Answer:
1) There are 100 carbon-14 atoms in the wood when it died
2) A function that models the number 'N' of carbon-14 atoms present in the wood (t) years after it died is presented as follows;
[tex]N = 100 \times \left (\dfrac{1}{2} \right )^{\dfrac{t}{5,730} }[/tex]
Step-by-step explanation:
The given parameters are;
The number of carbon-12 for each carbon-14 atom ≈ 10¹² carbon-12 atoms
The number of carbon-12 in the piece of wood = 10¹⁴ carbon-12 atoms
The number of carbon-14 in the piece of wood = 40 carbon-14 atoms
The number of carbon-12 in an organism = Constant
The number of carbon-14 in an organism = Decays
1) Given that the number of carbon-12 in an organism is constant, and there are 10¹² carbon-12 atoms per each carbon-14 atom, therefore, we have;
The number of carbon-12 atoms in the wood when it died = 10¹⁴ carbon-12 atoms
The number of carbon-14 atoms in the wood when it died = (10¹⁴ carbon-12 atoms)/(10¹² carbon-12 atoms/(carbon-14 atom)) = 100 carbon-14 atoms
The number of carbon-14 atoms in the wood when it died = 100 carbon-14 atoms
2) The half life of a radioactive isotope is given by the following formula;
[tex]N(t) = N_0 \cdot \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{\frac{1}{2} }} }[/tex]
The half life of carbon-14 atoms, [tex]t_{\frac{1}{2} }[/tex] ≈ 5,730 years
N₀ = The amount of carbon-14 present in the wood when it died = 100 carbon-14 atoms
Therefore, we have;
The number, N, of carbon-14 atoms present in the wood (t) years after it died is given as follows;
[tex]N = 100 \times \left (\dfrac{1}{2} \right )^{\dfrac{t}{5,730} }[/tex]
What is the distance from -36 to 36 on a number line?
Answer:
The distance is 20
Step-by-step explanation:
8 - 4+ (3 · 6)2 =
E. 22
F. 112
G. 328
Answer:
Step-by-step explanation:
8 - 4+ (3.6)2
= 8 - 4 + 7.2
= 11.2
hope it helps :)
Calculate the value
of the unknown
coefficient b of a
quadratic equation
when the
discriminant of that
equation is known.
3x² + bx + 2 = 0; Coefficient = 12
Answer:
The value of b is either + 6 or -6
Step-by-step explanation:
Here, given that we have the value for the discriminant, we want to calculate the value for the coefficient of x
mathematically, the discriminant can be calculated using the equation;
D = b^2 - 4ac
a represents the coefficient of x^2 which is 3
b represents the coefficient of x given as b
2 represents the last number
D is the discriminant = 12
So we have that;
12 = b^2 - 4(3)(2)
12 = b^2 - 24
b^2 = 24 + 12
b^2 = 36
b = √36
b = +6 or -6
The dimensions of an ancient Egyptian rug are 6 feet by 8 feet. Priscilla is creating a drawing of the rug with the scale 4 cm = 1 ft. What are the dimensions of Priscila's drawing in cm?
Answer:
12 x 18 CM.
Step-by-step explanation:
Because 3 cm is 1 ft so if it is 4 you multiply that by 3 which equals 12 , and for 6 feet you multiply that by 3 cm and get 18. SO it is 12 x 18 cm.
What is BD? Plzzzsss Helppp
Answer:
Step-by-step explanation:
since the two angles are the same we can set up a relationship between the two triangles and set them equal to each other and solve for X :) , as follows
SOH sin = Opp / Hyp
triangle 1 ) sin(Ф) = x / 12
triangle 2 ) sin(Ф) = x + 5 / 27
since sin(Ф) is the same for each triangle.. set those other sides equal to each other
x/12 = x+5 /27
now solve for x using your mad algebra skilz :P
27 / 12 = x + 5 / x
2 3/12 = x/x + 5/x
2 1/4 = 1 + 5/x
1 1/4 = 5/x
x = 5 / 1 1/4
x = 4 nice :)
So BD is then
4 + 4+5
so BD = 13
tell your professor / teacher that you figured it out all on your own :D
( yes.. that was tricky to figure out )
4. Which expression is equivalent to - (6x + 9) - (x - 2)?
A. 5x - 3
B. - 2x + 7.5
C. -4x - 3
D. -4x - 6
is this correct (random words because brainly is mhm
Answer: this is correct
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
The transformation of the shape is most definitely correct.
expand 2x(5x+4) please
Answer:
10x²+8x
Step-by-step explanation:
times everything in the bracket by 2x
What is the volume???
Answer:
First find out the other side measurements. Then split the shape into seperate squares and find the area then add them all up.
Step-by-step explanation:
volume is length × width × height.
Answer:
240 cm cubed
Step-by-step explanation:
If you separate the shape into 2 figures, the first figures area is 180
and the second is 60.
180 + 60 = 240
Hope this helps!
which letter would be the most meaningful variable for the problem situation the weight of a box increase by 5
Answer:i
Step-by-step explanation:
What is the area of this
what can you double and then add -6 to get -16
Answer:
- 5
Step-by-step explanation:
let the number be n then double is 2n , so
2n + (- 6) = - 16
2n - 6 = - 16 ( add 6 to both sides )
2n = - 10 ( divide both sides by 2 )
n = - 5
The number is - 5
Need help plzzzz ??????????????
A car is purchased for £11 500 In its first year, the value of the car will depreciate by 15%. Each year after that, the value of the car will depreciate by 10%. What is the value of the car at the end of 3 years?
Answer:
Value of the car at the end of 3 years is £7917.75
Step-by-step explanation:
The car is purchased for £11500.
In the first year, 15% depriciation.
So, depreciation on first year =11500 *[tex]\frac{15}{100}[/tex] =1725
After first year depreciation the value of car =11500-1725 =£9775
Now, second year depreciation is 10%
So, 10% of 9775 =0.10*9775 =977.5
Value of car after 2 years = 9775 -977.5 =8797.5
Now, for third year depreciation is 10%.
So, depreciation on 3 year = 10% *8797.5
=0.10*8797.5
=879.75
So, value of car after 3 years = 8797.5 -879.75 =£7917.75
What is the range of the function shown in the graph?
у
A
8
6
4
2
-8
f
- 2
X
4
6
8
-2
-4
-64
-8-1
Answer:
A
Step-by-step explanation:
The range of the given function from the given graph are: all values of y that are greater than or equal to -3. Therefore, the correct option is option D.
What is range of function?It is seen to be best practice to define the word "range" the first time it appears in a book or article because it might have several different meanings. When the word "range" is used in older literature, it frequently refers to what is today known as the codomain.
If more recent texts use the phrase "range" at all, they typically do so to refer to what is now known as the image. Several contemporary novels shouldn't use the term "range" at all to avoid any misunderstandings.
A function's range is the set of each of its potential outputs1,2,3,4. That's the output that the function generates when all of its inputs are used3,5. The range of the given function from the given graph are: all values of y that are greater than or equal to -3.
Therefore, the correct option is option D.
To know more about range of function, here:
https://brainly.com/question/29051369
#SPJ7
Your question is incomplete but most probably your full question was,
What is the range of the function shown in the graph?
. In a school 58of the students are boys. If there are 240 girls. Find the total number students in the school
Identify two segments that are marked congruent to each other on the diagram below. ANSWER CORRECTLY !!!!!!!!!! WILL
MARK BRIANLIEST !!!!!!!!!!! (three capital letters each)
Answer:
IM and JM
Step-by-step explanation:
They both have congruency marks that correspond to each other, indicated by the three short lines in the middle of each.
Does the table below represents a linear function why or why not
Answer:
No, it's not linear function.
Step-by-step explanation:
The x value repeatedly adds 3.
So far its a linear function.
If you look at the y value, it does NOT have a pattern, therefore that means it is NOT a linear function.
Nakato Nobuki, a Japanese artist, intends to withdraw $ 24,000.00 from his savings at the end of 5 years. Mr. Nobuki deposits $ 1,500.00 in savings annually and today has a balance of $ 8,000.00. What should be the savings interest rate for Nobuki to achieve his goals?
Answer:
The savings interest rate of Nakato Nobuki is 3 %
Step-by-step explanation:
Given;
Final amount of Nakato Nobuki, A = $ 24,000.00
time period of his investment, t = 5 years
principla amount, P = $ 1,500.00
The savings interest rate of Nakato Nobuki can be calculated on a simple interest basis.
A = P(1 + rt)
r is the savings interest rate
Substitute the given values and solve for r
24,000 = 1,500(1 + 5r)
24,000 = 1,500 + 7,500r
7,500r = 24,000 - 1,500
7,500r = 22,500
r = 22,500/7,500
r = 3 %
Therefore, the savings interest rate of Nakato Nobuki is 3 %
Solve using Square Roots.
16x² - 34=15
Answer:
[tex]\sqrt{\frac{49}{16}[/tex]
Step-by-step explanation:
The area of a bookmark is 140 square centimeters. The perimeter is 54 centimeters. What are the dimensions of the bookmark?
Answer:
See explanation
Step-by-step explanation:
Recall that all the sides of the square are equal
Hence;
Area of a rectangle= l * b ------- equation 1
Perimeter of a rectangle = 2(l + b)----------equation 2
Area of the rectangle = 140 square centimeters
140 = lb
l = 140/b
Perimeter of the rectangle = 54 centimeters
substituting l = 140/b into equation 2
54 = 2(140/b + b)
Multiplying through by b
54b = 280 + 2b^2
Hence;
2b^2 - 54b + 280 = 0
Solving the quadratic equation
b=20 or b=7
substituting b=20 or b=7 into l = 140/b
l = 140/20 or l = 140/7
l = 7 or 20
THEREFORE;
b=20 cm or b=7 cm
l = 7cm or 20cm
The chess club has a budget of at least $300 that the members can spend for the field trip. There are 20 people in the chess club. They get a discount of $60 for transportation for the field trip. What is the minimum that each member
of the chess club can spend on the trip?
Answer:
$12
Step-by-step explanation:
We are told that there are 20 people in the chess club and each got a discount of $60 for transportation on the field trip.
Let the amount spent by each member is x
Since there are 20 of them and the budget is at least $300 and they get a discount of $60, it means that;
20x ≥ 300 - 60
20x ≥ 240
Divide both sides by 20 to get;
x ≥ 12
Thus, minimum amount each member can spend is $12.
pls help i will rate u 5 stars and possibly mark u brainless HELP PLS.
Can someone pls help me asap!!!
Answer:
balloons
Step-by-step explanation:
to make it easier,there are only four tradic colors combination on basic color wheels Red,Yellow,Blue,
Write an integer to match the following descriptions. a. A debit of $40 b. A deposit of $225 c. 14,000 feet above sea level d. A temperature increase of 40°F e. A withdrawal of $225 f. 14,000 feet below sea level
Glee
Hehehejdjjdhchchhdhd
What is the first step to solving the equation 12 - y = 18?
Answer:
subtract 12 from 18
Step-by-step explanation:
Answer:
No real "first step" as there are many ways to do it. If I were to do it, I would add the y to the other side to make it positive. This thus eliminates any negative variables in the equation
Step-by-step explanation:
ez
AABC = AGHL Complete the congruence statement AB =
Answer:
AB = AH
Step-by-step explanation:
Hope This Helps!!
Help please I really need help, thank you
Answer:
What do you need help with? Answer and I will tell you anything you need.
Step-by-step explanation:
Who watching temptation island, The oval and Ruthless tonight?
Answer:
MMEEEE but im SOOO behinnnd
Step-by-step explanation:
Answer:
Not me sorry.
Step-by-step explanation:
A basketball shaped like a sphere has a diameter of 8 inches. Which measurement is
to the volume of the basketball in cubic inches?
Answer:
268
Step-by-step explanation:
The volume formula for a sphere is: V= [tex]\frac{4}{3}\pi r^{3}[/tex]
We also know that [tex]\pi[/tex] is approximately 3.14.
You have to know these in order to solve the question..
Since we also know the diameter is 8 we can also find the radius (r) ,which is half of the diamater so 4.
Now all we need to do it plug in the numbers.
V= [tex]\frac{4}{3}[/tex](3.14)[tex]4^{3}[/tex]
Now solve for the equation.
V=267.94...
So rounded that is 268.