The requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
here,
Given expression,
[tex]F(x) = \int\limits^{x^2}_x {e^{t^7}} \, dx[/tex]
Following the Leibniz rule
[tex]F'(x) = \frac{d}{dx}[ \int\limits^{x^2}_x {e^{t^7}} \, dx]\\F'(x) = \int\limits^{x^2}_x \delta/\delta x (e^{t^7}) + (e^{(x^2)^7}) d/dx (x^2) - e^{x^7}d/dx [x] \\F'(x) = 0 + 2xe^{x^{14}} - e^{x^7}\\F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex]
Thus, the requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
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What is the length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in?
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the length of the other two sides (a and b).
In this case, a = b = 9 in, so:
c2 = 92 + 92
c2 = 81 + 81
c2 = 162
c = √162
c = 12.73 in
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in, calculated using the Pythagorean theorem.The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
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In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the computer? Explain your answer
If Shapera mowed 7 lawns and worked for 36 hours at pet store and delivered newspapers 7 days , then she earned $497 which is not enough to buy the computer .
the amount that she earns in mowing each lawn is = $15 ;
So , the amount earned for mowing 7 lawns is = [tex]15\times 7[/tex] = $105 ;
the amount that she earns per hour working at pet store is = $7 ;
So , amount earned for working 36 hours is = [tex]36\times 7[/tex] = $252 ;
the amount that she earns by delivering newspapers per day is = $20 ;
So , amount earned by delivering newspapers for 7 days =[tex]20\times7[/tex] = $140 ;
The total amount earned by Shapera is = [tex]\$ 105 + \$252+\$140[/tex]
On adding all the amount earned ,
we get ;
= $497 ;
The amount earned by Shapera is $497 .
Therefore , Shapera will not be able to buy the $499 computer as she is $2 less than the price .
The given question is incomplete , the complete question is
Shapera has three sources of income. She earns $15 for each lawn she mows. She earns $7 per hour working part-time at a pet store She earns $20 each day she delivers newspapers.
In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the $499 computer ?
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HELP ME PLEASE . THESE ARE RATIONAL NUMBERS BTW.
Answer:
15. -3 1/4
16. -4 1/2 OR -4 2/4
17. 1 1/4
18. -5 3/4
19. 1/2 OR 2/4
20. -2 1/2 OR -2 2/4
Step-by-step explanation:
Answer:
15) -3.25
16) -4.5
17)1.25
18)-5.75
19).5
20)-2.5
Ash and her 2 friends went to dinner. If the bill was $124.72, and they left an 18% tip, how much did each person pay
Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
Which percentage is it?A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Amount of bill = $124.72
and tip they left = 18% of $124.72
total amount is =$124.72 + $124.72*18%=$147.1696
so, each person pay= $147.1696/3=$49.056
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these ar the numbers and i need the ratio
thank you!
help me please its due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer:
1:3
Step-by-step explanation:
The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 12°F. What was the lowest temperature overnight in that city?
Answer:-14°F
Step-by-step explanation:
-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it
Find output, g, when the input, r, is 4. g= 25-3r
when the input r, is 4, then the output g, is 13.
The function g = 25 - 3r gives the output g when the input r is given.
If we substitute r = 4 into the equation, we get:
g = 25 - 3×4
g = 25 - 12
g = 13
Therefore, when the input, r is 4, the output g, is 13.
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In ΔABC, if AB = BC and
Answer: not enough to answer
Hint: your answer will be a fraction or decimal. ex: 3/5 or 0.6 *
Find the probability that a point chosen at random on the part of the number line shown will lie
between points B and C.
On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.
What is probability?A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.
Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.
Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.
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11c+ 8) (-9c - 1)
Help plssss
Answer:
Step-by-step explanation: (11c + 8) (-9c - 1)
Then expand
which would be 11c ( -9c - 1) + 8 ( -9c - 1)
-99c^2 -11c - 72c - 8
It becomes -99c^2 - 83c -8
I hope this was helpful
Please help me with this problem.
In the year 1582, January 1st was adopted for the new year celebration
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.
The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear
The year that January 1st was adopted as new year can be gotten using the function:
f(x) = 3x³ - 7x² - 5x + 7
f(9) gives the year that it was adopted. Substituting x = 9 gives:
f(9) = 3(9)³ - 7(9)² - 5(9) + 7
f(9) = 1582
In the year 1582, the new year was celebrated at January 1st
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Carlos saves aluminum cans to sell to the recycling center. He recently recycled 43 pounds of cans and received $23. 65. How many dollars would he get at this rate for recycling 200 pounds of cans?
The rate of recycling 200 pounds of cans based on the mentioned information is $110.
Firstly calculating the cost of cans per pounds. Then we will proceed to actual calculation about rate of recycling 200 pounds.
Cost of recycling one pound of can = total cost ÷ number of recycled cans
Keep the values in formula
Cost of recycling one pound of can = 23.65/43
Performing division
Cost of recycling one pound of can = 0.55
Cost of recycling 200 pounds of cans = 0.55 × 200
Performing multiplication
Cost of recycling 200 pounds of cans = 110
Therefore, the required rate is $110.
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What is the slope of an absolute value function?
Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.
Absolute Value Function:
An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values of x and find some ordered pairs.
In mathematics, the absolute value or modulus of the real number x, represented as.
|x| is the non-negative value of x, regardless of sign.
x is positive and |xI =-x}. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.
Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.
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What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?
Answer: To find an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35, we can use the fact that two lines are parallel if and only if they have the same slope.
The slope of the line 4x−5y=35 is -4/5. Therefore, we can find an equation of the line that passes through (-5,-6) and is parallel to 4x−5y=35 by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
Substituting the values into the slope-intercept form, we get:
y = (-4/5)x + b
To find the value of b, we can substitute the coordinates of the point (-5,-6) into the equation:
-6 = (-4/5)(-5) + b
-6 = 8/5 + b
-6 - 8/5 = b
-24/5 = b
Therefore, the equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35 is:
y = (-4/5)x - 24/5
This can also be written as:
y = -4/5x - 24/5
Step-by-step explanation:
A grocery tore ha 13%-off ale on all bread. You decide to purchae 6 loave of bread. Let b be the original price of a loaf of bread. Expand the expreion 6(b-0. 13b). Once the expreion i expanded, who do the term repreent
6b - 0.78b it will result after expanding the expression.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.
There are three different expression types:
There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.Let, b represent the original price of a loaf of bread.
Given that,
A grocery store has 13%-off sale on all bread.
This means that the amount by which the price of bread was reduced would be
13/100 × b = 0.13 × b = 0.13b
The new price for the loaf of bread would be: b - 0.13b
you decide to purchase 6 loaves of bread. The expression would be:
6(b - 0.13b)
Expanding the expression, it becomes: 6b - 0.78b
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find the total surface area of this cuboid.
The total surface area of the cuboid is 2 (lh + lw+ hw) square units.
What is surface?A surface is the part of solid matter that can be touched by hand or seen with eyes. In other words, it is the place where the solid matter encounters the outside world through contact, light, etc. Solid matter not only effects humans with its surface, but also air, water, and other solid matter. Therefore, things around us work cooperatively with the outside world and with other things through surfaces, without a surface, solid matter would not be able to interact with anything.By changing the characteristics of solid matter, interactions such as the impact on the solid matter from other things (such as environmental conditions and people) as well as the effect that solid matter has on other things can be changed. In other words, certain features of the solid matter can be controlled as needed.To learn more about surface refer to:
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Find the product of the factors 8.075*0.08
Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8
Step-by-step explanation:
Did this with a classmate couple months ago. Hope this helps. :)
A DVD player had a $108. Price tags the store gave a 25% discount. What was the amount of the discount?
Answer:
$27
Step-by-step explanation:
If we know that %25 is equal to 1/4, or 0.25, then we can use an equation that look like this:
108 × 0.25 = 27
Therefore, the amount of the discount was $27
How can you solve for percentages?Solving for percentages can be tricky, and you may need help on trying to solve a problem including one. If you need to find a percentage of a number, the easiest way to do that is to convert the percentage into a fraction or decimal and multiply the total by that number.
For ex.
What is 15% of 60?
To do this, convert the percentage into a decimal.
15% converted into a decimal is 0.15.
Now multiply 60 by 0.15.
60 ÷ 0.15 = 9
So, the answer to this example would be 9.
simplifying radicals worksheet algebra 2
Therefore , the solution of the given problem of expression comes out to be √14q × 2√4q = 4q√14.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
The simplified expressions are 20 = 25, 56x2 = 2x14, [150x3k4] = 5xk26x, and 14q 24q = 4q14 given the facts from the question.
Simplifying the surd
A perfect square must be one of the components for a number to be written as just surds.
How to Make 20 Recall Simpler
20 = 4 × 5
Thus,
√20 = √(4 × 5)
√20 = 2√5
simple methods √(56x²)\s√(56x²) = √56 × √x²
Recall
√56 = √(4 × 14) = 2√14
√x² = x
Thus,
√(56x²) = 2√14 × x
√(56x²) = 2x√14
simple methods [150x3k4] = [150x3k4] = [150x3k4]
Recall
√150 = √(25 × 6) = 5√6
√x³ = √(x² × x) = x√x
√k⁴ = k²
Thus,
√[150x³k⁴] = 5√6 × x√x × k²
√[150x³k⁴] = 5k²x√6x
How to simplify 14q 2 4q: 14q 2 4q = 2
(14q × 4q)
√14q × 2√4q = 2 × 2q√14
√14q × 2√4q = 4q√14
Therefore , the solution of the given problem of eexpression comes out to be √14q × 2√4q = 4q√14.
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The width of a rectangle is the length minus 2 units. The area of the rectangle is 8 square units. What is the length, in units, of the rectangle?
The length of the rectangle is 4 units.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Let n be the length of the rectangle.
The width of a rectangle is the length minus 2 units.
The width = n - 2
The area of the rectangle is 8 square units.
The area of the rectangle = length x width
8 = n (n-2)
n²-2n - 8 = 0
n²-4n+2n - 8 = 0
n(n-4)+2(n-4) = 0
(n+2)(n-4) = 0
n = 4 and -2.
So the length is 4 units.
Therefore, 4 units are the length of the rectangle.
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PLS HELP :[
The graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.
A graph shows Number of Pepperoni Rolls on x-axis and Price of Pepperoni Rolls on y-axis. The x-axis scale is shown from 0 to 24 at increments of 4, and the y-axis scale is shown from 0 to 160 at increments of 20. A straight line joins the ordered pairs 4, 20 and 8, 40 and 12, 60 and 16, 80 and 20, 100 and 24, 120.
Kaiser Roll Packet
Number of Kaiser Roll Packet
Price of Kaiser Roll Packet (dollars)
4
24
8
48
12
72
16
96
How many dollars more is the price of a Kaiser roll packet than the price of a pepperoni roll at Luis's store? (1 point)
a
$1
b
$4
c
$5
d
$6
Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.
The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6
The price of a Kaiser roll = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5
$6 - $5 = 1
Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.
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Toss a coin 10 times and record how many times you tossed heads.
a) What is your experimental probability of tossing heads?
b) What is the theoretical probability of tossing heads?
c) Compare the two probabilities and determine if you are considered to be
"lucky" at tossing heads.
d) If you were to toss the coin 100 times, what would you expect the
experimental probability of heads to be? Defend your answer.
To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the probability of tossing heads is 0.000976.
What is probability?Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.
Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.
P(getting heads on one toss) = 1/2
P(getting all heads in 10 tosses)=(1/2)¹⁰
=1/1024
=0.000976
Therefore, the probability of tossing heads is 0.000976.
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It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold is given by n = a/(x-c) + b(95-x), where a and b are positive constants. What selling price will bring a maximum profit? Express the total profit P in terms of X. P(x) The selling price that will maximize profit is $
The total profit P in terms of x can be expressed as
P(x) = (a - c) (a/(x-c) + b(95-x))
The selling price that will maximize profit is the positive constant, a in dollars.
To find the selling price that will bring a maximum profit, we need to find the derivative of the profit function P(x) and set it equal to 0.
The profit function P(x) is given by P(x) = nx - nc,
where n is the number of backpacks sold and c is the cost to manufacture and distribute each backpack.
Substituting the given expression for n into the profit function gives:
P(x) = (a/(x-c) + b(95-x))x - c(a/(x-c) + b(95-x))
P(x) = (a - c) (a/(x-c) + b(95-x))
To find the selling price that will maximize profit, we need to find the critical points of P(x) by taking the derivative of P(x) with respect to x and setting it equal to 0:
P'(x) = (a - c) (-a/(x - c)² - b) = 0
Thus P'(x) = 0 at c = a or (x - c)² = -a/ b
a and b are positive constants, so -a/ b is negative but (x - c)² is never negative, so it is not a possible solution.
So only solution is c = a, that is for maximum profit selling price, c should be equal to the positive constant, a.
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A heavy rainstorm damages this year's crop of peanuts. The price of peanut butter increases. What will happen to the demand of jelly?
Answer the 3 questions below related to this scenario.
Complete sentences are not required. Please number each answer.
1. Will there be an increase or decrease?
2. Which way will the graph shift?
3. What is the determinant?
On solving the provided question, we got to know that - to plot the graph, required equation is 3x +y -8 = 0
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value. To plot the graph,we need to find the equation first.
and to find the equation -
(y - y1) = m( x - x1)
y1 = -4
x1 = -2
y = 3
x = -5)
equation -
(-3)(x-1) = y-5
-3x + 3 = y-5
3x - 3 = 5-y
3x +y -8 = 0
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find the gradient of a line passing through each of the following pair of points (0,-5) and (6,3)
When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a
histogram
standard deviation distribution
percentile distribution
bar graph
scatter-plot or scatter-gram
When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a scatter-plot or scatter-gram.
What is scatter-plot or scatter-gram?Scatter-plot: A scatter-plot is a form of mathematical diagram or plot that employs Cartesian coordinates to illustrate distinct values associated to two variables for a specific set of data. It is also known as a scatter-gram, scatter-graph, scatter-chatter, or scatter-diagram.
It is being utilized to determine how one variable influences the other.
The supplied statement in the question above represents the scatter plot.
Here,
When you observe a graphed cluster of dots reflecting the values and relationship of two separate variables, you are looking at a scatter-plot or scatter-gram, which is a visual explanation of relatedness.
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Please help me! I don't understand
Answer: 12
Step-by-step explanation:
The smaller triangles on the right can be proven congruent, so the other side also equals 6. 6+6=12
What is the value of 5 by 2?
The value of 5 divided by 2 is 2.5.
Therefore the answer is 2.5.
When dividing 5 by 2, we are trying to find out how many times 2 can fit into 5. The answer is 2 with a remainder of 1, this is why it can also be written as 2 and 1/2.
When dividing 5 by 2, we can also write the result as a fraction, in this case, it is 2 and 1/2 or 2.5 in decimal form. It is the exact same thing as 2.5, just represented in a different way.
It's important to note that, in general, dividing integers will give a decimal number. If you want the result to be a fraction, you will have to express it as such.
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estimate the product of 5,398 x 47 by rounding to the nearest thousand and ten.
a) 200,000
b)250,000
c)253,706
d)300,000
pls help me
Answer:
b) 250,000
Step-by-step explanation:
You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.
Rounded valuesRounding 5,398 to the nearest thousand gives 5000.
Rounding 47 to the nearest ten gives 50.
Estimated productThe product of these is the estimate you want:
5000·50 = 250,000
A team of scientists is developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time. Which variable would most likely affect the temperatures that the model predicts
Scientists are developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time.
These variables include:
Carbon dioxide emissions from human activity (x) - This variable is considered to have the greatest impact on temperature predictions as human activities have significantly increased the amount of carbon dioxide in the atmosphere, which is a major greenhouse gas that causes global warming. Carbon dioxide emissions from activities in nature (y) - This variable also plays a role in temperature predictions as it contributes to the overall amount of carbon dioxide in the atmosphere.Global sea level (z) - The time interval is sufficiently large for the global sea level to have a greater impact on temperature predictions as rising sea levels can affect coastal regions and weather patterns.Global rates of photosynthesis (p) - Changes in the Earth's orbital path can affect the global rates of photosynthesis, which in turn can affect temperature predictions.The acidity of ocean water (q) - While the acidity of ocean water is an important variable, it is considered to have a less significant impact on temperature predictions compared to the other variables listed above.In summary, the variables are ranked in order of their likely impact on temperature predictions, with carbon dioxide emissions from the human activity being the most significant variable, followed by carbon dioxide emissions from activities in nature, global sea level, global rates of photosynthesis, and acidity of ocean water.
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