I Need help to graph these and need explanation

Step-by-step explanation:

Using perfect square trinomial rules,

[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

Here, a is sin x

b is cos x

So

[tex]( \sin(x) + \cos(x) ) {}^{2} = \sin {}^{2} (x) + 2 \sin(x) \cos(x) + \cos {}^{2} (x) [/tex]

We know

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

So we know have

[tex]1 + 2 \sin(x) \cos(x) [/tex]

[tex] \sin(2x) = 2 \sin(x) \cos(x) [/tex]

So our final answer is

[tex]1 + \sin(2x) [/tex]

1:1.618 (the golden ratio).

To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.

Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.

Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).

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use the slope formula

5 - 9/4-2 = -4/2 = -2

slope = -2

Therefore , the solution of the given problem of function comes out to be the limit may not exist, if the function is not continuous at x = 0.

The mathematical discipline encompasses arithmetic, symbols, and their divisions, as well as histology, construction, and both real and imagined geographic places. A function describes the connections between various elements, which all have an associated outcome. A function is composed of an array of different parts that, when combined, result in particular outcomes for each input.

Here,

We must be aware of the precise function or expression under consideration in order to respond to this query.

The action as x moves towards zero from the negative direction can change depending on the function.

If a function is continuous at x = 0, then in general, if the function has a limit as x gets smaller from the downward direction, however this limit will be the same as the limit as x reaches zero from the positive direction.

The limit as x approaches zero from the downward direction may vary from the limit as x approaches zero from the better way, or the limit may not exist, if the function is not continuous at x = 0.

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The inequality that represents the maximum possible height that Raimundo reached is given as follows:

h - (-10) ≤ 40.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The difference between the maximum height and the maximum depth is given as follows:

h - (-10).

As the maximum depth is of 10 feet below.

The difference is at most 40 feet, hence the inequality is given as follows:

h - (-10) ≤ 40.

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Answer:

Zoe will save 30% of the original cost of the sweater, which is $40. To calculate the amount saved, we must multiply 30% by the original cost of the sweater, which gives us 0.30 x $40 = $12. Therefore, Zoe will save $12 on the sweater with the 30% discount

Step-by-step explanation:

Answer:

She will save $12.00

Step-by-step explanation:

.3 x 40 = 12

30% as a decimal is .3.

The cost of the sweater on sale would be

.7 x 40 = 28

If we take 30% off, we are leaving 70% on.

28 + 12 = 40 the original cost.

Helping in the name of Jesus.

The volume of the right circular cylinder is approximately 14,864.77 cubic meters.

What is the right circular cylinder?

A right circular cylinder is a three-dimensional solid shape that consists of a circular base and a curved side that is perpendicular to the base. The term "right" refers to the fact that the axis of the cylinder is perpendicular to the base, and the term "circular" refers to the shape of the base, which is a circle.

The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. The formula for the surface area of a right circular cylinder is A = 2πrh + 2πr^2, where r is the radius of the base and h is the height of the cylinder.

Right circular cylinders are commonly used in engineering, architecture, and everyday objects such as cans, pipes, and containers.

The formula for the volume of a right circular cylinder is [tex]V = \pi r^2h[/tex], where r is the radius of the base and h is the height of the cylinder.

In this case, the radius is 17.2 meters and the height is 15.3 meters.

Plugging in these values, we get:

[tex]V = \pi (17.2)^2(15.3)[/tex]

V ≈ 14,864.77 cubic meters

Therefore, the volume of the right circular cylinder is approximately 14,864.77 cubic meters.

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Hypothesis 1: There is a positive correlation between gender and GPA.
Hypothesis 2: There is a positive correlation between age and midterm score.
Hypothesis 3: There is a negative correlation between nationality and income.
Hypothesis 4: There is a negative correlation between expenditure and no. of credits.
Hypothesis 5: There is a positive correlation between no. of absences and learning preference.
Hypothesis 6: There is a positive correlation between online device usage and income.

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Answer:

$456

Step-by-step explanation:

12% = 0.12

3800 x 0.12 = $456

So, the down payment is  $456

It will take about 5.18 years for the car to be worth 8,200.

We can use the given formula to find the value of the car after x years:

[tex]V = 20,000(0.8)^x[/tex]

We want to know how long it will take for the car to be worth 8,200. So we can set V equal to 8,200 and solve for x:

[tex]8,200 = 20,000(0.8)^x[/tex]

Dividing both sides by 20,000 gives:

[tex]0.41 = (0.8)^x[/tex]

Taking the logarithm of both sides with base 0.8, we get:

[tex]log0.8(0.41) = x[/tex]

Using a calculator, we can find:

x ≈ 5.18

Therefore, it will take about 5.18 years for the car to be worth 8,200.

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The equation which represents the cost of one square foot of flooring is   x = $3.45.

Let the cost of one square foot of flooring be = x,

We know that the store is selling 60 square feet of flooring for $287, which includes a $80 installation fee.

So, the cost of 60 square feet of flooring is

⇒ $287.00 - $80.00 = $207

To find the cost of one square foot of flooring, we divide the cost of 60 square feet by 60,

Which is,

⇒ $207/60 = $3.45

Therefore, the cost of one square foot of flooring is represented by the equation x=$3.45.

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The given question is incomplete, the complete question is

A home improvement store advertises 60 square feet of flooring for $287.00 including a $80 installation fee. Write an equation to represent the cost of one square foot of flooring.

The surface area of the frustrum, obtained summing the areas of the trapezium-shaped faces, and the square base and top is 2720 mm²

A frustrum is the part of a pyramid formed when the top is removed by a plane parallel to the base of the pyramid.

The slant height of the small square-based pyramid, is the same as the slant height of the frustrum. The base of the small pyramid therefore intersects the sides of the large pyramid at the midpoint of the sides, which indicates that the base of the small rectangle is a midsegment of the triangular sides of the square-based pyramid.

The midsegment theorem indicates that the side length of the base of the small pyramid is half the side length of the base of the large square-based pyramid. Therefore;

Length of the base of the smaller pyramid = 32 mm/2 = 16 mm

Height of the trapezium-shaped face = √(17² - ((32 - 16)/2)²) = √(17² - 8²) = 15

Area of the trapezium-shaped face = (16 mm + 32 mm) × 15 mm/2 = 360 mm²

The surface area of the four trapezium-shaped faces = 4 × 360 mm² = 1,440 mm²

The area of the square at the top of the frustrum = 16 mm × 16 mm = 256 mm²

The area of the square base = 32 mm × 32 mm = 1024 mm²

The surface area of the frustrum is therefore;

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(a) The mode, median, first quartile, and third quartile of the data set is 24, 24, 12, and 43, respectively. There are no outliers.

(b) The data value corresponding to the 60th percentile is 33.8.

(c) The percentile rank of the age 40 is 70th percentile.

(a) The mode of the data set is 24, as it appears twice in the data set.
The median of the data set is 24, as it is the middle value when the data set is arranged in ascending order.
The first quartile (Q1) is 12, as it is the median of the lower half of the data set.
The third quartile (Q3) is 43, as it is the median of the upper half of the data set.
To check for outliers, we can use the interquartile range (IQR), which is Q3 - Q1 = 43 - 12 = 31.
The lower outlier boundary is Q1 - 1.5(IQR) = 12 - 1.5(31) = -34.5.
The upper outlier boundary is Q3 + 1.5(IQR) = 43 + 1.5(31) = 89.5.
Since all the values in the data set are within the outlier boundaries, there are no outliers.

(b) To find the data value corresponding to the 60th percentile, we can use the formula:
Percentile rank = (p/100)(n + 1)
where p is the percentile, and n is the number of data values.
In this case, p = 60 and n = 25, so the percentile rank is (60/100)(25 + 1) = 15.6.
Since the percentile rank is not a whole number, we can use interpolation to find the data value corresponding to the 60th percentile.
The data value corresponding to the 60th percentile is 32 + (0.6)(35 - 32) = 33.8.

(c) To find the percentile rank of the age 40, we can use the formula:
Percentile rank = (L + 0.5f)/n
where L is the number of data values less than 40, f is the frequency of 40, and n is the number of data values.
In this case, L = 17, f = 1, and n = 25, so the percentile rank of the age 40 is (17 + 0.5(1))/25 = 0.7 or 70th percentile.

(d) To draw a boxplot for the data set, we can use the values of the first quartile (Q1), median, and third quartile (Q3) that we found in part (a).
The boxplot would look like this:
[12]---[24]---[43]
    Q1    Median   Q3

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The two sides with lengths of 7 and 5 will never meet, which shows that the sum of the lengths of the two sides of a triangle must be equal to the length of the third side.

In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < n < b + c

Where:

n, b, and c represent the side lengths of this triangle.

b - c < n < b + c

7 - 5 < n < 7 + 5

2 < n < 12

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The comparison of textbooks is History textbooks > Science textbooks. The mass of the stacks of textbook differ by 0.15 kilograms.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Mass of science textbook = 1.15 kilograms

Mass of 4 science textbooks = 4 × 1.15 kilograms

                                                = 4.6 kilograms

Mass of a history textbook = 950 grams = 0.95 kilograms

Mass of 5 history textbooks = 5 × 0.95 kilograms

                                              = 4.75 kilograms

Part A :

History textbooks > Science textbooks

Part B :

Mass of History textbooks - Mass of science textbooks = 4.75 - 4.6

                                                                                            = 0.15 kilograms

Hence the history textbooks are 0.15 kilograms more.

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Answer:

6.74

Step-by-step explanation:

100 - 93.26

Answer:

$6.74

Step-by-step explanation:

100.00 - 93.26 = 6.74

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The values between[tex]7 * 10^-6[/tex] and [tex]6 * 10^-5 = 5.3 * 10^-5[/tex]

The result of subtracting one number from another. How much one number differs from another.

Example: The difference between 8 and 3 is 5.Another example is the difference between 100 and 50= 100-50 = 50

The difference simply means subtracting a number from another

Similarly the difference between [tex]7 * 10^-6 and 6 * 10^-5 = 6 * 10^-5 - 7 * 10^-6[/tex]

changing [tex]7 *10^-6 0.7 * 10^-5[/tex]= [tex](6 * 10^-5) - (0.7 * 10^-5)= 5.3 * 10^-5[/tex]

Therefore the values between [tex]7 * 10^-6[/tex] and [tex]6 * 10^-5[/tex] is [tex]5.3 * 10^-5[/tex]

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So the probabilities of the given events are:

P(X = 5) = 1/9
P(2 ≤ X ≤ 6) = 5/12
P(X = 5 or X = 10) = 7/36

To find the probabilities of the given events, we need to consider all the possible outcomes of the two dice-throwing experiments and the number of favorable outcomes for each event.

There are 6 possible outcomes for each die, so the total number of possible outcomes for the two dice is 6 × 6 = 36.

For the event X = 5, the favorable outcomes are (1, 4), (2, 3), (3, 2), and (4, 1). So the probability of this event is P(X = 5) = 4/36 = 1/9.

For the event 2 ≤ X ≤ 6, the favorable outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), and (5, 1). So the probability of this event is P(2 ≤ X ≤ 6) = 15/36 = 5/12.

For the event X = 5 or X = 10, the favorable outcomes are (1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), and (6, 4). So the probability of this event is P(X = 5 or X = 10) = 7/36.

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Answer: D

Step-by-step explanation: Its D because for every 6 units is 3/2 pi

Answer: y = 4 + 3x

Step-by-step explanation:

Input (x) = any number

Output (y) = 4 more than 3 times x

more: +

times: ×

Yes, Laura will have enough money to buy the computer before her brother's birthday.

Cost is the total amount of money, time, and resources required to produce or acquire a product, service, or outcome. It involves the initial outlay of money, time, and resources necessary to produce or acquire something. In addition, it involves any ongoing expenses required to maintain or improve that something. Cost can be a one-time purchase, a long-term investment, or a recurring expense.

At the time of her purchase, Laura had $427 which is $59 short of the $486 computer. She earns $42 each week from babysitting, so if she saves every penny she earns for the next 7 weeks she will have enough money to buy the computer. She will have $294 after the first week of saving, $336 after the second week, $378 after the third week, $420 after the fourth week, $462 after the fifth week, $504 after the sixth week, and $546 after the seventh week. The $546 is more than enough money to purchase the computer before her brother's birthday.

Additionally, the computer's price drops $14 each day, so if Laura waits an extra week to purchase the computer, it will cost her even less. She will have $588 after the eighth week and would only need to spend $400 to purchase the computer.

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Step-by-step explanation:

steps are in the image above

This code use to measures may be equivalent after some transformation.

<!DOCTYPE html>

<html lang="en">

<head>

<title>Cat in night</title>

</head>

<body>

<div id="wrapper">

<section class="sky">

<div class="moon"></div>

<ul>

<li class="cloud"></li>

<li class="cloud"></li>

<li class="cloud"></li>

</ul>

</section>

<section class="wall">

<section class="cat">

<div class="cat-head">

<div class="eyes">

<div class="eye"></div>

<div class="eye"></div>

</div>

</div>

<div class="cat-body">

<div class="tail"></div>

</div>

</section>

</section>

</div>

<style>

.sky {

height: 300px;

background: radial-gradient(#112A71, #000A31);

overflow: hidden;

position: relative; }

.sky .moon {

width: 80px;

height: 80px;

border-radius: 50%;

background-color: #FEFF79;

-webkit-box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

position: absolute;

top: 30px;

right: 100px; }

.sky .cloud {

width: 80px;

height: 30px;

background-color: #8D8D8D;

border-radius: 50px;

-webkit-box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

position: relative;

top: 60px;

left: 30px;

-webkit-animation: shift 100s infinite linear;

animation: shift 100s infinite linear; }

.sky .cloud:nth-child(2) {

-webkit-transform: scale(-1.5, 1.3);

transform: scale(-1.5, 1.3);

top: 100px;

left: 250px;

-webkit-animation-duration: 40s;

animation-duration: 40s; }

.sky .cloud:last-child {

top: 150px;

left: 100px;

Transformation refers to a significant change or shift in an entity, be it a person, organization, system, or society, towards a desired state or outcome. It is a process of evolving, improving, or adapting in response to internal or external pressures or opportunities. Transformation involves a fundamental shift in the way things are done, the mindset, values, and behavior of the entity undergoing the change.

Transformation can occur in various contexts, such as business, technology, education, social and political systems, and personal development. It often requires a clear vision, strategic planning, and effective execution to achieve the desired outcome. The process can be challenging and requires significant effort and resources, but the benefits of transformation can be substantial, leading to increased efficiency, innovation, growth, and social impact.

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Complete Question: -

It is important to define or select similarity measures in data analysis. However, there is no commonly-accepted subjective similarity measure. Results can vary depending on the similarity measures used. Nonetheless, seemingly different similarity measures may be equivalent after some transformation. Suppose we have the following two-dimensional data set:

A1

A2

X1

1.5

1.7

X2

2

1.9

X3

1.6

1.8

X4

1.2

1.5

X5

1.5

1.0

Consider the data as two-dimensional data points. Given a new data point, x = (1.4, 1.6) as a query, rank the database points based on similarity with the query using Euclidean distance, Manhattan distance, supremum distance, and cosine similarity.

The answer is V equals 355 over 113 times 6 squared times 8.

What is the volume of the cylinder?

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder, and h is the height of the cylinder.

Alternatively, the volume of a cylinder can be found by multiplying the area of the base (πr²) by the height (h).

The correct method to calculate the number of cubic units of cake batter needed to fill the mold is:

[tex]V = \pi r^2h[/tex], where r is the radius and h is the height of the cylinder.

The diameter of the cake mold is 12 inches, so the radius is half of that, which is 6 inches.

Therefore, the volume of the cake batter needed is:

V = (355/113) x 6² x 8

V = (355/113) x 36 x 8

V = 904.96 cubic inches

So the answer is: V equals 355 over 113 times 6 squared times 8.

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So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

How likely something is to happen can be determined using probability. For instance, while flipping a coin, there is a one in two chance of receiving heads because there is only one way to get a head and a total of two outcomes. the tail or the head. We set P(heads) = 12 in this case.

Let's represent the number of glitter pens Lindsey puts in each goody bag by the variable "p".

To find the value of "p", we can divide the total number of glitter pens by the number of goody bags:

p = 24 / b

So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

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Answer:

a = -2

Step-by-step explanation:

-18 = 2a - 2|1-3a|

-18 = 2a - 2 + 6a

-18 = 8a - 2

-16 = 8a

a = -2

The equation that has no solution is 2x+1=5x-3.

To find out which equation has no solution, we can use the process of elimination. First, let's look at the equation 2(x-7)=2x-14. If we simplify this equation, we get:
2x-14=2x-14
This equation is true for all values of x, so it has infinitely many solutions.

Next, let's look at the equation 15x-30=0. If we simplify this equation, we get:
15x=30
x=2
This equation has one solution, x=2.

Now, let's look at the equation 2x+1=5x-3. If we simplify this equation, we get:
-3x=-4
x=4/3
This equation has one solution, x=4/3.

Finally, let's look at the equation 3(2x+1)=6x+1. If we simplify this equation, we get:
6x+3=6x+1
3=1

This equation is never true, so it has no solution.

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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The equation of the line with gradient 2 and that passes through the point (1,1) is y= 2x -1.

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:

Gradient = 2

and, line passes through the point (1,1).

We know using Slope intercept form y= mx+ b

and, y= 2x+ b

Now, line passes through the point (1,1).

1 = 2(1) + b

b= -1

So, the equation of line is y= 2x -1.

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