The radius of a circle is 11 miles. What is the circle's circumference?

Answer:

A. 2

B.1

C.3

D. (should be x and 7x but that isnt an answer choice so) no

Step-by-step explanation:

For given expression x + 3 + 7x,

a) the number of terms in an algebraic expression = 2

b) the numerical coefficient of the first term = 1

c) the constant term = 3

d) the like terms are x and 7x

"It is a mathematical expression that consists of variables, numbers and operations."

"It is a value or number that never changes in expression."

"The like terms are defined as the terms that contain the same variable which is raised to the same power."

For given example,

We have been given an expression  x + 3 + 7x

a) x + 3 + 7x = 3 + (1 + 7)x

                    = 3 + 8x

So, the number of terms in the algebraic expression = 2

b) for given expression x + 3 + 7x,

the first term is x

x = (1) × (x)

the numerical coefficient of the first term is 1.

c) for given expression x + 3 + 7x,

the constant term = 3

d) for given expression x + 3 + 7x,

the like terms are x and 7x

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Answer:

option E, C

Step-by-step explanation:

From the graph we will find the equation of g(x).

g(x) is a parabola with vertex ( h, k) = ( 0, 9)

Standard equation of parabola is ,  y = a (x - h)² + k

                                                     y = a (x - 0)² + 9

                                                     y = ax² + 9 ----------  ( 1 )

Now we have to find a .

To find a we will take another point through which the parabola passes .

Let it be ( 3, 0).

Substitute ( 3 , 0 ) in  ( 1 ) =>  0 = a (3 )² + 9

                                     => - 9 = 9a

                                     => a = - 1

Substitute a = - 1 in ( 1 ) => y = -1 x² + 9

                                  => y = - x² + 9

Therefore , g(x) = -x² + 9

Now using the table we will find h(x)

 \(h(x) = 4^{x}\)

So g(x) = -x² + 9 and \(h(x) = 4^{x}\)

Option A : both function increases on ( 0, ∞ ) - False

               \(\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9\)

                                  \(= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty\)

g(x) decreases on ( 0 , ∞)

             \(\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}\)

                                \(= \infty\)

h(x) increases on ( 0, ∞)

option B : g(x) increasing on (- ∞, 0) - False

      g(x) = -x² + 9

       g( -2 ) = - (-2)² + 9

                 = - 4 + 9 = 5

       g ( -5) = - ( -5)² + 9

                =  - 25 + 9 = - 14

   As the value of x moves towards - ∞ , g(x) moves towards - ∞

   Therefore g(x) decreases on  (- ∞, 0)

Option C: y intercept of g(x) is greater than h(x) - True

         y intercept of g(x) = ( 0 , 9 )

         y intercept of h(x)  = ( 0 , 1 )

Option D : h(x) is a linear function - False

Option E : g(2) < h(2) - True

        g(x) =  -x² + 9

        g(2) = -(2)² + 9 = - 4 + 9 = 5

        h(x) = 4ˣ          

        h(2) = 4² = 16      

The sum of the geometric series infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ is {6 / (1 - x)}.

What is geometric series?

A geometric series in mathematics is made up of an unlimited number of terms with a fixed ratio between them.

As per data given,

The geometric series is infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ

Rewrite geometric series,

infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ = infinity ∑ (n = 0) {(x - 5)/6}ⁿ

Common ratio is r = (x - 5)/6

We know a geometric series converges when the radius is less than 1, so we have

I r I = I (x - 5)/6 I < 1

I x - 5 I < 6

-6 < x - 5 < 6

-1 < x < 11

Therefore, the series converges on ( -1, 11)

The sum of the series is, by using the formula {a / 1 - r}.

Substitute values in formula respectively,

a / 1 - r = 1 / {1 - (x - 5)/6}

           = 6 / {6 - (x - 5)}

           = 6 / (1 - x)

Hence, the sum of the geometric series infinity ∑ (n = 0) (x - 5)ⁿ / 6ⁿ is {6 / (1 - x)}.

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If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

The term taxable income refers to any gross income earned that is used to calculate the amount of tax you owe. Put simply, it is your adjusted gross income less any deductions. This includes any wages, tips, salaries, and bonuses from employers.

The minimum income amount depends on your filing status and age. In 2022, for example, the minimum for single filing status if under age 65 is $12,950. If your income is below that threshold, you generally do not need to file a federal tax return. Review the full list below for other filing statuses and ages.

Taxable income

a. Taxable income:

Taxable income=Gross income - Total taxes due

Taxable income=$63,000-$6,847.50

Taxable income=$56,152.5

b. The marginal tax rate for taxable income  under the income bracket of of $40,526 to $86,375 is 22%.

c. Effective tax rate:

Effective tax rate = Total taxes due/ Taxable income×100

Effective tax rate =$6,847.50/$56,152.5×100

Effective tax rate =10.869%

Effective tax rate =10.87% (Approximately)

Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

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Answer:

m<ABE = 109°

Step-by-step explanation:

Since the two chords intersect, we would have the following:

m<ABE = ½(Arc AE + Arc DC)

Substitute

m<ABE = ½(180° +38°)

m<ABE = ½(218)

m<ABE = 109°

To minimize the penalty cost, the linear programming problem is formulated as a goal programming problem by introducing deviation variables (d₁, d₂, d₃) and surplus variables (s₁, s₂), with the objective function Z = 100d₁ + 50d₂ + 10d₃ and the corresponding constraints.

To formulate the given linear programming problem as a goal programming problem to minimize the penalty cost, we can introduce deviation variables on each constraint and assign penalty weights to these variables. The goal is to minimize the total penalty cost:

d₁: Deviation variable for the first constraint (3x₁ + 2x₂ ≥ 30)

d₂: Deviation variable for the second constraint (2x₁ + x₂ ≥ 40)

d₃: Deviation variable for the third constraint (5x₁ + 3x₂ ≤ 50)

We also need to introduce positive surplus variables to ensure the original constraints are not violated:

s₁: Surplus variable for the first constraint (3x₁ + 2x₂ ≥ 30)

s₂: Surplus variable for the second constraint (2x₁ + x₂ ≥ 40)

Now, let's formulate the linear programming model with penalty costs and deviation variables:

Minimize:

Z = 100d₁ + 50d₂ + 10d₃

Subject to:

3x₁ + 2x₂ - d₁ + s₁ = 30

2x₁ + x₂ - d₂ + s₂ = 40

5x₁ + 3x₂ + d₃ ≤ 50

x₁, x₂, d₁, d₂, d₃, s₁, s₂ ≥ 0

The objective function minimizes the penalty cost by summing the products of deviation variables and their respective penalty weights.

The first constraint includes the deviation variable d₁ to measure the deviation from the minimum requirement of 30. The surplus variable s₁ ensures that the original constraint is not violated.

Similarly, the second constraint includes the deviation variable d₂ and the surplus variable s₂.

The third constraint includes the deviation variable d₃ to penalize any excess beyond the upper limit of 50.

All decision variables (x₁, x₂, d₁, d₂, d₃, s₁, s₂) are non-negative.

Solving this goal programming problem will minimize the penalty cost associated with failing to satisfy the original constraints.

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The ratio 3.4/2.2 can be expressed as a fraction in lowest terms as 17/11.

To find the fraction in lowest terms, we need to simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 17 and 11 is 1, as there are no common factors other than 1. Dividing 17 and 11 by 1 gives us the fraction 17/11, which is already in its simplest form.

In the given ratio 3.4/2.2, the numerator is 3.4 and the denominator is 2.2. To convert it into a fraction, we can express both the numerator and denominator as whole numbers by multiplying them by a power of 10. In this case, we multiply both 3.4 and 2.2 by 10 to get 34 and 22, respectively. The ratio then becomes 34/22. To simplify this fraction, we find the greatest common divisor of 34 and 22, which is 2. Dividing both the numerator and denominator by 2 gives us the fraction 17/11, which is the simplest form of the ratio.

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\(x + x^3\) is the simplified expression of \(x/4x + x^2\)

To simplify , we will find common denominator. A common denominator means the number which can be divided by all the denominators in a group of fractions.

The denominator of first fraction is 4x, so we will rewrite the expression as:

From \(x/4x + x^2\)

To: \((x/4x) + (x^2(4x)/4x).\)

Simplifying second fraction gives us:

(4x^3)/4x.

We will cancel out common factor of 4x, so, we are left with \(x + x^3\)as the simplified expression.

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Answer:

width = 14 feet

Step-by-step explanation:

the 7 part of the ratio relates to the length of the garden , then

24.5 feet ÷ 7 = 3.5 feet ← value of one part of the ratio , so

width = 4 × 3.5 feet = 14 feet

The given grammars (a) and (b) have been modified by applying left-factoring and eliminating left recursion, resulting in equivalent grammars suitable for recursive-descent parsing.

To eliminate left recursion and left-factoring in the given grammars, let's start with grammar (a) and then move on to grammar (b).

(a) Grammar: S + bccs | adaSa | adacSc | de

Left-Factoring

To apply left-factoring, we identify common prefixes in the productions.

S → bccs | adaSa | adacSc | de

We can see that "ada" is a common prefix in the second and third productions. Let's factor it out

S → bccs | ada(Sa | cSc) | de

Elimination of Left Recursion

To eliminate left recursion, we'll rewrite the grammar using new non-terminals.

S → bccsT | adaUT | de

T → Sa | cScT

U → daUT | cScU | ε

The grammar is now free of left recursion and left-factoring.

Moving on to grammar (b)

(b) Grammar: S + Scbc | Sbbc abs | dbSa

Left-Factoring

S → Scbc | Sbbc abs | dbSa

We can see that "Sb" is a common prefix in the second and third productions. Let's factor it out:

S → Scbc | Sb(bc | bc abs) | dbSa

Elimination of Left Recursion

S → ScbcT | SbUT | dbSa

T → ε

U → cbcT | bcUT | bc absT

The resulting grammar is free of left recursion and left-factoring.

Now, you have equivalent grammars for (a) and (b) where the problems preventing the use of recursive-descent parsing have been removed.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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The lowest test score that still qualifies for a scholarship is 632.

To discover the lowest test score that still qualifies for a scholarship, we will use the NORM.INV feature in Excel. This feature returns the inverse of the usual everyday cumulative distribution feature, which can be used to discover the score that corresponds to a given percentile.

The percentile we are interested by is the top 5%, which corresponds to a cumulative possibility of 0.95. we are able to use the formula:

NORM.INV(0.95, 600, 85)

Wherein 0.95 is the probability, 600 is the mean, and 85 is the standard deviation.

Evaluating these component in Excel offers us:

632.39

Rounding to the closest integer, we get:

632

Consequently, the test score which is lowest but still qualifies for a scholarship is 632.

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Answer:

10 km/h

228 km/h

Step-by-step explanation:

We are told the speed of one of the buses. Since we know that both buses only travelled 7 hours, we can multiply the speed of the first bus by 7 hours to get its total distance

10 km/h * 7 hours = 70 km

Now we subtract this amount from the total distance that the two buses are seperated initially

1666 / 70 = 1596 km

Finally, we can divide this remaining distance by the 7 hours that the second bus travelled to get the second buses rate of speed.

1596 / 7 = 228 km/h

**The total distance between both buses is probably wrong and may be 166km and not 1666 as the question states**

Part a: Ignoring those that are bigger than 4.

Part b: labeling the random number.

Part c: conclusion, Claire should plan to purchase 12 boxes.

Part a: random number table;

Part b: labeling the random number.

7318495907 05179 51002(10 boxes) 8337452297 07769 99792 78365 9348772753 36216 (15 boxes) 07230 35793 71907 65571 66784(10 boxes) 25548 91861 15725.

Part c: conclusion,

On average, Claire should plan to purchase 12 boxes.

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Answer:

5 feet

Step-by-step explanation:

The rose garden is trianglar and so the total of the two shorter sides need to equal more than the longest side. In this case 4+x=9. 6,7, and 8 all meet these requirments but 4+5 is 9, 9=9 which means 5 feet cannot be used

Answer:

A=l×b

18 = l × b

b = 18/6

b = 3

Answer:

B and C

Step-by-step explanation:

11 x 10³ is 11 with three zeros after the 11, or 11000

A is equal to 1100

B is equal to 11000

C is equal to 11 multiplied by 1000 which is 11000

E is equal to 1331

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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By evaluating the linear equation we can see that the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

Here we have a linear function:

y = -2x + 9

And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.

if x = -2

y = -2*-2 + 9 = 4 + 9 = 13

if x = 0

y = -2*0 + 9 = 9

if x = 2

y = -2*2 + 9 = 5

if x = 4

y = -2*4 +9 = 1

Then the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

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Answer:

At the end of 4 years, your savings will have grown to $6,077.

Step-by-step explanation:

result is 31+i in where 31 is real part and i is complex part as given i= √-1 and i²= -1

In mathematics complex number is an element which has two parts one is called real part and the remaining is termed as imaginary part. An example is 41+6i

here, 41 is real part, 6i is imaginary part

A real number cannot be added or subtracted with an imaginary number, but a real number can be multiplied or divided with an imaginary number.

We are given, (2+3i) (5-7i)

    at first, we expand it by removing parenthesis

2x5-2x7i+3ix5-3ix7i

10-14i+15i-21i²

now like term is added

10+i+21   as we are given i²= -1

    31+i

hence, we get 31+i

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The probability of getting all heads when flipping a coin four times is 1/16.

(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.

There were 16 total outcomes.

Probability going out of control

HHHH P(A) = P(getting all heads) = 1/16

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Answer:

x + 29 = 73

Step-by-step explanation:

Brandon  = x Videogames

Jerry = 29 Videogames

brandon + Jerry = 73

x + 29 = 73

Answer:

v + 29 = 73 This is the equation

44 is the answer to this equation. If you needed it

Step-by-step explanation:

Brandon has an unknown amount of video games, which we're selling v, adn Jerry has 29 video games. All together, they have 73 video games.

You can represent the amount of games that Jerry and Brandon have as a sum (addition)

v + 29

You know that together they have 73 games

You can set the two expressions equal to describe this situation with an equation

v + 29 = 73

You can write this as 29 + v = 73, 73 = 29 + v, or 73 = v + 29

Anyone of the equations is correct

So the equation is v + 29 = 73 or any of the equations I listed

Answer:

Step-by-step explanation:

The angle addition theorem tells you an angle is the sum of its parts:

  ∠ADC = ∠ADB +∠BDC

Angle BDC is marked as a right angle, so has a measure of 90°. Filling known values into the above equation gives ...

  (16x -55)° = (5x -13)° +90°

  11x = 132 . . . . . . . . . divide by °, add 55-5x

  x = 12 . . . . . . . . . . divide by 11

Then the measures of the angles are ...

  ∠ADB = (5x -13)° = (5(12) -13)° = 47°

  ∠ADC = (16x -55)° = (16(12) -55)° = 137° . . . . . . same as 47° +90°

Here <BDC is a right angled triangle i.e (90°) and rest of the two angles are <ADC and <ADB.

Here,

<ADC = (16x - 55)°

<ADB = (5x - 13)°

<BDC = 90°

Now by applying the addition theorem property of triangle we get,

\(:\implies\rm{16x - 55 = 5x - 13 + 90}\)

\(:\implies\rm{16x - 5x - 55 + 13 = 90}\)

\(:\implies\rm{11x - 42 = 90}\)

\(:\implies\rm{11x = 90 + 42}\)

\(:\implies\rm{11x = 132}\)

\(:\implies\rm{x = \frac{132}{11} }\)

\(:\implies\rm{x = 12}\)

For angle <ADC = (16x - 55)°

\(:\implies\rm{16\times 12 - 55}\)

\(:\implies\rm{192 - 55}\)

\(:\implies\rm{137}\)

For angle <ADB = (5x - 13)°

\(:\implies\rm{5 \times 12 - 13}\)

\(:\implies\rm{60 - 13}\)

\(:\implies\rm{47}\)

Step-by-step explanation:

from above figure calculate from the calculator and the right answer will be .....

The area of the indicated region bounded by y=7 and y=7/25x^2 is XXX square units.

To calculate the area using Green's Theorem, we need to express the region in terms of a curve. Green's states that closed the line Theorem line integral integral of over a a vector field around a closed curve is equal to the double integral of the curl of the vector field over the region bounded by the curve.

In this case, we can rewrite the given equations in terms of x and y to define the boundary of the region. The upper boundary is y=7, and the lower boundary is y=7/25x^2. To find the points of intersection between these two curves, we can equate them:

7 = 7/25x^2

Solving this equation, we find x = ±5. Now we have the boundaries of the region in terms of x values.

To express the region in terms of a line integral, we need to define a vector field F = (M, N). In this case, we can take M = 0 and N = x. Now we can apply Green's Theorem:

Area = ∬ D dA = ∮ C N dx = ∮ C x dx

To calculate the line integral, we need to parameterize the curve C that encloses the region. Since the region is bounded by two curves, we need to split the curve into two parts. Let's consider the upper curve C1: y = 7.

Parameterizing C1, we have:

x = t

y = 7, for t ∈ [5, -5]

Now we can calculate the line integral over C1:

∮ C1 x dx = ∫[5,-5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0

Next, let's consider the lower curve C2: y = 7/25x^2.

Parameterizing C2, we have:

x = t

y = 7/25t^2, for t ∈ [-5, 5]

Now we can calculate the line integral over C2:

∮ C2 x dx = ∫[-5,5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0

Since both line integrals are zero, the area of the region bounded by y=7 and y=7/25x^2 is 0 square units.

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Answer:

It is C.

Step-by-step explanation:

First thing you would do is go through all the information and read the options then what you would do is see the labels and its will try to throw you off at A. saying that its Prizes instead of students that has won the prizes so there for

C. Six prizes were won by 4, 5, 6, or 7 students.

is your answer

Answer:

$4.95

Step-by-step explanation:

Answer:

yes he thinks he is a good boy boy and he’s a boy and a very very important man and he is so important to him he has a very important man he has a very very important father

Step-by-step explanation:

he thinks he wants a little more and he understands the same answer and that is the same thing about this one and he’s being very very important he