How many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1. 4) to within 0. 0001?

The equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

In the question, we are asked to find the equation of the line of BEST FIT for the given scatter plot.

We let the time be the independent variable x, and velocity is the dependent variable y.

We find the line of best fit using the least square method.

First, we calculate the mean:

Now, we find the slope of the line of best fit, using the formula:

m = {∑(x - μ(x))(y - μ(y))}/{∑(x - μ(x))²}.

Taking value from the tables, which is attached, we get:

m = 239.35/109.2683333 = 2.190479096.

Now, we calculate the y-intercept of the line of best fit, using the formula:

b = μ(y) - m.μ(x),

or, b = 20.5 - 2.190479096*6.283333 = 6.736489681.

Now, the equation of the line of best fit, in the form of y = mx + b, can be written as, y = 2.190479096x + 6.736489681, which on approximation, and making y as v, the velocity, and x as t, the time, we get: v = 2.19t + 6.7.

Thus, the equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

Learn more about the least square method at

https://brainly.com/question/15088393

#SPJ1

[tex]direct \: variation \: lines \: pass \: through \: the \: origin[/tex]

Answer: 2

Step-by-step explanation:

Each of the two sides of the equation is set equal to y

By adding fractions, we conclude that the correct option is the third one:

"one and two sevenths tubes"

We know that:

The total amount of paint will be given by the direct addition of these two fractions, notice that the denominator is the same in both cases, so we can just add the numerators.

5/7 + 4/7 = (5 + 4)/7 = 9/7

We can rewrite this as:

9/7 = 7/7 + 2/7 = 1 + 2/7

Thus, the correct option is the third one

"one and two sevenths tubes"

If you want to learn more about fractions:

https://brainly.com/question/11562149

#SPJ1

A number line ranges from minus 5 to 5 with increment of 1 unit. Left, Point F is plotted on the number line at minus 3. Right, point G is plotted on the number line at 1.50, then the distance between F and G is 4.50.

Calculating the Distance between F and G:

It is given that, on a number line,

Point F is located at -3

Point G is at 1.50

Since, 1.5 > (-3) and each number is at a 1 unit difference form the adjacent number on the number line,

The difference between F and G = 1.50 - ( -3 )

This implies that the distance between F and G = 1.50 + 3

= 4.50 units

The numbers lying between the points F and G on the number line are: -2, -1, 0, and 1

Learn more about a number line here:

https://brainly.com/question/13189025

#SPJ1

Answer: 4 1/2

Step-by-step explanation:

Got it right

Answer:

Wayne used 2/5 more flour than sugar

Step-by-step explanation:

If you add 2/5 to 2/5 you get 4/5

The answer is C. 3√5.

[tex]g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2[/tex]

generate by:  Amplitude:5    Period:4

                      Phase shift:(3 to the right)    Vertical shift:-2

x=3,g(x)= 3

x=4,g(x)= -2

x=5,g(x)= -5

x=6,g(x)= -2

x=7,g(x)= 3

the graph is like cos(x)

learn more about trigonometric graphs here:

https://brainly.com/question/18265536

#SPJ1

The element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

To find the element:

As we have given two matrices A and B:

Therefore, the element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

Know more about matrix here:

https://brainly.com/question/24079385

#SPJ4

By the use of the completing the square method, the maximum height is 3 ±√29/4 + 9 m.

The maximum height has been modeled by the use of the equation f(x)= -4x^2 +24x -29. Now we know that f(x)= h so we can write;

h = -4x^2 +24x -29

Now we have;

0 = -4x^2 +24x -29

-4x^2 +24x -29= 0

x^2 - 6x = -29/4

(x - 3)^2 = -29/4 + 3^2

(x - 3)^2 =  -29/4 + 9

x = 3 ±√29/4 + 9 m

Learn more about completing the square:https://brainly.com/question/4822356

#SPJ1

The first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

In this question,

The nth term of the sequence is [tex]a_n=\frac{3^{(n-1)} }{n!}[/tex]

Now substitute the values of n = 1,2,3,4,5

For n = 1,

⇒ [tex]a_1=\frac{3^{(1-1)} }{1!}[/tex]

⇒ [tex]a_1=\frac{3^{0} }{1}[/tex]

⇒ a₁ = 1

For n = 2,

⇒ [tex]a_2=\frac{3^{(2-1)} }{2!}[/tex]

⇒ [tex]a_2=\frac{3^{(1)} }{(1)(2)}[/tex]

⇒ [tex]a_2=\frac{3}{2}[/tex]

For n = 3,

⇒ [tex]a_3=\frac{3^{(3-1)} }{3!}[/tex]

⇒ [tex]a_3=\frac{3^{(2)} }{(1)(2)(3)}[/tex]

⇒ [tex]a_3=\frac{9}{6}[/tex]

⇒ [tex]a_3=\frac{3}{2}[/tex]

For n = 4,

⇒ [tex]a_4=\frac{3^{(4-1)} }{4!}[/tex]

⇒ [tex]a_4=\frac{3^{(3)} }{(1)(2)(3)(4)}[/tex]

⇒ [tex]a_4=\frac{27}{24}[/tex]

⇒ [tex]a_4=\frac{9}{8}[/tex]

For n = 5,

⇒ [tex]a_5=\frac{3^{(5-1)} }{5!}[/tex]

⇒ [tex]a_5=\frac{3^{(4)} }{(1)(2)(3)(4)(5)}[/tex]

⇒ [tex]a_5=\frac{81}{120}[/tex]

⇒ [tex]a_5=\frac{27}{40}[/tex]

Hence we can conclude that the first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

Learn more about sequence here

https://brainly.com/question/14147167

#SPJ4

Answer:

7/10

Step-by-step explanation:

take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3

An inequality greater than (-3) but less than or equal to 3 is as follows:

- 3 < x ≤ 3

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

An inequality have the following signs:

Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:

Note the value we are comparing is x.

Hence,

- 3 < x ≤ 3

learn more on inequality here: https://brainly.com/question/1820270

#SPJ1

The perpendicular bisector of a chord passes through the center of a circle.

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.

The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.

Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.

Learn more about chord  at:

https://brainly.com/question/13950364

#SPJ1

Answer:

[tex] - 0.2026[/tex]

Step-by-step explanation:

I hope it is the right answer

1

Anything raised to the power of zero is 1, other than zero itself.

However, as it is given that x is not equal to zero, the answer must be 1.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathsf{(4x^2)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should:}[/tex]

[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable.

The variable you want to predict is called the dependent variable.

The variable you are using to predict the other variable's value is called the independent variable.

Learn more about linear regression here: https://brainly.in/question/14924595

Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.

Therefore, Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.

Know more about linear regression models here:

https://brainly.com/question/25987747

#SPJ4

The complete question is given below:

If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.

A) Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.

B) Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.

C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.

D) Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.

Answer:

  Order of exponentiation can be swapped here, and the fractional power written as a root.

Step-by-step explanation:

The commutative property of multiplication and the rules of exponents apply.

The rule is ...

  (a^b)^c = a^(bc)

The given expression can be rearranged to ...

  [tex]\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}[/tex]

Answer:

[tex]y = \sqrt{x+25} + 5[/tex]

Step-by-step explanation:

Swap x and y

x = y² – 10y

Add 25 to each side to complete the square

x + 25 = y² – 10y + 25

Factor

x + 25 = (y – 5)²

Take the square root of each side

[tex]\sqrt{x+25}[/tex] = y – 5

Add 5 to both sides

[tex]\sqrt{x+25}[/tex] + 5 = y

Answer:

-7624928000 is the right answer.

Step-by-step explanation:

(-7624928) × 997 + 7624928 × (-3)

= -7602053216 + (-22874784)

= -7624928000        Ans..

Hope its helpful :-)

If so, please mark me as brainlist :-)

Answer:

Step-by-step explanation:

=(-7624928) * 997 + 7624928 * (-3)

=-7602053216+(-22874784)

=-7624928000

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 64 }{ {a}^{2} - 10a + 24} \sdot \cfrac{ {a}^{2} - 12a + 36 }{ {a}^{2} + 4a - 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{2} - 6a - 4a+ 24} \sdot \cfrac{ {a}^{2} - 6a - 6a + 36 }{ {a}^{2} + 8a - 4a- 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{} (a - 6) - 4(a - 6)} \sdot \cfrac{ {a}^{} (a - 6) - 6(a - 6) }{ {a}^{}(a + 8) - 4(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{(a - 6) (a -4)} \sdot \cfrac{ (a - 6) (a - 6) }{ {}^{}(a - 4)(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8) }{(a -4)} \sdot \cfrac{ (a - 6) }{ {}^{}(a - 4)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8)(a - 6) }{(a -4) {}^{2} } [/tex]

Or [ in expanded form ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 8a - 6a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} -14a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

Answer:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a^2-64}{a^2-10a+24} \cdot \dfrac{a^2-12a+36}{a^2+4a-32}[/tex]

Factor the numerator and denominator of both fractions:

[tex]\textsf{Apply the Difference of Two Squares formula} \:\:\:x^2-y^2=(x-y)(x+y):[/tex]

[tex]\begin{aligned} a^2-64 & =a^2+8^2 \\ & =(a-8)(a+8)\end{aligned}[/tex]

[tex]\begin{aligned}a^2-10a+24 & =a^2-4a-6a+24\\& = a(a-4)-6(a-4)\\ & = (a-6)(a-4) \end{aligned}[/tex]

[tex]\begin{aligned}a^2-12a+36 & =a^2-6a-6a+36\\& = a(a-6)-6(a-6)\\ & = (a-6)(a-6) \end{aligned}[/tex]

[tex]\begin{aligned}a^2+4a-32 & =a^2+8a-4a-32\\& = a(a+8)-4(a+8)\\ & = (a-4)(a+8) \end{aligned}[/tex]

Therefore:

[tex]\dfrac{(a-8)(a+8)}{(a-6)(a-4)} \cdot \dfrac{(a-6)(a-6)}{(a-4)(a+8)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}[/tex]

[tex]\dfrac{(a-8)(a+8)(a-6)(a-6)}{(a-6)(a-4)(a-4)(a+8)}[/tex]

Cancel the common factors (a + 8) and (a - 6):

[tex]\dfrac{(a-8)(a-6)}{(a-4)(a-4)}[/tex]

Simplify the numerator:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

The value of P(4<X≤12) is 0.45

The complete question is added as an attachment

To calculate P(4<X≤12), we use the following equation

P(4<X≤12) = P(4<X≤8) + P(8<X≤12)

From the histogram, we have:

P(4<X≤8) = 0.1

P(8<X≤12) = 0.35

So, we have:

P(4<X≤12) = 0.1 + 0.35

Evaluate

P(4<X≤12) = 0.45

Hence, the value of P(4<X≤12) is 0.45

Read more about probability at:

https://brainly.com/question/10444337

#SPJ1

Answer:

=========================

We need to make a stem and leaf plot

Rearrange the data in the ascending order:

Group the data as follows:

The first two digits form a stem and the last digits form a leaf.

Make a plot:

       Stem   |  Leaf

The curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

The graph of a polynomial function is a smooth continuous curve. The point where the curve intersects the x-axis is the zero of the polynomial.

A polynomial is also known to have a degree of 3 and above. Hence the given polynomial has a leading degree of 3 and expressed as:

f(x)=−x^3+x^2+9x−9

The graph of the function is as plotted below. From the function, you can see that the curve pass through the y-axis at the coordinate point (0, 10) showing that the y-intercept of the function is (0, 10)

Learn more on polynomial graph here: https://brainly.com/question/10918240

#SPJ1

Answer:

1. Given.

2. <5 is supplementary to <4.

2. Angles 5 and 4 are consecutive angles, and by the consecutive angles theorem, the two are supplementary.

3. m<4 + m<5 = 180

3. By the definition of supplementary angles, m<4 + m<5 = 180.

4. m<2 = m<4

4. Angles 2 and 4 are corresponding angles, and by the corresponding angles postulate, the two are congruent. By the definition of congruent angles, m<2 = m<4.

5. m<5 + m<2 = 180

5. Substitution property of equality.

Pick 2 coordinates:

I choose first & last one (0,15) & (8-9)

Change in y is 24

(15--9 = 24)

Change in x is 8

(0 - 8) = - 8

24/-8 = - 3

So, slope = - 3

Hope this helps!

Answer:

-3

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: 0 --> 2 --> 4 --> 6 --> 8

y value: 15 --> 9 --> 3 --> -3 --> -9

When y changed from 15 to 9, the x changed from 0 to 2.

y: 15 --> 9

x: 0 --> 2

There was a difference of -6 in the y and a difference of 2 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -6 and 2 we found, we can say that the slope is -6/2.

If we simplify this answer, we end up with -3.

So -3 is the slope of the data.

Answer: C, 93m^2

Step-by-step explanation:

first step is to find the surface area of the base. it's 3x3, so that would be 9m^2. the sides of the rectangular prism are 5x3, so one side is 15m^2. there are 4, so 15x4=60m^2. now for the top, which is a triangular prism. each side has a height of 4 and a base of 3. the area of a triangle is 1/2bh, so 1/2(3)(4), which is 6. 4 of these makes 24 m^2. add up all of final numbers to get 9+60+24. this comes to 93m^2, or C.

The real statement is that the closer you get to the center of the vortex, the closer the current speed approaches infinity. option C is correct.

Given the speed s of the flow in a given vortex is modeled by x=300/d, where d is the distance to the center of the vortex.

speed is defined as the rate of change of an object's position in any direction. Speed ​​is measured as the ratio of distance traveled to time traveled.

As d approaches 0, you are approaching the center of the vortex.

[tex]\begin{aligned}S&=\lim_{d\rightarrow 0}\frac{300}{d}\\ &=\frac{300}{0}\\ &=\infty\end[/tex]

Thus, if the flow in a given vortex is modeled by x = 300/d, as one approaches the center of the vortex, the speed of the flow tends to infinity.

Learn more about speed from here brainly.com/question/18219085.

#SPJ1

Answer: C- As you move closer to the center of the whirlpool, the speed of the current approaches infinity.