What is the experimental probability of rolling a single die ten times and landing on 6?

The solution to the given linear equation, 4(x - 7)= 0.3(x + 2) + 2.11, is x = 8.3. The correct option is b) 8.3

From the questions, we are to determine the solution to the given linear equation.

The given linear equation is

4(x - 7)= 0.3(x + 2) + 2.11

To solve the equation, we will determine the value of x

Solving the equation

4(x - 7)= 0.3(x + 2) + 2.11

Clear the parentheses by applying the distributive property

4x - 28 = 0.3x + 0.6 + 2.11

Add 28 to both sides of the equation

4x - 28 + 28 = 0.3x + 0.6 + 2.11 + 28

4x = 0.3x + 30.71

Subtract 0.3x from both sides of the equation

4x - 0.3x = 0.3x - 0.3x + 30.71

3.7x = 30.71

Divide both sides by 3.7

3.7x/3.7 = 30.71/3.7

x = 8.3

Hence, the solution to the equation is x = 8.3

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The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.

A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.

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The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0 phenotypic ratio.

In the given question we have to explain about a 4:0 phenotypic ratio.

The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0. However, the genotypic ratio considers probable allele combinations rather than the observable trait (phenotype).

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When we multiply two decimal numbers less than 1 then their product will be less than 1.

What do you mean by fraction?

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. It is known as an improper fraction if the numerator is bigger and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder. By dividing the numerator by the denominator, any fraction can be expressed in decimal form. One or more digits may repeat indefinitely or the result may come to an end at some point.

If we multiply two decimal numbers less than 1 then their product will also be less than 1. Because we are determining a fractional portion of a quantity, this is the case.

Decimals are frequently multiplied by treating them as whole numbers before placing the decimal point in the result. Where the decimal point is placed in the solution depends on how many digits are present in the factors following the decimal points.

Therefore, when we multiply two decimal numbers less than 1 then their product will be less than 1.

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Zero extraneous solutions does the equation have (2m)/(2m+3)-(2m)/(2m-3) = 1.

What is Quadratic Equation?

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a ≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.

Given that;

[tex]\frac{2m}{2m+3}-\frac{2m}{2m-3} = 1[/tex]

⇒ [tex]\frac{2m(2m-3)-2m(2m+3)}{(2m+3)(2m-1)}=1[/tex]

⇒ [tex]\frac{4m^2-6m-4m^2-6m}{(4m^2-9)}=1[/tex]

⇒ [tex]\frac{-12m}{4m^2-9}=1\\[/tex]

⇒ [tex]-12m = 4m^2-9[/tex]

4m^2 +12m - 9 = 0(1)

The formula for calculating the roots of the quadratic equation ax^2 + bx + c can be utilized because (1) is a quadratic equation.

[tex]\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

Variable m is in equation (1), where a = 4, b = 12, and c = -9.

The roots are calculated as:

[tex]\frac{-12\pm \sqrt{12^2-4\times 4\times (-9)} }{2\times 4}[/tex]

[tex]\frac{-12\pm \sqrt{2\times 144} }{8}[/tex]

[tex]\frac{-12\pm 12\sqrt{2} }{8}[/tex]

[tex]\frac{-3}{2} \pm \frac{3}{2}\sqrt{2}[/tex]

[tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2} \ and \ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex]

Subsitituting [tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2}[/tex]  in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

The root -3/2 - 3([tex]\sqrt{2}[/tex])/2 is therefore not an auxiliary solution.

Now substituting [tex]\ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex] in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

Therefore, the root -3/2 + 3([tex]\sqrt{2}[/tex])/2 IS NOT AN ADDITIONAL SOLUTION.

The above problem can be solved using either of the two roots.

There is no superfluous solution to the equation (2m)/(2m+3)-(2m)/(2m-3) = 1 as a result.

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If each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, Gary Smith of Pomona College reviewed the test results of all 346 students who took his statistics course over a ten-year period.

Take into account that both the midterm and final tests were rated out of 100.

Let the midterm score (x) and the final score (y) be the same.

The data for the explanatory variable x and the response variable y will be the same if each student receives the same grade on the midterm and final.

The linear model will predict that the two variables are equal if the data for the two variables are the same, and as a result, the linear model will assume that the expected y-variable is equal to the predicted x-variable.

Thus, the following is how the least-square regression line appears:

[tex]\hat{y}=x[/tex]

Therefore, if each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

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Answer:

15/22

Step-by-step explanation:

15 red, 15 blue, 15 yellow

You draw a marble of any color.

Now the marbles left in the bag are 14 of the same color, and a total of 30 of different colors for a total of 44 marbles.

Your desired outcome is a marble of a different color.

There are 30 desired outcomes.

The total number of possible outcomes is all the marbles left in the bag: 44.

p(2 marbles of different colors) = 30/44 = 15/22

13.5 Hrs long a player would have to practice batting to have 27 hits.

Given:

TIME (Hrs) 1  5  9  13  17

HITS         2 11 18 25 34

To have 27 hits :

= 13 + 1 + 17 + 5 - 9 / 2

= 14 + 22 - 9 / 2

= 36  - 9 / 2

= 27 / 2

= 13.5 hours

Therefore 13.5 Hrs long a player would have to practice batting to have 27 hits.

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The expected value of winnings is 0.

The expected value will be calculated by taking the sum of winning and loosing = E(x) = ΣxP(x), where X is the outcome and P is the probability of that outcome.

The probability of winning = X P(x)

The probability of winning = 1 × 0.5

The probability of winning = 0.5

The probability of loosing = -1 × 0.5 (-1 because it will be the loss)

The probability of loosing = -0.5

Calculating their sum = 0.5 + (-0.5)

Expected value = 0.5 - 0.5

Expected value = 0

Hence, the expected value is 0.

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The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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The potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

What is function?

In arithmetic, a perform from a collection X to a collection Y assigns to every part of X specifically one part of Y.

Main body:

p(x) = x⁴+ 22x² - 16x - 12

From the rational root theorem,

All the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

In the given polynomial,

The constant term is - 12

The leading coefficient is 1

The factors of - 12 are ±1, ±2, ±3, ±4, ±6, ±12

Factors of 1 are ±1.

From the rational root theorem, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

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Answer:

just count 3 digit and round it off then the answer would be 34000

Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D.

Congruent triangles;-

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Here,

Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.

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Answer:

original price was $8

Step-by-step explanation:

Ashley buy a hamster wheel during the sale (25% off). If Ashley pay $6, what was the original price?

$6 = 75% of price

75% = 0.75

6 = 0.75x

divide both sides by 0.75:

6/0.75 = 0.75x/0.75

x = 8

original price was $8

Accountants and auditors create and review financial records, spot possible risk and opportunity areas, and provide individuals and organisations solutions. They guarantee the accuracy of financial records, the assessment of data and financial risks, and the correct payment of taxes.

Accountants;-

An accountant is a specialist who manages bookkeeping and organises the financial records you use to run your company, including balance sheets, profit and loss statements, and more. They simplify all the financial jargon associated with running a business, audit your records, create reports for tax purposes, and more.

Auditors;-

An organization's audit is to be conducted by an auditor, who may be an individual or a company. An audit is a planned, methodical procedure that involves looking over books, records, accounts, or other documentation.

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The volume of the composite figure is A) 69[tex]\pi ft^3[/tex].

What is volume?

 The area occupied within an object's three-dimensional bounds is referred to as its volume. Another name for it is an object's capacity. The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape.

Here the given figure contains cone and cylinder.

In cone height = 5f , radius r = 3 ft.

Then Volume of the cone is ,

=> V = 1/3 ([tex]\pi r^2[/tex]h) cubic unit

=> V = 1/3 (3.14*9*5)

=> V = 15[tex]\pi ft^3[/tex]

Now In cylinder Height = 6ft and radius = 3ft.

Then Volume of cylinder is ,

=> V=[tex]\pi r^2h[/tex] cubic unit.

=> V= [tex]\pi[/tex]*9*6

=> V=54 [tex]\pi[/tex][tex]ft^3[/tex]

Then Total volume of the figure is ,

=> Volume of cone+ volume of cylinder

=> 15[tex]\pi[/tex]+54[tex]\pi[/tex]

=> 69[tex]\pi ft^3[/tex].

Therefore the volume of the composite figure is  69[tex]\pi ft^3[/tex].

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Answer:

Is there a diagram or picture??

Step-by-step explanation:

Percentage by mass in sample will be 67.8%.

We know that volume of NaOH dispensed is 24.68 ml.

And mass of the NaOH is 39.997 g/mol.

Also mass of acid is 58.94 g/mol.

We have to find percentage by mass in sample.

To calculate the mass percent of an element in a compound, we divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100.

Therefore

Mass percent = (mass of chemical / total mass of compound) × 100

                       = (mass of NaOH/ mass of acid) × 100

                       = (39.997/58.94) × 100

                       = 0.678 × 100

Mass percent = 67.8

Hence percentage by mass in sample is 67.8%

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Answer:

See below

Step-by-step explanation:

= {(1, 3), (2, 5), (3, 7), (4, 9), (5, 9)}

Domain:

All the x-values of the relation are domain.

So,

Range:

All the y-values of the relation are range.

So,

[tex]\rule[225]{225}{2}[/tex]

The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.

The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.

Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.

The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.

Thus, vertex angle is defined as the angle opposite the base.

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The rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

According to the question,

We have the following information:

A spherical balloon is being inflated. We need to find the rate of increase of the surface area of a spherical balloon with respect to r.

Surface area = [tex]4\pi r^{2}[/tex]

Differentiating with respect to r:

ds/dr = 8πr

Now, we will put all the values of r in this formula.

(a) r = 1 ft

Rate of increase = 8π*1

Rate of increase = 8π square feet

(b) Radius = 8 ft

Rate of increase = 8π*8

Rate of increase of area = 64π square feet

(c) Radius = 9 ft

Rate of increase of area = 8π*9

Rate of increase of area = 72π square feet

(d) Radius = 2 ft

Rate of increase of surface area = 8π*2

Rate of increase = 16π square feet

Hence, the rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

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On average number of customers arrives at a grocery shop per minute is equal to 1.2 customers per minute.

As given in the question,

Following a Poisson distribution:

Number of customers arrives at grocery store

= Average rate of 70 per hours

Conversion hours to minutes

1 hour = 60 minutes

λ = average rate of 70 per hours

  = average rate of 70 per 60 minutes

  = average rate of ( 7 / 6 ) per minute

 = average rate of 1.1666...per minute

= average rate of 1.2 per minute

Therefore,  on average 1.2 number of customers arrives per minute.

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To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In a function for every single input (x), there must be one output(y).

In the given second table,

For x = 0 → y =2 and y = 1 thus it will not be a function.

In the fourth table,

For x = 2 → y =2 and y = 6 thus it will not be a function.

Hence "To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function".

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The equation for the direct variation will be 5y-3x=0.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, For the data in the table, does y vary directly with x

X: 5, 8, 9

Y: 3, 5, 7

y ∝ x

y=kx

3=k5

k=3/5

For x as 5 and y as 3, the obtained equation is,

y=kx

y=3/5x

5y=3x

5y-3x=0

Thus, the equation for the direct variation will be 5y-3x=0.

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Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

What is scaffold instruction?

Hence, Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

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The main activity that is performed by accountant include the safe keeping of financial records and preparation of financial statements that are helpful in order to represent the current financial positions of a company.

An accountant is a qualified personnel who is the responsibility of maintenance of accounting records and safe keeping of the books of accounts of a firm. apart from maintenance of the accounting records and accountant also has to ensure that the financial statements are true and fair.

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Answer:

factors : 1, 3, 5 and 15

Step-by-step explanation:

1 x 15 = 15

5 x 3 = 15

so those are the only factors of 15

The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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A cubic polynomial is a polynomial of degree 3. That is, it is a polynomial with three terms. The relationship between the zeros and the coefficients of a cubic polynomial can be found by using the factoring theorem.

This theorem states that if a polynomial has a factor of (x-a), then a is a zero of the polynomial. In other words, the zeros of a polynomial are the values of x that make the polynomial equal to zero.

To find the zeros of a cubic polynomial, we can use the factoring theorem to factor the polynomial into factors of the form (x-a). For example, if we have the cubic polynomial x³+ax²+bx+c, we can factor it as (x-a)(x²+px+q), where a, p, and q are constants. We can then use the factoring theorem to find the values of a, p, and q that make the polynomial equal to zero.

The coefficients of a cubic polynomial are the values of a, p, and q in the factored form of the polynomial. In other words, the coefficients of a cubic polynomial are the values that determine the zeros of the polynomial.

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Using the solution of Algebraic expression,

we get that total 28 games won by sports team.

We have given that,

let a sports team lost be x games .

then, total number of games won by sports team

= 2x

total number of games played by sports team

= 42

i.e , 2x + x = 42

=> 3x = 42

=> x = 42/3

=> x = 14

so, number of games lost by sports team is 14

but we have to calculate the total number of games won by spots team .

using the value of x , we get 2x = 2×14

=> 28 games

Hence, total 28 games out of 42 games are won by sports team.

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