Pharaoh Khufu has also requested that the outside of Cheops Pyramid be painted royal purple. If one gallon of paint covers 200 square feet, how many gallons of paint are needed for the project?

An approximate size which does not represent any of the actual dimensions of the unit is nominal value.

The phrase "nominal number" is said to be quite new and rarely used. It seems to have come from the statistical phrase "nominal data," which is reportedly defined as data revealing "...merely declarations of qualitative category of membership," as it is used in school textbooks. The meaning of the word "nominal" in this use is "name."

Nominal numbering is mathematically a one-to-one and onto function from a set of named objects to a set of numbers, which may change (typically growing) over time. It is a function because each named object is assigned a single number; it is one-to-one because different objects are assigned different numbers; and it is onto because every number in the set at a given time has a single named object associated with it.

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Answer:

Step-by-step explanation:

........................................................

Answer: No real solutions

Step-by-step explanation: to solve for x and find a solution you need to take the square root of -144

This is not possible as this a negative number . There is a solution if we use complex numbers, but this not included in the question

(a) The cost function is C(x) = 200 + 15x

(b) The revenue function is R(x) = 25x

(c) The profit function is P(x) = 10x - 200

(d) The break-even point is x = 20. Since the restriction is that no more than 19 units can be sold, the product should not be produced.

We shall determine the functions in the following way:

Given:

Fixed cost = $200

Variable cost = $15

Price of item = $25

(a) The cost function

C(x) = Fixed Cost + Variable Cost per unit * Number of units produced

C(x) = 200 + 15x

(b) The revenue function:

R(x) = Price per unit * Number of units sold

R(x) = 25x

(c) The profit function:

P(x) = R(x) - C(x)

P(x) = 25x - (200 + 15x)

P(x) = 10x - 200

(d) To find the break-even point, we shall set the profit function = 0 and solve for x:

P(x) = 0

10x - 200 = 0

10x = 200

x = 20

Therefore, the break-even point is 20 units. The restriction is that no more than 19 units can be sold, so, it is not profitable to produce this product.

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The numeric value of the function C(68) at f = 68 is given as follows:

C(68) = 20.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

C(f) = 5/9 x (f - 32).

The input at which we want to find the numeric value for the function is then given as follows:

f = 68.

Which means that the lone instance of f in the definition of the function is replaced by 68, and then the numeric value is calculated as follows:

C(68) = 5/9 x (68 - 32) = 5/9 x 36 = 5 x 4 = 20.

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Answer:

hope this will help you more

Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

b. Cannot be determined

b. The triangle have one congruent angles and one congruent sides, this is not enough information to conclude that they are congruent triangles.

The sum of functions f(x) and g(x) is calculated as (f+g)(x), and g(-1) is evaluated using the function g(x).


(a) To find (f+g)(x), we simply add the functions f(x) and g(x) together. Given f(x) = x² - 3x - 4 and g(x) = -2x + 7, we have:

(f+g)(x) = f(x) + g(x)
= (x² - 3x - 4) + (-2x + 7)
= x² - 3x - 4 - 2x + 7
= x² - 5x + 3.

Therefore, (f+g)(x) = x² - 5x + 3.

(b) To evaluate g(-1), we substitute x = -1 into the function g(x) = -2x + 7:

g(-1) = -2(-1) + 7
= 2 + 7
= 9.

Hence, g(-1) is equal to 9.

In summary, (a) (f+g)(x) is found by adding the functions f(x) and g(x), resulting in x² - 5x + 3. (b) Evaluating g(-1) gives a value of 9.


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The total length of two line segments is 80 cm

A line segment is just part of a line. It has two endpoints,

given that

the first line segment is 30cm

the second line segment is 500mm

now we need to convert it into cm from mm

To convert mm to cm, we need to multiply the length in mm by 0.1 cm since 1 mm is equal to 0.1 cm.

500 mm × 0.1 cm = 50cm

now we need to add two line segments

30 cm + 50 cm = 80 cm

The total length of two line segments is 80 cm

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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cos2x = (1+cos(2x))/2

The cosine power is odd (n odd): u = sin x and du = cos x dx should be used. d u = cos ⁡ To create an even number of cosine powers, replace dx with (a), canceling one power of cos x by substituting du. The Power Factor is the sine of the angle formed by Current and Voltage.

The ratio of the length of the side next to the angle to the length of the hypotenuse is known as the cosine, sometimes abbreviated as "cos." The ratio of the length of the side across from the angle to the length of the side next to it is called the tangent, which is frequently abbreviated as "tan."

cos2(2x) = (1+cos(4x))/2

cos4(2x)= [(1+cos(4x))/2]²

\(cos^{4}\)(2x) = [(1+cos(4x))/2]²

\(cos^{4}\) (2x) = (1/4) × [1 + cos(4x)]²

\(cos^{4}\)(2x) = (1/4) × (1 + 2cos(4x) + cos²(4x))

\(cos^{4}\)(2x) = (1/4)*[1 + 2cos(4x) + (1 + cos(2x))/2]

\(cos^{4}\)(2x) = (1/4)*[1 + 2cos(4x) + (1/2)*(1 + cos(2x))]

\(cos^{4}\)(2x) = (1/8)*[2 + 4cos(4x) + 1 + cos(2x)]  

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Answer:

D

Step-by-step explanation:

in this case, because it is being dilated by a factor of 2 this means that figure A´B´C´ will be double the size of its pre-image ABC.

each side will now be its double which means:

side A´C´= 10

side B´C´= 6

and side A´B´= 8

since the figure is only increasing its sides the angles of the right triangle remain the same.

<A= 37 degrees

The length of A'B' is, 8 units and the measure of angle A' is, 37 degree.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

ΔABC is dilated by a factor of 2 to produce ΔA'B'C'.

Now, When the triangle undergoes dilation, the length of its sides gets multiplied by 2 (dilation factor) but the angles remain the same ( since, the shape has to remain same).

Thus, The length of A'B' is,

= 4 x 2

= 8

And, the measure of angle A' is, 37 degree.

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Answer:

BD = 3 units

Step-by-step explanation:

Since, AD is an angle bisector of ∠BAC,

m∠BAD = m∠CAD = 20°

CD = 3 units

In ΔACD and ΔABD,

m∠BAD = m∠CAD = 20° (Given)

AD ≅ AD [Reflexive property]

Therefore, by H-A property of congruence both the triangles will be congruent.

And by CPCTC,

CD ≅ BD = 3 units

Calculation

Find the dependent variable by itself: \(y= \frac{4x}{9} -\frac{20}{9}\)

Find the function's x-intercept: x= 5

Find the dependent variable by itself: \(y= \frac{4x}{9} -\frac{20}{9}\)

Find the function's y-intercept: y = \(-\frac{20}{9}\)

The chart for : 4x-9y = 20

see the attachment

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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4

Given

x, 4x - 9y = 20  

x = 20 + 9 /4 y

Steps

4x - 9y = 20

Add 9 y to both sides

4x - 9y + 9y = 20 + 9y

Simplify

4x = 20 + 9y

Divide both sides by 4

4x/4 = 20/4 + 9y/4

Simplify

x = 20 + 9y /4

Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.

x = 20 + 9y /4

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In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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The dimensions of the column and row spaces of A are:

dim Col A = 3

dim Row A = 3

The nullity of a matrix A is the dimension of the null space of A. By the rank-nullity theorem, the rank of A plus the nullity of A equals the number of columns of A. Since A is a 4 x 6 matrix, it has 6 columns. Therefore, the rank of A is 6 - 3 = 3.

The dimension of the column space of A is equal to the rank of A, which is 3. This is because the column space is spanned by the columns of A, and the rank of A is the maximum number of linearly independent columns.

The dimension of the row space of A is also 3. This is because the row space is the orthogonal complement of the null space, and the null space has dimension 3. Therefore, the row space has dimension 6 - 3 = 3.

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Answer:

of the the sales tax of 7.25 percent is applied to an item that costs 28 dollars, then 2.03 dollars is the sales tax collected

The volume of sphere is 1437.33 if the given radius is 7 .

What is Surface area of sphere ?

Surface area of sphere can be defined as the product of four , pi and square of radius. And here the value of pi could be 3.14 or 22/7 .

Given ,

Volume of a sphere = 4/3πr³

π = 22/7

r = 7

Volume of a sphere = 4/3πr³

= 4/3 * 22/7 * 7³

= 4/3 * 22/7 * 7 * 7 * 7

= (4 * 22 * 7 * 7 * 7) / (3 * 7)

= 30,184/21

= 1437.3333333333

Volume of a sphere = 1,437.33

Therefore, the volume of sphere is 1437.33 if the given radius is 7 .

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Answer:

\(c=7\)

Step-by-step explanation:

\(8=-3c+29\)

⇒ Switch sides:-

\(-3c+29=8\)

⇒ Subtract 29 from both sides:-

\(-3c+29-29=8-29\)

\(-3c=-21\)

⇒ Divde both sides by -3:-

\(\frac{-3c}{-3}=\frac{-21}{-3}\)

\(c=7\)

OAmalOHopeO

Answer:

Thanks for free pnts

Step-by-step explanation:

The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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If this is an option, it should be Similar Triangles.

Solutions (a,b) = (3,8) or (8,3), which are not in Z11. Therefore, the polynomial x^2 + x + 4 is irreducible over Z11.

To show that the polynomial x^2 + x + 4 is irreducible over Z11, we need to ensure that it cannot be factored into simpler polynomials with integer coefficients modulo 11. In Z11, we can test the possible roots of the polynomial using the integers {0, 1, 2, ..., 10} and see if any of them satisfy the equation x^2 + x + 4 ≡ 0 (mod 11). If none of them do, then the polynomial is irreducible.
Testing each integer, we find:
0: (0^2 + 0 + 4) ≡ 4 (mod 11)
1: (1^2 + 1 + 4) ≡ 6 (mod 11)
2: (2^2 + 2 + 4) ≡ 2 (mod 11)
3: (3^2 + 3 + 4) ≡ 5 (mod 11)
4: (4^2 + 4 + 4) ≡ 3 (mod 11)
5: (5^2 + 5 + 4) ≡ 10 (mod 11)
6: (6^2 + 6 + 4) ≡ 8 (mod 11)
7: (7^2 + 7 + 4) ≡ 7 (mod 11)
8: (8^2 + 8 + 4) ≡ 9 (mod 11)
9: (9^2 + 9 + 4) ≡ 4 (mod 11)
10: (10^2 + 10 + 4) ≡ 6 (mod 11)
Since none of these integers satisfy the equation, the polynomial x^2 + x + 4 is irreducible over Z11.

To show that x^2 + x + 4 is irreducible over Z11, we can use the following steps:
Step 1: Substitute all possible values of x in the polynomial and check if it has any linear factors.
x = 0: 0^2 + 0 + 4 = 4 (not zero)
x = 1: 1^2 + 1 + 4 = 6 (not zero)
x = 2: 2^2 + 2 + 4 = 10 (not zero)
x = 3: 3^2 + 3 + 4 = 1 (zero)
x = 4: 4^2 + 4 + 4 = 7 (not zero)
x = 5: 5^2 + 5 + 4 = 10 (not zero)
x = 6: 6^2 + 6 + 4 = 2 (not zero)
x = 7: 7^2 + 7 + 4 = 10 (not zero)
x = 8: 8^2 + 8 + 4 = 5 (not zero)
x = 9: 9^2 + 9 + 4 = 9 (not zero)
x = 10: 10^2 + 10 + 4 = 5 (not zero)
Since there are no linear factors (i.e. no values of x that make the polynomial equal to zero), the polynomial is not reducible over Z11.
Step 2: Check if the polynomial has any quadratic factors by assuming it does, and then solving for the coefficients of the quadratic factors using the division algorithm.
Let the polynomial be factored as (x+a)(x+b), where a and b are in Z11. Then, expanding this expression gives:
x^2 + (a+b)x + ab
Comparing the coefficients of this expression with the coefficients of the original polynomial x^2 + x + 4, we get the following system of equations:
a + b = 1
ab = 4
Solving this system of equations gives the solutions (a,b) = (3,8) or (8,3), which are not in Z11. Therefore, the polynomial x^2 + x + 4 is irreducible over Z11.

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Answer: 2,641⇒3,000

Step-by-step explanation:

      2                       6                     4                 1

Thousand         Hundred            Ten             one

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

Question:

Round 2,641 to the nearest thousand

Solve:

When the number is less than 5, you move down

When the number is greater or equal to 5, you move up

2 is the thousands place

the number before 2 is 6 on the hundreds place

6 is greater than 5, so you move up

Hope this helps!! :)

Please let me know if you have any questions

a. To find the Maclaurin series for f(x) = 5e^-2x, we first need to find the derivatives of the function.

f(x) = 5e^-2x

f'(x) = -10e^-2x

f''(x) = 20e^-2x

f'''(x) = -40e^-2x

The Maclaurin series for f(x) can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

The first four nonzero terms of the Maclaurin series for f(x) are:

f(0) = 5

f'(0) = -10

f''(0) = 20

f'''(0) = -40

So the Maclaurin series for f(x) is:

f(x) = 5 - 10x + 20x^2/2! - 40x^3/3! + ...

b. The power series using summation notation can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

f(x) = Σ (n=0 to infinity) [(-1)^n * 10^n * x^n] / n!

c. To determine the interval of convergence of the series, we can use the ratio test.

lim |(-1)^(n+1) * 10^(n+1) * x^(n+1) / (n+1)!| / |(-1)^n * 10^n * x^n / n!|

= lim |10x / (n+1)|

As n approaches infinity, the limit approaches 0 for all values of x. Therefore, the series converges for all values of x.

The interval of convergence is (-infinity, infinity).

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Answer:

x² + 4x - 12

Step-by-step explanation:

Roots: -6 and 2

Leading coefficient: x²

(x + 6)(x - 2)

x(x - 2) + 6(x - 2)

x² - 2x + 6x - 12

x² + 4x - 12

I hope this helps!

Answer:

Step-by-step explanation:

you can find out the answer by subtracting 48 by 32, and if that number(16) times 3 equals 48( which it does) Then you know you are in the good.