HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE
WORD CONNECTION?

Answer:

(a+b)² - 11(a+b) -42

Step-by-step explanation:

Thoughtfully split the expression at hand into groups, each group having two terms,

Group 1:  -11b-11a 

Group 2:  a2+2ab 

Group 3:  b2-42 

Pull out from each group separately :

Group 1:   (a+b) (-11)

Group 2:   (a+2b) (a)

Group 3:   (b2-42) (1)

Looking for common sub-expressions :

Group 1:   (a+b) (-11)

Group 3:   (b2-42) (1)

Group 2:   (a+2b) (a)

final answer:(a+b)² - 11(a+b) -42

Answer:

(a+b+3)(a+b-14)

Step-by-step explanation:

let a+b be x,

= x²-11x-42

=x²-(14-3)x-42

=x²-14x+3x-42

=x(x-14)+3(x-14)

=(x+3)(x-14))

replacing x by a+b,

=(a+b+3)(a+b-14)

The complete statements are:

Part of a scatter plot

The parts of a scatter plot are

This means that the Key is not part of a scatter plot

The scale on the axes

Here, the scale is determined by the number of data points that exists on the scatter plot

This means that scatter plots that have 10 and 100 data points might not be represented on the same scale

The line of best fit

This is determined by drawing a line through the data points on the scatter plot.

The line is know as the line of best fit

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Answer:

Step-by-step explanation:

The amount of each brand can be found by writing and solving an equation that makes use of the given relations.

Let x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...

  0.55x +0.30(160 -x) = 0.45(160)

Subtracting 0.30(160), we have ...

  x(0.55 -0.30) = 160(0.45 -0.30)

  x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x

96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.

__

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109×50

100×50+9×50=5000+450

5450

Answer:

5450

Step-by-step explanation:

You can just use a caculater to get the answer.

For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.

Simply put, a set in mathematics is a grouping of different items.

An element of the set is any component of the set. When writing a set, curly brackets are utilized.

The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.

According to the question,

A = {11,22,33,44}

The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.

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The number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.

To minimize inventory costs, especially setup and holding costs, the economic order quantity (EOQ) technique is deployed.

The EOQ model refers to the ideal order or batch quantity a company should purchase per order or produce per batch to minimize its inventory costs.

Some of a company's inventory costs include holding costs, shortage costs, setup, and ordering costs.

Using the EOQ model shows the ideal minimum units that the manufacturer should produce per batch to minimize costs.

The EOQ formula is square root of: [2(setup costs)(demand rate)] / holding costs.

Annual demand = 22,638 cases

Storage cost per case = $7

Setup cost per batch = $33

Product unit cost = $15 per case

EOQ = square root of: [2(setup costs)(demand rate)] / holding costs.

= square root of 2 x $33 x 22,638/$7

= square root of 213,444

= 462

Number of batches = 49 (22,638/462)

Thus, the number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.

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Answer :LF is the abbreviation for linear feet Sq ft is the abbreviation for square feet L – lenght (e.g. room length) W – width (e.g. room width)

Liters to Cubic Feet formula. ft³ =. L * 0.035315. Show working Show result in exponential format More information: Cubic Feet.

Step-by-step explanation:

Answer:W ^10

Step-by-step explanation:

The solution is in the

The possible rational roots of the given equation are 1 and -3

From the question, we are to determine all the possible rational roots of the given equation

The given equation is

x⁴ -2x³ -6x² +22x -15 = 0

To determine the rational roots, we will test for values that make the equation equal to zero

(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15

1 + 2 - 6 - 22 -15

= -40

∴ -1 is not a root of the equation

(1)⁴ -2(1)³ -6(1)² +22(1) -15

1 - 2 - 6 + 22 -15

= 0

∴ 1 is one of the roots of the equation

(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15

16 + 16 - 24 - 44 -15

= -51

∴ -2 is not a root of the equation

(2)⁴ -2(2)³ -6(2)² +22(2) -15

16 - 16 - 24 + 44 -15

= 5

∴ 2 is not a root of the equation

(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15

81 + 54 - 54 -66 -15

= 0

∴ -3 is one of the roots of the equation

(3)⁴ -2(3)³ -6(3)² +22(3) -15

81 - 54 - 54 + 66 -15

= 24

∴ 3 is not a root of the equation

The other roots of the equation are irrational roots.

Hence, the possible rational roots of the given equation are 1 and -3

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Answer:

B

Step-by-step explanation:

Comment

√15 = 3.87

√12 = 3.46              Subtract these 2

Difference = 0.41

Answer:

[tex]\pi[/tex]([tex]r^{2}[/tex]h)

Step-by-step explanation:

r = radius

h = height

she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

she would pay $400 per month to rent a station and keep all of her earnings.

Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.

Therefore,

let

x = number of haircut

Hence,

4x = 400

divide both sides by 4

4x / 4  = 400 / 4

x = 100

Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

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The volume of the cord of wood will be similar to the volume of a rectangular prism. Then the correct option is C.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

The rectangular prism is the most typical geometric form used to approximate the volume of a cord of wood.

The wood is evenly cut into identical lengths, and when stacked, it forms a rectangular prism.

Therefore, C. rectangular prism is the right response.

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The answer is 756 m³.

The formula to find volume is : length × width × height

To estimate, round each dimension to the nearest whole number.

⇒ 12.3 ≅ 12

⇒ 7.2 ≅ 7

⇒ 8.6 ≅ 9

Volume = 12 × 7 × 9

Volume = 84 × 9

Volume = 756 m³

Answer:

The ans to this question is 756 which is Option (B)

Step-by-step explanation:

Estimate volume = rounding every digit

= 12.3 = 12

= 7.2 = 7

= 8.6 = 9

= 12x7x9 = 756

Answer:

  e)  y = √(x) +5

Step-by-step explanation:

The graph shown is the graph of the square root function shifted upward 5 units. There is no translation left or right.

A function can be translated h units right and k units up by the following:

  g(x) = f(x -h) +k

When the function is f(x) = √x, and it is translated 5 units up, but none left or right, we have ...

  g(x) = f(x-0) +5

  y = √(x) +5 . . . . . . matches choice e

Answer:

3:8 3 sodas for 8 drinks

Step-by-step explanation:

6/16

3/8

Using the probability concept, the likelihood of landing on 2 or 3 is given by:

[tex]p = \frac{3}{8}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, considering the areas of 2 and 5 counting twice, the spinner has 8 areas, out of which 3 are 2 or 3, hence the probability is given as follows:

[tex]p = \frac{3}{8}[/tex]

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Answer:

[tex]5x^{2} -4x-9[/tex]

Step-by-step explanation:

f(x)+g(x)

[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]

The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9

Given that:

Functions, f ( x ) = 3x² - 6x + 2

And g ( x ) = 2x² + 2x - 11.

Then find f ( x ) + g ( x ).

To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.

To find f(x) + g(x), add the coefficients of the corresponding terms:

f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)

Now, combine like terms:

f(x) + g(x) = 5x² - 4x - 9

So, the sum of the two functions is:

f(x) + g(x) = 5x² - 4x - 9

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If the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.

Given that the length of ladder is 12 feet and the base is 5 feet.

We are required to find the height of the windows from the ground.

When we graph all the things like ladder and all that we will get a right angled triangle.

We can find the height of window by using pythagoras theorem.

Pythagoras theorem says that the square of the hypotenuse is equal to sum of squares of base and perpendicular of right angled triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

P=[tex]\sqrt{H^{2} -B^{2} }[/tex]

Height of wall=[tex]\sqrt{12^{2} -5^{2} }[/tex]

=[tex]\sqrt{144-25}[/tex]

=[tex]\sqrt{119}[/tex]

=10.908

After rounding off it will be 10.91 feet.

Hence if the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.

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Answer:

20 is 50% of 40.

Step-by-step explanation:

1% = 1/100

50% = 50/100 or 1/2

1/2 = 20/n

1*20/2*20 = 20/n

20/40 = 20/n

n = 40

Answer: someone who is viewed as obsolete or a person you can use to save yourself from any problem/situation

Step-by-step explanation:

Answer:

The term "meat shield" is often used as an insult to refer to someone who is used by others as a protective barrier, especially in a dangerous or violent situation. The implication is that the person being referred to is expendable and not valued for their own merits or abilities.

Here are a few examples of insults that use the term "meat shield":

"You're nothing more than a meat shield for your boss."

"You're just a disposable meat shield to your friends."

"You're nothing but a human meat shield to your team."

"You're just a weak and pitiful meat shield."

"You're just a coward who hides behind others like a meat shield."

Again, it's important to remember that using insults is never a productive or kind way to communicate with others. It's always better to try to address the issue in a respectful and constructive manner.

Answer: 171.75

Step-by-step explanation:

[tex]687/4 = 171.75[/tex]

Answer:

To find the result we have to divide, in a fraction the numerator is always divided by the denominator and the final result is 171.75

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Thank you so much for participate in the community of Brainly.com

I hope help you :)

Kind regards, Antonio.

Complete the square.

[tex]z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0[/tex]

[tex]\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4[/tex]

Use de Moivre's theorem to compute the square roots of the right side.

[tex]w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)[/tex]

[tex]\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2[/tex]

Now, taking square roots on both sides, we have

[tex]z^2 + \dfrac12 = \pm w^{1/2}[/tex]

[tex]z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2[/tex]

Use de Moivre's theorem again to take square roots on both sides.

[tex]w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)[/tex]

[tex]\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}[/tex]

[tex]w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)[/tex]

[tex]\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}[/tex]

Step-by-step explanation:

=(7x)^2-(y)^2

=(7x+y) (7x-y)

Therefore, a^2-b^3

=(a+b) (a-b)

Answer:

The answer is 4'

Step-by-step explanation:

The answer is 4, 123456789, 6 12, 18, 24, 30, 36, 42, 48.

The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:

(x,y) -> (x - 3, y - 3).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:

(x,y) -> (x - 3, y - 3).

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Elena's height in centimeters is 142.24 cm.

Elena's height in meters is 1.42 meters.

The mathematical operations that would be used to determine the answers ae division and multiplication.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the operation that is used to determine the product of two or more numbers.

In order to determine the height in centimeters, first determine how many cenitmeters make 1 inch

1 inch = 254 / 100

1 inch = 2.54 cm

Now, convert 56 inches to cm : 56 inches x 2.54 = 142.24 cm

In order to determine the height in meters, first find the unit of conversion of inches to meters

1 inch = 0.0254 meters

0.0254 x 56 = 1.42 meters

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Answer:

12.63 weeks ~~ 13 weeks

Step-by-step explanation:

This is much like a banking question with compounded interest

FV = PV ( 1 + i)^n       FV = Future value = 1 m   PV = present value = .3

                                     i = periodic interest = .10     n = periods

1 = .3(1 + .1)^n      solve for n = the number of weeks

1/.3   = 1.1^n

log (1/.3) / log 1.1  = n = 12.63 weeks

a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.

b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.

According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.

According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.

a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]

Substitute

m∠AEB = 1/2(53 + 61)

m∠AEB = 57°

b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]

Multiply both sides by 2

2(35) = VW - 36

70 = VW - 36

Add 36 to both sides

70 + 36 = VW

VW = 106°

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