Factorise completely:

The amount that each person should pay is  $22.06   .

in the question ,

it is given that

total number of persons = 3 person + 1 = 4 persons

cost of the meal = $72.50

sales tax percent = 6.75%

tip percent = 15%

So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89

and , the amount of tip is = 15% of cost

= 0.15 * 72.50

= 10.87

So , the total amount payable is = cost + sales tax + tip

= 72.50 + 4.89 + 10.87

= 88.26

since the total number of persons is 4 ,

the amount per person is = 88.26/4 = 22.06

Therefore , The amount that each person should pay is  $22.06   .

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The table (D) values would produce the same graph as shown.

Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.

From the graph, find the intercepts,

At x = 0, the value of y is -1.

At, y = 0, the value of x is 4

So, from the given options, we can see that the values are given in table (D).

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Answer: Either C. or D.But I'm sure it's D.

Step-by-step explanation:

Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending

Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.

We are to multiply Pi to any equation

let the equation be (20.5 + 3x)[tex]\pi[/tex]

pi is represented in numbers by 3.14

Hence we would have the equation to be of the form

(20.5 + 3x)3.14

multiply through the bracket

64.37 + 9.42x

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The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is

y = (3/8)x - 13/4

How to find equation of line if one point and equation of perpendicular line is given?

To find the equation of line which is perpendicular to another line

According to the given question:

Let the required equation of line be y = mx + b

where m is the slope of line and b is the y-intercept

Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1

Standard form of the given line is

y = (-8/3)x + 1/3

∴ m₁ = -8/3

Finding m₂, (-8/3). m₂ = -1

∴ m₂ = 3/8 ------ (1)

Using the given point (6, -1) to find y-intercept in the equation

y = (3/8)x + b

-1 = (3/8)(6) + b

∴ b = -13/4

Therefore the required equation of line in standard form is

y = (3/8)x - 13/4

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The equation  y = 4x - 8 is discrete

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.

While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.

The main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.

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Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.

Given,

Volume = 2.5 cm³

Mass = 10 g

For density:

Mass ÷ volume

10 ÷ 2.5

4

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

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The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

Given :

Population Proportion ( p ) = ( 44 % ) = 0.44

Sample proportion ( p hat ) = ( 40 % ) =  0.4

Size of sample ( n ) = 853

To find : P ( p hat < 0.4 )

Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]

Substituting values in the above formula ,

z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]

z = - 2.3535

z - score = -2.3535

Finding the p - value :

p - value = 0.009299

Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

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A solution to −34x+2=(14)x+1 is x = 1/48

In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1

We need to find the solutions to −34x + 2 = (14)x + 1

i.e., we need to find the solution to f(x) = g(x)

Consider, f(x) = g(x)

-34x + 2 = (14)x + 1

-34x + 2 - 14x = 14x + 1 - 14x

-48x + 2 = 1

-48x = -1

x = 1/48

Therefore, a solution to −34x+2=(14)x+1 is x = 1/48

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The length of the shorter leg is 9 mm.

The length of the longer leg is 12 mm.

The length of the hypotenuse is 15 mm.

Pythagoras theory applies to every right triangle. If

Step-by-step explanation:

Known

Asked

Answer

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]

[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]

[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]

[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]

[tex]a^2 - 6a - 27 = 0[/tex]

[tex]a^2 - 9a + 3a - 27 = 0[/tex]

[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]

(a-9) (a+3)=0

a-9=0  or  a+3= 0

a=9     or  a=-3 (impossible)

Shorter leg

a=9 mm

Longer leg

b = a+3

b = 9+3

b = 12 mm

Hypotenuse

c = a+6

c = 9+6

c = 15 mm

Step-by-step explanation:

The answer is: A=210÷26.2=8.2

B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7

Answer:

A) 26.2/210= .125 miles per minute

B) 210/26.2= 8.02 minutes per mile

C) the other runner talks about the same rate as b), not a).

Step-by-step explanation:

A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)  

C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.

Answer:

Step-by-step explanation      a=0.32

The required simplified value of x in the given expression is 8.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
2.8x + 10 + 5.7x = 70+x

Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x  = 60
x = 60 / 7.5
x = 8

Thus, the required simplified value of x in the given expression is 8.

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The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months

The rent of a room for 4 months is Rs 20,000.

The rent of a room for 1 month is Rs 20,000./4

The rent of a room for 1 month is Rs 5000

The rent of a room for 7 months is Rs 5000 x 7

The rent of a room for 7 months is Rs 35000

Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent

The rent is 5000 for 1 month

The rent will be 55000 for 1/5000 x 55000 = 11 months

Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months

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The state population as a single-digit time power of 10 is approximately 4 × 10⁷.

Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.

To estimate something is to approximate it as accurately as possible.

To acquire a quick and approximate response is obtained by rounding down the values used in the computation.

Given the state estimated population = 38,332,521

Divide and multiply by 10

So,

= 3,833,252.1 × 10¹

= 383,325.21 × 10²

So, similarly, we can write

= 3.8332521 × 10⁷

So, we can write the state population as approximately 4 × 10⁷

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Answer:

so there are 3825 worker in total

Step-by-step explanation:

675=15%

women=85%

how much workers are 5%=675/3 =225

225=5%

how many workers is 85%= 85/5=17

                                    85%=225x17=3825

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Given,

12 fair dice rolled,

Probability that the product of the numbers on the top faces is prime:

⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁

6 × (1/6)⁵ × 3/6

1/2(1/6)⁴

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

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Answer: you are left with 17.1 or 17.10

HOW TO:  picture this. i'ma going to go to your store and you have 27 dollars. you owe me 9.90 for some reason. you give me the money and i go on my way. how much money are you left with?

The speed of each train is 125kph and 145kph.

Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.

The difference in their speed is 20 kph.

Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.

Formula to calculate speed is:

Speed = Distance / Time

Distance = Speed × Time

Distance covered by first train = x × 3

Distance covered by second train = (x + 20) × 3

Total distance = 810

So we get;

3x + (x + 20)3 = 810

3x + 3x + 60 = 810

6x = 750

x = 125

x + 20 = 125 + 20 = 145

Therefore we get the speed of both trains which is 125kpp and 145 kph.

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a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.

It is given that the number of bulbs in a given lot is 100.

The number of bulbs in the sample selected is 6

The life of the sample bulbs was

no.         life (hours)

1                      950

2                     1210

3                     1070

4                      840

5                     1420

6                      980

a)

The average life of the bulbs can be calculated by

the sum of the lives of the sample/ no. of samples

= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6

= 1078.3333 hrs

b) The total lives of the bulbs in the lot will be

average life X no. of bulbs

= 1078.3333 X 100

= 107833.33 hrs

c)

We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample

The bulbs

2, 3, and 5 have lives exceeding 1000 hrs.

Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.

Therefore the proportion

= 3/6

= 1/2

d)

The number of bulbs in the lot with a life exceeding 1000 will be

proportion X no. of bulbs

= 1/2 X 100

= 50 bulbs

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(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.

Latisha's total wealth is $17.

More than 10 veggies are the number of vegetables that Latisha wants to purchase.

A pumpkin costs $5.50.

An autumn squash costs $3.50.

Let n pumpkins purchased equal x.

Purchased number of autumn squash = y

There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.

With x acting as the independent variable, we may identify many y's.

x ( Pumpkin)                   y(Autumn squash) (integral value)

    8                                                                20

    6                                                                24

   10                                                              17

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The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5  .

In the question ,

it is given that

the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .

the slope is = (5 -(-2))/(-8 -6)

= 7/(-14)

= -1/2

so , the slope of the required line is = 2 .

The equation of the line passing through the point (3,1) with slope 2 is

(y - 1) = 2*(x-3)

y -1 = 2x - 6

y = 2x - 6 + 1

y = 2x - 5

the equation of line is y [tex]=[/tex] 2x - 5

the perpendicular slope is = 2

the y intercept is -5 .

Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5)  is y = 2x - 5 .

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According to the vertical angles theorem, m∠1 = 117°.

Based on the corresponding angles theorem, m∠2 = 117°.

The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.

When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.

Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.

Therefore:

m∠1 = 117° [vertical angles theorem]

Angles 1 and 2 are corresponding angles. Therefore:

m∠2 = m∠1

Substitute

m∠2 = 117° [corresponding angles theorem]

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The solution for x in the function when the equation  y=−4x+12 equals -12 is -6

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

y=−4x+12

To make the equation legible, we need to rewrite it

So, we have the following representation

y = −4x + 12

Also from the question, we have

y = -12

This means that we calculate x when y = -12

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

-12 = -4x + 12

So, we have the following equation

-4x + 12 = -12

Add -12 to both sides of the equation

So, we have the following representation

-4x + 12 - 12 = -12 - 12

Evaluate the like terms in the equation

-4x = -24

Divide both sides of the equation by -4

x = 6

Hence, the solution is 6

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Possible question

The equation below describes a function of x . y=−4x+12

Solve for x when y = -12

Answer:

if the root is 10 then the function is ²✓5

Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.

the ester's number is equal to one-tenth of the Sarai number.

= 1 / 10 × 0.09 = 0.009

to determine Kurry's number, multiply Sarai's number by 10

= 10 × 0.09 = 0.9

Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.

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Answer:

$2825,32

Step-by-step explanation:

Value of the car after 1 year

$3000 * 3% = 3000 * 0.03 = 90

3000 - 90 = $2910

Value of the car after 2 year

$2910 * 3% = 2910 * 0.03 = 87.3

2910 - 87.3 = $2912,7

Value of the car after 3 year

$2912,7 * 3% = 2912,7 * 0.03 = 87.381

2912,7 - 87.381 = $2825,319

"Round to the nearest cent"

$2825,32

The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

According to some of the laws of indices, we have;

[tex]\dfrac{1}{x^n} =x^{-n}[/tex]

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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The annual dividend for 500 shares was $710.

The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.

Dividends are always declared per share with a stated dollar amount or percentage.

Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.

Dividends are a kind of financial reward to stockholders for their investment in the entity.

The dividend per share = $1.42

Market price per share = $96

The number of shares held = 500

The dividend received for the year = $710 ($1.42 x 500)

Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.

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