size (n), and the Margin of error (E) is an inverse. That means
Sample size (n) ∝ 1/E
So, as the sample size increases, the margin of error decreases. This would be even more true if the accurate procedures for the experiment are followed.
How many 2/3 cup servings are in 28/3 cups of yogurt
The answer fam is..... 14
The living room of Ann's house is a square with an area of 121 square feet. What is the length of each side of the foyer
Answer:
30.25
Step-by-step explanation:
121 divided by 4 is 30.25
Please help me with this!
I will give you a thanks!
Which is equal to 0.63?
Answer:
63%
Step-by-step explanation:
A percentage is x/100. So 0.63 = x/100. So multiply by 100, and you'll get 63%.
Question 3 options: If 2y+13=y+5 then 2y + 1 = 3y + ___. What number would go in the blank? If you continued to solve, would y = - 14? state either yes or no
Answer:
Step-by-step explanation:
Given the expression 2y+13=y+5
To get the value of y, we willow the following steps:
Subtract 2y to both sides:
2y+13-2y = y+5-2y
13 = -y+5
subtract 5 from both sides:
13-5 = -y+5-5
8 = -y
-y = 8
multiply both sides by -1
-(-y) = -8
y = -8
Hence the value of y = -8 not -14
So NO,if you continue to solve, y would not be -14
Identify the terms, coefficients, and constants in the expression.
7h + 3
I need help now!!!!!
Step-by-step explanation:
7 is the coeffiecient
3 is the constant
1. A = {2, 4, 6, 8, 10), B = {1,2,3,4,5,6,7,8,9,10}
Find A UB and An B.
(7
Answer:
AUB=2,4,6,8,10 & AnB=1,3,5,7,9
PLEASE HELP!!! Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, l and the number of hours clearing tables, c, that Chloe can work in a given week.
Answer:
got u homie
Step-by-step explanation:
Answer:
l +c _> 12
Step-by-step explanation:
Selina didn't use the distributive property correctly. Where did she go wrong? Explain your thinking.
Answer:
PEMDAS
Step-by-step explanation:
Well, I don't know if there should be a picture of the problem that should go with the question. But a trick for solving distributive property is to use the trick PEMDAS In order.
For Example:
P-Paraenthese
E-Exponent
M-Multiply
D-Divide
A-Add
S-Subtract
NOTE!
Remember to always Multiply and divide BEFORE adding and subtracting.
Hoped this helped!
simplify these numbers
1. 125 5. 384
2. 458 6. 15710
3. 438 7. 2549
4. 10512 8. 8920
Help me plz
It’s 8th grade math
And ion know what the answer is..
Answer:
B slope = 1 and y intercept is 3
Step-by-step explanation:
The y intercept is where the line crosses the y axis (x is zero).
The slope can be figured by how far the line rises and runs to the next intersection of lines. In this case it goes up 1 and to the right 1. The slope would be 1/1 or 1
Answer:
Slope =1 ; Y-intercept=3
Step-by-step explanation:
The y intercept would be the point on the vertical line that touches the graph which in this case is three.
then to get to the next point that's on the line would have to move over 1 once to the right and one time up. so the slope is 1 over 1 which would equal 1.
The scatterplot and trend line show a positive correlation between advertising costs and sales.
Which two points can be used to find the slope of the trend line?
Point 1: ?
Point 2: ?
Answer:
Point 1: (6.4, 117)
Point 2: (6.6, 120)
Step-by-step explanation:
Answer:
Point 1: (6.4, 117)
Point 2: (6.6, 120)
Step-by-step explanation:
Please help
Trying to help daughter do virtual. And I stink in this stuff!
w(t) = 3t – 1; t = 5
what is 8 times 0.9 equal
Answer:
7.2
Step-by-step explanation:
Perform the indicated operation
3/4 divided by 1/3
Answer:
2 1/4
Step-by-step explanation:
3/4 ÷ 1/3 = ?
(to divide fractions faster you flip the second fraction so:)
3/4 x 3/1 = 2 1/4
You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?
Given:
You are given $893 in one, five, and ten dollar bills.
There are 165 bills.
There are twice as many five dollar bills as there are ones and tens combined.
To find:
How many bills of each type are there?
Solution:
Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.
According to the question,
Number of bills : [tex]x+y+z=165[/tex] ...(1)
Total amount : [tex]1x+5y+10z=893[/tex] ...(2)
Condition : [tex]y=2(x+z)[/tex] ...(3)
Equation (3) can be written as
[tex]\dfrac{y}{2}=x+z[/tex] ...(4)
Substituting [tex]x+z=\dfrac{y}{2}[/tex] in (1), we get
[tex]\dfrac{y}{2}+y=165[/tex]
[tex]\dfrac{3y}{2}=165[/tex]
[tex]3y=330[/tex]
[tex]y=110[/tex]
Substituting y=110 in (4), we get
[tex]x+z=\dfrac{165}{2}[/tex]
[tex]x+z=55[/tex]
[tex]x=55-z[/tex] ...(5)
Substituting y=110 and x=55-z in (2), we get
[tex](55-z)+5(110)+10z=893[/tex]
[tex]55-z+550+10z=893[/tex]
[tex]9z+605=893[/tex]
[tex]9z=893-605[/tex]
[tex]9z=288[/tex]
Dividing both sides by 9, we get
[tex]z=32[/tex]
Substituting z=32 in (5), we get
[tex]x=55-32[/tex]
[tex]x=23[/tex]
Therefore,
One dollar bills = 23
Five dollars bills= 110
Ten dollars bills = 32
Who’s good at 11 grade math pleasee help me comment o this :(
A government may create and regulate natural monopolies because:
Answer:
they can handle the costs of providing essential services
Step-by-step explanation:
A government may create and regulate natural monopolies because the government has the right to manage and regulate the resources available to the country in order to provide welfare and proper services to own citizens.
Given that,
A government may create and regulate natural monopolies because:,
The incomplete statement is to be complete.
An authority or claim controlled by the all-around people as the result of a constitution, law, ordinance, judicial precedent, or another type of law.
Here,
A government in any country has one motto rule of the country is to the people, for the people, and of the people. Whatever government does suppose to be for the welfare and proper livelihood in the country for its citizens. So in this manner,
Thus, a government may create and regulate natural monopolies because the government has the right to manage and regulate the resources available to the country in order to provide welfare and proper services to its own citizens.
Learn more about rights here,
https://brainly.com/question/8903161
#SPJ5
Help me with this question pleasee
Answer:
√23 = a
Step-by-step explanation:
/ab/²= /ac/²+/bc/² (Pythagoras theorem)
12² = a² +11²
144 = a² + 121
144 - 121 = a²
23 = a²
√23 = a
help me please !!!!!!!
Answer:
I don't see the screenshot and i'm not going to download it...
Step-by-step explanation:
yikes
Read 3 integer numbers from the user; these numbers represent the lengths of 3 straight lines. From the 3 lengths, determine whether a triangle can be formed with the corresponding lines. If it is possible to form a triangle, determine whether the triangle is a right triangle or not. The rules to be used are: 1. To form a triangle where all lines’ ends meet (form vertices), the sum of the lengths of two sides must be greater than the length of the third side. This short video illustrates this concept: How to determine if the three sides make up a triangle. 2. Per the Pythagorean theorem: in a straight triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. 3. The user can enter the lengths of each line in any order, i.e.: you may not assume that the first length is the longest or the smallest or the middle value.
Answer:
Written in Python
print("Enter three sides of a triangle: ")
length = []
for i in range(0,3):
inp = int(input(""))
length.append(inp)
length.sort()
if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:
print("Triangle")
if length[2]**2 == length[0]**2 + length[1] **2:
print("Right Angled")
else:
print("Not Right Angled")
else:
print("Not Triangle")
Step-by-step explanation:
This line prompts user for sides of triangle
print("Enter three sides of a triangle: ")
This line declares an empty list
length = []
The following iteration gets user input
for i in range(0,3):
inp = int(input(""))
length.append(inp)
This line sorts user input
length.sort()
The following if condition checks if user input is triangle
if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:
The following is executed is the if condition is true
print("Triangle")
The following if condition checks if user input forms a right angled triangle
if length[2]**2 == length[0]**2 + length[1] **2:
print("Right Angled")
else:
print("Not Right Angled")
This is executed if user input is not a triangle
else:
print("Not Triangle")
What is |-24| + |13| =?
Answer:
37
Step-by-step explanation:
just add the two numbers like they are not negative.
4x+2 = 2(2x+1) what is the answer?
Answer: 0=0
Step-by-step explanation: Simplify
w(t) = 3t – 1; t = 5
Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?
O Scale z by the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.
Answer: C
Step-by-step explanation:
I just took the quiz and I got it right
Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
What is Complex number?In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit
What is Modulus of a complex number?Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin
Given,
Complex number z divides by a second complex number w
To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction
From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w
Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
Learn more about Complex number and Modulus of a complex number here
https://brainly.com/question/19554199
#SPJ2