The simplified value of F'(4) = 14.
The solution provided above shows how to use the chain rule to find the derivative of the composite function F(x) = f(g(x)) at x = 4.
The chain rule is a formula for finding the derivative of a composite function, which involves taking the derivative of the outer function and multiplying it by the derivative of the inner function.
In this case, we are given information about the functions f and g, and we are asked to find F'(4), which is the derivative of F(x) evaluated at x = 4.
To do this, we first need to find the values of g(4) and f'(g(4)), which we can use to apply the chain rule.
Here to find F'(4), we will use the chain rule:
F'(x) = f'(g(x)) * g'(x)
So, to find F'(4), we need to find f'(g(4)) and g'(4).
We know that g'(4) = 2, so we just need to find g(4) to determine f'(g(4)).
To find g(4), we need to use the information we have about f and g:
F(x) = f(g(x))
We know that F(4) = f(g(4)), so we can solve for g(4):
F(4) = f(g(4))
f(g(4)) = f(g(4))
Since both sides are equal, we can take the derivative of both sides with respect to x:
F'(4) = f'(g(4)) * g'(4)
Now we just need to find f'(g(4)). We know that g(4) = 9(4) = -5, so we can substitute that into the equation:
f'(g(4)) = f'(-5)
We are given that f'(-5) = 7, so we can substitute that in:
F'(4) = 7 * 2
F'(4) = 14
Therefore, F'(4) = 14.
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assign pizzaslist's first element's caloriesinslice with the value in pizzaslist's second element's caloriesinslice.
This will update the value of pizzaslist's first element's caloriesinslice to be the same as the value of pizzaslist's second element's caloriesinslice.
To assign pizzaslist's first element's caloriesinslice with the value in pizzaslist's second element's caloriesinslice, you will need to use the assignment operator (=) to set the value of the first element's caloriesinslice to the value of the second element's caloriesinslice. Here's how you can do it in HTML:
```html
// Assign the value of pizzaslist's second element's caloriesinslice to pizzaslist's first element's caloriesinslice
pizzaslist[0].caloriesinslice = pizzaslist[1].caloriesinslice;
```
This will update the value of pizzaslist's first element's caloriesinslice to be the same as the value of pizzaslist's second element's caloriesinslice.
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whats the slope of a line that runs through (-10,11) and (8,-5)
Answer: m = -8/9
....................................
what is the answer to the equation 8n + 10 = 50 solve for n
Answer: \(n=5\)
Add -10 to each side of the equation
\(10 + -10 + 8n = 50 + -10\)
Combine like terms
\(0 + 8n = 50 + -10\\8n = 50 + -10\\8n = 40\)
Divide each side by 8
\(8n/8=40/8\\n=5\)
Answer:
n = 5
Step-by-step explanation:
8n +10 = 50
-10 -10
8n = 40
8 8
n = 5
**Yoxelt buys 4 1/ 2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pepsi did Yoxelt buy? Show all work below.
Answer:
1 1/8
Step-by-step explanation:
1/4 of 4 1/2 is Pepsi.
1/4 * 4 1/2 = (1/4) * 4 + (1/4) * (1/2) = 1 1/8
Find the measure of C
Would greatly appreciate it
The measure of angle C is 30°
How to find the measure of C?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Since polygon ABCD is quadrilateral, the sum of angles in a quadrilateral is 360°. That is:
m∠C = 360 - 230 - 50-50 = 30°
Therefore, the measure of C is 30°
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the product of 5 - 2i and i is
Answer:
5i + 2
Step-by-step explanation:
(5-2i)(i)
5i - 2i^2
i^2= -1
5i -2(-1)
= 5i + 2
Find the sum please!
The solution of expression is,
⇒ (6 + a⁴b) / a²b²
We have to given that,
An expression to solve is,
⇒ 6/a²b² + a²/b
Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, WE can simplify the expression as,
⇒ 6/a²b² + a²/b
Take LCM;
⇒ (6 + a² × a²b) / a²b²
⇒ (6 + a⁴b) / a²b²
Therefore, The solution of expression is,
⇒ (6 + a⁴b) / a²b²
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Is this the right answer?
Answer:
Hello!
Number 2 and 4 is wrong, other than that everything else is all good.
\(2)\) \(6x^4 - 12x^5 + 90x^1^{3}\)
The Greatest common factor is 6x^4.
The GCF needs to have the smallest exponent from the variables.
The correct answer should be 6x^4 ( 1 - 2x + 15x^9)
\(4)\) \(x^2 - 36\)
x (x - 36) is wrong because if we use the distributive property, the answer would be x^2 - 36x. Notice that there shouldn't be a variable multiplying 36.
The correct answer would be (x - 6)(x + 6)
x^2 + 6x - 6x - 36
x^2 - 36.
Hope this helps!
people i have 3528 last time i asked a summary of a scary movie now do a summary of godzilla 2 king of the monsters
Step-by-step explanation: Go.dzilla 2 king of monsters is one of the best movies out there in my opinion, right down to the CGI, the movie makers did a fantastic job of creating an emotional attachment to the family in the movie.
Basically in the movie it starts in a nuclear power plant, the power plant has a melt down, kil.ling the team that went into the core to see what the issue was, the director of the power plants wife died and he knew that it wasn.t normal for the plant to meltdown the way it did, so he dedicates the rest of his life to trying to figure out what really happened there. He even goes as far as to sneak in to the restricted area with his son, when there they find out that they are digging up something from the wreckage, this is the giant moth (it wont let me say the name), The giant moth was feeding on the nuclear radiation and that was what caused the plant to melt down all those years ago. the giant moth then flies across the country searching for nuclear radiation and in turn waking her mate and destroying the place, this awakens Go.dzilla so that he can reassert himself as the ap.ex predator. He finds both the giant moths and kil.ls them and then returns to the bottom of the ocean.
here is a table showing values of sequence p. define p recursively using function notation
n p(n)
1 5000
2 500
3 50
4 5
5 0.5
4y - 9 - 6y = 2 (y + 5) -3
Help
Answer:
y = −4
Step-by-step explanation:
Jaden writes an inequality that compares -16 to another number. The inequality shows that -16 is located to the right of the other number on a number line. Which of the following could be Jayden's inequality
Answer:
24>-16
Step my step explanation:
< View Policies Current Attempt in Progress Determine the values of r for which the differential equation - y = 0 has solutions of the form y = ert. y"? Number of values of r: Choose one Choose one none one two Save for Later Using multiple attempts will impact your score. 20% score reduction after attempt 3 > -/1 Attempts: 0 of 5 used Submit Answer
To determine the values of r for which the differential equation -y = 0 has solutions of the form y = ert, we need to find the roots of the characteristic equation.
The characteristic equation is obtained by substituting y = ert into the differential equation:
-ert = 0
Since \(e^x\) is never equal to zero for any value of x, we can divide both sides of the equation by \(e^{rt}\):
-1 = 0
This equation is a contradiction, as -1 is not equal to zero. Therefore, there are no values of r that satisfy the differential equation -y = 0 for the given form of y. In summary, there are no values of r for which the differential equation -y = 0 has solutions of the form y = ert.
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Suppose you are paid an annual salary, plus a bonus of 20% on annual sales over $500,000. Consider the two functions f(x) = x − 500,000 and g(x) = 0.2x where x equals your annual sales. Which function composition gives the bonus amount when your sales are over $500,000?
A) x(f(g))
B) x(g(f))
C) g(f(x))
D) f(g(x))
Answer:
C. \(g\,\circ \, f (x) =g(f(x))\)
Step-by-step explanation:
Let be \(f(x) = x-500000\) the excedent on annual sales and \(g(x) = 0.2\cdot x\) the bonus factor, to determine the bonus amount a composition of \(f(x)\) is \(g(x)\) must be done. That is:
\(g\,\circ \, f (x) =g(f(x))\)
Hence, the right answer is C.
Simplify 5^3 x 5^4
5^12
5^7
25^12
25^7
Please help ASAP. Please. The answer is one of those above.
Answer:
5⁷
Step-by-step explanation:
5³×5⁴
when bases are same powers are added
so..
5(³+⁴)
5⁷
Answer:
5^7
Step-by-step explanation:
Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)
You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!
Goblin Gryh can count the coins in a bag in 10 minutes. If goblin Girt counts with him, they can count all the coins in 6 minutes. How long would it take Goblin Girt to count the coins in the bag alone.
The Goblin Girt take 15 minutes to count the coins in the bag alone if Goblin Gryh can count the coins in a bag in 10 minutes. If goblin Girt counts with him, they can count all the coins in 6 minutes.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let's suppose the Goblin Girt take x minutes to count the coins in the bag alone.
Then we can frame an equation to find the value of x:
\(\rm \dfrac{1}{x}+\dfrac{1}{10}=\dfrac{1}{6}\)
\(\rm \dfrac{1}{x}=- \dfrac{1}{10}+\dfrac{1}{6}\)
\(\rm \dfrac{1}{x}=\dfrac{1}{15}\)
x = 15 minutes (reciprocal on both sides)
Thus, the Goblin Girt take 15 minutes to count the coins in the bag alone if Goblin Gryh can count the coins in a bag in 10 minutes. If goblin Girt counts with him, they can count all the coins in 6 minutes.
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a population of values has a normal distribution with and . find the probability that a single randomly selected value is between -0.2 and 32.7. round your answer to four decimal places. -0.2649 incorrect find the probability that a randomly selected sample of size has a mean between -0.2 and 32.7. round your answer to four decimal places.
The probability that a single randomly selected value is between -0.2 and 32.7 is 0.0039.
We have to find the required probability:
we have the normal distribution with u = 0.2 and 32.7
sample size = n = 108
the values have normal distribution,
let x be the values, so x follows normal distribution,
so x ~ n(u = 0.2, 32.7)
If x~ n then z = x-n ~(0,1)
let s = sample mean
a) to find the probability distribution of randomly selected value =
P (-0.2 < N (0,1) < 32.7)
when we solve for n, the probability that a single randomly selected value is between -0.2 and 32.7 is 0.0039.
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Answer quick plsssssssssss
Answer:
$64
Step-by-step explanation:
Let the pay of Bella be x and Glen be y.
ATQ, 7x-5y=46 and 6x+5y=188, x=18, y=16.
Glen earned 4*16=64 bucks on Friday.
Write the following linear equation in slope-intercept form given the following:
1) slope = 2/3, y-intercept = -1
2) slope = -1, y-intercept = 8
Answer:
1) Y= 2/3x -1
2) Y= -1x + 8
Step-by-step explanation:
I learned it in Middle school
What is the area of the figure?
Answer:
80 square feet
Step-by-step explanation:
You can split it into a rectangle and a triangle. The area of the rectangle would be 2 * 16 = 32 square feet.
Next, you need to find the height of the triangle. To do this, you can split the triangle into two right triangles and use the pythagorean theorem to find the height. The dimensions of one of the right triangle is 8 for one of the legs and 10 for the hypotenuse. Using the pythagorean theorem, 8^2 + b^2 = 10^2, which is 64 + b^2 = 100, so b^2 = 36 and b = 6. This means that the height is 6. Now, you find the area of the triangle and you get 16 * 6 / 2 = 48.
Adding the area of the rectangle and the triangle: 32 + 48 = 80
Not sure why that's not an answer choice, I'm fairly confident it's right.
6.
Consider the equation:
4(2 + px) = 12x
For what value of p does the equation have no solution?
A 1
B. 3
C 12
D. 48
Answer:
p = 3
Step-by-step explanation:
Given
4(2 + px) = 12x
If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.
Distributing gives
8 + 4px = 12x ( equate the coefficients of the x- term )
4p = 12 ( divide both sides by 4 )
p = 3
The value of p when the equation has no solution will be 3. Then the correct option is B.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
4(2 + px) = 12x
8 + 4px = 12x
If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.
4p = 12
p = 3
The value of p when the equation has no solution will be 3. Then the correct option is B.
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9 feet=___ yards please and thank you for your help
the ratio of feet to yards is:
\(\frac{3feet}{1yard}\)Now, the proportion to find the equivalent yards for 9 feet is:
\(\frac{3feet}{1yard}=\frac{9feet}{x\text{ yards}}\)Let's solve for x:
\(\begin{gathered} x=\frac{9ft\times1yard}{3ft} \\ x=3\text{yards} \end{gathered}\)Therefore, 9 feet=3 yards.
Please give some specific examples for significant zeros and
nonsignificant zeros?
Significant zeros are zeros that contribute to the precision of a number, while nonsignificant zeros are placeholders or indicate the magnitude of a number.
Significant zeros are zeros that are considered significant and contribute to the precision of a number. They are located between nonzero digits or at the end of a number with a decimal point.
For example:
In the number 4,503, the zeros between 4 and 3 are significant.
In the number 0.00856, the zeros after the decimal point and before the 8 are significant.
Nonsignificant zeros, on the other hand, are zeros that do not contribute to the precision of a number and are used for placeholders or to indicate the magnitude of a number. They are typically located at the beginning or end of a number without a decimal point. Examples include:
In the number 0420, the zero at the beginning is nonsignificant.
In the number 0.003, the zeros before the decimal point is nonsignificant and serve as placeholders.
It's important to note that the significance of zeros can vary depending on the context and the rules of significant figures or decimal places being used in a specific calculation or measurement.
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73
2
Evaluate the limit. lim
2.
13
a.
1
1
C.
2
b. 2
d. limit does not exist
Answer:
a 11
Step-by-step explanation:
helpppppppppp meeeeeeeeeee 50points
Answer:
1) 48
2)44
Step-by-step explanation:
Answer: 48 44 Are The Correct Answers
Step-by-step explanation:Hope This Helps
To show that
A
^
=∑
m
∑
n
A
m,n
∣ψ
m
Xψ
n
∣ we show that the action of L.H.S 2 R.H.S on ψ
1
0.n−b
basis {ψ
n
⟩} is identical. Indeed
A
^
∣ψ
l
⟩=L⋅H⋅S \&
(∑
m
∑
n
A
m,n
∣ψ
m
χ⟨ψ
n
∣)∣ψ
l
⟩=∑
m,n
A
m,n
∣ψ
m
⟩⟨ψ
n
∣ψ
l
⟩
=∑
m,n
A
m,n
∣ψ
m
⟩δ
nl
=∑
m,n
⟨ψ
m
∣
A
^
∣ψ
n
⟩∣ψ
m
⟩δ
nl
.
=∑
m,n
⟨ψ
m
∣ψ
m
⟩
A
^
∣ψ
n
⟩δ
nl
=ψ
l
⟩= L.H.S.
The LHS and RHS of the equation are identical on the basis of ψ, demonstrating that the relationship A ^ = ∑ m ∑ n A m,n ∣ψ m Xψ n ∣ is true.
The equation A ^ = ∑ m ∑ n A m,n ∣ψ m Xψ n ∣ is explained as below:To show that this equation is true, we have to demonstrate that the LHS and the RHS of the equation are identical on the basis of ψ. This can be shown as follows:A ^ ∣ψ l ⟩ =L⋅H⋅S & (∑ m ∑ n A m,n ∣ψ m χ⟨ψ n ∣) ∣ψ l ⟩= ∑ m,n A m,n ∣ψ m ⟩⟨ψ n ∣ψ l ⟩= ∑ m,n A m,n ∣ψ m ⟩δ nl = ∑ m,n ⟨ψ m ∣ A ^ ∣ψ n ⟩∣ψ m ⟩δ nl . = ∑ m,n ⟨ψ m ∣ψ m ⟩ A ^ ∣ψ n ⟩δ nl = ψ l ⟩= LHS.L.H.S. and R.H.S. are identical on the basis of ψ, and the relationship is true.
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An item sells for $75 and is on sale for 35% off. The sales tax is 9.8%. What is the final cost of the item?
The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.
The given problem is related to percentage discounts and sales tax and can be solved using the following steps:
Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25
Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75
Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79
Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.
Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54
Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!
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Write and solve a system of equations for the situation below. Be sure to define your variables, show all your steps, and interpret your solution. (8 points) Lily is a cross country skier. On Friday and Saturday, she skied a total of 63 miles. On Friday, she skied twice as many miles as she did on Saturday. How far did she ski on each day?
Answer:
friday: 42 miles
saturday: 21 miles
Step-by-step explanation:
f = distance skied on friday
s = distance skied on saturday
So the equations are:
f + s = 63
f = 2s
to solve them, fill in the second in the first:
2s + s = 63
3s = 63
s = 63/3 = 21
f = 2*21 = 42
Answer:
She ski 21 miles on Saturday and 42 miles on Friday
Step-by-step explanation:
Come on, she skated 63 miles on the two days, and on Friday I skated twice on Saturday, so let's assume that Friday is x and Saturday y
Then
\(x = 2y \\ x + y = 63 \\ 2y + y = 63 \\ y = 21 \\ x = 42 \)
Option t Suppose you have $150.00 with which to start a business. You have Exactly the skills and
training you have right now. What business will you start? How will you spend the money? What will you do
to make sure your business works? How would you advertise?
You can successfully begin a business that serves the requirements of expression your community by leveraging your existing skills and networks and investing in targeted marketing methods.
what is expression ?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
Offering a service that leverages your existing talents and training is one suggestion for beginning a business with $150.00. For example, if you are a graphic designer, you may offer logo creation or other graphic design services to local small businesses or people. Instead, if you have experience with social media marketing, you might offer to handle small businesses' social media accounts.
Ultimately, launching a firm on a tight budget necessitates ingenuity and resourcefulness. You can successfully begin a business that serves the requirements of your community by leveraging your existing skills and networks and investing in targeted marketing methods.
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There are 90 people going on this feild trip. The budget allows for $542.94 total for tickets to the Buccaneers game. There is a service fee of $45.82. How much does each ticket cost?