Find the perimeter of a regular pentagon with consecutive vertices at A(-3, 5) and B(7, 6).

Answer:

We do not have enough information to find the exact value of f(2.5) without additional assumptions about the nature of the exponential function. However, we can make an estimate using the given data and the properties of exponential functions.

First, we can write the general form of an exponential function as:

f(x) = a * b^x

where a is the initial value or y-intercept, and b is the base or growth factor. We can use the two given data points to set up a system of equations and solve for a and b:

f(-1) = a * b^(-1) = 18

f(5) = a * b^5 = 75

Dividing the second equation by the first equation, we get:

f(5) / f(-1) = (a * b^5) / (a * b^(-1)) = b^6 = 75 / 18 = 25 / 6

Taking the sixth root of both sides, we get:

b = (25 / 6)^(1/6) ≈ 1.472

Substituting this value of b into the first equation, we get:

a = f(-1) / b^(-1) = 18 / 1.472 ≈ 12.223

Therefore, we have the exponential function:

f(x) ≈ 12.223 * 1.472^x

Using this function, we can estimate the value of f(2.5) as:

f(2.5) ≈ 12.223 * 1.472^(2.5) ≈ 34.311

Note that this is only an estimate, and the exact value of f(2.5) may be different depending on the specific nature of the exponential function.

(a) Revenue will be zero when p = $0 and $2000.

(b) Revenue will exceed $1,400,000 when p > 500 or p > 700

(a) To find the prices at which revenue is zero, we need to set R(p) equal to 0 and solve for p:0 = -4p^2 + 8000p0 = 4p(p - 2000)So either 4p = 0 or p - 2000 = 0.

Solving for p gives us:

p = 0 or p = 2000

Therefore, the prices at which revenue is zero are $0 and $2000.

(b) To find the range of prices for which revenue exceeds $1,400,000, we need to set R(p) greater than 1,400,000 and solve for p:

1,400,000 < -4p^2 + 8000p

Rearranging the equation gives us:

0 < 4p^2 - 8000p + 1,400,000

Factoring the left side of the equation gives us:

0 < (p - 500)(4p - 2800)

So either p - 500 > 0 or 4p - 2800 > 0.

Solving for p gives us:

p > 500 or p > 700

Since we want the range of prices for which revenue exceeds $1,400,000, we need to take the larger value of p.

Therefore, the range of prices for which revenue exceeds $1,400,000 is p > 700, or prices greater than $700.

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Answer is SAS, we can solve this question by SAS theorem of triangle, for that we have to know more about triangle.

A triangle in geometry is a three-sided polygon or object with three edges and three vertices.

If two triangles satisfy one of the following conditions, they are congruent:

a. Each of the three sets of corresponding sides is equal. (SSS)

b. The comparable angles between two pairs of corresponding sides are equal.(SAS)

c. The corresponding sides between two pairs of corresponding angles are equal. (ASA)

d. One pair of corresponding sides (not between the angles) and two pairs of corresponding angles are equal. (AAS)

e. In two right triangles, the Hypotenuses pair and another pair of comparable sides are equal. (HL)

So, △MNP≅△OPN and NO II MP and NO ≅ MP

then, ∠ ONP = ∠ MPN and Side NP is common.

Therefore we can solve it by SAS Theorem.

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The solution is, distance from the point to the line is 22√10 feet.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The distance from point (x, y) to the line ax+by+c=0 is given by ...

 d = |ax +by +c|/√(a²+b²)

In general for, the equation of the line is ...

y = x/3 - 4

i.e. x -3y -12 = 0

so the distance formula is ...

 d = |x -y -12|/√(1² +(-3)²) = |x -y - 12|/√10

For the given point, the distance is ...

 d = |-6 -4 -12|/√10

   = 22/√10

 d = 22/√10 . . . .

distance from the point to the line = 22/√10

now, distance = 22/√10 * 10

                       =22√10 feet.

Hence, The solution is, distance from the point to the line is 22√10 feet.

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It is simply the largest of the common factors.

We have:

12x³- 18x² + 6x

We find GCF of 12, 18 and 6:

GCF(12, 18, 6) = 6

12 = 2 · 6

18 = 3 · 6

6 = 1 · 6

and GCF of x³, x² and x:

GCF(x³, x², x) = x

x³ = x² · x

x² = x · x

x = 1 · x

Therefore:

Emily can read 5 words per minute.

Minutes are often used to measure the duration of activities such as meetings, phone calls, or workouts. They are also used to express the duration of processes or events that occur over a short period of time.

To find out how many words Emily can read per minute, we need to divide the total number of words she can read by the amount of time it takes her to read them.

75 words in 15 minutes can be written as a ratio:

75 words / 15 minutes

To simplify this ratio, we can divide both the numerator and the denominator by 15:

(75 words / 15 minutes) ÷ (15 minutes / 15 minutes)

This gives us:

5 words / 1 minute

Therefore, Emily can read 5 words per minute.

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By answering the supplied question, we may infer that the response is percentage Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

A ratio or value stated as a percentage of 100 is referred to as a percentage in mathematics. The abbreviations "pct.," "pct," and "pc" are also sporadically used. Nonetheless, the percentage symbol "%" is frequently used to denote it. The percentage amount is dimensionally empty. When the denominator is 100, percentages are essentially fractions. To show that a number is a percentage, a percent symbol (%) should be used next to it. For instance, you receive a 75% grade if you correctly answer 75 out of 25 questions (75/100) on a test. For percentage calculations, multiply the outcome by 100 after dividing the amount by the total. The percentage is calculated by multiplying (value/total) by 100%.

We must divide the number of students who chose pizza (15) by the total number of students (20) and multiply the result by 100 to determine the percentage of students who chose pizza:

(15/20) x 100 = 75%

Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

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The approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

The boundary value problem given is y′′ − y = 0 with boundary conditions y(0) = 0 and y(2) = e2 − e−2.

(a) To find the exact solution y(t), we can use the characteristic equation r^2 - 1 = 0. This gives us r = 1 and r = -1. The general solution is therefore y(t) = c1e^t + c2e^-t.

Using the boundary conditions, we can find the constants c1 and c2.

For y(0) = 0, we have 0 = c1 + c2, which gives us c2 = -c1.

For y(2) = e2 − e−2, we have e2 − e−2 = c1e^2 + c2e^-2. Substituting c2 = -c1, we get e2 − e−2 = c1e^2 - c1e^-2.

Solving for c1, we get c1 = (e2 − e−2)/(e^2 - e^-2) = 1/2. Therefore, c2 = -1/2.

The exact solution is y(t) = (1/2)e^t - (1/2)e^-t.

(b) To use the three-point formula with step size h = 1/2, we can set up a table with tn and yn values.

tn | yn
---|---
0  | 0
1/2| y1
1  | y2
3/2| y3
2  | e2 - e-2

The three-point formula is yn+1 = yn-1 + 2h(y′n). We can use this formula to find the values of y1, y2, and y3.

For y1, we have y1 = 0 + 2(1/2)(y′0) = y′0. Since y′0 = y′(0) = (1/2)e^0 - (1/2)e^0 = 0, we have y1 = 0.

For y2, we have y2 = y0 + 2(1/2)(y′1) = 0 + 2(1/2)(0) = 0.

For y3, we have y3 = y1 + 2(1/2)(y′2) = 0 + 2(1/2)(0) = 0.

Therefore, the approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

It is important to note that the three-point formula is not accurate for this particular boundary value problem due to the size of the step and the nature of the differential equation. A smaller step size or a different numerical method may yield a more accurate approximation.

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Answer:

If 2 is a rational root of the equation x^3 - 5x^2 - 4x + 20 = 0, then (x - 2) is a factor of the polynomial. This is because of the rational root theorem, which states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is 20 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±4, ±5, ±10, and ±20.

Since 2 is a root, we can use long division or synthetic division to divide x^3 - 5x^2 - 4x + 20 by (x - 2). We get:

code

2 | 1 -5 -4 20 | 2 -6 -20 |------------ | 1 -3 -10 0

Therefore, we have:

x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10)

Now, we need to solve the quadratic equation x^2 - 3x - 10 = 0. We can use the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(-10))) / 2 x = (3 ± sqrt(49)) / 2 x = (3 ± 7) / 2

So the solutions to the equation x^3 - 5x^2 - 4x + 20 = 0 are:

x = 2, x = (3 + 7)/2 = 5, x = (3 - 7)/2 = -2

Therefore, the solution set is {2, 5, -2}.

Step-by-step explanation:

Step 1: Use the Rational Root Theorem to find possible rational roots The Rational Root Theorem states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is 20 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±4, ±5, ±10, and ±20. Since we are given that 2 is a root, we can conclude that (x - 2) is a factor of the polynomial.

Step 2: Use long division or synthetic division to divide the polynomial by (x - 2) We can use long division or synthetic division to divide the polynomial x^3 - 5x^2 - 4x + 20 by (x - 2). Both methods will give the same result, but I'll show the synthetic division method here:

code

2 | 1 -5 -4 20 | 2 -6 -20 |------------ | 1 -3 -10 0

The first row of the division represents the coefficients of the polynomial x^3 - 5x^2 - 4x + 20, starting with the highest degree term. We divide the first coefficient by the divisor, which gives us 1/1 = 1. Then we multiply the divisor (2) by the quotient (1), which gives us 2. We write 2 below the next coefficient (-5), and subtract to get (-5) - 2 = -7. We bring down the next coefficient (-4) to get -7 - (-4) = -3. We repeat the process with -3 as the new dividend, and so on, until we get a remainder of 0 in the last row.

The second row shows the partial quotients (in this case, just one quotient of 1), and the third row shows the coefficients of the quotient polynomial x^2 - 3x - 10. The last row shows the remainder, which is 0 in this case.

Step 3: Factor the quotient polynomial We now have x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10), since (x - 2) is a factor of the polynomial. We can factor the quadratic polynomial x^2 - 3x - 10 by finding two numbers that multiply to -10 and add to -3. These numbers are -5 and 2, so we can write:

x^2 - 3x - 10 = (x - 5)(x + 2)

Step 4: Find the solutions to the equation We now have:

x^3 - 5x^2 - 4x + 20 = (x - 2)(x^2 - 3x - 10) = (x - 2)(x - 5)(x + 2)

The solutions to the equation are the values of x that make the polynomial equal to 0. These values are the roots of the equation. We have:

x - 2 = 0, so x = 2 is a root x - 5 = 0, so x = 5 is a root x + 2 = 0, so x = -2 is a root

Therefore, the solution set is {2, 5, -2}.

The solution set of the equation x^(3)-5x^(2)-4x+20=0 is found to be {2, 5, -2}.

One rational root of the given equation is 2. We can use synthetic division to find the other roots.

Set up the synthetic division table by placing the root (2) in the leftmost column and the coefficients of the equation (1, -5, -4, 20) in the top row.

2|1-5-420|2-6-201-3-100

Multiply the root (2) by each of the numbers in the bottom row and place the result in the row below. Then add the numbers in the top and bottom rows to get the numbers in the final row.

The final row represents the coefficients of the reduced equation: x^(2)-3x-10=0. We can use the quadratic formula to find the remaining roots:

x = (-(-3) ± √((-3)^(2) - 4(1)(-10))) / (2(1))

x = (3 ± √(9 + 40)) / 2

x = (3 ± √49) / 2

x = (3 ± 7) / 2

x = 5 or x = -2

So the solution set of the equation is {2, 5, -2}.

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Yes, the fraction 4/9 will make each equation true.

Fraction is an element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. 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.

To see why, we can simplify the fraction 4/9 as follows:

4/9 = (4 x 7)/(9 x 7) = 28/63

Now, we can substitute 4/9 with 28/63 in each equation to see that they are all true:

63 x 28/63 = 28

18 x 28/63 = 8

96 x 28/63 = 42

36 x 28/63 = 16

We can also write it as:

63 × (4/9) = 28

18 × (4/9) = 8

96 × (4/9) = 42

36 × (4/9) = 16

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The zeros of the polynomial p(x)=x²+16 are x = 4i and x = -4i. The zeros of the polynomial can be found using the Quadratic Formula: x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = 0, and c = 16.

Plugging in these values into the Quadratic Formula, we get:

x = (-0 ± √(0²-4(1)(16)))/(2(1))

Simplifying the expression, we get:

x = (0 ± √(-64))/(2)

Since the square root of a negative number is a nonreal number, we can write this as:

x = (0 ± 8i)/(2)

Simplifying further, we get:

x = 0 ± 4i

So the zeros of the polynomial are x = 4i and x = -4i, both of which are nonreal numbers.

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Answer: The ones you have selected are correct

Step-by-step explanation:

Answer:

the ones you selected are all correct

Step-by-step explanation:

Answer:

To eliminate y, we can add the two equations.

5x + y + 3x - y = 48 + 16

Simplifying the left side, we get:

8x = 64

Dividing both sides by 8, we get:

x = 8

Now we can substitute x = 8 into either of the original equations and solve for y:

5x + y = 48

5(8) + y = 48

40 + y = 48

y = 8

So the solution is (x,y) = (8,8).

Answer:

25%

Step-by-step explanation:

Number of favorable outcomes 4

Total number of outcomes=4+5+2+3+2=16

4/16=0.25

0.25x100=25

25%

​

Answer:

The graph of y=1/2x-10 is a straight line with a slope of 1/2 and y-intercept of -10. It slopes upward from left to right and intersects the y-axis at -10.

On the other hand, the graph of y=1/x is a hyperbola that passes through the origin and has asymptotes at x=0 and y=0. It consists of two branches that curve towards the asymptotes in opposite directions.

Compared to the graph of y=1/x, the graph of y=1/2x-10 is a simpler and more predictable shape. It does not have asymptotes and has a constant slope. It also does not pass through the origin, unlike the graph of y=1/x.

We can conclude that the square pyramid has a volume of 111.5 in³.

A square pyramid in geometry is a pyramid with a square base.

It is a right square pyramid with C4v symmetry if the apex is perpendicular to and above the square's center.

It is an equilateral square pyramid, the Johnson solid J1 if all edge lengths are equal.

A polyhedron with seven faces is called a heptahedron.

One "normal" heptahedron exists, and it is formed up of a surface with one side made up of four triangles and three quadrilaterals.

So, 6.6 inches wide is the square pyramid's base.

The square pyramid's height is 7.7 inches or h.

V = a²(h/3) is the formula for the square pyramid's volume.

By changing the values given:
V = 6.6²(7.7/3)

V = 43.56(2.56)

V = 111.51 ≈ 111.5

Therefore, we can say that the square pyramid has a volume of 111.5 in³.

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None of the given options represents an amount of money equivalent to fife tenths of a dollar.

What is Money?

In mathematics, money is a unit of measure used to represent the value of goods or services. It is typically denoted in a currency unit, such as dollars, euros, or yen, and is often used to express prices, wages, or financial transactions. Money is a form of quantitative data and can be manipulated using various mathematical operations, such as addition, subtraction, multiplication, and division.

Fife tenths of a dollar is equivalent to $0.50, since there are 10 tenths in a dollar.

The amount of money that the digit 5 represents $0.50.

Looking at the given options, the only option that contains a total value of $0.50 is option B:

1 dollar bill = $1.00

quarter = $0.25

dime = $0.10

nickel = $0.05

5 Pennies = $0.05

Adding these values together, we get a total of $1.45, which is more than $0.50. Therefore, option B is incorrect.

Option D contains a total value of:

10 dollar bill = $10.00

quarter = $0.25

5 nickels = $0.25

2 Pennies = $0.02

Adding these values together, we get a total of $10.52, which is more than $0.50. Therefore, option D is incorrect.

Option A contains a total value of:

5 dollar bill = $5.00

quarter = $0.25

dime = $0.10

2 nickels = $0.10

4 Pennies = $0.04

Adding these values together, we get a total of $5.49, which is more than $0.50. Therefore, option A is incorrect.

The only remaining option is option C, which contains a total value of:

Two 20 dollar bills = $40.00

10 dollar bill = $10.00

quarter = $0.25

dime = $0.10

2 Pennies = $0.02

Adding these values together, we get a total of $50.37, which is more than $0.50. Therefore, option C is also incorrect.

Thus, none of the given options represents an amount of money equivalent to fife tenths of a dollar.

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Answer:

C

Step-by-step explanation:

Answer choice A implies that less than received an 80 or better, while according to the boxplot, at least 18 students did.

Answer choice B suggests that most students scored at least 90%, but that is false.

Answer choice C implies that the same number of students scored in the 70-80% range as in the 80-90% range, which is true according to the box plot.

Answer D says that more people scored 65-70% than 90-100%, but the opposite is true.

The required measure of y in the given triangle is 14 cm.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Following the property of proportionality of sides in similar triangles,
8 + 3.2 / 8 = y / 10
11.2/8 = y / 10
112 = 8y
y = 14

Thus, the required measure of y in the given triangle is 14 cm.

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The solution for c in the equation is 35/3

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

\(c = 5\frac{5}{6} \times 2 \)

Express the equation properly

So, we have the following representation

c = 5 5/6 * 2

Convert the fraction to improper​ fraction

So, we have the following representation

c = 35/6 * 2

Evaluate the products

c = 35/3

Hence, the solution is 35/3

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a. If 1,200 students are in the district, 165 students can be expected to oppose school uniforms.

b. From the sample, the most likely outcome is in favor, as it got the most responses, hence we should disagree with Bernice.

A proportion is a fraction of the total amount.

Out of 80, 11 opposed, hence, out of 1200, we apply the proportion and find that the amount will be of:

1200 x 11/80 = 165.

Hence, a - 165 students can be expected to oppose school uniforms.

b - We should disagree with Bernice because the sample indicates that the outcome in favor is the most likely because it received the most answers.

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The Simplex Algorithm to solve the given linear programming problem gives the solution [tex]x_{1}[/tex] = 16, , [tex]x_{2}[/tex] = 0,  [tex]x_{3}[/tex]  = 11; while the minimum value of objective function is "13.2".

The solution to the given linear programming problem can be obtained using the Simplex algorithm. Using the initial basic feasible solution ([tex]x_{1}[/tex] = 0,[tex]x_{2}[/tex] = 0, [tex]x_{3}[/tex] = 0), the following sequence of steps can be used to solve the problem:

The solution of the problem is: [tex]x_{1}[/tex] = 16, [tex]x_{2}[/tex] = 0, [tex]x_{3}[/tex] = 11.

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The answer as a single polynomial is x^(3) + 9x^(2) - 15.

To subtract the two polynomials as indicated, we need to distribute the constants in front of each polynomial and then combine like terms.

First, we distribute the 5 and -2 to each term in the respective polynomials:
5(x^(3)) + 5(x^(2)) - 5(3) - 2(2x^(3)) - 2(-2x^(2))

Simplifying each term gives us:
5x^(3) + 5x^(2) - 15 - 4x^(3) + 4x^(2)

Next, we combine like terms by adding the coefficients of each term with the same exponent:
(5x^(3) - 4x^(3)) + (5x^(2) + 4x^(2)) - 15

Simplifying the coefficients gives us:
x^(3) + 9x^(2) - 15

Therefore, the answer as a single polynomial is x^(3) + 9x^(2) - 15.

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The family uses 68.7 gallons of water every day for all purposes

If 22.9% of the water is used for cleaning, then the remaining 100% - 22.9% = 77.1% of the water is used for other purposes such as drinking and cooking.

To find out how much water the family uses every day, we need to add the amount of water used for cleaning to the amount of water used for other purposes.

Quantity of water used for cleaning = 22.9 percentage of the total amount of water used every day = 0.229 x 68.7 gallons = 15.71 gallons

Quantity of water used for other purposes = 77.1% of the total amount of water used every day = 0.771 x 68.7 gallons = 52.99 gallons

Total quantity of water used every day = amount of water used for cleaning + amount of water used for other purposes = 15.71 gallons + 52.99 gallons = 68.7 gallons

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Answer

the answer is b

If the selection is made randomly, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women. The probability that the committee consists of 5 men and 5 women is 0.129. The probability that there is no woman in the committee is  0.000000033.

1. The total number of ways to select a committee of size 10 from a group of 10 men and 20 women is given by the combination formula:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of people (10 men + 20 women = 30) and k is the size of the committee (10).
C(30,10) = 30! / (10! * (30-10)!)
C(30,10) = 30! / (10! * 20!)
C(30,10) = 30045015
Therefore, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women.

2. The probability that the committee consists of 5 men and 5 women is given by:
P(5 men and 5 women) = C(10,5) * C(20,5) / C(30,10)
P(5 men and 5 women) = (10! / (5! * 5!)) * (20! / (5! * 15!)) / (30! / (10! * 20!))
P(5 men and 5 women) = (252 * 15504) / 30045015
P(5 men and 5 women) = 0.129

3. The probability that there is no woman in the committee is given by:
P(no woman) = C(10,10) * C(20,0) / C(30,10)
P(no woman) = (10! / (10! * 0!)) * (20! / (0! * 20!)) / (30! / (10! * 20!))
P(no woman) = (1 * 1) / 30045015
P(no woman) = 0.000000033
Therefore, the probability that there is no woman in the committee is 0.000000033.

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Answer:

8290

Step-by-step explanation:

Explanation is on the pic

Wok out the probability of rolling one 6 from 2 throws on a biased dice rolling 6 1/5 of the time is 8/25

The given data is as follows:

Number of throws = 2

probability of rolling number = 6

The probability of getting dice one 6 from 2 throws can happen in two different ways.

1. Rolling a number 6 on the first throw and not getting a number 6 on the second throw.

2. Not rolling a number 6 on the first throw and getting a number 6 on the second throw.

Here, the multiplication rule of probability is used to find the probability of the above two different events.

1.

The probability of getting a 6 on the first throw = is 1/5

The Probability of not getting a 6 on the second throw = (4/5)

The Probability of both happening: (1/5) x (4/5) = 4/25

2.

The Probability of not getting a 6 on the first throw = (4/5)

The Probability of getting a 6 on the second throw = (1/5)

The Probability of both happening: (4/5) x (1/5) = 4/25

The probability of both events is = 4/25 + 4/25 = 8/25

Therefore we can conclude that the probability of getting one 6 from 2 throws on a  dice rolling 6 1/5 of the time is 8/25.

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Answer:

4x+3y

Step-by-step explanation:

Combining like terms, we get:

5x - x + 4y - y = 4x + 3y

Therefore, 5x+4y-x-y simplifies to 4x+3y.