Write Polynomial in a standard form.

7x-5-x^3+6x^4-3x^2
​

Answer:

Y = 1000 when X = 0

Since X is the time

1000 (units) were initially present at time t = 0

The Taylor series for the function f(x) = 1/x centered at a = 3 is given by:

1/(x-3) = -1/(3-x) = -1/3 - (x-3)/9 - (x-3)²/27 - (x-3)³/81 - ...

This is a Maclaurin series with the associated radius of convergence R = ∞, since the function is analytic everywhere except at x = 3.

To derive the Taylor series, we first find the derivatives of f(x) = 1/x:

f'(x) = -1/x², f''(x) = 2/x³, f'''(x) = -6/x⁴, f⁴(x) = 24/x⁵, ...

Evaluating these derivatives at x = 3 gives:

f(3) = 1/3, f'(3) = -1/9, f''(3) = 2/27, f'''(3) = -6/81, f⁴(3) = 24/243, ...

Using these values, we can write the Taylor series in sigma notation as:

1/(x-3) = Σ (-1)ⁿ (x-3)ⁿ / 3ⁿ⁺¹, n = 0 to ∞

This series converges for all x such that |x-3| < 3, which gives us the radius of convergence R = 3.

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Answer:

This would be a .04 or 4% decay.....

for every "time unit" (x in this case) you will be multiplying

the amount by .96 ... in other words if you started with one dollar

the results would be 96 cents... after two "time" steps you would have

only 92 cents (.96 *.96)

Step-by-step explanation:

(a) The product function would be f(x) * g(x) = x(4x^2 - 5) = 4x^3 - 5x.
(b) To find the rate-of-change function, we need to take the derivative of the product function. So, f'(x) = d/dx (4x^3 - 5x) = 12x^2 - 5. This is the rate-of-change function for the product of f(x) and g(x).

Let's define the functions and find the product function and the rate-of-change function.

Given:
g(x) = 4x^2 - 5
f(x) = x

(a) Product function:
To find the product function, we need to multiply g(x) and f(x) together.

Product function = f(x) * g(x) = x * (4x^2 - 5)

Product function = 4x^3 - 5x

(b) Rate-of-change function:
To find the rate-of-change function, we need to find the derivative of the product function with respect to x.

f'(x) = d(4x^3 - 5x) / dx

Using the power rule, we get:

f'(x) = 12x^2 - 5

So, the rate-of-change function is f'(x) = 12x^2 - 5.

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Answer:

This is a scatter plot . A scatter plot shows the association between two variables.

The variables in this graph tend to increase and decrease together, this means the association is positive. The straight line describes the relationship between the variables, the association is linear. The association is a linear relationship.

This graph has a wider and more variables/dots around it, meaning that more of the variables are uncorrelated.

This graph also has a few outlier variables.

Could you plz answer my question

Step-by-step explanation:

Those two trains met 4 hours after 1 pm or at 5 pm. They met at 350 miles from train A's starting point.

The relation between distance, speed, and time is given by:

distance = speed x time

In the given problem:

Train A leaf at 12.00 pm, with

speed = 70 mph

Since train B left at 1 pm, by the time train B left, train 1 has travelled a distance of:

distance train A = 70 mph x 1 hour = 70 miles.

Hence, when train A and train B left at 1 pm, they are 550 - 70 = 480 miles apart.

Let

sA = distance travelled by train A since 1 pm

sB = distance travelled by train B since 1 pm

Hence,

sA = 70 t

sB = 50 t

When they met:

sA + sB = 480

70t + 50t = 480

120t = 480

t = 480/120 = 4 hours

Therefore, the met at 5 pm. At that time, train A has travelled 5 hours and its position is:

distance = 70 x 5 = 350 miles from its starting point.

Your question seems incorrect, most probably the correct question was:

Two trains heading toward each other from 550 miles apart one leaves at noon with a speed of 70 mph and the other leaves at 1 with a speed of 50 mph when they meet how far are they from train a starting point

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In the given study, the correct symbols representing the underlined numbers are as follows:

- 6.8 hours is represented by μ (mu). The symbol μ is used to represent the population mean.

- 1.5 hours is represented by σ (sigma). The symbol σ is used to represent the population standard deviation.

- 30 NIACC students is represented by n. The lowercase letter n is commonly used to denote the sample size.

- < 6.4 hours is represented by\(x (x-bar)\). The symbol \(x bar\) is used to represent the sample mean.

Therefore, it's important to note that the study is comparing the sleep habits of college students (population) to a sample of NIACC students. The population mean and standard deviation are given for the college students, while the sample mean is provided for the NIACC students.

The sample size (number of NIACC students) is also given. These symbols allow for the distinction between population parameters and sample statistics, which is crucial in statistical analysis and inference.

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The down payment is 400, the monthly payment is 65 and the length of the plan is 7 months. An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive numbers is constant.

Arithmetic refers to the branch of mathematics that deals with numbers and the basic operations of addition, subtraction, multiplication, and division. An arithmetic sequence is a specific type of mathematical pattern where each term is obtained by adding a constant value to the previous term.

Here is the way to determine the monthly payment:

(1,060 - 400) / 7 = (660) / 7 = 65

As you can see the down payment is 400 and the last value in the sequence is 1060, so the total amount of the plan is 1060.

Also, the difference between any two consecutive terms is 110, as we can see that from the sequence:

510 - 400 = 110

620 - 510 = 110

730 - 620 = 110

840 - 730 = 110

950 - 840 = 110

1060 - 950 = 110

So the length of the plan is 7 months as the sequence contains 7 terms.

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Non-overlapping intervals:

If the intervals(say interval a & interval b) doesn't overlap then the set of pairs form by [a. end, b. start] is the non-overlapping interval.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers {\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Let's take the below mentioned overlapping intervals example to explain the idea: If both ranges have at least one common point, then we say that they're overlapping. In other words, we say that two ranges and are overlapping if: On the other hand, non-overlapping ranges don't have any points in common.

Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.

Examples:

interval (a) = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }

Output:  [5, 7]

The only interval which doesn’t overlaps with the other intervals is [5, 7].

interval (a) = { {1, 3}, {9, 12}, {2, 4}, {6, 8} }

Output: [4, 6]  and [8, 9]

There are two intervals which don’t overlap with other intervals are [4, 6], [8, 9].

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Answer:

D. 0.366

Step-by-step explanation:

Hello!

A stemplot is a way of arranging a data set.

In the stem you'll find the integer and first two decimal digits of the batting average, because these values are repeated several times.

In the leafs you'll find the third decimal digit.

So for the first value of the stem "0.32" there is only one observation:

0.329 ⇒  0.32 | 9

For the second value "0.33" correspond 14 observations: 0.330, 0.331, 0.331,0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336,  0.337, 0.338, 0.338, 0.338

0.33 | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

For the third value "0.34" correspond 12 observations: 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342,  0.344, 0.344, 0.345, 0.346, 0.349

0.34 | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

For the fifth value "0.35" and the sixth value "0.36" there is only one observation, so, as happened with the first one, these values of the stem will only have one "leaf"

0.358 ⇒ 0.35 | 8

0.366 ⇒ 0.36 | 6

So the whole stem plot for this 30 observations is:

Stem | Leafs

0.32  | 9

0.33  | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

0.34  | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

0.35  | 8

0.36  | 6

Considering this, the correct option is D

I hope this helps!

The correct first step in solving the equation 6x=24 is: D. log 6x = log 24.

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) and may contain variables, constants, and arithmetic operations. Equations are used to solve problems and find unknown values.

Here,

Then, using the logarithmic property of equality, we can simplify this to:

log 6x = log 24

log 6 + log x = log 24

log x = (log 24)/(log 6)

Finally, we can solve for x by taking the antilogarithm (exponentiating) of both sides:

\(x = 10^{log x}\)

\(=10^{log 24/log 6}\)

= 8.6587 (rounded to four decimal places).

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Answer: a = -8

Step-by-step explanation:

Given

-8a - 5 = -7a + 3

Subtract 3 on both sides

-8a - 5 - 3 = -7a + 3 - 3

-8a - 8 = -7a

Add 8a on both sides

-8a - 8 + 8a = -7a + 8a

a = -8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a = -8

Step-by-step explanation:

-8a-5=-7a+3                    Add 5 to both sides.

- 8a = - 7a + 3 + 5           Combine

-8a = - 7a + 8                  Add 7a to both sides

-8a + 7a = 8                    Combine

-a = 8                              Multiply by - 1

a = - 8                          

When you get a weird number like this, you should check it.

LHS = -8(-8) - 5

LHS = 64 - 5

LHS = 59

RHS = -(7*-8) + 3

RHS = -(-56) + 3

RHS = 56 + 3

RHS = 59

So a = - 8 must be right.

Answer:

2.5

Step-by-step explanation:

2x = 5

x = 5/2 = 2.5

I hope im right!!

When one outcome is favored over another, we call this favoritism or preference.

When one outcome is favored or chosen over another, it is referred to as favoritism or preference. Favoritism implies a bias towards a particular outcome or individual, while preference suggests a personal inclination or choice.

This concept is commonly encountered in various contexts. For example, in decision-making, individuals may show favoritism towards a specific option based on personal preferences or biases. In voting, people may have a preference for a particular candidate or party. In sports, teams or players may be favored over others due to their past performance or popularity. Similarly, in competitions, judges or audiences may exhibit favoritism towards certain participants.

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When one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

When one outcome is preferred or desired over another, we commonly refer to this as a preference or favoritism toward a particular result. It implies that there is a subjective inclination or bias towards a specific outcome due to various factors such as personal beliefs, values, or goals. This preference can arise from a range of contexts, including decision-making, competitions, or evaluations.

The concept of favoring one outcome over another is deeply rooted in human nature and can shape our choices and actions. It is important to recognize that preferences can vary among individuals and may change depending on the circumstances. Furthermore, the criteria for determining which outcome is favored can differ from person to person or situation to situation.

In summary, when one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

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The  slope of line is -4/3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

(5, 5) and (2, 9).

Using slope

slope= ( 9-5)/(2-5)

slope= 4/(-3)

slope= -4/3

Hence, the slope of line is -4/3.

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The correct command to plot vector x versus vector y on the 2nd row and 2nd column position of a figure divided into 2 rows and 3 columns is:

x=[1; 2; 3]; y=[4; 5; 6];

subplot(2, 3, 4);

plot(x, y)

To plot vector x versus vector y on the 2nd row and 2nd column position of a figure divided into 2 rows and 3 columns, the correct command is:

x = [1; 2; 3];

y = [4; 5; 6];

subplot(2, 3, 4);

plot(x, y);

Let's break down the command:

x = [1; 2; 3]; assigns the values [1, 2, 3] to the variable x, creating a column vector.

y = [4; 5; 6]; assigns the values [4, 5, 6] to the variable y, creating a column vector.

subplot(2, 3, 4); creates a subplot grid with 2 rows and 3 columns and selects the position for the current plot as the 4th subplot (2nd row and 2nd column).

plot(x, y); plots vector x versus vector y in the current subplot position.

This command will divide the current figure into 2 rows and 3 columns and plot vector x versus vector y on the 2nd row and 2nd column position.

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Answer:

21/4

Step-by-step explanation:

1/2[-8 +16 - ( -2 1/2)] = 1/2 ( - 8 + 16 +  2 1/2) = 1/2 ( 8 + 2 1/2) = 1/2 * \(10 \frac{1}{2}\) = 1/2 * 21/2 = 21/4

Answer:

The answer is 11.6 cm

Step-by-step explanation:

The equation of a right triangle is a^2+b^2=c^2 (a and b being its legs and c its hypothenuse.)

Now we must input 16 cm into c and 11 cm into either a or b.

a^2+11^2=16^2 which is equal to a^2+121=256.

subtract 121 from both sides to get a^2 by itself

a^2+(121-121)=(256-121)

a^2=135

to get "a" by itself, we must find the square root of 135.

√a^2=√135

a=11.6

Answer:

x=5

h = 5 sqrt 2

Step-by-step explanation:

isosceles right triangles are always 45-45-90, ratio of those triangles are always x:x:x*sqrt 2

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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you should know the observed frequencies or counts for different categories or levels of the variable you are examining. Therefore, the correct answer is B.

The chi-square test is a statistical test used to determine if there is a significant association between categorical variables. It compares the observed frequencies in each category to the expected frequencies, assuming there is no association or difference between the variables. By comparing the observed and expected frequencies, the test calculates a chi-square statistic, which follows a chi-square distribution.

In order to calculate the expected frequencies, you need to have the frequency distribution of the variables of interest. This means knowing the counts or frequencies for each category or level of the variable. The test then compares the observed frequencies with the expected frequencies to determine if there is a significant difference.

The mean, variance, and other measures of central tendency and dispersion are not directly involved in the chi-square test. Instead, the focus is on comparing observed and expected frequencies to test for associations or differences between categorical variables.

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Answer:

the answer would be A

Step-by-step explanation:

Answer:

answer is a

Step-by-step explanation:

I just answer it on edge

The inequality that best describes his morning commute is:

10 + x + y ≥ 210

We know that his commute each morning is:

So the total commute, in minutes, is:

10 + x + y

We know that he spends, at least, 3.5 hours in total, so we can write:

10 + x + y ≥ 3.5*(60) = 210

Where on the left side we wrote the 3.5 hours in minutes, by multiplying it by 60.

Then the inequality is:

10 + x + y ≥ 210

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The "Assume Non-Negative" option in Excel Solver is helpful when the solution to a problem appears to depend on the starting values for the decision variables.

This option is particularly useful when working with linear programming problems where the solution depends on the values of the decision variables, and there is no clear starting point.

The "Assume Non-Negative" option instructs Solver to assume that all decision variables have non-negative values. This means that the solution will only be searched for in the non-negative space, which can help to narrow down the solution space and make the search more efficient.

In other words, Solver will not search for solutions that violate the non-negative constraint, which can save time and computational resources.

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Answer:

Step-by-step explanation:

Formula for the volume of a cone:

((r^2)(height)(pi)) / 3

Since we are finding the answer in terms of pi, we will use the pi symbol.

The radius is 18.

The height is 30.

18^2 is 324.

324 x 30 is 9720.

9720 / 3 is 3240.

Answer : 3240 pi.

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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Another important mathematical contribution made by Fibonacci (Leonardo of Pisa) is the introduction of the Hindu-Arabic numeral system and its adoption in Western mathematics.

During the 13th century, Fibonacci traveled extensively and encountered the numeral system used in India and the Arab world, which is based on the concept of place value. Recognizing its efficiency and advantages over the existing Roman numeral system, Fibonacci popularized the Hindu-Arabic numeral system in Europe through his influential book "Liber Abaci" (Book of Calculation) published in 1202.

The Hindu-Arabic numeral system, which includes the use of the digits 0-9 and the concept of positional notation, revolutionized arithmetic and made calculations much simpler and more efficient. It introduced the concept of using place value to represent numbers, allowing for complex calculations to be performed with ease. This numeral system formed the foundation of modern arithmetic and laid the groundwork for the development of algebra and other branches of mathematics.

Fibonacci's introduction and promotion of the Hindu-Arabic numeral system had a profound impact on mathematics, commerce, and scientific endeavors. It enabled advancements in fields such as astronomy, engineering, and finance, making complex calculations more accessible and accurate. Fibonacci's contribution played a crucial role in the development of mathematics and its practical applications, and it remains a significant part of our everyday numerical representation and calculation systems today.

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Answer:

9 snacks

Step-by-step explanation:

50-9.2=40.8 40.8/4.25=9.6 soooooooo you can get 9 full snacks.