please help me answer this question

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

Step-by-step explanation:

It's a proportion rather than an equation that you might be more accustomed to.

2/0.05 = x/ 0.95       Cross multiply

2 * 0.95 = x * 0.05    Divide by 0.05

2 * 0.95/0.05 = x

x = 38 grams of sugar should be added to the 2 grams of cinnamon.

There's another way to do it.

2/0.05 = (x + 2)/1      Cross multiply

2*1 = 0.05x + 0.1       Subtract 0.1 from both sides

1.9 = 0.05x

1.9/0.05 = x

x = 38

Which ever way you understand better is the answer. 100 / 100% is 1

The number of souvenirs you can  buy if each one costs 450 Jamaican dollars is; 13

We are given;

Amount you have while on vacation in Jamaica = 40 US Dollars

Now, we are told that one souvenir costs 450 Jamaican dollars.

It should be noted that the money you have is in US Dollars and as such since the souvenir is purchased with Jamaican dollars, you will need to convert the money to Jamaican dollars to purchase the souvenirs.

We are given the conversion rate as;

1 U.S. dollar = 154.8 Jamaican dollars

Thus, your amount in Jamaican dollars is;

(40 * 154.8)/1 = 6192 Jamaican Dollars

Thus;

Number of souvenirs you can buy = 6192/450 = 13.76

Approximately 13.

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The perimeter and area of the given composite shape are respectively;  10a² + 10b and 37a²b

The perimeter of the composite figure here will simply be the sum of the entire boundary lengths and as such we have;'

Perimeter = 2(a² + 3a² + a²) + 2(4b) + b + b

= 10a² + 8b + 2b

= 10a² + 10b

The area of a rectangle is;

Area = Length * width.

Thus;

Area of composite shape = Overall area of rectangle - Area of cut out rectangle

Area = (10a² * 4b) - (3a² * b)

Area = 40a²b - 3a²b

Area = 37a²b

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Answer: the mean is 1.03

Step-by-step explanation: you multiple the days by the probability, 0 x .68= 0 1 x .05=.05 2 x .07=.14 and so on and you add what you get from multiplying them.

Answer:

C)  y = -1/4x

Step-by-step explanation:

find slope by selecting two points -- I used (0, 0) and (-4, 1)

slope is the difference of the y-values:  1 - 0  =  1

divided by the difference of the x-values:  -4 - 0  = -4

slope = -1/4

the other thing you need to know is the y-intercept, which in this case is zero

so the equation is y = -1/4x

Answer:

a is the answer..........

Answer:

That sounds delicious

Step-by-step explanation:

0.5:0.75  =   x:3

2 teaspoons of cinnamon needed

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

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Answer:

39%

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.

In this question, the binomial is (x + 2)².

You can expand this to be (x + 2)(x + 2).

When you expand it using the FOIL method, you get x times x, which is x².

Next, the outside/outer terms are x and 2, which is 2x.

Then, you multiply the inside/inner terms 2 and x, which is 2x.

Last, you multiply the last terms, which are 2 and 2, which is 4.

When you put them together, it looks like this:

x² + 2x + 2x + 4.

You can simplify this to x² + 4x + 4.

So your answer is 4.

Answer:

24

Step-by-step explanation:

6+2+0+4+1+3+8=24

All the numbers to see are, 6, 8, 0, 2, 4, 1.

And, The sum of all the numbers are 21.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Here,

In the figure,

All the numbers which can be seen are,

⇒ 6, 8, 0, 2, 4, 1

Now, Add all the numbers, we get;

⇒ 6 + 8 + 0 + 2 + 4 + 1

⇒ 21

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Answer: your answer should be 103

Answer: 0.155

Step-by-step explanation:

g / 1000 = kilograms

155 / 1000 = 0.155

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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Answer:

Horizontal Compress of 1/4.

Vertical compress of 1/4 as well.

Step-by-step explanation:

Looking at the graph the big Parallelogram HIJK gets becomes smaller parallelogram H'I'J'K'

I have counted the vertical and horizontal of the graph.

So the dilation is

Horizontal Compress of 1/4.

Vertical compress of 1/4.

Answer:

Here's a tree diagram to represent all of the possible outcomes for the coin landing on red or on yellow:

   / Red \

   /        \

  /          \

Start         End

  \          /

   \        /

     \Yellow/

The "Start" node represents the beginning of the experiment, and it has two branches: one for the coin landing on red, and one for the coin landing on yellow. The branches lead to the "Red" and "Yellow" nodes, respectively, which represent the possible outcomes. Finally, each outcome leads to the "End" node, which represents the end of the experiment.

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

Answer:

\(A = 125 \textrm{ yd}^2\)

Step-by-step explanation:

The area of a triangle can be solved for using the formula:

\(A_\triangle = \dfrac{1}{2}b h\)

where \(b\) is the length of the triangle's base and \(h\) is the length of its height (altitude).

Both \(b\) and \(h\) are given to us for the shown triangle, so all we have to do is plug the given values into the triangle area formula above.

\(A = \dfrac{1}{2} \cdot 10 \cdot 25\)

\(A = 5 \cdot 25\)

\(A = 125 \textrm{ yd}^2\)

Note that the height of the triangle is given on the outline of an auxiliary (dotted) right triangle. This is just to show that the height is in fact an altitude, meaning it is perpendicular to the base, not at the angle of the triangle's other sides.

Hello!

\(\large\boxed{b = 10in}\)

Formula for the area of a triangle:

A = 1/2(bh)

We are given the height and area, so we can plug those into the formula to solve for b:

90 = 1/2(18b)

Multiply both sides by 2:

180 = 18b

Divide both sides by 18:

b = 10 inches.

Answer:

10inches is equal to the base

Step-by-step explanation:

formula for finding the area of a triangle is

½bh which is half times base times height

-base is unknown, height is 18 and area is 90.

-½x*18=90

½of 18 is 9

1x*9=90

9*x=9x

therefore:9x=90

we devide both sides by the co-efficient of x which is 9

9 dividing 90 is 10.

therefore x is equal 10

Answer:

He bought 7 erasers take 10 dollars and keep adding 2

Answer:

x = 80

Step-by-step explanation:

We have, 150% · x = 120

or, 150/100 · x = 120

Multiplying both sides by 100 and dividing both sides by 150,

we have x = 120 · 100/150

x = 80

If you are using a calculator, simply enter 120×100÷150, which will give you the answer.

[RevyBreeze]

Answer:80

Step-by-step explanation:

we have,

150x/100 = 120

x = 120 x 150/100

x= 80

The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

We have to given that;

Expression to find exact value is,

⇒ sin 9π/4

Now, WE can change it into degree as,

⇒ 9π/4

⇒ 9 × 180 / 4

⇒ 9 × 45

⇒ 405 degree

Hence, We get;

⇒ sin 9π/4

⇒ sin 405°

⇒ sin (360 + 45°)

⇒ sin 45°

⇒ 1 / √2

Thus, The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

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Applying the system of equations given, we can conclude that: a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

To solve the system of equations, let's substitute the value of x from the first equation into the second equation:

x = 4y

8 + 2y = 4y

Simplifying the equation, we get:

8 = 2y

Dividing both sides by 2:

4 = y

Now, substitute the value of y back into the first equation to find x:

x = 4y

x = 4(4)

x = 16

Therefore, Nikhil has been employed by the company for 16 years, and Mae has been employed for 4 years.

The correct answer is option a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

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Answer:

Hope this helps ;)

Step-by-step explanation:

If you stretch the square root function F(x)=√x vertically by four units, the new function can be represented by the equation:

G(x) = 4 * √x

This can be written as:

G(x) = 2 * √(2x)

Alternatively, you can write the equation as:

G(x) = √(4x)

Either way, the vertical stretch of the square root function by four units is given by the equation G(x) = 4 * √x or G(x) = 2 * √(2x) or G(x) = √(4x).

No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.

Mark's answer is not correct.

When dividing a number line into equal sections, the value of each section represents a fraction of the whole.

In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.

Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.

So far, this is correct.

However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.

So, each of these smaller divisions represents 1/2 \(\times\) 1/3 = 1/6 (one-sixth) of the whole.

Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.

Mark made an error by mistakenly assuming that each smaller division represents the number 3.

In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.

The correct representation for dividing the number line as described is 1/6.

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It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

£21.216

Step-by-step explanation:

1 litre=£1.04

20.4 litre=£20.4*1.04

=£21.216

Answer:

=£21.216

Step-by-step explanation:

1 litre=£1.04

20.4 litre=£20.4*1.04

=£21.216