The function f(g(x)) is ((x^10+1)^(9/2), the derivative f'(u) is (9/2)u^(7/2), the derivative f'(g(x)) is (9/2)(x^10+1)^(7/2), the derivative g'(x) is 10x^9, and the derivative (f ∘ g)'(x) is the product of g'(x) and f'(g(x)) which equals to 10x^9 * (9/2)(x^10+1)^(7/2).
Explanation:The functions are defined as f(u)=u9/2 whereas g(x)=x10+1.
To find f(g(x)), input g(x) into the f function. Thus, f(g(x))=((x10+1)9/2.
Next, the derivative of f(u) would be: f'(u)= (9/2)u7/2.
For f'(g(x)), replace u with g(x) in f'(u): f'(g(x))=(9/2)(x10+1)7/2.
The derivative of g(x) is: g'(x)=10x9.
Lastly, to find (f ∘ g)'(x), use the chain rule which states that (f ∘ g)'(x) = g'(x) * f'(g(x) : (f ∘ g)'(x) = 10x9 * (9/2)(x10+1)7/2.
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Suppose that 21 girls and 21 boys enter a mathemat- ics competition. furthermore, suppose that each entrant solves at most six questions, and for every boy-girl pair, there is at least one question that they both solved. show that there is a question that was solved by at least three girls and at least three boys.
Individuals shall draw a table consisting of 21 boys in each column and 21 girls in each row as shown on the image below.
The table will have 21x21 = 441 boxes. Mark each box with a letter showing the problem solved by both that boy and girl. Since at least one problem was solved by a girl and a boy, therefore each box will have a letter. Each entrant solved at most six questions, so there can be at most six letters in any row or column. This means six different letters can be there in a row only if at least 11 of the boxes contain letters appearing three or more times in the row. Individuals go through each row and color all the boxes, say blue. Therefore, 11 boxes in each row must be colored blue.
The number of the boxes that must be colored blue = 21 x 11 = 231. Individuals can apply the same process to the columns and color at least 231 boxes, say green. But the total boxes are 441 only. Therefore, by Pigeonhole principle, there will be some boxes which will be both blue and green. The problem of doubly colored boxes represents a problem solved by at least three boys and three girls.
The Pigeonhole Principle is used to show that there must be a question solved by at least three girls and three boys in a math competition with 21 girls and 21 boys.
To show that there is a question solved by at least three girls and three boys, we will use the Pigeonhole Principle.
We have 21 girls and 21 boys, each solving at most six questions.Let's assume no question is solved by at least three girls and three boys.The total number of questions solved would be at most 21 x 6 = 126, which is fewer than 21 x 2 + 21 x 2 = 84, a contradiction.Therefore, there must be a question solved by at least three girls and three boys.there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
Q equal 1/2 p plus 15 solve for p
How would you write 1+1 in distributive property
What does n equal in: -6(n+1) = 42 . Need help quickly. Thank you!
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If (7^2)x = 1, what is the value of x? Explain your answer.
If (7^0)x = 1, what are the possible values of x? Explain your answer.
(7^2)x = 1
7^2 = 49
49x = 1
x = 1/49
(7^0)x=1
7^0 = 1 (anything raised to 0 = 1)
1x = 1
x = 1
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
6 rolls of dimes = $30.
6 rolls of quarters = $60.
Answer:
7 roll of quarter and 4 roll of dimes.
Step-by-step explanation:
Let x be the number of rolls of quarters and y be the number of rolls of dimes,
Given,
Total rolls = 11
⇒ x + y = 11 ------(1),
Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.
⇒ 10x + 5y = 90 ------(2),
Equation (2) - 5 × Equation (1),
We get,
5x = 90 - 55
⇒ 5x = 35 ⇒ x = 7
From equation (1),
7 + y = 11 ⇒ y = 4
Hence, the number of roll of quarters = 7,
And, the number of roll of dimes = 4
Kareem runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
In an eye color study, 25 out of 50 people in the sample had brown eyes. in this situation, what does the number .50 represent?
The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.
Explanation:In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).
Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.
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The sum of two integers is greater than 12. One integer is 10 less than the other. What are the values of the integers?
What is the difference of (4-5y)-2(3.5y-8)?
what percent of 176 is 17.6
There are 9 red and 6 green marbles in a bag. A child reaches in the bag and randomly takes one marble. What is the probability pf that child getting a green marble
Answer: The required probability that the child took a green marble is 40%.
Step-by-step explanation: Given that there are 9 red and 6 green marbles in a bag and a child reaches in the bag and randomly takes one marble.
We are to find the probability that the child took a green marble.
Let S denote the sample space of choosing a marble from the bag and A be the event of choosing a green marble.
Then,
n(S) = 9 + 6 = 15 and n(A) = 6.
Therefore, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{15}=\dfrac{2}{5}\times 100\%=40\%.[/tex]
Thus, the required probability that the child took a green marble is 40%.
What is factor out the coefficient of the variable of 4h-3
Find the critical points of the function. (enter your answers as a comma-separated list.) g(x) = 4 − x2
Mr. Thomas purchased a car for $30,000. in 4 years the value of the car decreased to $22,000. Which integer represents the average net change in value per year?
20. What percent of 392 is 98? 22. 33% of what number is 145? 24, 17 is 40% of what number?
69.5 is What precent of 85?
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
What is the greatest common factor of 49 and 84? 3 4 7 9
Help with #30 Please!
what is an angle between a side of a polygon and the extension of its adjacent side
The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.
Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.
Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)
The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\((-5, 6)\) and \((0, 1)\)[/tex]
Calculate the slope m:
[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]
Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
Now, simplify and compare with the given options:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
How l can write a brief summary about measurement for 3rd grade
Joanne has 2a^3 number of animals. Ronnie has 3a^3 number of animals . Odessa has a^4 number of animals . How many animals do Joanne , Ronnie, and Odessa have altogether?
Sara bought two pounds of strawberries for $5.12. What is price in dollars per ounce of strawberries 1 pound =16 ounces
Hello, I am taking Quantitative methods for business, which has a lot of excel based mathematics and I was wondering if anyone could help. Here is the question:
Refer to the table that illustrates customer’s complaints about a manufacturing company.
A. What is the probability a customer complained during the guarantee period?
B. What is the probability that a customer complained about an electrical problem or a mechanical problem?
Table is included in attachment. Also Thank you!!!
What is the smallest natural number that has three distinct prime factors in its factorization?
a girl is the same age if she takes 3/4 of her age +9 or 1/4 +21. what is her age?