The result of which expression will best estimate the actual product of (Negative four-fifths) (three-fifths) (Negative StartFraction 6 over 7 EndFraction) (five-sixths)?
(Negative 1) (one-fourth) (Negative 1) (negative 1)
(Negative 1) (one-half) (Negative 1) (1)
(Negative StartFraction 4 over 2 EndFraction) (Three-halves) (Negative two-fifths) (Five-halves)
(Negative three-fourths) (Negative three-fourths) (Negative one-fifth) (One-half)

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

Answer:

0.04

Step-by-step explanation:

0.03508772

Answer:

Step-by-step explanation:

Answer: II

Step-by-step explanation:

(a) The value of the investment after four years when interest is compounded yearly is $2629.76.

Investment is the act of committing money or capital to an endeavor with the expectation of obtaining an additional income or profit. It is the commitment of resources to a specific venture with the expectation of reaping a reward in the future. It is an important part of personal finance, as it is a way to increase wealth and build financial security.

This is calculated by taking the initial investment of $2100 and multiplying it by the interest rate of 6% for four years (1.06⁴).
(b) The value of the investment after four years when interest is compounded monthly is $2658.25. This is calculated by taking the initial investment of $2100 and multiplying it by the interest rate of 6% for four years with 12 compounding periods per year (1.005⁴⁸).

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7300\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=7300\left(1+\frac{0.042}{4}\right)^{4\cdot 5}\implies A=7300(1.0105)^{20}\implies A\approx 8996\)

1.

9 (3+2)

We have to distribute number 9 in the parenthesis, multiply each term in the parenthesis by 9:

9(3)+9(2)

27+18

45

2.

11(4-1)

11(4)+11(-1)=44-11=33

3.

12(7+7)

12(7)+12(7)

84+84

168

4.

5 (4+8)

5(4)+5(8)

20+40

60

5.

10(9-5)

90-50

40

Answer: the product is always positive.

Step-by-step explanation: Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.

Answer: No because the product of a positive integer and a negative integer is always negative.

-0.2

'0

-0.2 = - .2 = - 2/10 = - 1/5

so

answer is -1/5

Answer:

-0.2 = -1/5

Step-by-step explanation:

you have to turn the decimal to a fraction.

0.2/1

multiply 0.2/1 by 10/10 which is 2/10

Since the GCF is 2...

You want to divide 2/10 by 2/2

that is 1/5

Now add the negative number sign

BOOM

Now you got yourself -1/5

I hope I helped! :)

With regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W),

When, W = 10 then dw/dt = 6

When W = 35 then d²w/d²t = 0

where the point influx occurs, the weight of the carrying capacity is half

Therefore, 35 = a/2

Then the carrying capacity (a) = 35 x 2

a = 70

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable. Calculus's core tool is the derivative. It is a crucial idea that is incredibly helpful in a variety of contexts: in daily life, the derivative can inform you how fast you are driving or assist you in predicting stock market changes; in machine learning, derivatives are crucial for function optimization.

Therefore, with regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W), because the carrying capacity is 70 and the rate of change of the weight is 6 grams per hour when the weight is 10 grams.

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The correct option is C for the frequency table.

A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.

The correct two-way frequency table for the date will look like this:

                                               RAP      ROCK     COUNTRY     TOTAL

Grades 9-10             40           30            55                  125

Grades 11-12            60           25            35                  120

TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total

125 + 120 = 100 + 55 + 90

245 = 245

The correct option for the frequency table is C.

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Answer:

okay i'll keep this in mind

Step-by-step explanation:

Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

3

Step-by-step explanation:

i gotchu homie, dont even sweat

Answer: Yes

Step-by-step explanation:

∛1728= ∛(2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3)

= 2 x 2 x 3

=12

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Answer:

$2.50/pound

Step-by-step explanation:

Because if its $5for 2 pounds divide by 5 by 2 to see how much 1 pound costs

Given, base of the right angled triangle, b=40.

The altitude of the right angled triangle, h=9.

The hypotenuse of the right angled triangle can be calculated using Pythagoras theorem as,

Therefore, the the missing side (hypotenuse) of the triangle

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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In order to find the amount each person gets we divide the number of pies by the number of persons

The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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The interval notation for the inequality statement "5 less than m is at most 70" is (-∞, 75].

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The statement given is - 5 less than m is at most 70.

The given sentence can be translated into a mathematical inequality as -

m - 5 ≤ 70

To solve for m, we can add 5 to both sides of the inequality -

m - 5 + 5 ≤ 70 + 5

m ≤ 75

Therefore, m is less than or equal to 75.

In interval notation, we can represent this solution as -

(-∞, 75]

Therefore, the interval value is (-∞, 75].

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To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

The length and width of the rectangle are 5 inches and 1 inches respectively.

The length and width of the rectangle can be found as follows;

l = 3 + 2w

area of a rectangle = lw

where

Therefore,

5 = lw

5 = (3 + 2w)w

5 = 3w + 2w²

2w² + 3w - 5 = 0

Hence,

2w² + 3w - 5 = 0

Therefore,

w = 1  and w = - 5 / 2

width = 1 inches

length =  3 + 2(1) = 5 inches

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Answer:

y = -x - 2

Step-by-step explanation:

Use equation: y = mx + b, where "m" is the slope and "b" is the y intercept. You are given a slope of -1 for the m. This is usually expressed as just a "-", as the 1 is inferred.

Since you are given a point, plug the x and y values in to the equation.

-7 = -(5) + b

Solve for b:

-7 = -5 + b

-2 = b

Knowing "m" and "b", plug these in to get your final equation

y = -x - 2

Answer:

\(C)\:\:\frac{\sqrt 2}{ 2 } \)

Step-by-step explanation:

\( \sin \bigg( \frac{3\pi}{4} \bigg) \\ \\ = \sin \bigg( \pi - \frac{\pi}{4} \bigg) \\ \\ = \sin \bigg(\frac{\pi}{4} \bigg) \\ \\ = \frac{1}{ \sqrt{2} }\\\\= \frac{\sqrt 2}{ 2 }\)

Answer:

both have the same amount of dots I know that.

Step-by-step explanation:

also, I love the profile picture:)

Answer: 1, 2, and 5

Step-by-step explanation:

I did it myself