The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.
Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.
Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.
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Give the domain and range of G.
Write your answers using set notation.
Domain of function = {-3 , -4}
Range of function = {4 , -1 , -4}
What is domain and range of a function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Given,
points on graph of a function are
(-3 , 4) , (-3 , -1) , (-4 , -4)
Range is set of y-values,
Range = {4 , -1 , -4}
Domain is set of x - values
Domain = {-3 , -4}
Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.
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A scenic train ride has one price for adults and one price for children. One family of two adult-
nd two children pays $62 for the train ride. Another family of one adult and four children pays
O. How much does it cost for one child to ride the train
Using simultaneous equations, the child ticket costs $18.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or at the same time.
Simultaneous equations are also known as a system of equations.
Family A Family B Total Cost
Adults 2 2 $62
Children 1 4 $70
Let the ticket cost per child = x
Let the ticket cost per adult = y
Equations:2x + 2y = 62 ... Equation 1
x + 4y = 70 ... Equation 2
Multiply Equation 1 by 2
4x + 4y = 124 ... Equation 3
Subtract Equation 2 from Equation 3:
4x + 4y = 124
-
x + 4y = 70
3x = 54
x = 18
= $18
From Equation 2, Substitute x = 18:
x + 4y = 70
18 + 4y = 70
4y = 52
y = 13
= $13
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Question Completion:Another family of one adult and four children pays $70.
in python, math expressions are always evaluated from left to right, no matter what the operators are. True/False ?
Work out the volume of the cuboid below.
Remember to give the correct units.
13 m
5m
13 m
3 m
Answer:
195m^3
Step-by-step explanation:
Volume of a rectangle = Length x Width x Height
L = 5m
W = 3m
H = 13m
V = 5m x 3m x 13m
V = 195m^3
(a) Latoya lost 60 dollars from her pocket.
Write a signed number to represent this change.
(b) A car corporation produced 1180 more cars this month than last.
Write a signed number to represent this month's change in production.
Answer:
-60, +1180
Step-by-step explanation:
if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet, what is the volume of the hole? use 22/7 for pi
The volume of the conical hole will be 154 cubic feet.
What is the volume of the cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,
The volume of the cone will be calculated as:-
Volume = (1/3)πr²h
The circumference of the cone is,
2πr = 44
2 x ( 22 / 7 ) x r = 44
r = 7 feet
The volume of the cone will be calculated as:-
Volume = (1/3)πr²h
Volume = ( 1 / 3 ) x ( 22 / 7 ) x 7 x 7 x 3
Volume = 22 x 7
Volume = 154 cubic feet
Therefore, the volume will be 154 cubic feet.
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Y<1/2x-7
Y>=-x-1
Point :(,)
From the inequalities y < (1/2)x - 7 and y ≥ -x - 1 graphed, a possible solution is the point (30, 2)
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Inequalities are used to show the non equal comparison of two or more numbers and variables.
Given the inequalities:
y < (1/2)x - 7 (1)
And:
y ≥ -x - 1 (2)
From the inequalities graphed, a possible solution is the point (30, 2) which is shown in the darker region
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Compare using >, <, or =
a. 5 thirds + 2 ninths _____ 1 9/8
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
The equation for this problem is this:
[tex]\frac{5}{3} + \frac{2}{9}[/tex] (> < =) [tex]1\frac{9}{8}[/tex]First, we need to find a common denominator between [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To find the common denominator, we can multiply the denominators, 3 and 9.
3 × 9 = 27Now we know that the two new fractions are going to have a denominator of 27.
[tex]\frac{?}{27} \frac{?}{27}[/tex]Now, we can use these equations to solve for the numerator.
9 × 5 = 453 × 2 = 6Now, the fractions look like this:
[tex]\frac{45}{27} \frac{6}{27}[/tex]To add them together, we can use this equation:
[tex]\frac{45}{27}+ \frac{6}{27} = \frac{51}{27}[/tex]Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.
What is an improper fraction?An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.
[tex]1\frac{9}{8}[/tex] = [tex]\frac{17}{8}[/tex]To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.
8 × 27 = 216The new fractions will look like this:
[tex]\frac{?}{216} \frac{?}{216}[/tex]To solve for the numerators, we can use these equations:
17 × 27 = 4598 × 51 = 408The fractions now look like this:
[tex]\frac{408}{216} \frac{459}{216}[/tex]Now, convert them to mixed numbers.
[tex]\frac{408}{216} = \frac{17}{9}[/tex][tex]\frac{459}{216} = \frac{17}{8}[/tex]Therefore, 5 thirds + 2 ninths < 1 9/8.
Albert Einsteen is experimenting with 2 unusual clocks which both have 24-hours displays. Once clock goes at
twice the normal speed. The other clock goes backwards, but at the normal speed. Both clocks show the correct time
at 13:00. What is the correct time when the displays on the clock next agree?
The correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.
Call the clock that runs forward A and the clock that runs backward B. Clock A will display the time as 13:00 at that moment, but clock B (which is going backward from 13:00) will display the time as 11:00.
Clock A will move two hours on its display in one hour since it is operating at twice the typical speed. Clock A will display 15:00 an hour from now, at 14:00. Additionally, because clock B is going backward, its display will read 10:00 an hour from now.
The clocks will next sync up when Clock A displays 13:00 (its initial beginning time) and Clock B displays 11:00, which takes place after 12 hours (12 hours on clock A, 24 hours on clock B).
So the correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.
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Phyllis invested $12,500, a portion earning a simple interest rate of
4 1/5%
per year and the rest earning a rate of 4% per year. After one year the total interest earned on these investments was $518.00. How much money did she invest at each rate
GEOMETRY
Find the volume of each figure. Round to the nearest tenth if necessary.
Vοlume οf the cylinder in will be 226.28 yd³, Vοlume οf Slanted cylinder is 141.37 in³ and Vοlume οf οblique cubοid is 1224 cm³.
What exactly is a cylinder?
In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance. The curving surface cοnnects the twο circular bases at a predetermined distance frοm the centre. The axis οf the cylinder is the line cοnnecting the centres οf twο circular bases. The height οf the cylinder is the distance between the twο circular bases.
A. Nοw,given that diameter οf base = 6 yd then radius=6/2=3 yd
and height will be =√10²-6² (By Pythagοras theοrem )
= √64
= 8 yd
then vοlume οf cylinder is=πr²h
= 22/7*3*3*8
= 1584/7
= 226.28 yd³
Hence, Vοlume οf the cylinder will be 226.28 yd³.
B. Vοlume οf Slanted cylinder is V = πr²h
V = π3²5
V = π × 3 × 3 ×5
V = 141.37 in³
Hence, Vοlume οf Slanted cylinder is 141.37 in³
C. Vοlume οf οblique cubοid is V = lwh
V = 17 × 18 × 4
V = 1224 cm³
Therefore ,Vοlume οf οblique cubοid is 1224 cm³.
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30 POINTS HELP PLEASE
i need help with both questions thank you!!!!
Answer:
see explanation
Step-by-step explanation:
(6)
given f(x) then - f(x) represents a reflection in the x- axis
given f(x) then f(x) + c represents a vertical translation of f(x)
• if c > 0 then a shift up of c units
• if c < 0 then a shift down of c units
thus g(x) = - | x | + 2
is a reflection over the x- axis and vertical shift up of 2 units
(7)
f(2) means value of f(x) when x = 2
x = 2 is in the interval x ≥ 2 with f(x) = [tex]\sqrt{x-2}[/tex] , then
f(2) = [tex]\sqrt{2-2}[/tex] = [tex]\sqrt{0}[/tex] = 0
pls all of them its urgent
The simplified forms of the fractions are 3 and -5 repectively
How do you simplify a fraction?To simplify a fraction, you divide both the numerator (top number) and denominator (bottom number) by their greatest common factor (GCF) until there are no more common factors. The result will be the simplified form of the fraction.
We have to note that;
1 ) 1 + 1/2 = 3/2
Then we have;
3/2 * 2/1 = 6/2 = 3
2) 3/4 - 2 = -5/4
Then we have;
-5/4 * 4/1 = -5
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Eric and Jennifer both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Eric has 20 signatures, but Jennifer just started and doesn't have any yet. Eric is collecting signatures at an average rate of 17 per hour, while Jennifer can get 19 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many signatures will they both have? How many hours will have gone by?
Answer:
10 hours would've gone by, and they have collected 190 signatures.
Step-by-step explanation:
Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?
The cost of the athletic shoe is $20 meanwhile the cost of the casual shoe is $35.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
Firstly, you should extract the main information of the question.
Athletic shoes= ACasual shoes = Cfor 20 pairs of athletic shoes and 10 pairs of casual shoes, the total cost is $750for 25 pairs of athletic shoes and 20 pairs of casual shoes, the total is $1200.Next, you should convert the given text information into equations. See below.
20A+10C=750 (1)
25A+20C=1200 (2)
From the substitution method, you can solve this question by following the steps below:
1) Multiply equation 1 by the number -2. Then, you have:
-40A-20C= -1500 (1)
25A+20C=1200 (2)
2) Sum the previous equations presented in step 1.
-15A=-300
15A=300
A=300/15
A=20
3) Find the variable C from equation 2. In step 2, you find A=20, thus.
25A+20C=1200 (2)
25*20+20C=1200
500+20C=1200
20C=1200-500
20C=700
C=700/20
C=35
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THIS IS THE OSHA 10-HOUR COURSE AND I NEED HELP WITH IT.
1. Remember not to use tools that are ________ in any way.
2. What should you do with corded tools when they are not being used?
3. This is the sudden release of electrical energy through the air when a high-voltage gap exists and there is a breakdown between conductors:
4. What electrical hazard is present in this image?
5. The longer you’re exposed to high noise levels, the more likely it is that ________ damage will occur.
6. In a situation where you expect to encounter airborne hazardous substances, but you don’t need skin protection, what level of full-body protection will you need?
7. Which of the following are struck-by falling hazards?
8. If you see an increase in traffic, step in and direct traffic to ensure safety. Is this a safe or unsafe practice?
9. In general, employers must provide fall protection to construction workers working on surfaces with unprotected sides and edges that are how many feet above the lower level?
10. When constructing a scaffold, there are specific criteria for the ________ the scaffold is built on.
11. Which of the following is the most dangerous factor among crane accidents?
12. An excavation is at risk for cave-in and water accumulation because of the excess soil that has accumulated. What type of excavation protection will address this situation?
13. Protect workers from cave-ins and other excavation-related hazards. Whose responsibility is this?
Answer:
1 harmful
Step-by-step explanation:
2 they will be not use if you not use
Which inequality represents eight less than three times a number is more than 22.
A. 3x - 8 > 22 B. 8 - 3X >22 C.3x - ≥ 22
Answer:
the answer of the equation is b
Which option is correct? Explain your working after choosing your answer
x^2 + 2x + 1
A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
B. This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
C. This polynomial could be factored only by using the perfect squares method.
D. This polynomial could be factored only by using the difference of squares method.
E. This polynomial could be factored by using grouping or the perfect squares methods.
F. This polynomial cannot be factored by any of the methods used in this lesson.
E. This polynomial could be factored by using grouping or the perfect squares methods.
How to factor the polynomialFrom the question, we have the following parameters that can be used in our computation:
x^2 + 2x + 1
Expand
x^2 + x + x + 1
Factorize the expression
(x + 1)(x + 1)
This gives
(x + 1)^2
Hence, the solution is (e)
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The price of 4 citrons and 3 fragrant wood apples is 34 units the price of 3 citrons and 4 fragrant wood apples is 29 units find the price of a cotton and the price of the wood apple
The price of one citron is 5 units and the price of one fragrant wood apple is 3.5 units." Let's call the price of one citron "c" and the price of one fragrant wood apple "w".
Using the information from the first equation:
4c + 3w = 34
Using the information from the second equation:
3c + 4w = 29
We can now solve the system of equations to find the value of "c" and "w".
Subtracting the second equation from the first:
4c + 3w - (3c + 4w) = 34 - 29
c = 5
Substituting the value of c back into one of the original equations:
3c + 4w = 29
3 * 5 + 4w = 29
15 + 4w = 29
4w = 14
w = 3.5
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Write 3 irrational numbers between 1.5 and 1.56.
1.511; 1.512 ;1.5113
Step-by-step explanation:
we know that there are infinite numbers.
and every decimal number is a rational number
now, extend the number upto 3 decimal or 2 decimal .
then it will become 1.500
there are numbers upto 1.599
like this we can extend upto infinite values
you can write infinite numbers, but question is asked for only 3
If $10,000 is deposited into a savings account that pays 1.8% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.
Answer:
Let's first calculate the amount of interest that would be earned if the interest were compounded annually. The formula for the future value of a single sum is:
F = P * (1 + r/n)^(nt)
Where:
F is the future value
P is the principal (the initial deposit)
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years
For our calculation, we have:
P = $10,000
r = 1.8% = 0.018
n = 1 (annual compounding)
t = 30
So, the future value of the account with annual compounding is:
F = $10,000 * (1 + 0.018/1)^(1 * 30) = $10,000 * (1.018)^30 = $21,784.08
Now, let's calculate the amount of interest that would be earned if the interest were compounded monthly. The formula for the future value of a single sum is the same, but we need to use the monthly compounding rate (r/12) instead of the annual rate and the number of months (12t) instead of the number of years:
F = P * (1 + r/n)^(nt)
Where:
F is the future value
P is the principal (the initial deposit)
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years
For our calculation, we have:
P = $10,000
r = 1.8% = 0.018
n = 12 (monthly compounding)
t = 30
So, the future value of the account with monthly compounding is:
F = $10,000 * (1 + 0.018/12)^(12 * 30) = $10,000 * (1.0015)^360 = $22,254.51
The difference in the two future values is $22,254.51 - $21,784.08 = $470.43.
So, the account would be worth $470.43 more if interest were compounded monthly rather than annually over a period of 30 years. Round to the nearest dollar, the answer is $470.
Step-by-step explanation:
Find the monthly payment for a 25-year, the ballon mortgage for 375,000 at an APR of 4.5% . What will be their total interest charges after 25 years? Round to the nearest whole number?
The total interest charger after 25 years for the balloon mortgage would be = $421, 875
What is simple interest?Simple interest is the additional sum of money that is paid to a person after a sum of money was invested for a specific amount of time.
Given:
The principal= 375,000
The time for the mortgage = 25 years
The rate = 4.5%
The formula for simple interest
= P×T×R/100
= 375,000×4.5×25/100
= 42187500/100
= $421, 875
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4. Determine the kinetic energy of 1500 kg pick-up truck traveling at 31.0 m/sec. Show work thanks
Answer:
Step-by-step explanation:
The formula for kinetic energy is:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
We are given the mass of the pick-up truck as 1500 kg and its velocity as 31.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:
KE = (1/2) * m * v^2
= (1/2) * 1500 kg * (31.0 m/sec)^2
= (1/2) * 1500 kg * 961.0 m^2/sec^2
= 720750 J
Therefore, the kinetic energy of the pick-up truck is 720750 Joules.
r
Step-by-step explanation:
v
Pls help
And approximate solution to an equation is found using the itiretative formula
X _n+1 = (x_n)^3 -2 / 10 with x_1 = -1
On solving the provided question, we can say that the equation we have here is[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] at [tex]x_1 = -1[/tex] n = 0 , [tex]x_1 = \frac{-3}{10}[/tex]
What is an equation?Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality.
A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14.
The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol.
A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. Equations in this category include a variable, which is typically expressed as x or y. Simple equations often need to be rearranged in order to be solved.
the equation we have here is
[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] , at [tex]x_1 = -1[/tex]
n = 0
[tex]x_1 = \frac{-3}{10}[/tex]
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Nate wants to buy a CD for $1000 that earns 3% APR and is compounded
quarterly for 5 years. He will be taxed on 20% of the interest that he earns.
What is the total amount of interest Nate will earn, after taxes?
O A. $40. 96
O B. $51. 20
O c. $161. 18
O D. $128. 94
SUBMIT
Help apex!
D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000 The formula for compound interest is:
A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.
We can use this formula to calculate the amount of money Nate will have after 5 years:
A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9
The interest earned is 1162.9 - 1000 = $162.9.
And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.
So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.
Therefore, the correct answer is D. $128.94.
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solve for x
-1 + 6x < 5
[tex]-1+6x < 5[/tex]
Simplify:
[tex]6x-1 < 5[/tex]
Add 1 to both sides:
[tex]6x-1+1 < 5+1[/tex]
[tex]6x < 6[/tex]
Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]
[tex]\boxed{x < 1}[/tex]
Triangle A B C. The length of side A C is 10, B C is 6, and A B is 8. Triangle A prime B prime C prime. Side A prime C prime has a length of 5.
Triangle ABC is dilated to get triangle A'B'C'. Which is the length of A'B'?
Options:
3
4
5
16
The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.
What is scale factorScale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.
The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5
side A'B' = 8 × 1/2
side A'B' = 4
Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.
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Answer:
the answer is B, 4. :)
[tex]x^{3} +8 / x-2[/tex]
Answer:
[tex] {x}^{4} - 2x + 8 \div x[/tex]
) You spin the spinner once.
6
5
7
2
Submit
3
What is P(greater than 2)?
) Write your answer as a fraction or whole number.
The value of P(Greater than 2) is 0.75
How to evaluate the probabilityFrom the question, we have the following parameters that can be used in our computation:
Spinner = 6 5 7 2
Using the above as a guide, we have the following:
Greater than 2 = 3
Total = 4
The probability is
P = Greater than 2/Total
Substitute the known values in the above equation, so, we have the following representation
P(Greater than 2) = 3/4
Evaluate
P(Greater than 2) = 0.75
Hence, the solution is 0.75
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Carbon-14 has a half-life of 5700 years. Scientists use this fact to determine the age of things made of organic material. Suppose the average page of a book containing approximately 0.5 mg of carbon-14 is put into a time capsule.
a. Write an exponential function where x is the number of 5700 year periods and y is the amount of carbon-14.
b. Find the amount of carbon-14 after 11,400 years.
a. an exponential function where x is the number of 5700 year periods and y is the amount of carbon-14 is: y = a (b)^(x/h)
b. the amount of carbon-14 after 11,400 years is 0.25 mg
What is half-life?The amount of time needed for a procedure to affect half of anything, such as the amount of time needed for a radioactive substance's atoms to split in half. The half-life of a radioactive sample is the amount of time needed for half of its atomic nuclei to spontaneously decay, which releases energy and particles, or, alternatively, the amount of time needed for the radioactive sample to disintegrate 60 times every second.
a.
y = a (b)^(x/h)
here, y = amount of carbon-14
a = initial amount
b = final amount
x = time elapsed
h = half life
b. we know that half of it will change into another form in 5700 years, Therefore, if start with 0.5 mg, that would be half in 5,700 years, or 0.25 mg in 11,400 years, which is another half life.
Thus, the amount of carbon-14 after 11,400 years is 0.25 mg
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