A rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out of it to find the area of the paperboard that remains.

The formula for the nth term in an arithmetic sequence is an=a1+(n−1)d, and a10 = 10/5.

An=a1+(n1)d is the formula for the nth term in an arithmetic series. Any term in an arithmetic sequence may be determined using this formula. Every phrase in an arithmetic series has a common difference. For instance: 25,8,11. The order of operations in mathematics defines the priority with which complicated problems are solved. Your parenthesis comes first, followed by exponents, multiplication and division, and then addition and subtraction (PEMDAS).

A sequence is an ordered set of elements that follow a pattern. For example, 3, 7, 11, 15,… is a series because each term is formed by adding 4 to the preceding term.

This equation is a sequence of numbers that follow a pattern of increasing by 2 each time. The sequence begins with -3, then increases to -1, then increases again to 1, and finally increases to 3. From there, the pattern continues, with each number increasing by 2 each time. For example, the fourth number in the sequence would be 5, the fifth number would be 7, and the tenth number would be 17.

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Answer: To find the solution of the system of equations:

y = 3x^2 + 5x + 4

y = 2x + 10

We set the two expressions for y equal to each other:

3x^2 + 5x + 4 = 2x + 10

Subtracting 2x and 10 from both sides:

3x^2 + 5x - 2x + 4 - 10 = 0

3x^2 + 3x - 6 = 0

We can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 3, b = 3, and c = -6. Plugging these values into the formula:

x = (-3 ± √(3^2 - 4 * 3 * -6)) / 2 * 3

x = (-3 ± √(9 + 72)) / 6

x = (-3 ± √(81)) / 6

x = (-3 ± 9) / 6

x = (-3 + 9) / 6 or (-3 - 9) / 6

x = 6 / 6 or -12 / 6

x = 1 or -2

So the solution of the system of equations is (1, 17) or (-2, 4).

Step-by-step explanation:

Therefore, when CD is divided by XX, Is standard form 20

The fixed positive integers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively

We know that

CD = (D – C)

CD = (500 – 100)

CD = 400

XX = (X + X)

XX = (10 + 10)

XX = 20

CD = 400 and XX = 20 in numbers.

On dividing 400 by 20

Now, 20

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1. The slope of the secant line in terms of x and h is m(sec) =18x - 6 + 9h.

2. The m(sec) for h= 0.5, 0.1, and 0.01 at x = 1 is 16.5, 12.9 and 12.09 respectively.

3. The equation for the secant line at x = 1 with h = 0.01 is y = 12.09x - 0.09.

The function is g(x) = 9x^2 - 6x + 9

m(sec) = [tex]\frac{g(x+h)-g(h)}{h}[/tex]

m(sec) = [tex]\frac{(9(x+h)^2 - 6(x+h)+9)-(9x^2 - 6x+9))}{h}[/tex]

Simplifying

m(sec) = [tex]\frac{((9x^2+18xh+9h^2) - (6x+6h)+9)-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(9x^2+18xh+9h^2 - 6x+6h+9-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(18xh+9h^2 +6h)}{h}[/tex]

Taking h common

m(sec) =18x - 6 + 9h

At x = 1

m(sec) =18 - 6 + 9h

m(sec) = 12 + 9h

At h = 0.5

m(0.5) = 12 + 4.5 = 16.5

At h = 0.1

m(0.1) = 12 + .9 = 12.9

At h = 0.01

m(0.01) = 12 + .09 = 12.09

as h = 0 , m(sec) = 12

point-slope form

y - 12 = 12.09(x - 1)

y - 12 = 12.09x - 12.09

Add 12 on both side, we get

y = 12.09x - 0.09

The graph of the part c is given below.

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Answer:

9 hours

Step-by-step explanation:

The time taken is inversely proportional to the number of men; if M = number of men and D = number of days this can be expressed as
[tex]D \displaystyle \propto } \dfrac{1}{M}\\\\\text{which can be expressed as an equation: }\\\\D = k \cdot \dfrac{1}{M}\\\\or\\\\D = \dfrac{k}{M}\\\\[/tex]

k is known as the constant of proportionality which can be expressed as

[tex]k = D\cdot M[/tex]

Inversely proportional means:
As the number of men increases, the time taken decreases

As the number of men decreases, the time taken  increases

We can find k from the given information with M = 3 and D = 6 hours

[tex]k = 6 \cdot 3 = 18[/tex]

[tex]\textrm{Therefore, given M= 2, D = $\dfrac{18}{2} = 9$ \;hours}[/tex]

For 2 men it will take 9 hours to repair the road

By applying the concept of the pyramid, it can be concluded that the height of the larger pyramid is 5 m.

Pyramid is a 3-D shape that has a polygonal base and flat triangular faces, which join at a common point (the apex).

To find the volume of a pyramid, we multiply the area of its base by the height of the pyramid and divide by 3.

We have two similar pyramids. Let Va be the volume of the larger pyramid and Vb be the volume of the smaller pyramid:

Va = 123 m³

Vb = 27 m³

Let Ha be the height of the larger pyramid and Hb be the height of the smaller pyramid:

Hb = 3 m

Since these are similar pyramids, then their volume is proportional to their height.

For smaller pyramid:

Vb = 27 m³

     = 3³ = Hb³

So we can determine Ha as follows:

Ha = ∛Va

     = ∛125

     = 5 m

Thus, the height of the larger pyramid is 5 m.

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For ε = 0.1, c = 3, and l = 3.2, we can choose δ = 0.2. This means that for all x, 0 < |x - 3| < 0.2 → |f(x) - 3.2| < 0.1.  the values of ε, c, and δ into the equation to check if it satisfies the given condition.

1. Choose an epsilon (ε) value of 0.1 which is the maximum allowed difference between f(x) and l.

2. Identify the value of c which is 3 in this case.

3. Choose a δ value (δ) such that it is greater than 0 and when combined with c, it satisfies the condition 0 < |x - 3| < 0.2.

4. Substitute the values of ε, c, and δ into the equation to check if it satisfies the given condition.

5. If it does, then the answer is 0.2.

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Answer:-3, -1/2

Step-by-step explanation:

bro this was tough for me i f u kin hate algebra but yeah theres your answer my guy

Answer:

got to combine like terms and I think you got your answer

Step-by-step explanation:

The volume of a pyramid is 10x² /3 -40x/ 3 - 40.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.

The area that any three-dimensional solid occupies is known as its volume.

We have,

The area of the rectangular base of a pyramid is given by the polynomial equation, B = x²-4x-12.

Now, Volume of Pyramid

= 1/3 x (base area) x height

= 1/3 x ( x²-4x-12) x 10

= 10x² /3 -40x/ 3 - 40

Thus, the Volume is 10x² /3 -40x/ 3 - 40.

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The sample standard deviation between two of the given independent sets is 15.3.

A standard deviation can be defined as the amount of variation or difference between a given set of values. If we have a low standard deviation, it means that the values are closer to the mean of the data set. A higher standard deviation just means that the opposite - the values are far off in the range.

Given data items 84, 85, 83, 63, 61, 100, 98,

Number of data items, N = 7,

Let x represent the data item. The Mean of the data points can be calculated using the -

= 84+ 85+ 83+ 63+ 61+ 100+ 98 / 7

= 82

Hence, the sample standard deviation would be -

= [tex]\sqrt{\frac{x}{y} }[/tex]   where x = Σ(x₁ - μ)² and y = N

= 15.3

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For the given statement is 2/7, numerator = 2, denominator = 7

The line that divides the numbers 4 and 5 is an example of a fraction and is known as the fraction bar. Here, the number above and below the fraction bar represent the numerator and denominator, respectively. A numerator is used to symbolise the denominator, or the number of parts that make up the whole.

Fractions are used to represent the parts of an entire or collection of items. A fraction is made up of two parts. The number at the top of the line is known as the numerator. It shows the number of identically sized pieces that were taken from the full product or collection. The quantity specified below the line serves as the denominator.

Following division, the quotient is converted to whole numbers, the remainder becomes the new numerator, and the denominator remains constant.

As he ate 2 pieces out of 7 pieces,

the fraction would be 2/7

numerator = 2

denominator = 7

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By applying the definite integral concept, it can be concluded that ∫₀¹²⁰ r(t) dt represents the number of gallons of oil that leaked from the tank in the first two hours.

Integral is a form of continuous addition that is the inverse of the derivative (anti-derivative)

Definite integral is an integral form in which the integration variables have limits (upper and lower limits) written at the top and bottom of the integral notation.

If y = f(x) is continuous on the interval a ≤ x ≤ b, where a is the lower limit and b is the upper limit, then:

∫ₐᵇ f(x) dx = F(x) |ₐᵇ

               = F(b) - F(a) , where

F(x) = anti-derivative of f(x) on the interval a ≤ x ≤ b

In everyday life, integrals can be used to calculate the volume of a container when the flow rate is known.

r(t) = V'(t) , where:

r(t) = flow rate

V'(t) = anti-derivative of volume

We have a function ∫₀¹²⁰ r(t) dt where r(t) is the oil leaks rate.

As we know that r(t) = V'(t), we can substitute this into the function:

∫₀¹²⁰ r(t) dt = ∫₀¹²⁰ V'(t) dt

                = V(120) - V(0)

Now we understand that this function represents the change of volume from t = 0 to t = 120 minutes (2 hours).

Or in the other words, this function represents the number of gallons of oil that leaked from the tank in the first two hours.

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The final result for c will be -90 degrees.

Since triangle ABC is a right triangle (with angles A and E equal to 90 degrees), we know that the sum of its interior angles must equal 180 degrees. Therefore, we can set up the following equation to solve for c:

c + 90 + 60 + 30 = 180

Simplifying and solving for c:

c = 180 - 90 - 60 - 30

c = 0 - 60 - 30

c = -90

So c = -90 degrees.

The problem we face is a problem in geometry, specifically concerning the calculation of the measurement of angles in a triangle. It involves using the properties of triangles and the fact that the sum of the interior angles of a triangle is equal to 180 degrees.

I determined that this is a problem in geometry based on the given information about the triangle and the calculation of its interior angles. The use of the sum of the interior angles being equal to 180 degrees, as well as the given values of angles G, A and E, and F, are common in geometry problems, indicating that this is likely a geometry problem.

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The period of the function given by the graph of cosine is 2pi.

A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods. In other terms, a periodic function is one whose values recur after a specific interval. The period of a function that has the formula f(x+k)=f is known as the basic period of a function (x)

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function.

The given function is a cosine function.

The period of the cosine function is given as:

P = 2pi /B

Here, the value of B = 1

Hence, the period of the function is 2pi.

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The period of the function given by the graph of cosine would be 2π.

A periodic function is one whose values repeat at regular intervals or periods, whereas a period is the amount of time between two waves. In other words, a periodic function is one whose values repeat every predetermined amount of time. The basic period of a function is the duration of a function whose formula is f(x+k)=f (x)

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. For any trigonometry graph function, we can take x = 0 as a starting point.

The given function is a cosine function.

Let the period of the cosine function be P = 2π/B

The value of B = 1

Therefore, the period of the function be 2π.

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The probability that all five of the children get the disease is 0.012.

The probability of a single child getting the disease from the mother is 0.41. The probability that all five children will get the disease from their mother can be found by multiplying the probability of each child getting the disease. So, the probability that all five of the children get the disease is

= 0.41 * 5

= 0.41 * 0.41 * 0.41 * 0.41 * 0.41

= 0.012.

= 1.2%

This means that there is a 0.012, or 1.2%, chance that all five of the children will get the disease from their mother.

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The correct option for the given question of the vector is none of these.

Physical values may be represented mathematically using vectors, which have both magnitude and direction. They are helpful for resolving issues in physics, engineering, and many other disciplines. They are frequently depicted as directed line segments or arrows. The addition, subtraction, and scaling of vectors make it simple and flexible to express physical quantities and carry out mathematical operations. They are crucial for characterizing geometric objects and carrying out spatial transformations.

According to the question

The vector projection of a vector u onto a vector v is given by:

proj_v u = (u . v) / ||v||^2 * v

where (u . v) is the dot product of vectors u and v, and ||v|| is the magnitude of vector v.

For the vectors u = i + 2j + 3k and v = 3i - j + 2k, the projection of u onto v is:

proj_v u = (u . v) / ||v||^2 * v = ((i + 2j + 3k) . (3i - j + 2k)) / ||3i - j + 2k||^2 * (3i - j + 2k) = (15 + 4 - 3) / 14 * (3i - j + 2k) = 16 / 14 * (3i - j + 2k) = (8/7) * (3i - j + 2k) = 8/7 * 3i - 8/7 * j + 8/7 * 2k = 8/7 * i + 2/7 * j + 16/7 * k

Therefore, the vector projection proj_v u of u onto v is:

proj_v u = 8/7 i + 2/7 j + 16/7 k

The "None of the above", option is correct.

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Steel: σs = p/A_s; Brass: σb = p/A_b; Copper: σc = p/A_c , where A_s, A_b, A_c are the areas of the steel, brass, and copper, respectively.

To calculate the tensile stresses in the steel, brass, and copper due to the force p, we use the formula: σ = p/A, where σ is the tensile stress and A is the area of the material. For the steel, the area is A_s, so the tensile stress σs is equal to p divided by A_s. For the brass, the area is A_b, so the tensile stress σb is equal to p divided by A_b. Finally, for the copper, the area is A_c, so the tensile stress σc is equal to p divided by A_c. Therefore, the tensile stresses in the steel, brass, and copper due to the force p can be calculated using the formula σ = p/A, where A is the area of the material.

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The given function is a radical expression with a coefficient of -3, a radicand of x-5, and a constant of 1.

A function is a process or set of instructions that takes inputs, performs a specific task, and produces an output. Functions are key components of programming languages, allowing the coder to create complex commands with simple instructions. For example, a function can be used to add two numbers together or to generate a random number. Functions can also be combined to create more complex sequences of instructions.


This function can be graphed on a coordinate plane by plotting the points that satisfy the equation. The graph of the given function will look like a parabola that is shifted up 1 unit and shifted left 5 units. It can also be seen that this function has been vertically stretched by a factor of 3.

To transform this function, we can use the same rules that apply to linear functions. For example, we can shift the graph up 3 units by adding 3 to the constant of 1, making the new equation f(x) = -3√x-5+4. We can also shift the graph down 5 units by subtracting 5 from the radicand, making the new equation f(x) = -3√x-10+1. Additionally, we can shift the graph left 2 units by subtracting 2 from the radicand, making the new equation f(x) = -3√x-7+1. Finally, we can shift the graph right 4 units by adding 4 to the radicand, making the new equation f(x) = -3√x-1+1.

Overall, by applying the same transformation rules that apply to linear functions, it is possible to transform the given radical expression. The transformation will result in a graph that is shifted up or down, left or right, and vertically stretched or compressed.

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The polygon above has 7 sides. it is an heptagon.

A polygon is a plane figure enclosed by line segments called sides. A polygon is named according to the number of sides.  For example polygon with 5 sides is called pentagon, the polygon with 6 sides is called hexagon, the polygon with 7 sides is called heptagon and the polygon with 8 sides is called octagon

A polygon with equal sides of angle is called a regular polygon.

Therefore, let's count he sides of the polygon to know the polygon name.

Hence the polygon has 7 sides and it is called an heptagon.

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The value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect

The given equation is written in slope-intercept form as y=6x. This is a linear equation where 'y' is a function of 'x', and the slope is 6.

To calculate the value of y when x=4, first substitute the value of x in the given equation.

y = 6x

 = 6 x 4

 = 24

Therefore, the value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect.

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Notice that points ( i ), ., (vi) are approaching x=1 from the right and points

(vii), ., (xi) are approaching from the left.

The closer is a point Q to x=1, the closer is the slope of the line PQ to the slope of the tangent at x=1.

For this articular function you can treat a pair like (xi),(vi) as an upper and lower

bound on the slope of the tangent.

If you can find a pair (something like Q1=0.999, Q2=1.001) so close to x=1 that the two secant lines PQ1 and PQ2 have identical slopes within two decimal places, then you have your estimate.

The exact value of the slope at x=1 is -14π.

The thing about this function is that it alternates between up and down extremely quickly.

If I could attach a graph I would; I would recommend that you look at it in some graphing tool.

Just imagine what is happening around x=1:

The argument of sin is 14π, making the value of the function 0.

If you keep increasing x beyond 1, the argument of sin gets smaller;

when the argument of sin gets to 13.5π the value of the function reaches -1

and the direction of the slope reverses.

That means that to get any meaningful estimate of the slope you need x

such that 14π/x is in the interval (13.5π, 14.5π).

That means x must be in the interval (0.97, 1.03).

And you probably need to try values even closer to 1 to get accuracy to 2 decimal digits.

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Answer:

6(2g+1) (2g-1)

Answer:

6(2g - 1)(2g + 1)

Step-by-step explanation:

24g² - 6 ← factor out the common factor of 6 from both terms

= 6(4g² - 1) ← 4g² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4g² - 1

= (2g)² - 1²

= (2g - 1)(2g + 1)

then

24g² - 6 = 6(2g - 1)(2g + 1) ← in factored form

volume= 127.31

if base side is 7 and height is 6

Answer: 14

Step-by-step explanation:

Volume = 1/3 x 7 x 6

Volume = 1/3 x 42

Volume = 14

Answer:

[tex] {10}^{6} = x[/tex]

Step-by-step explanation:

When transforming an expression from logarithm form to exponential form, remember:

[tex] log_{a}(x) = n [/tex]

is also equal to

[tex] {a}^{n} = x[/tex]

The Exponential Form of log of x is given as 10⁶.

The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 103, its logarithm in base 10 is 3, or log₁₀ = 3.

The use of a logarithm can be used to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to express exponents. Log interpretation is not that tough. It suffices to know that an exponential equation may also be written as a logarithmic equation in order to comprehend logarithms.

Logarithmic Graph Properties :

A > 0 and a ≠ 1 

When a > 1, the logarithmic graph rises, and when 0 a 1, it falls.

By increasing the function's input above 0, the domain is acquired.

The set of all real numbers is known as the range.

The natural logarithm is e so

lnx = 6

or, x = e⁶

for log of 6 we can also write

log₁₀x = 6

or, x = 10⁶

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Answer: Add 1/8 to 1/8, or multiply 1.8 by 2

Step-by-step explanation:

1/8 + 1/8 = 2/8, which is 1/4

or

1/8 x 2 = 2/8 which is 1/4

The value of k that makes the given function continuous would be k=3

What is continuous function ?

A continuous function is one in which the interval specified for the function is continuous. A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].

The function f(x) = 5 - 3x - 2 is defined for all real values of x. To make the function continuous, the value of f(0) must be equal to the value of the function at x = 0 from the second piecewise definition:

f(x) = k if x = 0

Setting these two values equal to each other and solving for k, we find:

5 - 3(0) - 2 = k

k = 3

So, the value of k that makes the given function continuous is k = 3. This means that the function is continuous at x = 0 if f(x) = 5 - 3x - 2 for x ≠ 0 and f(0) = 3.

Hence, The value of k that makes the given function continuous would be k=3

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Answer:

Tom is 30 years old. Danny is 31 years old, Pablo is 32 years old, and Adam is 36 years old.

There are 64 combinations possible with 4 numbers without repeating. The solution has been obtained by using permutations.

What is permutation?

A permutation is a grouping of objects in a certain order or sequence. When dealing with permutation, it's crucial to consider both the selection and the arrangement. In a nutshell, permutations heavily rely on ordering. In other terms, an ordered combination is a permutation.

Using permutations, the total number of combinations will be as follows:

⇒4P1 + 4P2 + 4P3 + 4P4

⇒4 + 12 + 24 + 24

⇒64

Hence, there are 64 combinations possible with 4 numbers without repeating.

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The fencing around the perimeter of semicircular statuary garden of diameter 21 feet will altogether cost $300

given that the diameter of the garden is 21 feet

cost per linear foot is  $9.50

perimeter of semicircle = [tex]\pi r[/tex]

hence the perimeter of the garden will be  [tex]3.14*\frac{21}{2}[/tex]

which is equal to 32.97 feet

now since the cost of fencing per linear foot is $9.50

the cost of fencing the perimeter will be [tex]32.97*9.50[/tex]

i.e $313.215≈  $300

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The hypotenuse is 5 of a right triangle with legs of length3 and4

The Pythagoras theorem goes as follows:

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

a²+b²=c²

'A' and 'B' are the other two legs, and '=' is the hypotenuse of the right triangle. As a result, the Pythagoras equation can be used for any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Here: a=3,b=4

32+42=c²

9+16=c²

25=c²

=√25=5

So, the hypotenuse is 5

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