How do we explain the Riemann sum process that leads to the definite integral that computes arc length?

Answer:

c

Step-by-step explanation:

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

Learn more about dependent variables here:

https://brainly.com/question/30386143

#SPJ1

Answer: No solutions

Step-by-step explanation:

\(5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9\)

However, as absolute value is non-negative, there are no solutions.

The first step is to rewrite the equations in standard form by subtracting the constant from each side.

Standard form is a type of numerical notation used to express large numbers in a concise form. It is based on powers of 10, which means each place value of a number is multiplied by a power of 10. Standard form is typically used in scientific and mathematical applications, and it is also known as scientific notation. To write a number in standard form, the number is written as a coefficient, followed by the base of 10, raised to an exponent.

3x - 2y = 10  becomes  3x - 2y - 10 = 0

3x - y = 17 becomes 3x - y - 17 = 0

Let's multiply the first equation by 2 and the second equation by 3.

2(3x - 2y - 10) = 0

3(3x - y - 17) = 0

6x - 4y - 20 = 0

9x - 3y - 51 = 0

The next step is to add the two equations together.

6x - 4y - 20 + 9x - 3y - 51 = 0

15x - 7y - 71 = 0

The last step is to solve for the variable.

15x - 7y = 71

15x = 71 + 7y

x = (71 + 7y)/15

To learn more about standard form
https://brainly.com/question/19169731
#SPJ1

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

Learn more about the total Surface Area of the Cone :

https://brainly.com/question/15153049

The part of Jillian's plan which requires revision is that,

C. Jillian should have found the intersection of two perpendicular bisectors of triangle QRS instead of two altitudes.

Given an acute, scalene triangle QRS.

Jillian has to draw a circle which passes through all of the vertices of the triangle, that is, Q, R and S.

This circle is the circumcircle of the triangle.

In order to draw a circumcircle, it is first required to draw the perpendicular bisectors of any of the two sides.

Then the intersecting point has to be kept as the center and then draw a circle which passes through any of the vertex and it will automatically pass through all vertices.

Hence the correct option is C.

Learn more about Perpendicular Bisectors here :

https://brainly.com/question/24753075

#SPJ1

Step-by-step explanation:

Multiply (4/10) by 10 to find the sum using common denominators:

\( \frac{4 \times 10}{10 \times 10} = \frac{40}{100} \)

Add:

\( \frac{40}{100} + \frac{20}{100} = \frac{60}{100} \)

60/100 is your unsimplified answer.

Divide (60/100) by 20:

\( \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \)

3/5 is your simplified answer.

Answer:

Step-by-step explanation:

This is the answer

The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place

In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.

From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :

     =>  x ≥ 12.25   and x < 12.35

So, the x lies between 12.25 and 12.35 which defines the error of interval for x.

Hence, the error of interval for x will be [12.25, 12.35)

To know more about Error of Interval, Click here :

https://brainly.com/question/17588303

#SPJ1

Answer:

The company needs to sell either 30 or 40 items.

Step-by-step explanation:

We are given that the cost for selling x items given by the function:

\(C(x)=40x+180\)

And the revenue for selling x items is given by:

\(R(x)=68x-0.4x^2\)

The profit function is the cost function subtracted from the revenue function:

\(P(x)=R(x)-C(x)\)

Substitute and simplify:

\(\displaystyle \begin{aligned} P(x)&=(68x-0.4x^2)-(40x+180)\\&=68x-0.4x^2-40x-180\\&=-0.4x^2+28x-180\end{aligned}\)

To find how many items must be sold in order to obtain a weekly profit of $300, we can let P equal 300 and solve for x. So:

\(300=-0.4x^2+28x-180\)

Solve for x. Subtract 300 from both sides:

\(-0.4x^2+28x-480=0\)

We can divide both sides by -0.4:

\(x^2-70x+1200=0\)

Factor:

\((x-40)(x-30)=0\)

Zero Product Property:

\(x-40=0\text{ or } x-30=0\)

Solve for each case:

\(x=40\text{ or } x=30\)

So, in order to obtain a weekly profit of $300, the company need to sell either 30 or 40 items.

There is no proportional relationship between x and y.

No, all ratios yx are not equivalent.

We have,

"Two or more number or variable are said to be in proportion if the ratio between them are equivalent to each other."

According to the question,

Given x : 8 , 10, 12, 14

        y : 5, 7, 9, 11

Ratio between different values of x and y are not equivalent

( 8 /5) ≠ (10 / 7)≠ (12 /9) ≠(14 /11)

We conclude there is no proportional relationship between x and y.

Hence, Option(1) is the correct answer.

Learn more about Proportion here

brainly.com/question/2548537

#SPJ1

complete question:

Is there a proportional relationship between x and y? Explain.

x 8 10 12 14

y 5 7 9 11

1. No; all ratios yx are not equivalent.

2.Yes; each x value and y value increases by 2.

3.Yes; the difference between each x value and y value is 3.

4.No; all ratios xy are greater than 1.

Answer: Below

Step-by-step explanation:

so using slope intercept form, we know that y = mx + b. We plug in our values. Since -10 is the x value and -7 is the y value, and 2 is the slope:

-7 = 2(-10) + b

Simplify.

-7 = -20 + b
13 = b

We plug b into the slope intercept form, this time without an x or y value to make it apply to all points on the line.

y = 2x + 13

That's our answer.

The given points are,

x1, y1 = 5, 6

x2, y2 = -10, -15

The general line equation is,

y = mx +b

Here, m is the slope and b is the y intercept.

The slope m can be calculated as,

Now, b can be calculated by taking a point and susbtituting the values in the line equation.

Let us here take, th points (5,6). Therefore we have,

Thus, the equation is,

Answer:

Step-by-step explanation:

7a - 4a

a = 8

so

7(8) - 4(8)

56 - 32 = 23

FINALLY! Someone asks for a step-by-step! TYSM!

Since a=8, we ae going to replace the a variables with 8.

7(8)-4(8)

7x8=56

4x8=32.

Now we subtract.

56-32=24.

---

hope it helps

Answer:

x=-14

Step-by-step explanation:

7x+156=9x+184

2x=-28

x=-14

The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.

Here we want to find the solution set of the inequality below:

x ≤ -4

First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so  we need to have a closed set at that end)

This is written as:

(-∞, -4]

The use of the symbols [ ] means that the element belongs to the set.

Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1

Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

30 % loss means 70 % remains  (.7)

y =  8 (.7)^x       =   battery life after 'x' years

2 =  8(.7)^x     solve for 'x'

2/8 = .7^x       LOG both sides

log.25 / log.7   = x = ~ 3.9 years

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

The correct option that result the data with variability:

C. The shoe size of the various 5 year olds.

D. The number of patients at the doctor's office each day.

The term "variability" refers to the distance between data points within a distribution and their distance from its centre. Measures of variability provide you summary statistics that summarise your data in addition to measurements of central tendency.

Spread, scatter, and dispersion are other terms for variation. It is often assessed using the following:

Thus, the result the data with variability:

C. The shoe size of the various 5 year olds as it will vary for different children.

D. The number of patients at the doctor's office each day is also variable.

Know more about the variability of data

https://brainly.com/question/30693581

#SPJ1

Answer:

Step-by-step explanation:

\(x^{2} + 6x-6= 10\\x^{2} +6x-16=0\\x^{2} -2x+8x-16=0\\x(x-2)+8(x-2)=0\\(x-2)(x+8)=0\\x = 2\\or\\x = -8\)

Answer:

X = 2 and X = -8

Step-by-step explanation:

X2 + 6X - 6-10 = 0 ....... when +10 pass the equality sign it will become -10

X2 + 6X -16 =0

here we need to find if there are two numbers there sum is +6 and there product is -16.

here we need to find if there are two numbers there sum is +6 and there product is -16.The two numbers are -2 and +8

-2+8= +6

-2*8= -16

( X - 2 ) * ( X + 8 ) =0

X - 2 = 0 ...... when -2 pass equality sign it will become+2

X = 2

X + 8 =0 ..... when +8 pass equality sign it will become -8

X = -8

Answer:

Step-by-step explanation:

5x+9y=-3             Multiply both sides by 8

40x+72y=-24

-53x-8y=-3  Multiply both sides by 9

-477x -72y= -27

sum the equations vertically to eliminate one variable  

40x+72y= -24

-477x-72y= -27       (the y cancels out )

-477x =-51                (-24 + -27=-51)

-477x=-51 / -477       divide both sides by -477

x =51/437

5x 51/437=9y= -3   substitute the value of x

y= -174 /437

(x,y) = (51/437,  -174/437)

Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.

We can see this by comparing the growth rates of the three functions for larger and larger values of x.

As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.

if we plug in x = 10, we get:

f(10) = 4×2¹⁰ = 4×1024 = 4096

h(10) = 9×10² + 25 = 925

g(10) = 15×10 + 6 = 156

As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

For such more questions on Sustainable Energy Bill Study

https://brainly.com/question/3159537

#SPJ8

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

Learn more about area here : brainly.com/question/2607596

#SPJ1

The language is generated by the following grammars are

a) s 0S1 | 01 is string

b) s + S S | -SS | a is arithmetic expressions

c) S S (S)S |  is string

d) s a Sb S | b S a S | e  is string

e) s a | S+S | SS S*|(S) is expression

Grammar is a set of rules that define the structure of a language. It provides a set of guidelines for constructing sentences that are grammatically correct.

a) The grammar s -> 0S1 | 01 generates a language consisting of all strings that begin with 0, end with 1, and have any number of 0's and 1's in between.

The justification for this is that the grammar provides rules for constructing such strings by either appending a 0 and a 1 to an existing string or by directly generating the string "01".

Thus, all strings in the language can be generated by the given grammar.

b) The grammar s -> +SS | -SS | a generates a language consisting of all valid arithmetic expressions using the symbols +, -, and a single variable "a".

The justification for this is that the grammar provides rules for constructing such expressions by recursively applying the rules to generate sub-expressions.

Thus, all valid arithmetic expressions can be generated by the given grammar.

c) The grammar S -> SS(S)S | ε generates a language consisting of all strings of balanced parentheses.

The justification for this is that the grammar provides rules for constructing such strings by recursively generating balanced strings and surrounding them with parentheses.

Thus, all balanced strings of parentheses can be generated by the given grammar.

d) The grammar s -> aSbS | bSaS | e generates a language consisting of all strings that contain an equal number of "a"s and "b"s.

The justification for this is that the grammar provides rules for constructing such strings by recursively generating pairs of "a" and "b" surrounded by two new substrings.

Thus, all strings containing an equal number of "a"s and "b"s can be generated by the given grammar.

e) The grammar s -> a | S+S | SS | S* | (S) generates a language consisting of regular expressions over the alphabet {a, +, *, (, )}.

The justification for this is that the grammar provides rules for constructing regular expressions using the provided operators and the variable S.

Thus, all regular expressions over the given alphabet can be generated by the given grammar.

To know more about grammar here.

https://brainly.com/question/917076

#SPJ4