A support pole for an ancient structure is found to have one-sixth of the carbon-14 of a modern, living tree. How long ago did the tree used to make the support pole die? Give your answer to the nearest whole number. (Assume that half-life of carbon-14 is 5770 years.)
Answers
14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.
Assume that the half-life of carbon-14 is 5770 years
As per the given condition, the expression would be
\(A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}\)
\((0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\)
\((0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}\)
Take the logarithms of both sides to get:
\(log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}\)
Using logₐ(xⁿ) = n logₐx.
⇒ log 0.167= (t/5770) log (0.5)
⇒ log 0.167/ log (0.5)= (t/5770)
⇒ 3 = (t/5770)
⇒ t = 3 × 5770
⇒ t = 14912
Hence, 14912 years ago, the tree that was used to kill the support pole died.
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Related Questions
If the graph of y = - x ^ 2 translated horizontally 7 units to the right and translated vertically 6 units upwards, what’s the new equation?
Answers
9514 1404 393
Answer:
y = -(x -7)² +6
Step-by-step explanation:
Replacing x with (x-h) translates the graph h units to the right. You want h=7.
Replacing f(x) with f(x)+k translates the graph k units upward. You want k=6.
These transformations make the new equation be ...
y = -(x -7)² +6
I need help can you help me please
Answers
Answer:
with i cant see the problem so i dont lnow
find the inverse of each function
Answers
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
\( \frac{1}{ log(y) } = x\)
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
show that the volume of the unit cube is one
Answers
Check the picture below.
1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
10 points: Write the vertex form equation for g(x) below.
Answers
A graph of f(x) is shown in the image below.
A graph of f(x) is shown in the image below.
The vertex form equation for g(x) is g(x) = -x²
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;
f(x) = (x + 3)² - 2
g(x) = -[(x + 3 - 3)² - 2 + 2]
g(x) = -x²
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WHAT IS THE AVERAGE OF -2.5, 5.2, 1.7, -0.8?
Answers
-2.5 + 5.2 + 1.7 + (-0.8) = 3.6
3.6 / 4 = 0.9
Answer:
0.9
Step-by-step explanation:
-2.5 + 5.2 + 1.7 + -0.8 = 3.6
3.6 / 4 = 0.9
the current l in an electrical current conductor varies inversely as the resistance R of the conductor. the current is 1/3 ampere when the resistance is 1701 ohms. what is the current when the resistance is 9261 ohms
Answers
Answer:
Step-by-step explanation:
V=IR
V=1/3×1701=567
567=IR
567=9261 I
I=567/9161
x = 13, ¿cuál ecuación es verdadera?
3(18 - x) = 67
4(9x) = 23
2(x-3)=7
5(x-9) = 20
Answers
When x = 13, the equation that is true is option D) 5(x - 9) = 20.
To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:
A) 3(18 - x) = 67
Substituting x = 13:
3(18 - 13) = 67
3(5) = 67
15 = 67
The equation is not true when x = 13. Therefore, option A is false.
B) 4(9x) = 23
Substituting x = 13:
4(9*13) = 23
4(117) = 23
468 = 23
Again, the equation is not true when x = 13. Therefore, option B is also false.
C) 2(x - 3) = 7
Substituting x = 13:
2(13 - 3) = 7
2(10) = 7
20 = 7
Once again, the equation is not true when x = 13. Therefore, option C is false as well.
D) 5(x - 9) = 20
Substituting x = 13:
5(13 - 9) = 20
5(4) = 20
20 = 20
Finally, the equation is true when x = 13. Therefore, option D is true.
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Note: the translated questions is
X = 13, which equation is true?
What is the value of X in this question?? I need help please!
Answers
Answer:
The value of x would be 23
Step-by-step explanation:
You must first find the angles of triangle CDE. So to find angle C you must know that a straight line is equal to 180 degrees, 180-117=63 So angle C would be 63 degrees. Angle D is congruent to Angle B so Angle D would equal 24 Degrees. Then to find the angle of Angle E simply subtract 87 from 180 (You Get 87 From Adding 24 and 63), 180-87=93. Know that you know that Angle E is 93 Degrees set up the equation, 4x+1 = 93 SOLVE.
4x+1=93
4x = 92
x = 23.
Riley is saving up to buy a new television. She needs a total of $1,200.17 Riley has saved $200.34 already and earns $76.91 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answers
To enable Riley to save up to buy a new television priced $1,200.17, and since he already has $200.34 saved and earns $76.91 per week at her job, she needs to work for 13 more weeks.
How is the amount determined?To determine the number of weeks Riley has to work to earn enough to buy the new television, we apply the mathematical operations of subtraction and division.
Subtraction and division are two of the four basic mathematical operations, including addition and multiplication.
The total amount that Riley requires = $1,200.17
The amount of savings Riley already has = $200.34
The remaining amount that Riley needs to earn = $999.83 ($1,200.17 - $200.34)
Riley's earnings per week = $76.91
The number of weeks Riley needs to work to save enough money = 13 weeks ($999.83 ÷ $76.91)
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write a story problem to represnt 3÷1/2
Answers
Answer:
Story in Explanation
Step-by-step explanation:
There are three different types of sandwiches available for you and your friend to eat. They all look yummy, and you and your friend decide to get half of every sandwich. When you cut sandwiches in half, how many do you now end up with?
Determine if the ordered pair (6, 4) is a solution to the inequality y is greater than negative one half times x plus 7. Yes, because (6, 4) is above the line No, because (6, 4) is below the line Yes, because (6, 4) is on the line No, because (6, 4) is on the line
Answers
Answer:
No, because (6, 4) is on the line
Step-by-step explanation:
y>-1/2(x)+7
4>-1/2(6)+7
4>-3+7
4>4
15 greater than y is at least 150 interval notation
Answers
Step-by-step explanation:
I think this is the ans and I have got this ans from brainly.
Michelle had 7 paperback books and 4 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books
Answers
Answer:
7:4 that would be the ratio
Lydia is organizing a cooking competition at her school. She ordered some basic supplies to share among the teams that are competing.
The teams will be bringing other ingredients as well.
Use the list at the right to answer the questions.
1. If 10 of the teams divide the olive oil equally, how
much will each team receive? Write an equation
to model your work.
738.4 grams, flour
8.25 liters, milk
5.4 liters, olive oil
87.6 grams, salt
36 eggs
Answers
The equation to model the given work is 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.
The teams will share 5.4 liters of olive oil. To find out how much each team will receive, we can divide the total amount of olive oil by the number of teams:
5.4 liters ÷ 10 teams = 0.54 liters per team
However, it's usually more convenient to express this in grams for equation, so we need to convert liters to grams.
The conversion factor for olive oil is approximately 0.92 grams per milliliter (or 920 grams per liter). So, we can multiply 0.54 liters per team by 920 grams per liter to get:
0.54 liters per team × 920 grams per liter = 497.28 grams per team
Therefore, each team will receive 497.28 grams of olive oil as per the work.
Equation: 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.
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Select all the expressions that are equal to 1/6
Answers
The equivalent expression will be 2 / 12 and 6 / 36.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that the fraction is 1 / 6. The equivalent expression to 1 / 6 will be calculated as:-
To calculate the equivalent expression solve the given expressions and check whether they are equivalent to 1 /6 or not,
2 / 12 = 1 / 6
6 / 36 = 1 / 6
Therefore, the equivalent expression will be 2 / 12 and 6 / 36.
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Rasberry Crazy Ants, a species found in wall sockets, cellphones, and television sets are
slowly spreading across Texas and are poised to spread across the entire South. Named for
Texas exterminator Tom Rasberry, who spotted ants moving in an erratic swarm in 2002,
the destructive ants are now in 23 counties in Texas, the Austin American-Statesman
recently reported. Although their march in impossible to stop, it is also quite slow. They travel at an average speed of 1.8 feet per day.
a. At that rate, how long will the swarm that is presently centered in Austin, Texas, take to reach your home? Express your answer in the timeframe that is most appropriate.
b. Do you need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren? Explain why or why
not.
Answers
The average time taken to travel to Toronto by the swarm of Rasberry Crazy Ants is 12,947 Years
What is the calculation for the above Solution?To arrive at the solution above, we need to look at the information given and the information assumed.
Step 1 - Information given:
Step 2 - Information assumed:
The swarm are travelling to the location of the student which is assumed to be Toronto.
Hence,
Time taken for the swam to get to Toronto (TTS) =
Distance between Austin, Texas and Toronto (DBTT) / Average distance covered per day by the Rasberry Ants. (ADC)
Estimated distance between Austin Texas and Toronto = 2592.6 Kilometers
Time travelled per day by the ants (In Km) = 0.00054864
Thus,
TTS = DBTT/ADC
= 2592.6 /0.00054864
≈ 4,725,503.06 days or
≈ 12,947 Years
Do I need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren?The answer to both questions is NO.
The average life expectancy in Toronto (as at 2022) is 80 years. Assuming I was born today, it is expected that the time between now and when my last grand child will die is about:
80 x 3 = 240 years.
Given that the ants have to travel 12,947 to get to Toronto, the possibility of my grand children seeing them is zero.
Besides, even if they by chance got to Toronto and infested my grandchildren's residence, they would have nothing to worry about because Rasberry Crazy Ants are 100% harmless.
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Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 6,100 units per year. The cost of each unit is $101, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $31 per order. It take about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and the are 250 working days per year.)A) What is the EOQ?B) What is the average inventory if the EOQ is used?C) What is the optimal number of orders per year?D) What is the optimal number of days in between any two orders?E) What is the annual cost of ordering and holding inventory?F) What is the total annual inventory cost, including cost of the 6,100 units?
Answers
Answer and Step-by-step explanation:
The computation is shown below:
a. The economic order quantity is
\(= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}\)
\(= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}\)
= 217 units
b. The average inventory used is
\(= \frac{economic\ order\ quantity}{2}\)
\(= \frac{217}{2}\)
= 108.5 units
c. The optimal order per year
\(= \frac{annual\ demand}{economic\ order\ quantity}\)
\(= \frac{6,100}{217}\)
= 28 orders
d. The optima number of days is
\(= \frac{working\ days}{optimal\ number\ of\ orders}\)
\(= \frac{250}{28}\)
= 8.9 days
e. The total annual inventory cost is
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost is
\(= \$6,100 \times \$101\)
= $616,100
Ordering cost = Number of orders × ordering cost per order
= 28 orders × $31
= $868
Carrying cost = average inventory × carrying cost per unit
= 108.50 units × $8
= $868
So, the total would be
= $616,100 + $868 + $868
= $617,836
72 = 0.6J I need help plz
Answers
What’s the volume for this shape?
Answers
Answer:
60 m^3
Step-by-step explanation:
3 x 4 x 5 = 60
The others are self explanatory
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
which table does not show y as a function of x?
Answers
Answer:
I am confident the answer is H.
translate the sentence into an inequality.
The product of x and 3 is greater than -25.
Answers
Answer:
x · 3 > -25
I hope that this helped!
Answer:
x · 3 > -25
Step-by-step explanation:
Pls help I’ll brainlest ASAP
Answers
Answer:
November 1st and 2nd
5. pan de Muerto
6. ofrenda
7. Mexico
Step-by-step explanation:
sorry i am Hispanic but i don't know the others :(.
find the value of k if the roots
of 3x²-5x+k=0, differ by 2
Answers
By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as
3x ² - 5x + k = 3 (x - a) (x - b)
and upon expanding, we have
3x ² - 5x + k = 3x ² - (a + b) x + ab
Two polynomials are equivalent if their coefficients are equal, so
a + b = 5
ab = k
We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :
a + (a - 2) = 5
2a - 2 = 5
2a = 7
a = 7/2
Solve for b :
b = 7/2 - 2
b = 3/2
Solve for k :
k = 7/2 × 3/2 = 21/4
Please help!
What is the area in square units?
Answers
Solve the equation 3x +10=40.
x=
Answers
Answer:
x = 10
Step-by-step explanation:
3x + 10 = 40
which X in this case means 10. Hope this helps!
X=30
Because we need x in a side and the constant numbers in the opposite side
Go step by step to reduce the radical.
Square Root 200
Answers
Answer:
10 root 2
Step-by-step explanation:
root 200 = root 2 × root 100 = 10 root 2
What is the common ratio of the Fibonacci sequence called
Answers
Answer:
1.618
The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.
Step-by-step explanation:
Plz Mark me as brainliest
\(\Large \boxed{\sf golden \ ratio}\)
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
rechna notices her car driving at 40km/hr and knows that at that speed she will reach home in 2 hours if she wants to reach her home only in an half hour by what percentage does she need to increase her speed choose the correct answer 50%,100%,200%,400%
Answers
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.
What is speed?Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.
To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.
If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.
By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.
Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.
The time taken to reach her destination while travelling at her initial speed is 2 hours.
To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.
Therefore, the percentage increase in speed
= (30/120) x 100
= 25%.
Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.
Therefore, the correct answer is 200%.
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