Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home.

Use the graph to answer questions about this scenario.
1. What does the x-axis represent in this situation?


2. What does the y-axis represent?


3. During which parts of the graph does Arthur's distance from home decrease?

4. When is Arthur waiting for bagels? Explain how you know.


5. If Arthur's pace had not been constant after leaving the bagel shop, which part of the graph would change? Explain how that part of the graph would change.



6. If Arthur had spent less time reading his newspaper, which part of the graph would change? How would that part change?

There are total of 12 girls in the class.

A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.

Let the number of girls in the class be x and the number of boys in the class be y

so total number of students in the class is x+y

ration of number of girls to the total number of students is x/(x+y)

given that total number of student is x+y which is 21

so x/21 = 4/7

=> x= (21*4)/7

=> x= 3*4

=> x=12

so the total number of girls in the class is 12.

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Complete question:

The ratio of girls to the total number of students in class is 4 to 7. How many students are girls if class has 21 students in all?

Answer:

[tex]\boxed{\mathrm{Option \;D: 5x^4-37x^3-6x^2+41x-6}}[/tex]

Step-by-step explanation:

You can solve such multiple choice questions using a trick. This especially is useful in a time constrained question

Consider only the coefficients of the terms relating to x⁴ and the constant

If you expand (-4x³ + 5x - 1)(2x - 7) this will work out to

(--4x³) (2x) +..... + (-1)(-7)

This will result in (- 8x⁴ +..... + 7)

Since there is a negative sign before this last term, expanding will change the signs of the terms

-(-8x⁴ + ..... + 7) = 8x⁴ -7

Add the coefficients of the x⁴ terms to get

(5 - 8 + 8)x⁴ = 5x⁴

Add the constants of the individual terms

--1 + 2 - 7 which is -6

So the simplified polynomial is of the form

5x⁴ +....... - 6

Only option D fits these values, so the correct choice is Option D:
[tex]\mathrm{5x^4-37x^3-6x^2+41x-6}[/tex]  

ANSWER

--------------------------------------------------------------------------------------------------

If you want to do it the hard way,

First evaluate the last product using FOIL:
[tex]\left(-4x^3+5x-1\right)\left(2x-7\right)\\\\= \left(-4x^3\cdot \:2x-4x^3\left(-7\right)+5x\cdot \:2x+5x\left(-7\right)-1\cdot \:2x-1\cdot \left(-7\right)\right)\\\\= \left(-8x^4+28x^3+10x^2-37x+7\right)\\\\[/tex]

With the negative sign in front of this expression this becomes:

[tex]-\left(-8x^4+28x^3+10x^2-37x+7\right)\\\\= 8x^4-28x^3-10x^2+37x-7\\\\[/tex]

From the original polynomial expression, group like terms:

[tex]\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right)-\left(-4x^3+5x\:-1\right)\left(2x-7\right)\\\\[/tex]

[tex]=\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right) + (8x^4-28x^3-10x^2+37x-7)\\\\[/tex]

The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2) = 9 + 4√2

Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.

Given:

u(x) = x^2 + 3

w(x) = √x+2

We have to find (w о u)(2) and (u о w)(2).

First to find (w о u)(x)

(w о u) = w(u(x))

         = w(x^2 + 3)

(w о u) = √(x^2 + 3) + 2

(w о u)(2) = √(2^2 + 3) + 2

 (w о u)(2) = √7 + 2

Now to find (u о w).

(u о w)(x) = u(w(x))

= u(√x+2)

= (√x+2)^2 + 3

= x + 4√x + 4 + 3

(u о w)(x) = x +  4√x + 7

(u о w)(2)  = 2 + 4√2 + 7

 (u о w)(2)  = 9 + 4√2

Hence,

The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2)  = 9 + 4√2

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The formula of median is Med(x) = X [n=1/2].

The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to consider the entire data set as a representation; in these cases, median is helpful. The median is a simple metric to calculate among statistical summary metrics. Since the data that is in the center of a sequence is used as the median, the median is also known as the Place Average.

Median Formula When n is Odd

Median = [(n + 1)/2] th term

Median Formula When n is Even

Median = [(n/2) th term + ((n/2) + 1) th term]/2

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Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]

The given system of equations:

k x + 2y = 5  

⇒ k x + 2y - 5 = 0 ….( i)  

3x - 4y = 10

⇒3x - 4y - 10 = 0 …(ii)

These equations are of the forms:

a1x + b1y + c1 = 0

a2x + b2y + c2 =0

where, a1 = k

            b1 = 2

             c1 = -5

            a2= 3

            b2 =-4

             c2 = -10

[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex]

[tex]\frac{k}{3} \neq \frac{2}{-4}[/tex]

[tex]k\neq \frac{-3}{2}[/tex]

Thus for all real values of k other than −3/2 ,

the given system of equations will have a unique solution.

(ii) For the given system of equations to have no solutions, we must have:

[tex]\frac{a1}{a2} = \frac{b1}{b2}\neq \frac{c1}{c2} \\\\ \frac{k}{3} = \frac{2}{-4}\neq \frac{-5}{-10} \\ \\ \frac{k}{3} = \frac{2}{-4}\\ \\ \frac{k}{3} \neq \frac{1}{2} \\ \\ \\k \neq \frac{3}{2} \\\\k =\frac{-3}{2} \\[/tex]

Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]

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An equation to model the data that India is witnessing is f(x) = 2757(0.95)^x.

A graph of this exponential equation is shown in the image attached below.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since her colonies is dying at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 5 = 95% = 0.95.

Substituting the parameters into the exponential equation, we have the following;

f(x) = 2757(0.95)^x

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Nelly's gross pay is $451.20 + $84.60 = $535.80.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

First, we calculate her regular pay.

She worked 45 hours last week, and her regular hourly rate is $11.28 per hour. Therefore, her regular pay for the week is 40*$11.28 = $451.20. This is the pay she receives for the hours she worked up to 40 hours, which is considered the standard workweek.

Next, we calculate her overtime pay. Nelly worked 45 hours last week, and she is entitled to overtime pay for hours exceeding 40 hours. Therefore, she worked 45-40 = 5 hours of overtime.

Since she is paid time and a half for overtime, her overtime pay is calculated by multiplying her regular hourly rate by 1.5. Therefore, her overtime pay is 5*$11.28*1.5 = $84.60.

Finally, we add her regular pay and her overtime pay to get her gross pay. Her gross pay is the total amount she earns for the week, including both her regular pay and her overtime pay.

Therefore, her gross pay is $451.20 + $84.60 = $535.80.

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The dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

Given is the volume of the cylinder as -

V = 500 cm³

We can write -

V = 500

So, we can write -

πr²h = 500

So, we can write -

{r} = √500/πh

{h} = (500/r²)

Therefore, the dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

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{Question in english -

What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}

-8 hshdjdbdkdndidjdndjdodjfodjdjd

Step-by-step explanation:

2*(-2)-4=

-4-4=

-8

The minimum number of hikers that could have walked between 8 miles and 19 miles is given as follows:

7.

The maximum number of hikers that could have walked between 8 miles and 19 miles is given as follows:

17.

The frequency table gives the number of observations on each interval.

Then the minimum number of hikers that could have walked between 8 miles and 19 miles is obtained when:

Hence the minimum amount is of 7.

The maximum number of hikers that could have walked between 8 miles and 19 miles is obtained when:

Hence the maximum amount is of 4 + 7 + 6 = 17.

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By using the point-slope form, the equation of a line that passes through the point (-14, 6) with slope -7/4 is equal to y = -7x/4 + 30.5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (-14, 6), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = -7/4(x - (-14))

y - 6 = -7/4(x + 14)

y = -7x/4 + 24.5 + 6

y = -7x/4 + 30.5

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The weight of the cashews plus the weight of the peanuts cannot be more than 192 ounces and the weight of the cashews must be at least one-fourth of the total weight of the mixture.

Step 1: Let c = weight of cashews

Step 2: Let p = weight of peanuts

Step 3: 0.25c + p ≤ 48

Step 4: Multiply both sides by 4

Step 5: 4(0.25c + p) ≤ 4(48)

Step 6: c + p ≤ 192

This system of inequalities models the situation of combining cashews and peanuts to make a nut mixture. The first inequality states that the weight of the cashews plus the weight of the peanuts cannot exceed 48 ounces, and the second inequality states that the weight of the cashews must be at least one-fourth of the total weight of the mixture. To model this situation, we let c equal the weight of the cashews and p equal the weight of the peanuts. We then multiplied both sides of the first inequality by four to get the second inequality, which states that the weight of the cashews plus the weight of the peanuts cannot exceed 192 ounces. This system of inequalities accurately models the situation of combining cashews and peanuts to make a nut mixture, and it ensures that the weight of the cashews is at least one-fourth of the total weight of the mixture.

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The probability that a student studied for exactly 1 hour is 0.23 Or 23%. The correct option is A.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

A table is given where the first column represents the number of hours a student studied math and the second column represents the number of students.

The sum of the second column is 30. So it is the total number of students. And only 7 of them studied mathematics for 5 hours.

Therefore, The probability that a student studied for 5 hours is,

= 7/30.

= 0.23 or 23%.

Therefore, the correct option is A. 23.0.

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The question is incomplete. Your most probably complete question is given below:

23.0

0.70

0.23

0.16

The range is calculated as follows by combining the lowest and highest values. Organize the information in ascending or descending order first, then calculate the maximum and minimum values.

The range of a particular data set is the distinction between those maximum and minimum values. Range = Maximum Value–Minimum Value

The range of a set of data is the differential between the collective's maximum and minimum values.

Domain and range are keywords in relations and functions. The range is the set of all potential dependent values produced by a relation from a domain value.

To identify the range, first, arrange the data in ascending or descending order to gain a clear picture of the data's Maximum and Minimum terms.

Then, to get the data range, subtract the lowest value from the largest value in the collection.

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Answer:

Step-by-step explanation:

ttt

The percentage of the students that do not like camping like travelling out of state is 33% and this can be determined by using the given data.

what is meant by camping?

To the complete questions is;

Likes Traveling Out of State Does Not Like Traveling Out of State Row totals Likes Camping 52 38 90

Does Not Like Camping 36 74 110

Column totals 88 112 200

a)32% b)34% c)38% d)42%

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The coordinates of point E on the parallelogram are given as follows:

(3, -2).

The coordinates of point E are obtained considering that the point E is the midpoint of segment AC, hence it's coordinates are the mean of the coordinates of A and C.

Then the x-coordinate of point E is obtained as follows:

x = (1 + 5)/2 = 3.

The y-coordinate of point E is obtained as follows:

y = (1 - 5)/2 = -4.

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1 in 4 angle of slope in degree is 90°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.

The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.

So to find the 1 in 3 angle we have to put the value 1/3 in arctan function

which is tan inverse function.

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Answer:

lol i don't know this

Step-by-step explanation:

lol= laugh out loud

Answer: We know that sound travels about 343 meters per second. To convert the distance in meters to miles, we need to use the conversion factor that there are 3.28 feet in a meter and 5280 feet in a mile.

1 mile = 5280 feet = 5280/3.28 meters = 1600 meters

Therefore, the distance in miles from Alyssa to the lightning bolt can be calculated by dividing the distance in meters by the number of meters per mile:

distance in miles = distance in meters/1600

So, the distance in miles from Alyssa to the lightning bolt is 343 meters/1600 miles = 0.215 miles (approx)

Note that this calculation is based on the assumption that sound travels 343 meters per second and it's an approximation.

Step-by-step explanation:

Standard form of the quadratic function is,

⇒ y = 4x² - 32x + 28

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ y = 4 (x - 7) (x - 1)

Now, We can simplify the equation in standard from as;

⇒ y = 4 (x - 7) (x - 1)

⇒ y = 4 (x² - x - 7x + 7)

⇒ y = 4 (x² - 8x + 7)

⇒ y = 4x² - 32x + 28

Thus, The standard form is,

⇒ y = 4x² - 32x + 28

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The area of a triangle with a base of 4.8 cm and height of 3.6 cm is 8.64 cm².

Area of triangle = ½ × base × height

= ½ × 4.8 × 3.6

= 8.64 cm²

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The roots are hypothetical, meaning that they have two false roots. As a result, a quadratic equation has real, unequal, and irrational roots.

The quadratic equation with roots ax2 + bx + c = 0 has real and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive.

5x 2 2x+3=0 a=5, b=2, c=3, D=b 2 4ac D=56 0

The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.

A degree two equation of the form ax2+bx+c = 0—where an is not equal to 0—is a quadratic equation. The quadratic equation's roots are the value of x in this equation. The only roots of a quadratic equation are two. These roots can have both real and made-up characteristics.

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Full Question = Write the nature of roots of the quadratic equation 5x2 - 2x + 3 = 0.

Answer: [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA

Step-by-step explanation:

Therefore, [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA.

The exact probability that would make the three marbles to be blue is  6/273,

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that exactly three marbles drawn would be blue = (number of blue marbles / total number of marbles) x [(number of blue marbles / total number of marbles) - 1] x [((number of blue marbles / total number of marbles) - 1]

Total number of marbles = 6 + 5 + 4 = 15

= (5/15) x (4/14) x (3/13) = 6/273

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The process to identify if the function is inverse is identified through the horizontal line test.

Function in math is known as a correspondence from one value x of the first set A to another value y of the second set B.

Here we need to identify the way to know that whether the given unction is inverse function or not.

By using the horizontal line test that is If any horizontal line intersects the graph of f more than once then the function f does not have an inverse.

Where as If no horizontal line intersects the graph of f more than once, then the function f does have an inverse.

Here we have also have the property of having an inverse is very important in mathematics, and it has a name.

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To simplify 9x, you need to use the distributive property.

The distributive property states that when you multiply a number by a group of numbers or variables, you can separate the group into individual components, multiply each component by the number, and then add the products together.

For example, 9x can be simplified as follows:

9x = 9x(1)

Using the distributive property, you can separate the 1 into individual components:

9x = 9x(1) = 9x(1 + 0)

Then, you multiply each component by the number:

9x = 9x(1) = 9x(1 + 0) = 9x(1) + 9x(0)

And finally, you add the products together:

9x = 9x(1) + 9x(0) = 9x + 0

Therefore, 9x can be simplified to 9x.

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The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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Answer:

V ≈ 13036 ft³

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height )

here diameter = 19, then r = 19 ÷ 2 = 9.5 and h = 46 , then

V = 3.14 × 9.5² × 46

   = 3.14 × 90.25 × 46

  ≈ 13036 ft³  ( to the nearest whole number )