19. The equation y = -x + 9.6 models the data in the table
shown. Identify the number of positive and negative residuals,
the residual with the greatest absolute value, and the residual
with the least absolute value. Is the model a good fit?

X| 1 | 2 | 3 | 4 | 5 | 6 |
Y| 5.8| 8.7 | 2.9 | 0.8 | 5.1 | 1.7|

Irving states women are strong but nagging; the slave trade is not morally correct; the puritans are exterminators, and being a moneylender is a controversial but yet acceptable job.

Tom Walker and the Devil is a short story by Washington Irving. In this story, a man called Tom Walker decides to make a deal with the devil and this has awful consequences by the end of this story.

Moreover, this story written by Washinton Irving indirectly describes the ideas of the author about different aspects. Let's analyze some of these.

Women: Irving refers to women mainly through Tom's wife, about her he mentions Tom’s wife was a tall termagant, fierce of temper, loud of tongue, and strong of arm from this, we can conclude women are strong but also nagging.

Slave trade: Irvings seems to reject the slave trade, this is because in the story the devil proposes Tom to be part of the slave trade and Tom does not agree with this. Tom should employ it in the black traffic... This, however, Tom resolutely refused.

Puritans attitude: Irving seems to reject puritans' attitude because he blames puritans for the extermination of native people. This can be seen in the red men have been exterminated by you white savages.

Moneylender: Irving refers to moneylenders as usurers, this has a negative connotation but is not as morally incorrect as being a slave trader.

Note: This question is incomplete because the text it refers to is not given; here is the missing information.

"Tom Walker and the Devil" by Washing Irving

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Answer:

75

Step-by-step explanation:

(0.45)(30) = (0.18)x

x = (0.45)(30) / (0.18)

x = 13.5 / 0.18 = 75

Check the answer:

(0.45)(30) = (0.18)(75)

13.5 = 13.5   answer is correct!

Answer:

Step-by-step explanation:

45% of 30 = 18% of some number

In this kind of questions, we usually assume the missing number as as something

Let the number be x

So assuming the number is x, the equation will be as follows:

45% of 30 is equal to 18% of x

45/ 100 * 30 = 18/100 * x

This means that 0.45 *30= 0.18 * x

Therefore, 13.5 = 0.18 x

Thus X = 13.5 / 0.18

Which is equal to 75

Thus 45% of 30 is equal to 18% of 75

Proving the above situation as follows:

45% OF 30 = 13.5

And 18% of 75 = 13.5

Thus both equations are equal.

Solution =75

The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Central angle Θ of the circle is equal to π/3 radians.

A radian is another unit of measurement that is used to measure angles. A degree is a unit of measurement that is used to measure circles, spheres, and angles. The radian, or one pi radian, is only half the diameter of a circle, which has 360 degrees, or its entire area.

Central angle of the circle is equal to:

\(\pi=3\times\Phi\)

\(\Phi=\dfrac{\pi }{3} \ \text{radians}\)

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Answer:

See explanation

Step-by-step explanation:

Your question is different from the attachment

Statement 1

1 adult + 5 Children

$4 for adult and total of $16 for both adult and children

Let

Cost of children skating = x

The equation is

4 + 5x = 16

Statement 2:

Cost of making a bike bag= $4

Selling price of the bike bag = $5

Profit = $16

Let x = number of bike bag

Profit = selling price - cost price

16 = 5x - 4x

16 = x(5 - 4)

Also written as

(5 - 4)x = 16

Statement 3:

Initial temperature = 16°C

Change in temperature per hour = 4°C

Final temperature = 5°C

Let

x = number of hours it changes

16 - 4x = 5

Hope made 3 different yo-yos. She used 1 3/4 meters of string for the first yo-yo, 1 meter of string for the second yo-yo, and a total of meters of string 4 1/3

length of first yo-yo = 1 3/4

length of second yo-yo = 1

Length of third yo-yo = x

Total = 4 1/3

Total length = length of first yo-yo + length of second yo-yo + length of third yo-yo

4 1/3 = 1 3/4 + 1 + x

4 1/3 = 2 3/4 + x

4 1/3 - 2 3/4 = x

13/3 - 11/4 = x

(52-33) / 12 = x

19/12 = x

x = 1 7/12

Answer:

1. true

2. false

3. true

4. true

Answer:

30 centimeters

Step-by-step explanation:

120 ÷2 =60 now you must use only .5 of that number so you have thirty

The slope in improper fraction form is 10/11, in integer form 0.91.

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

We have an equation of a line;

y+3= 10/11 (x+7).

Rearranging,

y+3 = 10x/11 + 70/11

y = 10x/11 + 70/11 - 3

y = 10x/11 + 67/11 {equation 1}

And we have the slope-intercept form

y = mx +b

Comparing the equation 1 to standard form

we have the slope m = 10/11

Therefore, the slope in improper fraction form is 10/11, in integer form 0.91.

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Step-by-step explanation:

2y - 4x + 6 = 0

2y = 4x - 6

y = 4x/2 - 6/2

y = 2x - 3

Answer:

\(y = 2x - 3\)

Step-by-step explanation:

Simply make the y as the subject

\(2y - 4x + 6 = 0 \\ 2y - 4x = - 6 \\ 2y = - 6 + 4x \\ \frac{2y}{2} = \frac{ - 6 + 4x}{2} \\ y = - 3 + 2x \\ y = 2x - 3\)

So,

\(y = mx + b \\ y = 2x - 3\)

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

Pretty sure it is option 4

It´s that or option 3

Step-by-step explanation:

The two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

Given the equation; 6x² - 35 = -11x

The quadratic formula is expressed as;

x = [ -b±√( b² - 4(ac)  ]/2a

First, we re-arrange our equation in the form of ax² + bx + c = 0

6x² + 11x - 35 = 0

We substitute into the formula.

x = [ -b±√( b² - 4(ac)  ]/2a

x = [ -11±√( 11² - 4( 6 × -35 )  ]/2×6

x = [ -11±√( 121 + 840 ]/12

x = [ -11±√961 ]/12

x = [ -11 ± 31 ]/12

x = (-11 + 31)/12,  (-11 + 31 )/12

x = 20/12,  -42/12

x = 5/3, -7/2

Therefore, the two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

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The area of the playground of dimensions 18 and 240is 432 \(m^{2}\).

Given  If the dimensions of the playground in the layout are given by 180 cm x 240 cm.

The area of rectangle is length *breadth.

The given playground is in the shape of rectangle because there are two sides given and both the sides are different. In a rectangle length of opposite side found to be equal and each side form an angle of 90 degree.

Area=length*breadth

=180*240

=43200 \(cm^{2}\)

We have to convert in meters so we have to divide by 100.

Area=43200 \(cm^{2}\)

=43200/100

=432 \(m^{2}\)

Hence the area of playground having dimensions 180 cm and 240 cm is 432\(m^{2}\).

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Answer:

1/-32

Step-by-step explanation:

As my first step, I turn the problem into a fraction since the exponent is negative.

The problem is now 1/-2^5

Now that the exponent is positive, you can finish the problem by finding out what -2 raised to the fifth power is which is -32.

The expression \((-2)^{-5}\) in fraction form will be equal to \(\frac{-1}{32}\) .

A mathematical expression is given which is \((-2)^{-5}\).

We have to change this to the fraction in simplest form.

What do you mean by fractions ?

A fraction can be defined as a portion or part of any quantity or it defines a part of a whole.

As per the question ;

The mathematical expression is ; \((-2)^{-5}\).

Let's change \((-2)^{-5}\) as a fraction in simplest form.

As the power to number is negative , while changing the number into fraction form , we will invert it , i.e.,

\(\frac{1} {(-2)^{5}}\)

= \(\frac{-1}{32}\)

Thus , the expression \((-2)^{-5}\) in fraction form will be equal to \(\frac{-1}{32}\) .

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Answer:

x=34, z=26 degrees, y=74 degrees

Step-by-step explanation:

We can find x because the triangles are equal to each other, meaning that we can set 2x-20 equal to 4x-88. When solved, x=34. This now means that the expression 2x-20 and 4x-88 both equal to 48 degrees.

Now looking at the triangle on the left, we can find the angle using supplementary angles, setting 180-154, which is 26 degrees. This means z on the triangle to the right is also 26 degrees since the triangles are equal to each other.

Because of knowing two angles, we can now find the 3rd one by adding both of them up and subtracing it from 180. That will get you 106 degrees, then using vertical angles we can find that the angle measure of 106 degrees carries over to the second triangle.

To find y now, you simply subtract 106 from 180 to get 74 degrees.

(I believe this is right, hopefully it made sense!)  

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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I think the the answer is b Answer:

Step-by-step explanation:

Answer: only one line

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

plz mark the brainliest. if that is adding not multiplying, you will do 3 divide by 8 first and then add 12. I think its a typo and it is multiply so if it is multiply, it is B. plz mark the brainliest

In this case, the actual rational roots of the equation 8x³ + 2x² - 5x + 1 = 0 can only be determined by performing the calculations using the possible rational roots mentioned above.

The Rational Root Theorem can be used to identify the possible rational roots of a polynomial equation. In the case of the equation 8x³ + 2x² - 5x + 1 = 0, the possible rational roots can be determined by considering the factors of the constant term (1) divided by the factors of the leading coefficient (8). By testing these potential roots using synthetic division or substitution, we can find the actual rational roots of the equation.

The Rational Root Theorem states that any rational root of a polynomial equation with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

For the equation 8x³ + 2x² - 5x + 1 = 0, the constant term is 1, and the leading coefficient is 8. The factors of 1 are ±1, and the factors of 8 are ±1, ±2, ±4, and ±8. Combining these factors, the possible rational roots are ±1, ±1/2, ±1/4, ±1/8.

To find the actual rational roots, we can substitute these values one by one into the equation and check if they satisfy the equation. Using synthetic division or direct substitution, we can test each potential root. By doing so, we can determine if any of the possible rational roots are indeed solutions to the equation.

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Answer: d = √(5² + 9²) = √106, or approximately 10.3 units.

Answer:

Option B.

Step-by-step explanation:

We have to find the quotient of the expression \((3x^4+6x^3+2x^2+9x+10)\) when divided by (x + 2) by synthetic division.

-2 | 3     6     2     9     10

   | ↓    -6     0    -4    -10

     3     0     2     5     0

Solution of the synthetic division will be = (3x³ + 2x + 5)

Therefore, quotient after division will be, (3x³ + 2x + 5) and the remainder is 0.

Therefore, (3x³ + 2x + 5) will be the answer.

Option (B) will be the correct option.

Answer:

B

Step-by-step explanation:

I did the work and this one is very tough

The variance of this binomial random variable is 2.4 .

The variance of a binomial random variable with parameters n and p is given by the formula:

The variance of the binomial distribution  where n is the number of trials, p is the probability of success, and 1-p is the probability of failure.

Variance = n × p × (1 - p)

In this case, n = 10 and p = 0.4

Putting these values into the formula, we get:

Variance = 10 × 0.4 × (1 - 0.4)

Variance = 4 × 0.6

Variance = 2.4

Therefore, the variance of this binomial random variable is 2.4 .

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The longer leg of the right triangle measures 160m. This is found by setting up and solving an equation based on the Pythagorean theorem.

Let's denote the longer leg of the right triangle as x. According to the given information, the shorter leg measures 120m.

Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can set up the equation:

x^2 + 120^2 = (x + 40)^2

Simplifying this equation, we have:

x^2 + 14400 = x^2 + 80x + 1600

Subtracting x^2 from both sides, we get:

14400 = 80x + 1600

Subtracting 1600 from both sides, we have:

12800 = 80x

Dividing both sides by 80, we find:

x = 160

Therefore, the longer leg of the right triangle measures 160m.

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Answer:

(1,-2)

Step-by-step explanation:

x= 1

y= 2

Answer: the answer is no solution

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.

If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.

See image.

h(x) = -4 + 6

h(x) = 2

h(-2) = 2 because It's a constant function, when you substitute any x-values, you still get the same y-value.

Even if you substitute x = 1000, you still get y = 2.

Therefore, h(-2) = 2

-----------

If you mean h(x) = -4x+6

then h(-2) = 8+6 = 14

therefore, h(-2) = 14 for h(x) = -4x+6

Answer:

1/1

Step-by-step explanation:

i hate math do you hate math?