Georgie buys a pack of chocolate which has 18 small chocolate bars. She ate three bars in the morning, Later in the
day, Georgie's brother ate three fifth of the chocolates bar that were left, what fraction of the chocolate bars is left in
the packet?

Polynomial [tex]$-1+x^3-\frac{1}{3} x^3$[/tex] and its conventional form, [tex]x^5-\frac{x^2}{3}-1$$[/tex] , are both used.

[tex]$$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$[/tex]

steps

[tex]$$-1+x^5-\frac{1}{3} x^2$$[/tex]

[tex]\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}[/tex]

rephrase in proper grammar

[tex]=x^5-\frac{x^2}{3}-1$$[/tex]

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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To enlarge a shape by a scale factor of 1/3, you would need to reduce its size by multiplying the dimensions of the shape by 1/3. This can be done by dividing the length and width of the shape by 3.

when we say "enlarge a shape by a scale factor" it means to change the size of the shape by a certain percentage. A scale factor of 1/3 means that the new shape will be 1/3 the size of the original.

To accomplish this, you would need to multiply the length and width of each side of the shape by 1/3.

For example, If a shape has a length of 6 and a width of 4, to reduce it by 1/3, the new shape will have a length of 61/3=2 and a width of 41/3=1.3(approximately).

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Answer:

17°

Step-by-step explanation:

m∠1 = m∠2.

Set the expressions for 1 and 2 equal to each other.

6x + 5 = 9x - 46

Separate x's on one side.

3x = 51

x = 17

Calculation for the videorecorder:

A) Hire Purchase Price: $2700

B) Monthly Instalment: $233.33

C) Difference between the hire purchase price and the cash price: $540

D) Difference as a percentage of the cash price: 20%

Solution:

A) The hire purchase price is the total cost of the item, which in this case is $2700.

B) The monthly instalment is calculated by taking the total cost of the item and subtracting the initial deposit (20% of the cash price), which is $540, and then dividing this amount by 12 (the number of months). Therefore, the monthly instalment is $233.33.

C) The difference between the hire purchase price and the cash price is calculated by taking the hire purchase price of $2700 and subtracting the cash price of $2160 (which is 80% of the hire purchase price). Therefore, the difference is $540.

D) The difference as a percentage of the cash price is calculated by taking the difference between the hire purchase price and the cash price ($540) and dividing it by the cash price ($2160). Therefore, the difference is 20%.

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The number of meters that he travel farther will be 2,000 meters.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

Shawn take 2 minutes to cycle 800 m. Then the average speed is calculated as,

Average speed = 800 / 2

Average speed = 400 meters per minute

If he continues to cycle for another 5 minutes at the same average speed. Then the total distance is calculated as,

400 = Total distance / 5

Total distance = 400 x 5

Total distance = 2,000 meters

The number of meters that he travel farther will be 2,000 meters.

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The average speed is 400 m/ min and the distance covered in 5 minutes is 2000 m.

Given:

Time= 2 min

Distance = 800 m

So, speed= Distance / time

speed = 800/ 2

speed = 400 m/ min

Now, fir time= 5 min

Distance= speed x time

D = 400 x 5

D= 2000m

Hence, the distance covered is 2000m.

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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The cost of 1 water canteen will be $12.6 using the equation 54+10w=182.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations.

When performing calculations but unsure of the precise amount, algebra is used.

So, we have:

Subtotal of $182.

Each lantern costs $5.40 and each water canteen costs w dollars.

Now, an equation that will determine total cost using w will be:

Let C be the total cost, then calculate as the cost of 1 water canteen:

10*5.40 + 10w = 182

54+10w=182

10w = 180 - 54

10w = 126

w = 126/10

w = $12.6

Therefore, the cost of 1 water canteen will be $12.6 using the equation 54+10w=182.

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The value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

The Integral is [tex]$$\int \frac{t}{t^4+5} d t$$[/tex]

Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f, and it returns a function of the independent variable.

Let [tex]$t^2=u= > t d t=\frac{d u}{2}$[/tex]

The above Integral becomes

[tex]$\frac{1}{2} \int \frac{1}{u^2+(\sqrt{5})^2} d u=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{u}{\sqrt{5}}\right)+C$$[/tex]

Substitute u In terms of t

[tex]$$\int \frac{t}{t^4+5} d t=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

Therefore, the value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex].

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Answer:

2x^7

Step-by-step explanation:

To simplify this expression, there are two steps. You have to act as though the exponents are whole numbers and add them together to combine like terms.

[tex]2x^4 \times x^3\\= 2x^{4+3}\\= 2x^7[/tex]

Hope this helps!

The color of Everett's jumpsuit is given as follows:

Pink.

The color of Everett's jumpsuit is obtained considering the patterns in this problem, which are given by each of the sentences.

The jumper who wears the yellow suit started skydiving 1 year after Everett, which means that Everett does not wear yellow.

The jumper who wears the aquamarine suit started skydiving sometime before Gordon, which means that Everett could have worn the aquamarine suit.

Francisco started skydiving 2 years after Everett, which means that Everett jumped either in 1982 or in 1983.

Rodney started skydiving sometime after the skydiver who wears the pink suit, hence the order is given as follows:

Everett - Rodney - Francisco - Gordon.

From 4, we have that Everett wore the pink suit.

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If a certain store is selling packages of 10 pencils and 4 pens for back to school . The number of pencils that are in the larger package is 25 pencils.

First step is to find the  number of pencils per pen

Number of pencils per pen = 10 / 4

Number of pencils per pen = 2. 5

Now let find the number of pencils  that are in the larger package

Number of pencils = Number of pens x Pencils per pen

Number of pencils  = 10 x 2.5

Number of pencils = 25 pencils

Therefore we can conclude that the number of pencils is 25 pencils.

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yes there is no work show below

The result for the error interval has already been rounded to the nearest integer, which is 4.8.

The numbers 10.3 and 10.5 are below and above, respectively (to 1 decimal place)

For the lower bound, we need to look halfway between 10.3 and 10.4 and for the upper bound, we need to look halfway between 10.4 and 10.5.

For the number to be rounded to 10.4 with one decimal point, it has to be between 10.35 and 10.45.

An inequality can be used to describe this.

10.35 ≤ x < 10.45

Thus, the error interval with the lower bound and upper bound are: 10.35 ≤ x < 10.45.

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Answer:

  4y

Step-by-step explanation:

You want to simplify the expression (12x²y)/(3x²).

When reducing any fractions, common factors in the numerator and denominator are cancelled. Here, the factor 3x² in the numerator is cancelled by the same factor in the denominator.

  [tex]\dfrac{12x^2y}{3x^2}=\dfrac{(3x^2)(4y)}{(3x^2)}=\boxed{4y}[/tex]

Answer:

Three lines of symmetry.

Step-by-step explanation:

A figure is symmetrical when it is made up of exactly similar parts facing each other or around an axis.

See the attached photo.

There are 3 symmetrical lines:

Please let me know it this helped!!!

Answer: B

Step-by-step explanation: You are adding the shirts times the amount, hence X the variable plus the money already spent to then be less then the 200 dollar maximum.

The solution to the given system of equations y = x² + 10x + 11, y = x² + x - 7 is x = -2, y = -5.

The given set of equations

y = x² + 10x + 11 --- eqn(1)

y = x² + x - 7 --- eqn(2)

Solving the equations by elimination method

⇒ Subtracting eqn 2 from eqn 1, we get

⇒ y - y = x² + 10x + 11 - (x² + x - 7)

⇒ 0 = x² + 10x + 11 - x² - x + 7

⇒ 0 = 9x + 18

⇒ 9x = -18

⇒ x = -2

Put the value of x in eqn 1, and we get

⇒ y = (-2)² + 10(-2) + 11

⇒ y = 4 - 20 + 11

⇒ y = -5

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Answer:

To find the final balance of an account earning interest compounded continuously, you can use the formula:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

A = 500 * e^(0.07 * 20)

The percentage of his income that he pays in taxes would be = 32%

Taxes is defined as the amount that is paid to the government by working class individuals as a way of generating internal revenue for the country.

The total amount of money made by Mr. Sullivan = $24,000

The amount of tax paid for the wedges = $7,700

The percentage of the income paid as tax would be calculated as;

= 7700/24000 × 100

= 770000/24000

= 32.01

= 32%

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The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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The Area of a triangle whose height is 8 feet and has a base length of t feet is; 20 ft².

It follows from the task content that the area of the triangle whose height is 8 feet and base length is 5 feet be determined.

Since the area of a triangle is given by;

A = 1/2 × b × h

Therefore, the area of the triangle in discuss can be determined as follows;

Area, A = 1/2 × 8 × 5

Area, A = 20 ft².

On this note, it follows that the area of the triangle is; 20 ft².

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Answer:

20 square feet

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

Given the base of the triangle is 5 feet, and the height is 8 feet, substitute b = 5 and h = 8 into the formula and solve for A:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot 5 \cdot 8\\\\&=\dfrac{5}{2} \cdot 8\\\\&=\dfrac{5 \cdot 8}{2}\\\\&=\dfrac{40}{2}\\\\&=20\; \sf ft^2\end{aligned}[/tex]

Therefore, the area of a triangle that has a height of 8 feet and a base length of 5 feet is 20 square feet.

What graph are you talking about?

Using the quadratic function for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

A quadratic function is an equation in which the highest power of the unknown is 2.

Since we have the function f(x) = -0.5x² + 32.5x - 375, to determine the value of x at which the company breaks even, we equate f(x) to zero and solve for x.

So, f(x) = 0

⇒ -0.5x² + 32.5x - 375 = 0

So, using the quadratic formula, we solve for x

so, [tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where

So, substituting the values of the variables into the equation, we have that

[tex]x = \frac{-32.5 +/- \sqrt{(32.5)^{2} - 4\times(-0.5)\times(-375)} }{2\times(-0.5)}\\= \frac{-32.5 +/- \sqrt{1056.25 - 750} }{-1}\\= \frac{-32.5 +/- \sqrt{306.25} }{-1}\\= \frac{-32.5 +/- 17.5 }{-1} \\x = \frac{-32.5 - 17.5 }{-1} or x = = \frac{-32.5 + 17.5 }{-1} \\x = \frac{-50}{-1} or x = \frac{-15}{-1} \\x = 50 or x = 15[/tex]

So, for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

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The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=5/2 x.

Substitute x=0, 1, 2, 3, 4,......

When x=0

y=0

When x=1

y=5/2=2.5

When x=2

y=5

When x=3

y=7.5

Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

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"Your question is incomplete, probably the complete question/missing part is:"

Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

Given that,

An open box length [tex]l[/tex] = 5 feet

An open box breadth b = 5 feet

An open box height = h

An open box area = 605 cubic feet

A square is a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The shape of the square is such as, if it is cut by a plane from the center, then both the halves are symmetrical. Each half of the square then looks like a rectangle with opposite sides equal.

Area = [tex]l * b * h[/tex]    (Equation - 1)

So,

We can substitute l , b , h values in the equation - 1,

605 = 5 * 5 * h

605 = 25 * h

605/25 = h

24.2 = h

Therefore,

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

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The amplitude of a sine or cosine function is the vertical stretch or compression factor of the function. In this case, the function f(x) = sin(x) has been stretched vertically by a factor of 3. Therefore, the amplitude of the function g(x) is A = 3.

The function g(x) = 3sin(12x) + (-5)

Answer: Value of p= 28

Step-by-step explanation:

Use remainder theorem to find the value of p

K(x) = 2x^3+4x^2+px-12  is take f(x)

           (x + 3)  

 f(3)  = 21

f(3)    = 2*3^3+4*3^2+p*3-12

           = 2*27+4*9+3p-12

           = 54+36+3p-12= -6

           =  90-12+3p = -6

           =78+3p = -6

           = 3p = 78--6

                     =78+6

              3p  = 84

              p = 84/3

                 = 28

The value of p is 28

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Sound decibel are not additive because humans listen to sound logarithmically and LaTrenda is correct

Osman is not correct in his claim that 88 + 75 decibels would be 163 decibels. The decibel unit is not an additive unit, meaning that when you add the decibel levels of two different sound sources, you do not simply add the decibel levels.

Instead, adding the decibel levels of two different sound sources together would give you the total sound pressure level (SPL) of the combined sound.

To calculate the SPL of the combined sound, you would need to add the intensities of the two sounds and then calculate the decibel level of the combined sound using the formula:

SPL (dB) = 10 log10 (I1/I0) + 10 log10 (I2/I0)

Where I1 and I2 are the intensities of the two sound sources and I0 is the reference intensity, which is the threshold of human hearing.

It would make more sense to add the intensities of the two sounds and then calculate the number of decibels, because the human ear perceives loudness of sounds logarithmically, not linearly.

So, LaTrenda would be correct in this scenario.

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The value 255 in pixels means the code for the image is white. Therefore, any image with 255 pixels means it is white color.

Pixel values are the numerical values that make up the matrix in which images are stored in computers. The byte image, the most popular pixel format, stores this number as an 8-bit integer with a possible value range of 0 to 255.

Normally, zero and 255 are considered to be black and white, respectively. The many colors of gray are composed of values in between. This has the tremendous benefit of allowing computers to operate with color values that can be stored in a tidy number of bytes.

It is represented in 8 bits because 2⁸ equals 256 (from 0 to 255).

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