Kristen is mixing sweet tea and lemonade to make her favorite beverage. She mixes 24 fluid ounces of sweet tea with 18 fluid ounces of lemonade. How many liters of the beverage did she mix? Round to the nearest hundredth.

The largest possible total area of the six pens is 33750 square feet.

Given:

An ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job.

Let L and W  be the length and width.

900 = L + 6W

L =  900 -6W

Area = A = LW = (900-6W)W = 900W -6W^2

A' = 990-12W = 0

W = 900/12 =  75 feet wide

L = 900 -6W = 900 - 6(75)

L = 900 - 450 = 450 feet.

Maximum area = 450 * 75

= 33750 square feet.

Therefore the largest possible total area of the six pens is 33750 square feet.

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Answer:

+1

Step-by-step explanation:

So, you just first multiply the denominator to whole then add to the numerator after that the denominator will remain the same and the numerator will be the remainder

The zeros of the function R(x) will be 0 , 4 , -4 , -5.

The equation given to us is

[tex]x^{4}[/tex] + 5[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] - 80x = 0

Take x common

x( [tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 ) = 0

from here we get one factor of x as 0.

Now

[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 = 0

It is given that  x + 5) is a factor of this equation. so we will divide the equation by (x + 5).

After dividing it by (x + 5) we get [tex]x^{2}[/tex] - 16

Which can be written as [tex]x^{2}[/tex] - [tex]4^{2}[/tex] = (x + 4) (x - 4)

From here we get rest of the two roots of the equation.

Therefore four zeros of the function will be 0 , 4 , -4 , -5.

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Answer:

D)  0, 4, -4, -5

Step-by-step explanation:

Given polynomial:

[tex]R(x)=x^4+5x^3-16x^2-80x[/tex]

Given (x + 5) is a factor of R(x), use long division to find the other factor:

[tex]\large \begin{array}{r}x^3-16x\phantom{)}\\x+5{\overline{\smash{\big)}\,x^4+5x^3-16x^2-80x\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+5x^3)\phantom{-b))))))))))))}}\\-16x^2-80x\phantom{)}\\-~\phantom{()}\underline{(-16x^2-80x)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]

Therefore:

[tex]R(x)=(x^3-16x)(x+5)[/tex]

Factor out x from the first factor:

[tex]R(x)=x(x^2-16)(x+5)[/tex]

Apply the Difference of Two Square Formula: a²-b²=(a-b)(a+b)

[tex]\begin{aligned}\implies x^2-16&=x^2-4^2\\&=(x-4)(x+4)\end{aligned}[/tex]

Therefore:

[tex]R(x)=x(x-4)(x+4)(x+5)[/tex]

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

To find the zeros of the function, apply the zero-product property by setting each factor equal to zero and solving for x:

[tex]\implies x=0[/tex]

[tex]\implies x-4=0 \implies x=4[/tex]

[tex]\implies x+4=0 \implies x=-4[/tex]

[tex]\implies x+5=0 \implies x=-5[/tex]

Therefore, the zeros of the function R(x) are:

The maximum possible number of elements in B = 68.

A subset B of the set of integers from 1 to 100, inclusive, has the property that no two elements of B sum to 137.

Maximum possible number of elements in B =?

Set of integers = {1, 2, 3, 4, 5......100}

If we divide 137/2 = 68.5

If we add 68+69 = 137

So, we cannot consider number 69 in the subset, it gives us the total numbers we can consider are till 68.

Set B = {1,2,3,4,5,6,7....60,61,68}.

The maximum possible number of elements in B = 68.

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Answer: 69/11

Step-by-step explanation:

-69/-11=

-69*(-1)/(-11*(-1))=

69/11

As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°

As per the reference document attached thereby along with the question statement, (∠SOX = 160°), and it's constituent angles

[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],

And we are required to determine the measure of ∠2.

Since, [(∠SOW + ∠WOX) = ∠SOX],

Therefore, [{(x + 14) + (3x – 10)} = 160°]

Or, [{(x + 3x) + (14 - 10)} = 160°]

Or, [(4x - 4) = 160°]

Or, [4x = (160 + 4)°]

Or, (4x = 164°)

Or, [x = (164/4)°]

Or, (x = 41°)

Or, [(3x – 10) = {(3 * 41) - 10}°]

Or, [∠2 = (123 - 10)°]

Or, (∠2 = 113°)

That is, if (∠SOX = 160°), and it's constituent angles (∠1) and (∠2) measure as [∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)], then the measure of ∠2 in degrees will be 113°

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The equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.

What is the percent increase?

The formula for percentage increase is the ratio of the increased value to the original value multiplied by 100. It is expressed as a percentage. If the price of something rises, the percentage rises as well.

a) c + 4.99 = 14.84.

c = 14.84.- 4.99

c = 9.84

(b) 14.84 - 9.84 = 5

(c) Store owner increased the original price of the toy by adding $5.

hence, the equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.

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Answer:

Girls

Step-by-step explanation:

out of children there are 15 girl therefore percentage of girl = 15 x 100 =60

25

there are 60% girls in class

The individual error rate needs to be for each of those 5 comparisons is Option B which is 0.01.

Individual error rate = α/m = 0.05/5 = 0.01

The individual error rate is the most extreme likelihood that at least one correlation will inaccurately infer that the noticed contrast is essentially unique in relation to the invalid speculation.

Individual error rates are careful in all cases. Family error rates are careful with equivalent gathering sizes. Assuming that gathering sizes are inconsistent, the true family error rate for Tukey, Fisher, and MCB will be somewhat more modest than expressed, bringing about moderate certainty spans. The Dunnett family error rates are careful with inconsistent example sizes.

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The value of the expression is 698.

What is an expression?

A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).

Given expression 3*(14+c²) +2d

3*(14+12²)+2*112

= 42+3*12²+224

= 42+3*144+224

= 42+432+224

= 698

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Answer: 60

Step-by-step explanation:

first multiply like terms,

-4 x -5 = 20 [Multiplying two negative signs equal to positive]

3 x 20= 60

The slope of the line that goes through these two points is -19/13.

Given points:

(–6, −3), (–19, 16)

slope:

Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.

slope m = y2-y1 / x2-x1

= 16-(-3) / -19-(-6)

= 16+3/-19+6

= 19/-13

= -19/13

Therefore The slope of the line that goes through these two points is -19/13.

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Answer:

17x^2-5x-17

Step-by-step explanation:

(8x^2-6x-8)-(-9x^2-x+9)

8x^2-6x-8+9x^2+x-9

17x^2-5x-17

The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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The linear equation to represent the cost of C of an NFL ticket y years after 2006 is y=2.54x+62.38.

Given that the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.

we want to write a linear equation to represent the cost c of an nfl ticket y years after 2006.

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The equation can be written in the form y=mx+b.

Let us assume x represent the duration or stipulated years after the year 2006, y represent the amount of ticket that is sold and m represent the average increase in the price every year.

y=mx+c

y=2.54x+62.38

Hence, a linear equation to represent the cost c of an nfl ticket y years after 2006 is y=2.54x+62.38 when the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.

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The point (2,3) translated 2 units to the right is (4,3)

Rotated 90 degrees clockwise around the origin becomes (3,-4)

Then (2,3) is translated 2 units to the right and rotated 90 degrees counterclockwise to become (3,-2). (5,-2)

One of two numbers and/or letters indicating a point's precise location on a map or graph: Zoom in on the map after entering the GPS coordinates.

In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. An object's x-coordinate, also referred to as the abscissa, is its perpendicular distance from the y-axis as measured along the x-axis.

The domain refers to the first coordinate, which is typically the x-coordinate, and the range refers to the second coordinate, which is typically the y-coordinate.

You do the opposite to determine a point's coordinates in a coordinate system. Starting at the point, move vertically up or down until you reach the x-axis.

The complete question is : The point (2, 3), translated 2 units to the right, becomes (___, ____), then rotated

90° clockwise around the origin it becomes (___, ____). The point (2, 3) rotated

90° clockwise around the origin becomes (____, ____), then translated 2 units to the right it becomes (___,____), which is not the same.

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Answer:

:)......................

Bao's age is 12 years old.

Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.

Let's call Bao's age "x".

Since their ages are consecutive even integers, the next sibling's age would be x + 2, the next one x + 4, and the last one x + 6.

The sum of all their ages is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12 = 60.

Solving for x, we get 4x + 12 = 60, and subtracting 12 from both sides gives 4x = 48.

Dividing both sides by 4 gives x = 12.

Therefore, Bao's age is 12 years old.

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Answer:

35

Step-by-step explanation:

I did 1/5 into a decimal which is 0.2 and then i did 7/0.2 because 7 miles and 0.2 miles they stop and then you divide them and get 35

The correct answer is the pilot should expect the visibility required to be reported in lieu of the published RVR as a ground visibility of 1/2SM.

       Visibility is half of a statute mile (SM). Persuading visibility is described in statute miles and fractions. The visibility having 15+ is encrypted as 15SM. Lower visibilities which are half or less of the visibility are detailed in the remarks section. Low visibility procedures (LVP) refer to procedures related to an aerodrome for the cause of ensuring safe operations in the course of lower-than-standard value and low visibility take-offs.

                Reduced visibility operations are operations that take place at an aerodrome during the visibility is lower than Runway Visual Range which is 2600 RVR and 1/2 statute mile sm down to and including 1200 RVR and 1/4 statute mile sm.

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The equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x, so option B is correct.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

The time taken to complete the work = 6 hrs,

The no of worker = 4,

The no of workers = The time taken by four workers / no of workers,

w (x) = 6 /4x

w (x) = 1.5x

Therefore, the equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x.

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Dave will need 8 boxes, out of which 7 will be completely full and 2 sweaters will be kept in eighth box.

Number of boxes required for 23 sweaters = total number of sweaters ÷ number of sweaters in each box

Keep the values in above mentioned formula to find the number of boxes required for 23 sweaters.

Number of boxes required for 23 sweaters = 23 ÷ 3

On performing division, we get 7 as quotient and 2 as remainder. This indicates that 7 boxes will be accomodate the sweaters and 2 indicates the remaining sweaters.

Thus, there will be need of 8 boxes in total.

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The correct option regarding Sara's and Sam's position between 40 minutes and 80 minutes is given as follows:

C. Were not moving since there was not a change in position.

The graph is given by the image shown at the end of the answer, and the relation graphed is defined as follows:

Distance x Time.

Hence the input and the output variables are given as follows:

Between 40 minutes and 80 minutes, which is a symmetric period around the time of one hour, the graph is constant.

The constant graph means that the position was not changed, that is, they were not moving, hence the correct statement is given by option C.

The problem is given by the image shown at the end of the answer.

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Answer:

[tex]20[/tex]

Explanation:

[tex]5[/tex] ÷ [tex]\frac{1}{4}[/tex]

To change the division sign into a multiplication sign, you need to change (1/4) into its reciprocal.

[tex]5[/tex] × [tex]\frac{4}{1}[/tex]

[tex]5[/tex] × [tex]4[/tex]

[tex]20[/tex]

After 1st Translation  (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)

What is translation?

And image After Composition means resultant image after you plot the translated points.

So, Given Vertices are X(2,4), Y(6,0), Z(7,2)

Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation = X(4,11), Y(8,7), Z(9,9)

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The answer to the expositional growing account will be $14838.

What is exponential function?

The mathematical formula for an exponential function is f (x) = ax, where x is a variable and a constant known as the base of the function, which must be greater than zero. The transcendental number, or e, which is roughly equivalent to 2.71828, is the most frequently used exponential function base.

Let suppose in the xth year, the value of the money is 6300* [tex]a^{4}[/tex]

⇒8200 = 6300* [tex]a^{4}[/tex]

⇒a = 1.068

So 6300 *[tex]a^{13}[/tex]

= $14838

Hence the value of the account will be $14838.

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The cost of a swim club membership for a year is $170. The price consists of 12 monthly payments of $20 and a $20 registration fee. From equation, the mth payment is $12.5 per month.

Finding the value m of each monthly payment can be done using the equation 12m+20=170.

To find the amount(m), solve the equation 12m+20=170.

12m=150

M = 150/12

M= $12.5

Consequently, each monthly payment will cost 12.5 in total.

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We are given the following:

[tex]8-3(1-x)=2(x+1)-3[/tex]

To solve for x, simplify both sides of the equation, then isolate the variable.

Hope this helps!

The mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics

The vector graphics is defined as the computer graphics that the  visual images are created directly from geometric shapes. It is defined on the Cartesian plane such as lines, curves, texts, ovals and other geometric shapes

The vector artworks are the artwork that created by vector graphics. There will be lines curves, text, oval and other geometric shapes according to the mathematical expression

Therefore, the vector graphics is the mathematical instruction that defines the geometric shapes

Hence, the mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics

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The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔABC and ΔLMN, we have

AB = LM = 8 cm

∠B = ∠M = 90°

AC = LN = 12 cm

The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate.

The triangles ΔFGH and ΔLMN are similar triangles, then we have

x / 12 = 4 / 8

x / 12 = 1 / 2

x = 12 / 2

x = 6 cm

The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.

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