Using the chain rule, Therefore, f'(0) = 2.
Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) to obtain :
f'(x) = f'(g(x)) * g'(x)
substitute x = 0, we get:
f'(0) = f'(g(0)) * g'(0)
We are given that g(0) = -2 and g'(0) = 3. Therefore, we need to find g(0) and g'(0) in order to determine f'(0).
To do this, we can use the fact that f(x) = f(g(x)). Substituting x = 0 into this equation, we get:
f(0) = f(g(0))
Since f(-2) = 2, we have:
f(g(0)) = f(-2)
Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) with respect to x to obtain:
f'(x) = f'(g(x)) * g'(x)
substitute x = -2, we get:
f'(-2) = f'(g(-2)) * g'(-2)
We are given that f'(-2) = 2 and g'(-2) = 3. Therefore, we can solve for f'(g(-2)):
f'(g(-2)) = f'(-2) / g'(-2) = 2/3
Since f'(x) = f'(g(x)) * g'(x), we can substitute g(0) = -2 and f'(g(-2)) = 2/3 into the equation f'(0) = f'(g(0)) * g'(0) to obtain:
f'(0) = f'(g(0)) * g'(0) = f'(g(-2)) * g'(0) = (2/3) * 3 = 2
Therefore, f'(0) = 2.
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please help I domt understand
PLS HELP!! right answer = gets
The awnswer is (1,-3) (if I'm not right try typing it it an app called math away it can solve that no problems)
Solve the equation : 12/x+2
Answer:
the third answer x= 18 only is correct
Felipe bought a collection of 525 old sports cards at a
garage sale. He decided to sort them into piles of baseball
players, football players, soccer players, basketball players
and hockey players . He was surprised to find that each
pile of cards had an equal amount. How many of each type
of card was in his collection?
Answer:
105 in each pile of cards .5 types of card in his collection
Solve for a? Please help
we can answer it as follow
The red one show the GCF factor form it is -7 then you you ommit negative of numinator by negative of denominator . then you multiply both side by 4/7
the you simplify and solve a .
PLS HELP WRITE EACH EXPRESSION AS A SINGLE POWER DO NOT EVALUATE
Answer:
1. 3³
2. (-5)⁴
3. 3¹⁰
4. 4⁰
Step-by-step explanation:
When multiplying exponents with the same base, you add the exponents. When dividing exponents with the same base, you subtract the exponents. When raising a number with an exponent to another power, multiply the exponents.
1. \(\frac{3^4*3^6}{3^2*3^5} =\frac{3^{10}}{3^7}=3^3\)
2. \(\frac{(-5)^{12}}{(-5)^3*(-5)^5} =\frac{(-5)^{12}}{(-5)^8}=(-5)^4\)
3. \((3^2)^5=3^{10}\)
4. \(\frac{4^0*4^4}{4^1 * 4^3} =\frac{4^4}{4^4}=4^0\)
Explain how to modify the graphs F(x) and g(x) to graph the solution to set the following system of inequalities. How can the solution set be identified? Y>x^2-1
Y<-x^2+4
The following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is found by the fact that the domain of quadratic functions is the entire real domain.
How to apply rigid transformations to understand the differences between two given functions
According to the Euclidean geometry, rigid transformations are those transformations applied on geometrical loci such that Euclidean distances are conserved in every point of the loci. Reflections and translations are sound examples of rigid transformations.
In this question we must derive all needed rigid transformations to turn f(x) into g(x), both quadratic functions. After a careful analysis we conclude that the following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is represent by all x-values such that the function exists. According to real algebra we remember that the domain of quadratic functions is the real domain. Thus, the solution sets of f(x) and g(x) are the real domain.
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The Anderson family is preparing for a family reunion they think they will need 18 juice boxes for every six children who attend how many juice boxes will they need if they are expecting 28 children
Answer:
84
Step-by-step explanation:
If it's 18 juice boxes for 6 children then the ration is 6:18. Since both numbers are divisible by 3, do that. You then get a ratio of 2:6, both of those are divisible by 2, do that and get 1:3. So there's 3 juice boxes per kid, so multiply 28x3 and get 84.
according to your text, which of the following is the primary source of primate endangerment today? habitat destruction human diseases social stress and dislocation use of primates for pets
Based on the text, the primary source of primate endangerment today is habitat destruction.
Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.
Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.
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If a student picked is 10 years old, what
are the chances that they skip breakfast?
Answer:
There are 29% chance that they will skip their breakfast
Step-by-step explanation:
40 / 14 x 10 = the percentage of the kid skipping his breakfast
40 / 14 x 10 = 28.5%
28.5 = (rounded off) = 29%
The kid has a 29% chance of skipping the breakfast
Does anyone know the last two? Match the correct property to the equation showing that property.
Explanation: The 4th one is the distributive property because it shows an equal sign and the 5th one is the inverse property of addition because it uses more than addition.
Answer: 4th one is distributive property 5th one is inverse property of addition
P.S. I am sure 95% sure that I am correct.
a rectangular prism has a length of 8 in., a width of 4 in., and a height of 214 in.the prism is filled with cubes that have edge lengths of 14 in.how many cubes are needed to fill the rectangular prism?
To fill the rectangular prism we need 1 cube.
To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of a single cube.
The volume of the rectangular prism is given by the formula:
Volume = Length × Width × Height
Substituting the given values:
Volume = 8 in. × 4 in. × 21 in.
Volume = 672 in³
The volume of a cube is given by the formula:
Volume = Edge Length³
Substituting the given edge length:
Volume of a cube = (14 in.)³
Volume of a cube = 2744 in³
Now, we can divide the volume of the prism by the volume of a single cube to find the number of cubes needed:
Number of cubes = Volume of prism / Volume of a single cube
Number of cubes = 672 in³ / 2744 in³
Calculating this division gives:
Number of cubes ≈ 0.245
Since we cannot have a fraction of a cube, we need to round up to the nearest whole number. Therefore, we would need 1 cube to fill the rectangular prism.
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4 3/7 + 6 1/5 = ?
Please EXPLAIN!!!
I'm too lazy and when I lazy I not so smart ;)
Answer:
Welp here is the answer to your question, 372/35 in exact form. in mixed number form it is 10 22/35
Find the difference of (t−8)−(t+15)
Answer:
Step-by-step explanation:
(t-8)-(t+15)
t-8-t-15
t-t-8-15
-23
The value of the expression after subtraction will be;
⇒ - 23
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (t - 8) - (t + 15)
Now,
Subtract the expression as;
⇒ (t - 8) - (t + 15)
⇒ t - 8 - t - 15
⇒ t - t - 8 - 15
⇒ - 23
Thus, The value of the expression after subtraction will be;
⇒ - 23
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which of the following equations represent a line that is parallel y=5x-4 ad passes through the point (3,4)
The equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
How to write the point-slope form equation?We are given that
The slope of given line = 5And passed through point (3, 4)Slope of parallel lines is the same, so slope of the line parallel to the given line will be m = 5
We have the slope and a point, using the point-slope form we can write the equation of the line:
\(\rightarrow\text{y} - 4 =5 \ (\text{x} - 3)\)
\(\rightarrow\text{y} = 5\text{x} - 15 + 4\)
\(\rightarrow\bold{y = 5x - 11}\)
Hence, the equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
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Your question is incomplete. The complete question is-
Which of the following equations represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4)?
A. y = 5x - 7
B. y = 5x + 19
C. y = -1/5x -4
D. y = 5x - 11
what is 32z-48 factored with gcf
Answer:
We found the factors and prime factorization of 32 and 48. The biggest common factor number is the GCF number. So the greatest common factor 32 and 48 is 16.
Step-by-step explanation:
What is the GCF of 32and 48?
16
Greatest common factor (GCF) of 32 and 48 is 16.
i if (x == null) return alreadyreversed; node y = x.next; x.next = alreadyreversed; return reverse (y, x);
The code snippet is a recursive function to reverse a singly linked list.
When the current node (x) is null, it returns the already reversed list. Otherwise, it reverses the remaining list and returns the result.
The code is a part of a recursive function that aims to reverse a singly linked list. It starts by checking if the current node (x) is null, meaning that the end of the list has been reached. If true, it returns the already reversed part (alreadyreversed).
If the current node is not null, it proceeds to the next step by assigning the next node (y) as x.next. Then, it changes the next pointer of the current node (x) to point to the already reversed part (x.next = alreadyreversed).
Finally, it calls the same function again with the updated parameters (reverse(y, x)) to continue reversing the remaining list. This process continues until the base case (x == null) is encountered, and the fully reversed list is returned.
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3. true or false? (ln n) 2 is big-o of n. justify your answer
False.
To determine whether (ln n)^2 is big-O of n, we need to examine the growth rates of both functions as n approaches infinity.
The function (ln n)^2 grows much slower than the function n. Taking the logarithm of n twice results in a logarithmic growth rate, which is significantly slower than the linear growth rate of n.
In the big-O notation, we are concerned with the worst-case behavior of a function. For (ln n)^2 to be big-O of n, there must exist constants c and n0 such that (ln n)^2 ≤ c * n for all n ≥ n0.
However, no matter what constants c and n0 we choose, there will always be an n large enough where (ln n)^2 exceeds c * n. Therefore, (ln n)^2 is not big-O of n.
Hence, the statement is false.
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The latest online craze is a new game,khan on seven. You get 100 points for playing the game. In addition,you get 50 points for each seven-letter word you make with the ten letter you receive.sal wants to break the record,and he needs 18,000 or more points to do so
Answer:
how do I get started here
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
\(w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5\)
A standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than 8? express your answer as a fraction or a decimal number rounded to four
The answer is 0.5833 using probability.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
When two dice are rolled sample space is of 36 elements.
The elements which give sum less than 8 are given as follow
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5)
(3,1),(3,2),(3,3),(3,4)
(4,1),(4,2),(4,3)
(5,1),(5,2)
(6,1)
Here the total number of elements that satisfy conditions is 21
Hence probability is given by (21/36)
Probability=0.5833
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Which of this is NOT a family of antiderivative of 2(3x + 2) ? a. 3 2(3x + 2)4 - +C 12 (3x + 2)4 - -C 6 b. 4(3x + 2)4 12 + K (3x + 2) 6 + K
4(3x + 2)4 12 + K (3x + 2) 6 + K is NOT a family of antiderivative of 2(3x + 2). The correct answer is Option b.
To find the antiderivative of 2(3x + 2), follow these steps:
1. Notice the function is 2(3x + 2).
2. Apply the power rule of integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.
3. In this case, n = 1, so the antiderivative is (2(3x + 2)^2)/(2) + C.
4. Simplify to obtain (3x + 2)^2 + C.
Option b doesn't match this result, so it is NOT a family of antiderivatives of 2(3x + 2).
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there are 15 different colored marbles in a bag and you have one six-sided die. if you roll the die and choose a marble, how many possible combinations of marble color and die number are possible?
There are 90 possible combinations of marble color and die number that are possible from a bag of 15 different colored marbles and rolling one six-sided die.
This can be determined using the multiplication principle of counting.
The multiplication principle of counting can be used to find the number of ways two or more tasks can be performed together. The principle states that if there are m ways to perform task A and n ways to perform task B, then there are m × n ways to perform both tasks A and B.
To apply the multiplication principle of counting to this problem, we need to determine the number of ways the die can land and the number of ways a marble can be chosen. There are six possible outcomes of rolling a six-sided die, and there are 15 different colored marbles to choose from. Thus, the number of possible combinations of marble color and die number is: 15 different colored marbles × 6 possible die numbers= 90 possible combinations.
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A rectangle has an area of 36 square centimeters. The width of the rectangle is 4 centimeters.
What is the length of the rectangle?
Compute the range for a distribution where the highest score is 89 and the lowest score is 27.
Answer:
The range of the distribution is 62
Step-by-step explanation:
Here in this question, we are interested in computing the value for the range.
Mathematically;
range = Highest value - lowest value
from the question, highest valve = 89 while lowest value = 27
Plugging the values into the range equation, we have;
Range = 89-27 = 62
Nadya deposited $1,000 into a savings account that pays 3. 5% simple interest per year. Which expression represents the value of her investment after 8 years?
The expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)So, the expression that can represent the above situation is:
The total money Nadya deposited is $1000.
Interest is 3.15%.
Total years are 8.
Simple interest formula: A = P (1 + rt)
Where a is the final amount, p is the principal amount, r is the interest return and t is the time in years.
Then, we have:
A = 1000 (1 + 3.5(8))
A = 1000(29)
A = 29,000
Therefore, the expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).
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Find the area of each figure. Round to the nearest hundredth where necessary. Only 1 and 5 please!
Answer:
See below
Step-by-step explanation:
To begin, it is volume, not area
1. 8 x 12 x 17 = 1632 in ^3
5. 9 x 9 x 13.5 = 1093.5 in^3
If you want to find SURFACE AREA:
1. 2(8 x 12) + 2(8 x 17) + 2(17 x 12) = 872 in^2
5. 2(9 x 9) + 4(9 x 17) = 774 in^2
for the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest. a: ∫80f(x)dxb: ∫30f(x)dxc: ∫85f(x)dxd: ∫50f(x)dx
Therefore, we can order the integrals as follows, from smallest to largest:
a: ∫80f(x)dx (interval [3, 0], negative values, short length)
b: ∫30f(x)dx (interval [0, 5], positive values, longer length)
d: ∫50f(x)dx (interval [0, 5] and part of [5, 8], positive values, longest length)
c: ∫85f(x)dx (interval [5, 8], positive values, short length)
However, we can compare the given intervals in terms of their length and the position of the function on those intervals to determine the order of the integrals. From left to right, the intervals and their approximate lengths are:
Interval [3, 0]: length 3
Interval [0, 5]: length 5
Interval [5, 8]: length 3
Now we need to examine the position of the function on each interval. From the graph, we can see that the function is negative on the interval [3, 0] and positive on the intervals [0, 5] and [5, 8].
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Complete question:
For the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest.
a: ∫80f(x)dx
b: ∫30f(x)dx
c: ∫85f(x)dxd: ∫50f(x)dx
i need help with this question, thx to anyone who helps! :)
Answer:
Golf balls
Step-by-step explanation:
There is a much higher chance of her picking an even number in the golf ball tank because there are way more golf balls with even numbers. (2, 4, 6, 8, etc.)
How do you find the inverse of a matrix in Matlab?
In Matlab, you can find the inverse of a matrix using the "inv" function. This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.
Suppose you have a matrix "A", and you want to find its inverse. You can do this by typing:
B = inv(A);
This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.
Note that calculating the inverse of a matrix can be computationally expensive and should be avoided if possible. In some cases, it may be more efficient to use other methods, such as solving a system of linear equations using the backslash operator.
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