xavier is a teacher and takes home 90 papers to grade over the weekend. he can grade at a rate of 6 papers per hour. how many papers would xavier have remaining to grade after working for 12 hours?

Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

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Sec x is the simplified expression cos(−x)+tan(−x)sin(−x) involving a single trigonometric function with no fractions.

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

The Given expression is

cos(−x)+tan(−x)sin(−x)

Now,

cos(−x) + tan(−x)sin(−x)

= cos x + (- tan x) (- sin x)

= cos x + tan x * sin x

= cos x + (sin x / cos x) * sin x

= (cos²x + sin²x) / cos x     ( As sin²x + cos²x = 1)

= 1/ cos x

= sec x       (As sec x = 1/cos x)

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The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).

To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.

We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .

The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).

We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.

The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.

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Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

The unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel. This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

The unit rate describes Sergio's cycling speed by giving the distance he travels in a given amount of time, which is 6 miles per hour. This means that for every hour he cycles, he travels a distance of 6 miles.

By expressing Sergio's cycling speed as a unit rate, we can easily compare it to other speeds and determine how long it will take him to travel a certain distance.

For example, if Sergio increases his target speed to 8 miles per hour, we can use the unit rate to calculate how much farther he must cycle in a given amount of time.

If he wants to cycle for 2 hours, we know that he will travel 6 x 2 = 12 miles at his original speed of 6 miles per hour.

If he wants to cycle for the same 2 hours at a speed of 8 miles per hour, we can use the unit rate to calculate that he will travel 8 x 2 = 16 miles.

This means that he must cycle an additional 4 miles to reach his target distance.

Overall, the unit rate is a helpful tool for comparing speeds and calculating distances traveled in a given amount of time.

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Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth

The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and

a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:

4,500 dives x 2 scientists per dive = 9,000 scientists

Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.

2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:

4,500 dives x (1 pilot + 2 scientists)

= 4,500 x 3

= 13,500 people

Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

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Answer: The one that has the best deals.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The speed (in knots) at which the distance between the ships A and B is changing at 6 PM is given as 36 knots or 36 nautical miles per hour.

Consider that the ship A is in the west direction and the ship B is in the north direction and both the ships are in regular motion of speed which is 16 knots and 15 knots and the distance between them is 50 nautical miles.

Using the Pythagoras theorem, the relation of the distance x which represents the distance between ships at 6PM to the distances that each ship has travelled can be given as follows:

x^2 = (50 + 16t)^2 + (15t)^2

where, t is the number of hours that has passed since noon.

Differentiating both sides of the above equation with respect to time, we get:

2x*(dx/dt) = 2(50 + 16t)*(16) + 2*(15t)*(15)

t = 6, at 6 PM, therefore substituting the value and solving, we get:

2x(dx/dt) = 2[(50 + 16(6)]*(16) + 2*[15(6)]*(15)

2x(dx/dt) = 4194

dx/dt = 2097/x

Now substituting the value of x that corresponds to 6 PM:

x^2 = (50 + 16(6))^2 + (15(6))^2

x^2 = 3385

x = √3385 ≅ 58.19

Putting this value in dx/dt, we get:

dx/dt = 2097/58.19 ≅ 36.00 knots

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Answer:3.79*10^14

Step-by-step explanation:

370000000000000+9000000000000=379000000000000

=3.79 x 10^14

Answer:

(3.79×10^14)

Step-by-step explanation:

sjskakakzks

The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer:

345.6

Or 345 full cubes

Step-by-step explanation:

To answer this question we first need to find the volume of the cuboid!

To find volume we use the equation...

For the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...

We now need to the the volume of the cube which we can just do by cubing the value given

We now need to divide the two results together to find out how many cubes would fit...

Hope this helps, have a lovely day!

As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.

The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.

given

We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:

[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]

where h is the height of the frustum, r is the small radius, and R is the large radius.

Given the numbers, we can determine:

R = 5 in.

3 centimeters is r.

24 inches tall

With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]

As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.

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Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.

Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.

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To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.

For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.

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Answer:

54

Step-by-step explanation:

Answer:

y=54

as x=3

so y=2*x^3

y= 2*3^3

y=2*27

y=54

Answer: Let x be the number of hamburgers sold.

Then, the number of cheeseburgers sold is 3x.

The total number of burgers sold is x + 3x = 4x.

Given that the total number of burgers sold is 416, we have:

4x = 416

x = 416/4

x = 104

Therefore, 104 hamburgers were sold.

Step-by-step explanation:

Grace need to buy the jump rope, the game, and the ball $8.

$7 will get you a jump rope.

$10 will get you a board game.

$4 will get you a playground ball.

total amount to be spent: $7 + $10 + $4 = $21

She has ten dollars.

$3 was all her uncle gave her.

13 dollars are all she has.

She needed $8, therefore 21 - 13 = $8.

a sum of money awarded as compensation, a bounty, or to cover costs. a wage that comes with a cost-of-living supplement. especially: a regular amount set aside for household or personal costs.

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Using pythagoras' theorem in the right-angled triangle

A right-angled triangle is a polygon with 3 sides in which one angle is a right angle

Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have

h² + (12 - x)² = 12² - 6² (1)

Also, h² + x² = 6²  (2)

So, h² + (12 - x)² = 12² - 6²

h² + (12 - x)² = 144 - 36

h² + (12 - x)² = 108  (3)

From equation (2), h² = 36 - x²

Substituting this into equation (3), we have that

h² + (12 - x)² = 108  (3)

36 - x² + (12 - x)² = 108  (3)

Expanding the brackets, we have that

36 - x² + 144 - 24x + x² = 108

36 + 144 - 24x = 108

180 - 24x = 108

-24x = 108 - 180

-24x = -72

x = -72/-24

x = 3

Since  h² = 36 - x²

h = √(36 - x²)

So, substituting the value of x = 3 into the equation, we have that

h = √(36 - x²)

h = √(36 - 3²)

h = √(36 - 9)

h = √27

h = 3√3

So,

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Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for  5,445 is 3²×5×7².

The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.

Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:

The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,

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The area of the square base = x².

we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...

The dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.

Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x

Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x²  A'(x) = 0 when x =  (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

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Answer:

x = -13/7

y = 54/7

Step-by-step explanation:

Y = 5x + 17                          Y = -2x + 4

5x + 17 = -2x + 4

7x + 17 = 4

7x = -13

x = -13/7

Not put -13/7 in for x and solve for y

y = 5(-13/7) + 17

y = 54/7

So, the answer is x = -13/7 and y = 54/7

Answer:   x = -13 / 7, y = 54/7

Step-by-step explanation:

To eliminate a variable, we can substitute y for 5x + 17

We get 5x + 17 = -2x + 4

7x = -13

x = -13 / 7

Substituting x into the 2nd equation y = 5 * -13 / 7 + 17

y = 119/7 - 65/7

y = 54/7

The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:

x + y ≥ 10 and 0.25x + 0.1y < 2

These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.

Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:

Thus, the first inequality is x + y ≥ 10.

Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+

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Therefore, we have the values of:

a = -g(x) for -10 < x < -8

b = lower limit of the range where g(x) = -6

c = -C for -1 < x < 1

d = upper limit of the range where g(x) = 4

e = we cannot determine the value of e based on the given information.

In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.

Here,

We can find the values of a, b, c, d, and e by examining the given information:

For -15 < x < -10: g(x) = -(-10) = 10

For -10 < x < -8: g(x) = -a

For -1 < x < 1: g(x) = -C

For b < x < l: g(x) = -(-6) = 6

For 10 < x < 15: g(x) = -8

For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.

To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we need to find the antiderivative of f(x):

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx

To do this, we can use a technique called partial fraction decomposition:

1 / (x² + 10x + 25)

= A / (x + 5) + B / (x + 5)²

Multiplying both sides by the denominator (x² + 10x + 25), we get:

1 = A(x + 5) + B

Setting x = -5, we get:

1 = B

Setting x = 0, we get:

A + B = 1

A + 1 = 1

A = 0

Therefore, the partial fraction decomposition of f(x) is:

1 / (x² + 10x + 25) = 1 / (x + 5)²

Now we can find the antiderivative:

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx

Using the substitution u = x + 5, du = dx, we get:

∫ 1 / (x + 5)² dx = -1 / (x + 5) + C

where C is the constant of integration.

Now we can evaluate the definite integral over the interval [5, 7]:

∫[5,7] f(x) dx = F(7) - F(5)

∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]

∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]

∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C

∫[5,7] f(x) dx = -1 / 60

Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.

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According to the given information, the solution to H(x) = 3 is x = 2.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS

To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:

H(x) = -x + 5

3 = -x + 5

Subtracting 5 from both sides, we get:

-2 = -x

Multiplying both sides by -1, we get:

2 = x

Therefore, the solution to H(x) = 3 is x = 2.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The theoretical probability for the 1 horned, 1 eyed,  flying, people eater purple is found to be 1/120.

Experimental Probability: Based on actual results rather than mathematical calculations, the experimental probability of an occurrence is the likelihood that the event will actually occur.

Theoretical Probability: Considering that the event is ideal, the theoretical chance that it will occur is the theoretically ideal probability of a specific result. The flaws in the system are not taken into consideration by theoretical probability.

Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.

The given probability are;

Let P(E)  be the theoretical probability  1 horned, 1 eyed,  flying, people eater purple.

Then,

P(E) =  3/4 * 1/5* 2/3* 3/8* 1/2

P(E) =  1/120

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