A cereal company estimates that its monthly cost is
C(x) = 400x2 + 300x and its monthly revenue is
R(x) = -0.6x3 + 900x2 – 400x + 700, where x is in thousands of
boxes sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?

SOLUTION

From this, the number of combinations possible for 1 flavor, 1 topping and 1 cone becomes

hence the answer is 72 combinations

Answer:

D, the volume of the rectangular prism is 36 cm

Step-by-step explanation:

2 x 3 x 6 = 36

Given:

The inequality is \(y<-2x-4\).

To find:

The graph of the given inequality.

Solution:

The inequality is

\(y<-2x-4\)

The related equation is

\(y=-2x-4\)

For x=0,

\(y=-2(0)-4\)

\(y=0-4\)

\(y=-4\)

For y=0,

\(0=-2x-4\)

\(4=-2x\)

\(\dfrac{4}{-2}=x\)

\(-2=x\)

So, the related line passes through two points (0,-4) and (-2,0).

Sign of inequality is <, so the related line is a dotted line and shaded region is below the related line.

Therefore, the correct option is B.

Answer:

hopefully this helps :] 16th line down I think

Step-by-step explanation:

here is the answer to your question

Answer:

C. 22 degrees

Step-by-step explanation:

<CBD = 90-68=22

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

\(\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)  

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                             \(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = 9x^{10} \tan^{-1}(x)\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The domain of a function h(x) is x < 5, and the range is y< 4. The domain and range of its inverse function, h-¹ (x) will be  domain is x < 5 and range: y < 4.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

Given,

The domain of a function h(x) is x < 5, and the range is y< 4.

The domain and range of its inverse function, h-¹ (x)

The domain and range switch places when the function is inverted.

This indicates that x < 4 and y < 5 are the domain and range of its inverse function, h-1(x).

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Answer:

0.500000

Step-by-step explanation:

Answer:

It is non repeating

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

The side lengths satisfy the Pythagorean theorem.

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Answer:

8

Step-by-step explanation:

3/4 = 6/8

Answer:

8 cause common can be like

In-state corresponds to students who are residents of the same state as the university, out-of-state corresponds to students from different states, and foreign corresponds to students from countries other than the university's country.

To match the vocabulary word with its corresponding example in the context of the state university survey, we need to understand the terms and their meanings.

Here are the vocabulary words and their corresponding examples:

Vocabulary Word: In-state

Example: A student who is a resident of the same state where the university is located.

They pay lower tuition fees compared to out-of-state or foreign students.

Vocabulary Word: Out-of-state

Example: A student who is not a resident of the state where the university is located.

They typically pay higher tuition fees compared to in-state students.

Vocabulary Word: Foreign

Example: A student who is from a country other than the country where the university is located.

They are international students who may have different visa requirements and tuition fees.

To match these vocabulary words with their corresponding examples:

In-state: A student from the same state as the university, paying lower tuition fees.

Out-of-state: A student from a different state than the university, paying higher tuition fees.

Foreign: A student from a country other than the country where the university is located, with potential differences in visa requirements and tuition fees.

By associating each vocabulary word with its respective example, we can accurately describe the three categories of students based on their residency and origin in the context of the state university's survey.

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Answer:

I'm pretty sure the answer is 40.

Step-by-step explanation:

1:4 meaning

1-10 inches

10 x 4 equals 40ft.

Because of the scale being 1:4 .

Answer:

8000

Step-by-step explanation:

Answer:

g(4) = 10

f⁻¹(11) = 1

h{g(4)} =

if h(x) = (10/x) – 3 = 7

if h(x) = 10/(x – 3) = 10/7

____________

f⁻¹(x) = (x - 4) / 7

Answer:

x = 4

Step-by-step explanation:

fFs

Answer:

Step-by-step explanation:2 ( + 4 )

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

On Julie's door, the images will span 210 square inches.

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.

The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.

From the question:

Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.

One image's area is as follows:

5 inches x 7 inches = 35 square inches

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Consequently, 210 square inches of Julie's door will be covered by the images.

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The minimum possible volume of this rectangular prism is 176.78 ft³.

The maximum possible volume of this rectangular prism is 131.11 ft³.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

In order to determine the minimum possible volume of this rectangular prism, we would add the greatest possible error to each measurement and then multiply as follows:

Vmin = (3.5 + 0.25) × (8.4 + 0.25) × (5.2 + 0.25)

Vmin = 3.75 × 8.65 × 5.45

Minimum possible volume, Vmin = 176.78 ft³.

In order to determine the maximum possible volume of this rectangular prism, we would subtract the greatest possible error from each measurement and then multiply as follows:

Vmax = (3.5 - 0.25) × (8.4 - 0.25) × (5.2 - 0.25)

Vmax = 3.25 × 8.15 × 4.95

Maximum possible volume, Vmax = 131.11 ft³.

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Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Answer:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

Step-by-step explanation:

Which ordered pairs are in the relation {(x, y) | x > y + 1} on the set {1, 2, 3, 4}

Assuming that:

R should be the set of real numbers such that:

R = { (x,y) | x > y + 1}  on the set {1, 2, 3, 4}

Then:

The ordered pairs for the relation can be computed as:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Weight of Omar after 4 weeks is 9.4375 pounds.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Weight of Omar at the time of birth = 8 pound 3 ounces

Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces

New weight of Omar

= (8 lb 3 ounces) + 20 ounces

= 8 lb + 23 oz

As, we know 16 ounces = 1 pound

23 ounces = 1.4375 pound

Now, total weight of Omar after 4 weeks = 8 lb + 23 oz

                                                                  ≈ 8 lb + (1.4375) lb

                                                                   ≈ 9.4375 pounds

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Answer:

here ya go.

Step-by-step explanation:

15=j+9

subtract 9 from both sides.

j= 6