You spin the spinner once. What is P (5 or divisor of 16)

Answer:

216 inches of ribbon is needed.

216 inches of ribbon will cost Bryon $108.

Step-by-step explanation:

multiply 12 x 18

12 x 18 = 216

216 inches of ribbon need to be used to cover the frame.

To find the cost multiply 216 and 0.5

216 x 0.5 = 108

It will cost Bryon $108 for 216 inches of ribbon.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Ways can n identical balls be distributed into r bins such that each bin contains at least two balls are 20 ways.

1 ball in each of 3 boxes: 4 ways

3 balls in one box: 4 ways

2 balls in one box and 1 ball in another box: 3*4=12 ways

There are 20 ways to arrange the balls .

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination can also be represented as: –nCr, nCr, C(n,r), Crn

Proof:

nPr = nCr.r!

= [n!/r!(n-r)!].r!

= n!/(n-r)!

Hence the theorem states true.

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

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The volume of the prism is 21 * 5 = 105 cubic feet.

To find the volume of a prism with a triangular base, you need to follow these steps:

1. Determine the area of the triangular base: Since the base is a right triangle with leg lengths of 6 feet and 7 feet, you can use the formula for the area of a right triangle: (1/2) * base * height. In this case, the area would be (1/2) * 6 * 7 = 21 square feet.

2. Multiply the area of the triangular base by the height of the prism: The prism is 5 feet tall, so the volume can be calculated by multiplying the area of the base (21 square feet) by the height (5 feet).

Thus, the volume of the prism is 21 * 5 = 105 cubic feet.

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The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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If chuck earns additional 40,000 of taxable income, 23.52% the marginal tax rate on this income

Chuck, a single taxpayer, earns $76,000 in taxable income and $1 in interest from an investment in city of heflin bonds.

Tax on $76,000

4,617.5 + (76,000 - 40,125) * 22% = 12,510.0

Taxable income 76,000 + 40,000 = 116,000

Tax on $116,000  

14,605.5 + (116,000 - 85,525) * 24% = 21,919.5

Marginal tax rate

(21,919.5 - 12,510) / 40,000 = 23.52%

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The line integral of xy dx + x^2 dy around the given rectangle is 0.

To evaluate the line integral ∮C (xy dx + x^2 dy) along the given rectangle C with vertices (0, 0), (5, 0), (5, 1), and (0, 1), we can break it down into four line integrals along each side of the rectangle and sum them up.

Along the bottom side:

Parametrize the line segment from (0, 0) to (5, 0) as r(t) = (t, 0), where t ranges from 0 to 5. The differential element along this line segment is dr = (dt, 0). Substituting these values into the line integral, we get:

∫[0,5] (t*0) dt = 0.

Along the right side:

Parametrize the line segment from (5, 0) to (5, 1) as r(t) = (5, t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, dt). Substituting these values into the line integral, we get:

∫[0,1] (5t0 + 25dt) = ∫[0,1] 25*dt = 25.

Along the top side:

Parametrize the line segment from (5, 1) to (0, 1) as r(t) = (5-t, 1), where t ranges from 0 to 5. The differential element along this line segment is dr = (-dt, 0). Substituting these values into the line integral, we get:

∫[0,5] ((5-t)*0 + (5-t)^2 * 0) dt = 0.

Along the left side:

Parametrize the line segment from (0, 1) to (0, 0) as r(t) = (0, 1-t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, -dt). Substituting these values into the line integral, we get:

∫[0,1] (0*(1-t) + 0) dt = 0.

Summing up all the line integrals, we have:

0 + 25 + 0 + 0 = 25.

Therefore, the line integral of xy dx + x^2 dy around the given rectangle is 25.

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We can use partial fraction decomposition method.                       Suppose that: x / (x - 4) (x - 3) (x - 2) = A / (x - 4) + B / (x - 3) + C / (x - 2)      A, B, C are constants to be determined by comparing the numerators.

Now, let us add the fractions on the right side together, since the denominators are the same as:                                                                      x / (x - 4) (x - 3) (x - 2)

= A / (x - 4) + B / (x - 3) + C / (x - 2)

=> x

= A (x - 3) (x - 2) + B (x - 4) (x - 2) + C (x - 4) (x - 3)

Now, the three denominators have the values x = 4, x = 3, x = 2 respectively. Therefore, we have, for each of these values:

when x = 4:

         A = 4 / (4 - 3) (4 - 2)

            = 4 / 2

            = 2

when x = 3:

         B = 3 / (3 - 4) (3 - 2)

            = -3

when x = 2:

         C = 2 / (2 - 4) (2 - 3)

            = -2

Thus, the partial fraction decomposition is:

x / (x - 4) (x - 3) (x - 2) = 2 / (x - 4) - 3 / (x - 3) - 2 / (x - 2)

Partial Fraction Decomposition is a method for breaking down a fraction into simpler fractions. This method is usually used in calculus to solve indefinite integrals of algebraic functions. It is used in integration by partial fractions and differential equations. If we have a fraction, the partial fraction decomposition helps us to re-write it in a way that makes it easy to integrate.

This method can be useful in simplifying complex expressions, especially if they involve rational functions with multiple terms in the denominator, as it allows us to break down the rational function into smaller, more manageable pieces.

In the given problem, we can see that the denominator of the rational expression is a product of three linear factors. Therefore, we can use partial fraction decomposition to write the expression as a sum of simpler fractions with linear denominators. By equating the numerators on both sides, we can find the values of the constants A, B, and C. Finally, we can put the fractions back together to get the partial fraction decomposition of the original expression.

Hence, the answer is:

x / (x - 4) (x - 3) (x - 2) = 2 / (x - 4) - 3 / (x - 3) - 2 / (x - 2).

Partial fraction decomposition can be a useful technique for simplifying complex expressions, especially those involving rational functions with multiple terms in the denominator. By breaking down the fraction into simpler fractions with linear denominators, we can make it easier to integrate and perform other algebraic manipulations. The method involves equating the numerators of the fractions, solving for the constants, and putting the fractions back together.

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Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

Answer:

c

Step-by-step explanation:

i took algebra and i know.

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

Answer:

the square foot is 5

Step-by-step explanation:

The square root of 5 is 5^(1/2)the cube root of 5 is 5^(1/3)so square root of five times cube root of five= 5^(1/2)*5^(1/3)=5^(1/2+1/3

Answer:

a soln

x+52=180(co interior angles)

x=180-52

x=128

x= 6+√-16/2

or

x= 6-√-16/2

Answer:

-6 and -13

Step-by-step explanation:

Divide both sides by 8

-48/8

and

-104/8

The required ventilation rate for a particle board manufacturing facility operating 24 hours per day is 220,534,854.6 m3/hr

Dimensions of workspace=30m × 10m × 5m

HCHO generation=25,000 micrograms/dm2/hr

Formaldehyde (HCHO) concentration = 0.10 ppm

Let the required ventilation rate for a particle board manufacturing facility operating 24 hours per day be V.

Volume of workspace=30m × 10m × 5m

                                    = 1500m^3

Conversion of formaldehyde (HCHO) concentration from ppm to micrograms/m3= 0.10 ppm × 1000,000/24.45

                         = 4088.67 micrograms/m3

Let the concentration of formaldehyde (HCHO) in the facility be equal to the concentration of formaldehyde (HCHO) in the exhaust air.

Concentration of HCHO in the exhaust air= 4088.67 micrograms/m3

Volume of air exhausted in one hour= V/3600m3/sec

Concentration of HCHO in the exhaust air= HCHO generation/Volume of air exhausted in one hour4088.67 micrograms/m3

= (25,000 micrograms/dm2/hr × 10000 dm2)/(V/3600m3/sec)4088.67

= (25,000 × 10,000)/(V/3600)4088.67

= 25,000,000,000/ V / 36004088.67 V / 3600

= 25,000,000,000V

= 25,000,000,000 × 3600 / 4088.67

= 220,534,854.6 m3/hr

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The domain of f(x), g(x), and h(x) can be represented in interval notation as (-∞, ∞) for all three functions since they are defined for all real numbers.

The domain of the function f(x) is all real numbers since there are no restrictions or limitations stated. Therefore, the domain can be represented as (-∞, ∞).

For the function g(x) = x² - 13x + 40, we need to find the values of x for which the function is defined. Since it is a quadratic function, it is defined for all real numbers. Thus, the domain of g(x) is also (-∞, ∞).

Considering the function h(x) = 5 - 2x, we have a linear function. It is defined for all real numbers, so the domain of h(x) is (-∞, ∞).

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Answer:

first option

Step-by-step explanation:

Given

\(\frac{3x}{x+1}\) ÷ x + 1 = \(\frac{3x}{x+1}\) ÷ \(\frac{x+1}{1}\)

To perform the division

Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is

= \(\frac{3x}{x+1}\) × \(\frac{1}{x+1}\)

Option A is correct, (3x/x+1).(1/x+1) is the equivalent expression of the expression  3x/x+1 divided by x+1.

An expression is combination of variables, numbers and operators.

The given expression is 3x/x+1 divided by x+1.

We need to find the equivalent expression of it.

3x/x+1 divided by x+1 can be mathematically written as below

(3x/x+1)/x+1

(3x/x+1) is the numerator and x+1 is in denominator

(3x/x+1)/(x+1/1)

When a fraction is divided by another fraction the denominator is multiplied to numerator as a reciprocal.

(3x/x+1).(1/x+1)

Hence, Option A is correct, (3x/x+1).(1/x+1) is the equivalent expression of the expression  3x/x+1 divided by x+1.

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1. Inside the spherical shell (r < R), the potential is given by V(r, θ) = ∑[(2l + 1)σ₀/(2ε₀\(R^{2l+1}\))] * (\(r^l\)) * \(P_l\)(cosθ).

2. Outside the spherical shell (r > R), the potential is given by V(r, θ) = ∑[σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^l\)) * \(P_l\)(cosθ).

3. The electric field inside the shell is E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(r^l\)) * \(P_l\)(cosθ) * ∇r

4. The outside the shell is E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^{l+2}\)) * \(P_l\)(cosθ) * ∇r.

To solve the given problem, let's go through the steps:

1. Boundary Conditions:

Inside the sphere (r < R), the potential must be finite, so we set the coefficients \(A_l\) = 0 for all l.

Outside the sphere (r > R), the potential must match the potential of a point charge at the center of the sphere, so we set \(B_l\) = σ₀ / (2l + 1) for all l.

2. Maxwell's Equation and Boundary Conditions:

Using the equation ∇²V = -ρ/ε₀, where ε₀ is the permittivity of free space, and ρ is the charge density, we have ∇²V = 0 outside the sphere (r > R) and ∇²V = -σ₀/ε₀ inside the sphere (r < R).

Applying the appropriate boundary conditions, we find that \(B_l\) = (2l + 1)σ₀/(2ε₀\(R^{2l+1}\)) for all l.

3. Potentials:

Using the expressions for the constants obtained in step 2, the potentials inside and outside the sphere are:

Inside (r < R): V(r, θ) = ∑[(2l + 1)σ₀/(2ε₀\(R^{2l+1}\))] * (\(r^l\)) * \(P_l\)(cosθ)

Outside (r > R): V(r, θ) = ∑[σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^l\)) * \(P_l\)(cosθ)

4. Electric Fields:

The electric field can be obtained from the potential using the relation E = -∇V.

Outside the sphere (r > R): E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(R^{l+1}\)/\(r^{l+2}\)) * \(P_l\)(cosθ) * ∇r

Inside the sphere (r < R): E(r, θ) = -∑[(l+1)σ₀/(2l + 1)] * (\(r^l\)) * \(P_l\)(cosθ) * ∇r

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Step-by-step explanation:

the sum of all angles in any quadrilateral is 360°.

so,

x + x + 3x + 8 + 3x + 8 = 360

8x + 16 = 360

8x = 344

x = 344/8 = 43°

3x + 8 = 3×43 + 8 = 129 + 8 = 137°

so, the angles are

43°

137°

43°

137°

In the given image, \(a_{23}\) is 5. The correct option is the first option 5

From the question, we are to determine which entry in the given matrix represents \(a_{23}\)

NOTE: For any entry denoted as \(a_{mn}\), it represents the entry in the m-th row and n-th column.

Thus,  

 \(a_{23}\) represents the entry in the 2nd row and 3rd column.

In the given image, the entry in the 2nd row and 3rd column is 5.

Hence, in the given image, \(a_{23}\) is 5. The correct option is the first option 5

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Answer:

blah blah blah blah

Step-by-step explanation:

karma :)

Answer:

\(x = 6\)

Step-by-step explanation:

\( \sin(45) = \frac{opposite}{hypotenuse} \)

\( \sin(45) = \frac{3 \sqrt{2} }{x} \)

\((x) \sin(45) = \frac{3 \sqrt{2} }{x} (x)\)

\((x) \sin(45) = 3 \sqrt{2} \)

\( \frac{(x) \sin(45) }{ \sin(45) } = \frac{3 \sqrt{2} }{ \sin(45) } \)

\(x = \frac{3 \sqrt{2} }{ \sin(45) } \)

\(x = 6\)

Answer:

15 weeks.

Step-by-step explanation:

Answer:

$2.45

Step-by-step explanation:

To find the unit cost, you divide the total cost by the number of units

19.60 ÷ 8 = 4.45

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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The product in scientific notation is 1.36 x 10^22

The product expression is given as:

3.2 x 1012 and 4.25 x 109

Express the product, properly

3.2 x 10^12 x 4.25 x 10^9

Regroup the factors

3.2  x 4.25 x 10^12 x 10^9

Evaluate the product

13.6 x 10^21

Rewrite as:

1.36 x 10^22

Hence, the product in scientific notation is 1.36 x 10^22

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Answer:

c 1.36 x 1012

explanation:

The median of the given data set is 259.

To find the median of a set of data, we arrange the data in ascending or descending order and locate the middle value.

If there is an odd number of data points, the median is the middle value. If there is an even number of data points, the median is the average of the two middle values.

Arranging the given data in ascending order, we have:

{154, 215, 224, 253, 254, 259, 263, 267, 276, 293, 389}

There are 11 data points, which is an odd number.

Therefore, the median is the middle value of the ordered data set.

The middle value is the 6th number in the ordered list, which is 259.

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The value of (c) that makes the equation \(\(19x^2 + 266x + c = 0\)\) have exactly one solution is approximately (930.526).

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13. Here, 2x – 5 and 13 are expressions The sign that connects these two expressions is “=”.

The equation \(\(19x^2 + 266x + c = 0\)\) is a quadratic equation in the form \(\(ax^2 + bx + c = 0\)\). For this equation to have exactly one solution, the discriminant \((\(b^2 - 4ac\))\) must be equal to zero.

In this case, we have (a = 19), (b = 266), and (c) is unknown. We can plug these values into the discriminant formula and set it equal to zero:

\(\((266)^2 - 4(19)(c) = 0\)\)

Simplifying this equation gives:

(70756 - 76c = 0)

To solve for (c), we isolate the variable:

(76c = 70756)

\(\(c = \frac{70756}{76}\)\)

Evaluating this expression gives:

(c = 930.526)

Therefore, the value of (c) that makes the equation \(\(19x^2 + 266x + c = 0\)\) have exactly one solution is approximately (930.526).

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The transfer price set by the selling division should be equal to the selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally. Option D.

The transfer price refers to the price at which goods or services are transferred between divisions within the same organization. When the selling division sets the transfer price, it needs to consider various factors. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, is the most appropriate choice.

The selling price less the variable costs ensures that the selling division covers its direct costs associated with the transferred goods or services. This ensures that the division remains financially viable and does not incur losses. However, it is also important to consider the opportunity cost of making the transfer internally.

The foregone contribution to the organization represents the potential profit or contribution that the selling division could have made if it had sold the goods or services to external customers instead of transferring them internally. By including this foregone contribution in the transfer price, the selling division accounts for the potential value it could have added to the organization.

In conclusion, the transfer price set by the selling division should consider both the variable costs associated with the transfer and the foregone contribution to the organization. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, captures both of these factors and provides a comprehensive approach to setting the transfer price.

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The slope of a line that passes through the points is 3

A slope is defined as the ratio of rise to run of a line. It is expressed according to the formula below;

Slope = rise/run

Slope = y₂-y₁/x₂-x₁

Using the coordinate points (1, 3) and. (2, 6), the slope is expressed as:

Slope = 6-3/2-1

Slope = 3/1

Slope = 3

Hence the slope of a line that passes through the points is 3

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As we can see the value of root 6 does not terminate after 3 decimal places. It can still be extended further. Hence, this makes √6 an irrational number.

hope it will help you..