An experiment relating factors x and y
resulted in the data graphed below.
y
40
35
30
25
20
15
10
5
(1, 1) |
0 1 2 3
(2, 4)
J
K
y = x²
y = 6x - 8
L x + y = 10
M x - y² = 0
N x² - y² = 0
(3,9)
4
(4, 16)
(6, 36).
(5, 25).
Which equation represents the graph
through the data points?
5 6 7 8
x

Answer:

Expression: 5y+3x+9

Coefficients: (of y) 5, (of x) 3

Constant: 9

Hope this helps :)

Step-by-step explanation:

The coefficient(s) of an equation will always be the number that sits next to/attached to a variable. The constant of an equation will always be the number(s) that stands alone.

The vertex for the graph is at (2, 0).

A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)

Focus is a fixed point.

Directrix is the name for fixed lines.

Given the graph is a parabola,

A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola whose equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.

The minimum point in graph is (2, 0)

Hence vertex is (2, 0).

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The complete question is in image,

To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour we need to use a graphing calculator or computer.

1. Enter the velocity data into the graphing calculator or computer.

2. Select the "Polynomial Regression" option.

3. Choose the degree of the polynomial (third degree).

4. Enter the polynomial regression equation displayed.

5. Select the "Graph" option to view the polynomial model.

A third-degree polynomial model can be used to accurately represent data points. To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour, we need to use a graphing calculator or computer. First, we enter the velocity data into the graphing calculator or computer. Then we select the "Polynomial Regression" option and choose the degree of the polynomial (third degree). This will generate the polynomial regression equation which can then be entered. Finally, we select the "Graph" option to view the polynomial model. This will show us a graph of the velocity data points with the third-degree polynomial fitted to the points. This can be used to accurately predict the velocity of the shuttle Endeavour throughout its mission STS-49.

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The probability of rolling an even number on an unfair die is 0.65, which means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65.

So, the probability of rolling an even number is closest to option c) 0.65

A die is a cube with numbers on each face that are used in games or gambling. A fair die is a die that is equally likely to land on any of its faces, meaning that each face has a probability of 1/6 of being the face that lands up. An unfair die is a die that does not have an equal probability of landing on each face. It means that the probability of landing on each face is not the same.

In the given scenario, it is said that the probability of rolling an even number on an unfair die is 0.65. This means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65. It means that the die is not fair, and it is more likely to roll an even number.

Therefore, the probability of rolling an even number is closest to 0.65, it is the probability of rolling an even number on an unfair die.

--The question is incomplete, answering to the question below--

"The probability of rolling an even number on an unfair die is 0.65 which of the following is closest to the probability that an even number

a. 0.35

b. 0.40

c. 0.65

d. 0.70"

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The probability that an even number is rolled 15 or fewer times when the die is rolled 25 times total can be calculated using the binomial probability formula. In this case, the probability of success is rolling an even number (0.65) and the number of trials is 25.

Using the binomial probability formula, we can calculate the probability of getting 15 or fewer even numbers when the die is rolled 25 times as follows:

P (X <= 15) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 15)

Where X is the number of even numbers rolled and P(X) is the probability of getting X even numbers.

Using the binomial probability formula:

P(X) = (25 choose X) * (0.65)^X * (0.35)^(25-X)

Plugging in the values, we get:

P(X <= 15) = (25 choose 0) * (0.65)^0 * (0.35)^25 + (25 choose 1) * (0.65)^1 * (0.35)^24 + (25 choose 2) * (0.65)^2 * (0.35)^23 + ... + (25 choose 15) * (0.65)^15 * (0.35)^10

After calculating all the values, we get that the probability of rolling an even number 15 or fewer times when the die is rolled 25 times is about 0.28.

Therefore, the closest answer choice to the probability that an even number is rolled 15 or fewer times when the die is rolled 25 times is 0.25.

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Answer:

h = 6 m

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

given A = 51 , b₁ = 10 and b₂ = 7 , then

[tex]\frac{1}{2}[/tex] h (10 + 7) = 51 ( multiply both sides by 2 to clear the fraction )

17h = 102 ( divide both sides by 17 )

h = 6 m

Find the height of the trapezoid.

if the area of the trapezoid is [tex]51m^{2}[/tex] and parallel sides are [tex]7m[/tex] and [tex]10m[/tex].

To find the height of the trapezoid, substitute the area and parallel sides into the formula for the area of the trapezoid.

Trapezoid area formula is

[tex]L=\frac{1}{2}(number of parallel sides)(height)\\ L=\frac{1}{2} (a+b)(t)[/tex]

The next step is substitute the area and parallel sides into the formula for the area of the trapezoid.

[tex]51=\frac{1}{2}(7+10)(t)[/tex]

Complete the arithmetic operation

[tex]51=\frac{1}{2}(17)(t)\\ 51=\frac{17}{2}(t)[/tex]

Multiply each side by [tex]\frac{2}{17}[/tex]

[tex]51(\frac{2}{17}) =\frac{17}{2}(\frac{2}{17})(t)\\ 6=t[/tex]

So the height of the trapezoid is [tex]6m[/tex]

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The difference in salary will be $71,250.

What is multiplication in mathematics?

Multiplication is a mathematical operation that is used to find the product of two or more numbers. It is usually represented by the symbol "x" or "*", and is often referred to as repeated addition.

Career Preparation and Development (Career SMART Goals) worth 50 points.

Denise Diligence scored 95/100 on all of the assignments and reports, so she earned a total of 47.5 points.

Since each point earned will result in a $1500 increase in salary 20 years from now, Denise's salary will be $1500 x 47.5 = $71,250 higher than Slacker's.

Sam Slacker did not complete any of the career smart goals assignments and reports, so he earned a total of 0 points.

Hence, the difference in salary will be $71,250.

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It is false that x is a function of y

The given equation to be used to determine the truth and falsity of the statement is given as:

The given parameters are function of x

x = y²

determine whether the relation represents y as a function of x

x^2 + y^2 =25

x = y²

Set y = 2

x = (2)²

Taking the square root of the value

x = 4

Set y = -2

x = (-2)²

x = 4

From the experiment, the different values of y give the same x value.

therefore, this means that x is not a function of y

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The height of the tree is 8 feet.

Triangles which has the same shape but are different in size are said to be similar triangles for example all equilateral triangles are similar triangle.  

It is also defined as if the corresponding sides of two triangles are in proportion then the two triangles are said to be a similar triangles. The symbol ‘~’ is used to denote the similarity between two triangles.

If two triangles ΔABC and ΔXYZ are two similar triangles then the condition between corresponding sides is given by

Here we have

John's height is 6 feet

He standing 4 feet from a tree

Johns's shadow is 12 feet long  

We can represent the whole scenario as two similar triangles

[ Picture is given below ]

As we know in Similar triangles the ratio of corresponding sides is equal

Let 'x' be the height of the tree

From given figure  

=> AC: DE = BC: EB  

=> x : 6 = 16 : 12

=> x/6 = 16/12

=> 12x = 16 × 6  

Divided by 6

=> 2x = 16

Divided by 2

=> x = 8

Therefore,

The height of the tree is 8 feet.

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(15x+7)/(x-1) is the simplified rational expression

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.

Factors of 15x²-8x-7 are (15x+7)(x-1)

Factors of  x²–2x+1 are (x-1)²

15x²-8x-7 / x²–2x+1 = (15x+7)(x-1) / (x-1)²  

common factors cancel out

(15x+7)/(x-1) is the simplified rational expression

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Answer:

Step-by-step explanation:

Answer:

So the answer is

FMA Assignment 01

1. Jornal

2. Date (Mar) Accounts Title Debit ($) Credit ($)

1 Cash 60,000

Common Stock 60,000

3 Land 23,000

Buildings 9,000

Equipment 6,000

Cash 38,000

5 Advertising Expenses 1,600

Cash 1,600

6 Prepaid Insurance 1,480

Cash 1,480

10 Equipment 26,000

Accounts Payable 26,000

18 Cash 800

Golf Revenue 800

19 Cash (100 x 15) 1,500

Unearned Revenue 1,500

25 Dividends 1,000

Cash 1,000

30 Salaries Expenses 600

Cash 600

30 Accounts Payable 26,000

Cash 26,000

31 Cash 500

Golf Revenue 500

A constant is fixed, which is arbitrary since you don't know what that fixed number is the arbitrary denotes that no particular value has been ascribed.

The order of a differential equation is equal to the number of arbitrary constants in its general solution.

The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power. The formula:

c1=a1+ib1

and  c2=a2+ib2

the solution will be

y(x)=(a1+ib1+a2+ib2)cos(ax)+i(a1+ib1−a2−ib2)sin(ax)

If and only if

a2=a1

and  b2=−b1

will be the solution real because of complex conjugates using this property.

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Full question

Can arbitrary constants in solutions to 2nd-order linear differential equations be complex?

The total length of the metal strips needed in inches is 370.5 inches

Number of strip metals = 12

Length of each strip metal = 2 ft 6 7/8 in.

Convert feet to inches:

1 feet = 12 inches

2 feet = 24 inches

2 ft 6 7/8 in = 30 7/8 inches

Total length of strip metals= Number of strip metals × Length of each strip metal

= 12 × 30 7/8 inches

= 12 × 247/8

= 2,964/8

= 370.5 inches

So therefore, the total length of the metal strips is 370.5 inches

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Over the past few months, Brody has eaten 3 glazed donuts and 6 other donuts. we expect 1 to be glaized

Generally, Based on the data provided, it seems that Brody has eaten 3 glazed donuts out of a total of

3 + 6 = 9 donuts.

This means that 3/9, or approximately 1/3, of the donuts Brody has eaten are glazed.

So, if Brody eats 3 more donuts, we would expect 1/3 of them to be glazed,

or 3*(1/3)=1.

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The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.

The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.

1)a. 0.3333

2)c. 2.0794

1)The decay rate is found by dividing 1 by the average lifetime (in this case, 3 years). Therefore, the decay rate is 1/3 = 0.3333.

2)The median lifetime of these phones is found by taking the natural logarithm of 0.5 (which is the probability of the phone failing within 2 years) and dividing it by the decay rate (0.3333). Therefore, the median lifetime is ln(0.5)/0.3333 = 2.0794.

The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.

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Answer:

−16890

Step-by-step explanation:

Simplify the expression.

A person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.

d = 2 √(hR)

We can use the formula d = 2 √(hR) to calculate the distance d to the horizon that a person can see on a clear day from a 1461 feet above the given planet.

First, we need to convert the height of 1461 feet to miles. We can use the conversion factor of 1 mile = 5280 feet. Therefore, the height h = 1461/5280 ≈ 0.2772 miles.

Next, we need to find the radius of the planet. The radius of the planet is given as 3900 miles.

Finally, we can substitute h = 0.2772 miles and R = 3900 miles into the formula d = 2 √(hR).

d = 2 √(0.2772*3900) = 2 √(1083.08) ≈ 32.9 miles

Therefore, a person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.

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The slope of the line passing through (3, 7) and (-2, -1) is 1.6

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

The slope of the line passing through (3, 7) and (-2, -1) is:

Slope = (-1 - 7) / (-2 - 3)

Slope = -8/-5 = 8 / 5

Slope = 1.6

The slope is 1.6

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The slope of this situation is equal to: A. 0.80.

In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Points on x-axis = 12

Points on y-axis = 9.6.

Substituting the given data points into the slope formula, we have the following;

Rate of change (slope), m = 9.6/12

Rate of change (slope), m = 0.80.

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From the given points, it was found that the slope is m= -3.

You can correlate two data from a function. An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=9 and b=5.

The question gives some points of the linear function, see below.

x    y

−1  6

0   3

1   0

2  −3

From the given data you can find the slope by solving the system linear equation.

You can write a system linear equation using the points: (-1,6) and (2,-3), for example.

6=m*(-1)+b  (1)

-3=2m+b    (2)

Multiplying equation 2 by -1, you have

6=-m+b  (1)

3= -2m-b    (2)

Summing the previous equation, you have:

9=-3m

m= -9/3

m= -3

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Answer: the answer is A

Step-by-step explanation: I took the text and got it right

a) This equation holds true for all x values except x=0, because it would result in division by zero.

b) This equation holds true for all x values except x=0, because it would result in division by zero.

What is inequality?

An inequality is a statement that compares two expressions and is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).

a) 6x² - x³ = -x² + 2x + 3

b) 6x² - x³ ≤ -x² + 2x + 3

To solve for x in the given inequalities:

a) 6x² - x³ = -x² + 2x + 3

Start by isolating x³ on one side of the equation:

x³ = 6x² + (-x² + 2x + 3)

x³ = 6x² + 2x + 3

Now we can factor out x² from the right side of the equation:

x³ = (x²)(6 + 2/x) + 3

This equation holds true for all x values except x=0, because it would result in division by zero.

b) 6x² - x³ ≤ -x² + 2x + 3

Start by isolating x³ on one side of the inequality:

x³ ≤ 6x² + (-x² + 2x + 3)

x³ ≤ 6x² + 2x + 3

Now we can factor out x² from the right side of the inequality:

x³ ≤ (x²)(6 + 2/x) + 3

This inequality holds true for all x values except x=0, because it would result in division by zero.

Hence,

a) This equation holds true for all x values except x=0, because it would result in division by zero.

b) This equation holds true for all x values except x=0, because it would result in division by zero.

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Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It is used with 1000 labeled examples to minimize the sum of the squared errors of the model.

Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It adds a penalty term to the cost function that penalizes large coefficients, thus reducing their magnitude. The penalty term is a regularization term that is added to the cost function to minimize overfitting. To use ridge regression, one must select a value for the regularization parameter. This parameter determines how much the model weights the penalty term, and is usually determined through cross-validation. With 1000 labeled examples, ridge regression can be used to minimize the sum of the squared errors of the model. The model is then trained on the data, and predictions can be made. Ridge regression is a powerful tool for reducing the effects of multi-collinearity, and can be used to accurately model relationships between variables.

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The volume of the container is (x+6)(x-2)(x-1) cubic feet and it can be express as the form of polynomial.

Six faces make up the three-dimensional shape of a rectangular prism. The prism's faces are all rectangles. The shape of a rectangular prism is cuboidal.

There are two sets of parallel and congruent bases in this polyhedron. It has eight vertices, 12 sides, and six faces. Rectangular prisms are also known as a right rectangular prism, rectangular parallelepiped, and rectangular hexahedron.

Right rectangular prisms and oblique prisms are the two primary varieties of rectangular prisms. The bases of a right rectangular prism are parallel to the other faces.

The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given x

[tex](x+6)(x-2)(x-1)[/tex]

A polynomial is a sum (with some coefficients) of powers of x, so, if we expand the product just written, we have.

[tex]=(x+6)(x-2)(x-1)\\\\=(x^2-2x+6x-12)(x-1)\\\\=(x^3+4x^2-12x-x^2-4x+12)\\\\=(x^3+3x^2-16x+12)[/tex]

Which is a polynomial and expresses the volume of the prism.

the complete question is,

How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x-2, and height x-1?

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47 square centimeters is equal to 303.225 square inches.

Measure the length and width of an object, such as a rectangle, and multiply the results to get the number in square centimeters. In the event that the length and width are 15 cm and 10 cm, respectively, the formula is 15 cm*10 cm, which equals 150 cm2.

Any number that is multiplied by itself is transformed into a square. A different word for this is a number squared. The symbol for "squared" is 22 since 2 x 2 equals 4.

In mathematics, the squared sign (2), an arithmetic operator, stands in for multiplying an integer by itself. The "square" of an integer is the sum of that number and itself. Therefore, 10,000 square meters are represented by one square centimeter.

1 square inch = 6.4516 square centimeters.

47 in^2 = 47 × 6.4516

= 303.225 sq. cm

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The Equation For calculating the paver area is

Length(m) x width(m) = area(m²).

Concrete, natural stone, clay brick, or even porcelain can be used to make pavers. They are typically little fragments of varying sizes. Homeowners can choose from a variety of hues, patterns, and textures.

Divide your space into squares or rectangles and multiply the length by the width to find the square metres of paved surface. The total square metres should be included. There are about 38 pavers per square metre, although this varies depending on how many cuts are made and what laying pattern is used. Additionally, you must account for waste.

The area to be paved and the paver selected will determine how many pavers are required.

Determine the area that will be paved in square metres.

Equation : Length(m) x width(m) = area(m²).

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The class interval [15-19] has the greatest frequency, and the class interval [10-14] has the least frequency

From the question, we have the following parameters that can be used in our computation:

10. 9. 5. 19. 17

13. 2. 0. 4. 10

1. 16. 9. 7. 3

15. 17. 18. 16. 6

Using a class of 5, we have the following class intervals

0 - 4, 5 - 9, 10 - 14 and 15 - 19

When the frequencies of each class are counted, we have the following table

Interval Midpoint Frequency R/F        C/F

0 - 4 2           5                 5/20 5

5 - 9 7           5                 5/20 10

10 - 14 12           3                 3/20 13

15 - 19 17            7                 7/20 20

using the above as a guide, we have the following:

The class interval [15-19] has the greatest frequency 7

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Answer:

Step-by-step explanation:bmmmv m

As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

Circled portion of the shaded partition is 7/4 of the total.

Take 1/2's reciprocal and switch the sign to multiply. 7/4 * 1/2 = 3 1/2

As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .

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The answers are as follows:

1. Skewed to the right.

2. The center is about 2 or 3 servings of fruit.

3. From zero o eight servings.

4. No outliers

5. About 12%.

6. 26 girls

About Pennsylvania.

Although the original European immigrants were Swedes and Dutch, William Penn, a Quaker, gave the state of Pennsylvania its name in honor of his father by combining the name Penn with the Latin word Sylvania, which means "woodlands," to create "Penn's woodlands." Pennsylvania, also known as the "Keystone State," is one of the original 13 colonies (it entered the Union in 1787). The state is now dominated by two large cities: Pittsburgh, a bustling inland river port, and Philadelphia, the city of the Liberty Bell, Constitution Hall, and a vibrant metropolitan area. The Amish are a group of people who don't utilize technology and live in the Pennsylvania countryside. The ruffed grouse is the state bird and Harrisburg is home to it.

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The following question be maybe like:

We all know that fruit is good for us. Many of us do not eat enough. The figure provided is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls from a study in Pennsylvania.

Image given below:

1. Choose the term that best describes the shape of this distribution.

2. Provide the center of this distribution (Enter your answer as a whole number.)

3. Select the best description for the variability of this distribution.

4. Are there any outliers?

5. What percent of these girls ate six or more servings of fruit per day?

6. How many of these girls ate fewer than two servings of fruit per day?