A new refrigerator has a price of $480.00. The store will discount the price by 15% if the purchaser pays in cash. What is the cash price of the refrigerator?

The value of the line integral is 32/3.

To use Green's Theorem to evaluate f= eyz'dy+ r²dy, where C is the rectangle with vertices (0,0), (4,0), (4,1), and (0,1), it is first important to calculate the partial derivatives.

Therefore, we have;

∂f/∂y = r² and ∂f/∂z = ey and the region D is the rectangle R with vertices (0,0), (4,0), (4,1), and (0,1).

Thus,

∬D ( ∂f/∂y - ∂f/∂z ) dA = ∫(C) f.dr

Applying Green's Theorem to the left-hand side we have;

∬D ( ∂f/∂y - ∂f/∂z ) dA = ∫(C) f.dr

= ∫(C) (eyz'dy+ r²dy) dr

Where the positive orientation of C is counterclockwise.

The rectangle with vertices (0,0), (4,0), (4,1), and (0,1) can be seen in the figure below:

Using Green's Theorem, we have;

∬D ( ∂f/∂y - ∂f/∂z ) dA = ∫(C) (eyz'dy+ r²dy) dr

= ∫(C) (eyz'dy+ r²dy) dr

Now, we have the curve C made up of four line segments as shown below:

Since the curve C is a simple closed curve, we can apply Green's Theorem to evaluate the line integral. Thus, we have;

∫(C) (eyz'dy+ r²dy) dr

= ∫(0,0)^(4,0) r² dx + ∫(4,0)^(4,1) 4y² dy + ∫(4,1)^(0,1) 4 dx + ∫(0,1)^(0,0) 0 dy

= [r³/3]0,0^(4,0) + [4y³/3]4,0^(4,1) + [4x]4,1^(0,1) + [0]0,1^(0,0)

= (64/3) + (64/3) + (-16) + 0

= 32/3

Therefore,

∬D ( ∂f/∂y - ∂f/∂z ) dA = 32/3.

Thus, the value of the line integral is 32/3.

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a) The probability of extinction occurring in the first generation is (0.5).

b) The probability of extinction occurring in the second generation is 0.25

c) The probability of extinction occurring in the third generation is 0.125

d) The probability of extinction occurring in the fourth generation is 0.0625

e) The probability of extinction occurring in the fifth generation is 0.03125

In a branching process, each individual can either have zero offspring or one offspring with a probability of 0.5. The probability of extinction occurring at each generation is the probability that all individuals have zero offspring, which is equal to \((0.5)^n\), where n is the generation number.

Therefore, the probability of extinction occurring by a certain generation can be calculated by raising 0.5 to the power of the generation number.

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Answer:

The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.

Step-by-step explanation:

Given that:

Cost of each lunch = $2.50

Cost of monthly lunch pass = $40.00

Number of lunches = x

For making the monthly pass a better deal, the cost of lunches should be greater than the cost of monthly lunches, therefore

Cost of lunch * Number of lunches > Cost of monthly lunch pass

2.50x > 40.00

Hence,

The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.

Answer:

2.50x > 40.00

$2.50 times a number of lunches is greater than $40.

Step-by-step explanation:

The solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the Intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3

Given that the number graph ranges from negative eight to eight on the x-axis and negative eight to eight on the y-axis.

Two lines that are perpendicular to each other intersect at (three, zero). The line with a positive slope is labeled a, and the line with a negative slope is labeled b.

The system is given byx – y = 3 (line a)x + y = 3 (line b)We know that both the lines a and b pass through (3,0).

Let's first find the points of intersection of the line a with the x-axis and the y-axis.

To find the point of intersection of the line a with the x-axis, put y = 0 in the equation x - y = 3x - 0 = 3x = 3So, the point of intersection of line a with the x-axis is (3,0).

To find the point of intersection of the line a with the y-axis, put x = 0 in the equation x - y = 3 0 - y = 3y = -3So, the point of intersection of line a with the y-axis is (0,-3).

Similarly, let's find the points of intersection of the line b with the x-axis and the y-axis.

To find the point of intersection of the line b with the x-axis, put y = 0 in the equation x + y = 3x + 0 = 3x = -3So, the point of intersection of line b with the x-axis is (-3,0).

To find the point of intersection of the line b with the y-axis, put x = 0 in the equation x + y = 3 0 + y = 3y = 3So, the point of intersection of line b with the y-axis is (0,3).

Now, we can plot the graph of the two lines a and b and then find the points of intersection as follows:

Therefore, the solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3.

Hence, the answer is (0, 3).Option B. (0, 3)

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We need to find the general solution of the above PDE. Let's solve the above PDE by the method of characteristic. Let us first solve the PDE by using the method of characteristics.

The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations. To use this method, we first need to find the characteristic curves of the given PDE. Thus, the characteristic curves are given by $x = t + c_1$.

Now, we need to eliminate $t$ from the above equations in order to obtain the general solution. By eliminating $t$, we get the general solution as:$$u(x,y) = f(2x - 3y) + 3(x - 2y)$$ where $f$ is an arbitrary function of one variable. Hence, the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$ is given by the above equation. Thus, the main answer to the given question is $u(x,y) = f(2x - 3y) + 3(x - 2y)$. In order to find the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$, we first used the method of characteristics. The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations.

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The factors of the polynomial functions are 4p and p+8 and p+1

Given the polynomial function

4p^3 + 36p^2 + 32p

Factoring out 4p from the polynomial, we will have:

4p(p^2 + 9p + 8)

Factorize the function in parenthesis

= p^2 + 9p + 8

= p^2+p+8p+8

=p(p+1)+8(p+1)

=(p+8)(p+1)

Hence factors of the polynomial functions are 4p and p+8 and p+1

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Yes, it is a solution

y = -10x + - 4

The given point: (0, -4)

To know if it is a solution, we need to replace the y and x with the points given.

If the result on the left hand side is the same as the right hand side then, it is a solution

x =0, y = -4

-4 = -10(0) + -4

-4 = 0 + (-4)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

-4 = 0 - 4

-4 = -4

The left hand side is the same as the right hand side. Hence, it is a solution

Answer:

Yes it is a solution

Step-by-step explanation:

y = -10x + - 4

Point: (0, -4)

Answer:

The total amount of kids at the dance is 840

Step-by-step explanation:

100/20 equals 5

168 x 5 = 840

Answer:

there is not a complete question here ...

\(\sqrt{2} +1\) is not in a denominator to rationalize

if it were you would multiply the rational expression (the fraction)

by \(\frac{\sqrt{2} -1}{\sqrt{2} -1}\) the result (in the denominator would end up being "2 -1"

which is 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

(1/2)(1/2)=1/4

The value of P is approximately 0.0082027.

To find the probability of selecting exactly three claims from one coverage and exactly two claims from one of the other coverages, we need to calculate the total number of ways to choose three claims from one coverage and two claims from another coverage, and divide it by the total number of ways to choose five claims from the portfolio.

First, let's calculate the total number of ways to choose three claims from one coverage and two claims from another coverage. We have 10 bodily injury claims and 10 property damage claims to choose from, so the number of ways to choose three claims from one coverage is 10 choose 3 (denoted as C(10, 3)), and the number of ways to choose two claims from another coverage is 10 choose 2 (denoted as C(10, 2)). Multiplying these two combinations gives us the total number of ways to choose three claims from one coverage and two claims from another coverage.

Next, let's calculate the total number of ways to choose five claims from the portfolio. We have a total of 10 bodily injury claims, 10 property damage claims, 10 worker's compensation claims, and 10 comprehensive claims to choose from, so the number of ways to choose five claims from the portfolio is 40 choose 5 (denoted as C(40, 5)).

Finally, to find the probability, we divide the total number of ways to choose three claims from one coverage and two claims from another coverage by the total number of ways to choose five claims from the portfolio.

Therefore, the probability that the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverages can be calculated as:

P = (C(10, 3) * C(10, 2)) / C(40, 5)

P = (C(10, 3) * C(10, 2)) / C(40, 5)

ChatGPT

To solve the expression P = (C(10, 3) * C(10, 2)) / C(40, 5), we can substitute the values into the combination formulas and perform the calculations:

C(10, 3) = 10! / (3!(10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

C(10, 2) = 10! / (2!(10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45

C(40, 5) = 40! / (5!(40-5)!) = 40! / (5! * 35!) = (40 * 39 * 38 * 37 * 36) / (5 * 4 * 3 * 2 * 1) = 658,008

Now, we can substitute these values into the expression:

P = (C(10, 3) * C(10, 2)) / C(40, 5) = (120 * 45) / 658,008

Performing the calculation:

P = 5,400 / 658,008

Simplifying the fraction:

P ≈ 0.0082027

Therefore, the value of P is approximately 0.0082027.

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Answer:

1.2 ft per second

Step-by-step explanation:

The toy robot move 0.83 feet in one second.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A toy robot moves 10 feet in 12 seconds at a constant speed.

Now,

At a constant speed,

In 12 second = 10 feet

So, In 1 second = 10 / 12 feet

                        = 0.83 feet

Thus, The robot move 0.83 feet in one second.

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Answer:

2.5 feet

Step-by-step explanation:

DM

Answer:

2.5

Step-by-step explanation:

The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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Answer:

Step-by-step explanation:

yes

The ∠3 is an alternate angle of ∠4 so it is 35° while ∠3 is a complimentary angle of ∠4 so it will be 55°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Since we lack a measurement for angular rotation, the angle is a valuable tool for measuring angular distance. For instance, a meter or an inch is a unit of measurement for linear motion.

Given that AB and CD are parallel and AC is perpendicular to both.

So,

∠ACD = 90°

∠3 + ∠4 = 90°

∠3 = 90 - 35 = 55°.

Now,

Since ∠4 and ∠2 are alternative angles so both will be the same.

So,

∠2 = 35°

Hence "The ∠3 is an alternate angle of ∠4 so it is 35° while ∠3 is a complimentary angle of ∠4 so it will be 55°".

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Answer:

brah, where's the triangle

Step-by-step explanation:

looooooooooooooooooooooooooool

Answer:

32

Step-by-step explanation:

The first pattern has 7 sticks and you would count to see how many extras there are in the second and I got 5 and it was the same on the third one, so you would take the number of sticks you had on the previous pattern +5

Carla and Ben, siblings, walk to school together daily. Carla carries a blue backpack with flower prints, while Ben has a trolley bag. Their mother ensures they sleep early and wakes them up, fostering discipline.

Siblings Carla and Ben keep to their regular schedule by walking to school. Every single day, they set out on this journey together. One of the siblings, Carla, is wearing a blue rucksack with lovely floral patterns on it. It displays her distinct sense of style and individuality. Carla and Ben are prompt and punctual, never being late for school. Ben, meanwhile, has a handy trolley bag that he can easily lug around with him. Carla and Ben are put to bed at an early hour by their mother, who understands the need of sleep. In fact, she constantly monitors their sleep patterns and personally wakes them up early in the morning. The siblings' disciplined lifestyle is fostered by this caring routine.

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Mother sees to it that Carla and Ben sleep early because Mother wakes Carla and Ben up early too. (She, them)Therefore, the following personal pronouns replace the underlined words.

Activity 1: replace the underlined words with personal pronounsPersonal pronouns are words that take the place of nouns in a sentence. When replacing the underlined words with personal pronouns, we obtain the following:1. My sister Carla and brother Ben walk to school every day. (They)2. Carla carries a blue backpack. It has flower prints on it. (She)3. Carla and Ben are never late in going to school. (They)4. Ben has a trolley bag that he pulls around. (He)5. Mother sees to it that Carla and Ben sleep early because Mother wakes Carla and Ben up early too. (She, them)Therefore, the following personal pronouns replace the underlined words:1. They2. She3. They4. He5. She, them

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Answer:

the mountains bring Pat joy because it is beautiful

only one I know

Step-by-step explanation:

:)

The measure of x in the circle given below is calculated as:

x = 52.

To find the measure of x, recall that a full circle is equal to 360 degrees.

Angle APC is equal to 90 degrees. Therefore we have:

360 - 90 = 5x + 10

270 = 5x + 10

270 - 10 = 5x + 10 - 10 [subtraction property of equality]

260 = 5x

Divide both sides by 5:

260/5 = 5x/5

52 = x

x = 52

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Answer:

5

Step-by-step explanation:

20-30

10-5

5

Answer:

(x^5)(x^7)

Step-by-step explanation:

Answer:

x^5+7a

Step-by-step explanation:

Use the power rule to combine exponents

The simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).

Given the expression in the question;

√( 45 x⁸ w⁷ )

First, factor out 9 from 45

√( 9(5) x⁸ w⁷ )

√( 3²(5) x⁸ w⁷ )

Rewrite x⁸ as (x⁴)²

√( 3²(5) (x⁴)² w⁷ )

Rewrite w⁷ as ( w⁶ × w )

√( 3²(5) (x⁴)² ( w⁶ × w ) )

Rewrite w⁶ as (3³)²

√( 3²(5) (x⁴)² (w³)² × w  )

We can now take the square roots of all the terms with a power of 2 and take them out of the square root

(3)(x⁴)(w³)√(5w)

3x⁴w³√(5w)

Therefore, the simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).

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The number of solutions that are viable is; D: There are 2 solutions and only 1 is viable.

For the Rose Only Aisle;

Let the bouquets of roses be X.

Let the number of roses per bouquet be r.

Thus;

Number of bouquets of roses = Xr - 4

Number of rose Aisles = 6

Number of bouquets of dahlias = 2

Patio seating area;

Number of bouquets of roses = 4

Number of bouquet of dahlias (d) = 8

For the rose only aisle, the equation is;

6(Xr - 4r) + 2d = 100

For the patio seating area, equation for number of flowers is;

4r + 8d = 132

We can see the two simultaneous equations and we can solve for r and d but only one of them will be viable.

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Based on the given histograms, and the table on the city's monthly precipitation amounts, the histogram that corresponds to the table is Histogram 1.

The number of months with 0 - 1.992 inches is 8 months which means that the first bar on the histogram of between 0 to 2 inches should reach the 8 month mark.

6 months had 1.992 - 3.994 inches so the next bar should stop at the 6th month mark. The next bar should stop at the 4 month mark.

The one after that should stop at the 5 month mark. The last bar would stop at the 1 month mark.

The only histogram that has this is histogram 1 which is not shown clearly but it likely the only one with these qualities as the others don't have it.

Rest of the question:

Amount (inches) 0 - 1.992 - 3.99 4 -5.996 - 7.998 - 9.99

Number of Months 8           6          4          5            1

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The value of x in the similar figures is 2.33

When two figures have the same shape but their sizes are different, then such figures are called similar figures

The two polygons are similar

We have to find the value of x

Let us form a proportional equation

4590/21=510/x

4590x=21×510

4590x=10710

Divide both sides by 4540

x=10710/4590

x=2.33

Hence, the value of x in the similar figures is 2.33

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The decimal number system uses nine different symbols is False as the decimal number system actually uses ten different symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols, also known as digits, are used to represent all possible numerical values in the decimal system.

Each digit's position in a number determines its value, and the combination of digits creates unique numbers. This system is widely used in everyday life and forms the basis for arithmetic operations and mathematical calculations. Thus, the decimal number system consists of ten symbols, not nine.

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Currently we do not know the price of the PS5 but I believe it will be $550