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The area in square feet of the part of the backyard in which Shayne is allowed to dig is option D: 272 ft².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The length of the rectangle ADEH is 17 ft.

The breadth of the rectangle ADEH is 22 ft.

The length of the rectangle ABGH is 17 ft.

The breadth of the rectangle ABGH is -

GH = (EH - GE)

GH = [EH - (GF + EF)]

GH = [22 - (6 + 14)]

GH = [22 - 20]

GH = 2 ft

The formula for the area of a rectangle is -

Area = Length × Breadth

The area of part where Shayne is allowed to dig is -

Area = [Area of ABGH + Area of CDEF]

Area = [(17 × 2) + (17 × 14)]

Area = [34 + 238]

Area = 272 ft²

Therefore, the value for area is obtained as 272 ft².

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In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.

Employing the Box Method

For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.

The first step is to create a two by two grid, as shown here:

using a box

Following that, we place the first term in the upper left box and the last term in the lower right box.

The Complete Question.

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Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3

The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

step1:

calculate the slope m using the slope formula

slope m=y2-y1/x2-x1

with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)

step2:

m=-11-7/-5-1=-18/-6=18/6

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Answer: 2343.8 meters

Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together

The amount of sugar present in the milk chocolate bar is, 12000   milligrams.

Given,

Amount of milk chocolate bar = 20.00 grams

Amount of sugar = 12.00 grams

The conversion used for grams to milligram is :

1 gram = 1000 milligram

As per question we are given that, 12 grams of sugar

As, 1 gram of sugar = 1000 milligram of sugar

So, 12.00 grams of sugar = (12/1) x 1000

                                          = 12000 milligrams of sugar

Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.

(b) THe reduced size is 3 g

3 g bar has 12x3/20 g of sugar

i.e 7.2 g

hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.

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Answer: the decorator should order 2,844 square feet of carpet to replace the carpet in the east room of the White House.

Step-by-step explanation:

Area = Length x Width

Area = 79 feet x 36 feet

Area = 2,844 square feet

The number of scarves in 4 hours is 9.6

From the question, we have the following parameters that can be used in our computation:

Rate = 3 scarves in 75 minutes

Time = 4 hours

The number of scarves is then calculated as

Scarves = Rate * Time

substitute the known values in the above equation, so, we have the following representation

Scarves = (3/75 minutes) * 4 hours

Evaluate the product

Scarves = 9.6

Hence, the number of scarves is 9.6

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Answer:

Step-by-step explanation:

1/3 + 2i is a complex number, with the real part equal to 1/3 and the imaginary part equal to 2i. It can be represented in a Cartesian coordinate system as a point (1/3, 2)

The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35). To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). The answer is y = 4.51 feet.

y = 5.5sin(35)

y = 4.816

arcsin(4.816) = 35

4.816 = 5.5sin(35)

y = 5.5 arcsin(35)

y = 4.51 feet

The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35), which is the length of the shadow. To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). We can then use the Pythagorean Theorem to solve for y: 4.816 = 5.5sin(35), so y = 5.5 arcsin(35). The answer is y = 4.51 feet, so the length of the shadow is 4.51 feet. This demonstrates how trigonometry can be used to calculate the length of shadows, with the help of a clinometer.

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To solve for the volume of the rotated region we will use the integration and its formula is V=π∫ba(r21−r22)h where r1 and r2 are the radii of the washer and h is the height. Note that the limits a and b is determined by finding the volume of the solid .

Using the washer method, the volume of the solid is

V=π∫ba[(x14)2−(x4)2]dx

Find the limits, equate the two equations in terms of x

4√x=x4

Raising both sides to fourth power,

x=x8x8−x=0

Factor out x

x(x7−1)=0

x=0,1

Thus, the limits is from x =

V=π∫10[(x^1/4)^2−(x4)^2]dx

Integrate this equation with in limits 0 to 1

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The required value of d for the given function is given as d = 2.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

Here,
F(s) = 5s²+ 4s +4
F'(s) = 10s + 4

F'(1) = f(d) - f(0)/ d
10(1) + 4 = 5d² + 4d / d
14 = 5d +4
d = 2

Thus, the required value of d is given as d = 2.

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The slope of the given graph is 3/8 .

What is Graph ?

Graph can be defined as the visual representation in which we can represent the data.

Given in the graph,

We are given two points: (4, 5) and ( -4, 2 ). Slope is calculated as the change in y over the change in x, or rise over run.

The change in y is the difference of the two y coordinates (it doesn't matter the order): 5- (2) = 3

The change in x is the difference of the two x coordinates (this order depends on the order that you subtracted the y coordinates; they must be the same order): 4 - (-4) = 4+4 = 8.

So, the slope is 3/8

Therefore, The slope of the given graph is 3/8 .

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True. A data model is an abstract representation of the data structures used in a database.

It is typically used to represent the structure of the data and the relationships between different elements of the data. Data models are used to define the structure of the data in a database, as well as the relationships between different elements of the data. A data model is a combination of entities, attributes, relationships, and constraints. It is used to describe the data that is stored in a database and how the data can be accessed and manipulated. The data model also defines the relationships between the different elements of the data, such as which element of the data is related to which other element. The data model also defines the constraints that must be met in order to ensure the integrity of the data. A data model is also used to define the data types that are used in the database and the operations that can be performed on the data. For example, a data model may define data types such as integers, strings, and dates, as well as operations such as arithmetic, comparison, and sorting. A data model also defines rules for the structure and organization of the data, such as which fields must be present in a record, the order in which records must be stored, and the types of relationships that can exist between records.

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The explicit equation and domain for an arithmetic sequence is a_{n}=9+(n-1)-8, the correct option is C

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given;

A first term of 9 and a second term of 1

a=9

D=1-9=-8

We know that the explicit equation of an AP is

a_{n}=a_{1}+(n-1)d

So, substituting the values

a_{n}=9+(n-1)-8

Therefore, the arithmetic sequence will be a_{n}=9+(n-1)-8.

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Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.

Punnet square analysis indicates that the progeny of two heterozygous pea plants (Yy) will be 75% (3/4) dominant and 25% (1/4) recessive. In the event that 1000 individuals are created, 750 will therefore be dominating.

Tt will be the genotype of a tall heterozygous plant. It will actually prevail over the recessive t allele because T is primarily the dominant allele. Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.

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Answer:

5.80

Step-by-step explanation:

just to make the answer

The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23

upper bound of Valletta  = 16.8 -12+23

upper bound of Valletta = 27.8 °C

Lower bound of Valletta = 0.1 -12+23

Lower bound of Valletta = 10.9 °C

Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

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Answer:

148545

Step-by-step explanation:

it's easy enough

The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35

The vector that perpendicular to the plane is equal to the cross product of:

P ⨉ Q

Remember the properties of cross product of two vectors:

i ⨉ i = j ⨉ j = k⨉ k = 0

i ⨉ j = k

j ⨉ i = - k

j ⨉ k = i

k⨉ i = j

i⨉ k = -j

Hence,

P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)

          = k + j +4k + 2i +2j - i

          = i + 3j + 5k

The magnitude of P ⨉ Q is:

|| P ⨉ Q || = √(1² + 3² + 5²)

               = √35

Therefore, the unit vector = ( i + 3j + 5k )/√35

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The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).

What is meant by three-dimensional space?

A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.

For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.

a)  For the first hook there is no y-axis, it is hung in the xz plane.

So the coordinates are (4,0,7.5)

b) The second hook coordinates are given as (5, 12,8)

c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.

x= (x1 + x2)/2 = (4+5)/2 = 4.5

y = (y1 + y2) /2 = (0+12) / 2 = 6

z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75

Therefore the mid-point of the string is (4.5, 6, 7.75).

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The expression in the standard form  is 37.008

From the question, we have the following parameters that can be used in our computation:

3 x 10 + 6 x1 + 1 + 8 x 1/1,000

Evaluate the products

This gives

30 + 6 + 1 + 8/1,000

Evaluate the quotients

30 + 6 + 1 + 0.008

Evaluate the sum

37.008

Hence, the number in standard form is 37.008

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The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles

Distance is defined as the quantity that describes the space that exists between two locations in a field.

The number of miles Tonya covered on Saturday = 3 ⅓ miles

The number of miles that Tonya covered on Sunday = 2 ⅘

Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.

That is; 3⅓ - 2⅘ ( change to single fraction form)

= 10/3 - 14/5

= 50-42/15

= 8/15

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The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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For function f(x)= x² + 7 and g(x)= x² + 2,

a) f(x) + g(x) = 2x² + 9

b) f(x) - g(x) = 5

c) f(x) . g(x) = x⁴ + 9x² + 14

d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]

Consider given functions  f(x)= x² + 7 and g(x)= x² + 2

a) To find addition of functions: f(x) + g(x)

f(x) + g(x)

= (x² + 7) + (x² + 2)

= x² + x² + 7 + 2             .............(associative property of addition)

= 2x² + 9                       ................(combine like terms)

b) to find subtraction of functions : f(x) - g(x)

f(x) - g(x)

= ( x² + 7 ) - (x² + 2)

= 7 - 2

= 5

c) To find multiplication of functions: f(x).g(x)

f(x) . g(x)

= ( x² + 7 ).(x² + 2)

= x² (x² + 2) + 7(x² + 2)

= x⁴ + 2x² + 7x² + 14

= x⁴ + 9x² + 14              ................(combine like terms)

d) To find division of functions: f(x)/g(x)

[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]

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The values of  (f + g) (x),  (f - g) (x),  (fg) (x) and  (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and  1/ [x² (x + 9)] respectively

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Since f(x) = x/(x + 9), g(x) = x³

(a) (f + g) (x) will be the addition of f(x) and g(x). That is:

(f + g) (x) = x/(x + 9) + x³  or  x³ +  x/(x + 9)

(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:

(f - g) (x) = x/(x + 9) - x³

(c) (fg)(x) substitute x = x³ into f(x). That is:

f(x)= x/(x + 9), g(x) = x³

(fg)(x)  = x³/(x³ + 9)

(d) (f/g)(x) will be the division of f(x) by g(x). That is:

(f/g)(x) = [x/(x + 9)] / x³ =  x/ [x³ (x + 9)] = 1/ [x² (x + 9)]

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If you divide 11 by 2.5 you will end up with 4.4. Answer = 4.4

La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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Answer:

There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.