A circle has a circumference of 36 cm. What is the length
of an arc that has a measure of 190°?

Answer:

  (a)  A(x) = (12 -2x)√(3x -9)

Step-by-step explanation:

You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.

Heron's formula for the area of a triangle with side lengths a, b, c is ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

Given a perimeter of 12, and two sides x, this becomes ...

  A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))

  A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares

  A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6

The domain is such that the radical and the area are non-negative.

The derivative of the area function is ...

  [tex]A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}[/tex]

The derivative is zero at the maximum, so ...

  -9x +36 = 0   ⇒   x = 4 . . . . . . . an equilateral triangle

The maximum area is ...

  A(4) = (12 -2·4)√(3·4 -9) = 4√3

The maximum area is 4√3.

Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...

  2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4  ⇒  x = 1/3

The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.

The function ...

  z = 2A(3x+3) +1 = 2A(3(x+1)) +1

Compare this to ...

  z = p·A(q(x -r)) +s

which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.

We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.

Applying these transformations to the original A(x) domain and range, we find the domain is ...

  1/3[3, 6] -1 = [0, 1] . . . . . domain of z

And the range is ...

  2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z

The value of side length PS is found as 4 units for the given right angled triangles.

For the stated question:

PQ = 3x - 3

QR = 6x - 9

PS = 5x - 6

As, Q is the mid point of PR.

PQ = QR

3x - 3 =  6x - 9

On solving.

x = 2

Then,

PS = 5*2 - 6

PS = 4

Thus, the value of side length PS is found as 4 units for the given right angled triangles.

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The correct question is attached.

Steps to remove the quarter 1 data series from Dana's column chart in Microsoft Excel are given below.

You might need to add an additional data series to the chart after it has been created. A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart.

To remove the quarter 1 data series from Dana's column chart in Microsoft Excel:

Note: The steps may vary slightly depending on the version of Excel you are using.

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The area of each box would be proportional to the salaries of each group. Option C.

The use of models to represent data in mathematics is well known. In the case of the data we have, the salaries of the college graduates and the high school graduates have been shown by the use of squares.

We can see that the sizes of the squares respectively show the magnitudes of the salries of the high school graduate and that of the college graduate. The area of the boxes would be proportional to the salaries.

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The length of BC in simplest radical form is 2√19

The Pythagorean theorem states that the square of the hypotenuse side of a right angled triangle is equal to the square of the other sides.

It is represented mathematically as;

a² = b² + c²

Given that the parameters;

From the information given, we have that;

Hypotenuse side, a = 20

Adjacent side = 18

Substitute the values

20² = 18² + b²

Find the squares

400 =324 + b²

collect like terms

b² = 400 - 324

b² = 76

Make 'b' the subject of formula

b = 2√19

Hence, the value is 2√19

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Answer: 8/12

Step-by-step explanation:

First you multiply 1/6 with 1/2 that would give us 1/12

Then you add 1/12 with 7/12

Our answer would be 8/12

Answer:

2/3 or in Decimal its 0.6

Step-by-step explanation:

1/6x+7/12 when x= 1/2.

1/6(1/2)+7/12

The  inequality shown on the graph is x > -2 and x < 5 or -2 < x < 5

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

If you examine the graph, you will notice that there is one circle on -2 and another circle on 5. These give you the range of values. Also, notice that circles are not shaded. Thus, this can be written as:

x > -2 and x < 5 or  -2 < x and x < 5

Which can then be combined as:

-2 < x < 5

Note: The reason we did not use ≤ is because the circles are not shaded.

Thus, the inequality is x > -2 and x < 5 or -2 < x < 5

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A plate of spring roll is price of $7.5.

What is Linear System?

A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties.

Let n, b, and c represent the cost per plate of spring roll, chicken tenders , and pretzel dipper, respectively.

One party spends $23 and purchases two plates of chicken tenders and one plate of pretzel dipper.

i.e. 2b + 1c = 23

     2b + c = 23                                        --------------------- 1

Three plates of  spring roll and a plate of chicken tenders are purchased by another group for $30.75.

That is

          3n + 1b = 30.75

          3n + b = 30.75                                          ---------------------- 2

A third party spends $22.25 and purchases one of each appetizer.

That is

             n + b + c  = 22.25                                    --------------------- 3

On solving;

eqn2 - eqn3

            2n - c = 8.5                                           --------------------- 4

on solving;

eqn 1 + eqn 4

             2b+ 2n = 31.5

             b + n = 15.75                                           --------------------- 5

On solving;

eqn 3 - eqn 5

              c = 6.5

Substituting in eqn 4

           2n - 6.5 = 8.5

              n = 7.5

Substituting in eqn 3

           7.5 + b + 6.5  = 22.25

               b = 8.25

Price of spring roll n = $7.5 .

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Answer: Jayda finishes 39 pages in 1 hour

Step-by-step explanation:

156/4 gives us her rate since we have to find 1 hour, not 4 hours.
This is 39

I hope this way able to help you :D

Each bag of lemons costs $3.99

Let m represents the cost of eggs and n represents the cost of each bag of lemons.

He buys 6 bags of lemons that each cost the same amount.

so, the cost of six bags of lemons would be 6n

He pays a total of $29. 33

so, we get an equation,

m + 6n = 29. 33               ............(1)

Levi pays a total of $5. 39 for the eggs

So, m = 5.39

We need to find the value of n.

substitute above value of m in equation (1)

m + 6n = 29. 33

5.39 + 6n = 29. 33

6n = 23.94

n = 23.94 / 6

n = 3.99

Thus, the cost of each bag of lemon = 3.99 dollars

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The system of equation: 3(2x-5)=28 represent the dimensions of the play area.

As per the data given,

We have, the width of a rectangle play area is 5 meters less than the length.

Let us assume that the length of the rectangular field = x

So, the value of the width of the rectangular field will be = (x-5)

As we know,

The Perimeter of the rectangular field can be determined by using formula:

Perimeter = 2l+2b, where, l = length of the rectangle, while b = breadth of the rectangle.

From question,

We have a value of the rectangle as 38 m

So, writing the above in form of the equation,

We can write the above as:

2(length + breadth) = 38

=> 3(x+ (x-5) =38

=> 3(x+x-5) =28

=>3(2x+5)=28

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Answer:

1:2.42

Step-by-step explanation:

145/60 = 2.42

Answer: 1 : 29/12

Step-by-step explanation:

60/60 = 1
145/60 = 29/12 in simplest form
therefore 1 : 29/12

The area of the base of the parcel box is given by the expression A=2x²+8x+6. The dimensions (length and width) are determined from this expression as (2x+2) and (x+3).

In general, the volume of a rectangular box is calculated by the product of the height, width, and length of the box. From the given hint, we can write the volume of the parcel box as a product of the height and the area of the base. This is written as,

[tex]\begin{aligned}V&=A\times h\\6x^2+24x+18&=A\times 3\\A&=\frac{1}{3}(6x^2+24x+18)\\A&=2x^2+8x+6\end{aligned}[/tex]

The above equation gives the area of the base

Now solving the above quadratic equation to find dimensions, we get,

[tex]\begin{aligned}A&=2x^2+8x+6\\&=2x^2+6x+2x+6\\&=2x(x+3)+2(x+3)\\&=(2x+2)(x+3)\end{aligned}[/tex]

The dimensions are (2x+2) and (x+3).

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Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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Answer: 1

Step-by-step explanation:

Anything to the power of 0 is 1

Answer:

Multiplying by 10 would be the inverse operation

Answer:

Multiplication

Step-by-step explanation:

The inverse operation of division is multiplication and vice versa.

:)

The measure of the angle m∠ABD is 100°.

What is the measure of angle?

In mathematics, an angle is defined as the amount of rotation between two lines or planes that share a common point. The measure of an angle is typically given in degrees or radians. A full rotation is equal to 360 degrees or 2π radians, and the size of an angle can range from 0 degrees (no rotation) to 360 degrees (a full rotation).

In the given figure, m∠ABC = 130° and m∠DBC = 30° is given.

And we have to find the m∠ABD

so

m∠ABC = m∠ABD + m∠DBC

130° = m∠ABD +  30°

m∠ABD =  130° -  30°

m∠ABD = 100°

Hence, the measure of the angle m∠ABD is 100°.

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The inventory at the beginning of the day, given that 18 were sold earlier that day, is 70 units

The inventory at the beginning of the day can be found by the formula:

= Closing store inventory for the day + Inventory sold during the day

Closing store inventory for the day = 52 units

Inventory sold earlier that day = 18 units

The inventory at the beginning is therefore:

= 52 + 18

= 70 units

In conclusion, the inventory at the beginning of the day was 70 units.

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The coordinates of point A are given as follows:

A(19, 23).

The coordinates of point A are obtained applying the proportions in the context of this problem.

The segment AB is represented as follows:

AB = B - A.

Hence the segment 5AB is given as follows:

5AB = 5(B - A) = 5B - 5A.

Then the x-coordinate of A is obtained as follows:

5(16) - 5A = -15

5A = 95

A = 19.

The y-coordinate of A is obtained as follows:

5(30) - 5A = 35

5A = 115

A = 23.

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Answer:

3x = 42

Step-by-step explanation:

The correct equation is

3x = 42

However, because your formatting has been scrambled, I cannot tell you which choice it is

Compare this equation with your original question and see which is the correct choice

3x = 42 means

each kite = 42/3 = $14
but the question is only asking for the equation not the solution

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Answer:

(-4)^12

Step-by-step explanation:

Hello!

We can use exponent rules to rewrite the equation.

a^b * a^c = a^(b+c)

The value of the equation can be calculated by (-4)^12.

[tex](-4)^{12}[/tex]Answer:

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

[tex](-4)^{5}[/tex] × [tex](-4)^{7}[/tex]

= [tex](-4)^{(5+7)}[/tex]

= [tex](-4)^{12}[/tex]

If a player who is off the field of play to receive medical treatment trips a player who is on the field of play , then (c) the referee cautions the player and the play is restarted with a indirect free kick.

On the field of play of football , the medical treatment of any player is not permitted under any circumstances.

When the player is bleeding, the player is required to leave the field immediately.

When the play has been restarted, only time the injured player is allowed to return to field of play is after game has started again.

It is exclusive responsibility of match referee to decide whether or not an injured player may return to the game.

The given question is incomplete , the complete question is

A player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?

(a) A. The referee shows a red card and sends off the player. Play is restarted with an indirect free kick.

(b) The referee shows a yellow card and cautions the player. Play is restarted with an indirect free kick.

(c) The referee cautions the player and Play is restarted with an direct free kick.

(d) The referee cautions the player and restarts with a dropped ball.

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the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function  g(x) = − 4x + 8

The domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output

The range of a function means all possible outputs or all the numbers that are the result of all the inputs or values of y

Intercept is the point on a graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y-intercept where the value of the x coordinate is zero

The domain of the given function is all real numbers or - infinite < x< infinite

The range of the given function is all real numbers or - infinite < x< infinite

The x-intercept of the given function is where y = 0

so,  0 = -4x + 8

-8 = -4x

x = 2

The x-intercept is (2,0)

Therefore, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.

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Answer:

Good luck

:/ :/ :/ :/ :/ :/ :/

The correct statement is : The probability of landing on purple is equal to the probability of landing on yellow.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given here: A spinner with four different colors purple, yellow, blue and orange.

Now Section 1&8 = Blue

Section 2&3 = yellow

Section 4,5,6 = blue

Section 7 = orange

Total=8

Thus probability for each section are as follows

P(purple)=2/8

           =1/4

P(yellow)=2/8

              1/4

P(Blue)=3/8

P(orange)=1/8

∴ The probability of landing on purple is equal to the probability of landing on yellow.

Hence, The probabilities of all the individual sections are 1/4,1/4,3/8,1/8 for purple, yellow, blue and orange respectively.

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There is a 0.81 Probability that the breakdown entails a gas leak. Given that there is a gas leak, there is a 0.63 percent chance that there is evidence of electrical failure. Given that there is evidence of an electrical failure, the likelihood of a gas leak is 0.77.

A)

Total number of  units

= 55 + 32 + 17 + 3

= 107

Hence the Probability that  failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) Probability that there is  a evidence of electrical failure given that there is a gas leak

P ( A / B ) = P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

Hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

Hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

0-2-0

1-11-11

2-28-56

3-18-54

4-11-44

5-15-75

6-10-60

7-2-14

8-3-24

total number of tickets won - 100

mean number - 336 divided by 100 = 3.36