A rectangular box has a volume of 504 cubic inches the width of the box is 7 inches and a height of the box is 6 inches use the partial quotient method to find the length of the box

Therefore , the solution of the given problem of probability comes out to be the likelihood that 2 will not occur is 5/6, or roughly 0.8333, or 83.33%.

Any considerations technique's main objective is to determine the likelihood event that a claim is true or that a particular incident will happen. Any number from 0 to 1, where 0 traditionally represents a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The six possible results on a conventional six-sided die are 1, 2, 3, 4, 5, and 6.

Since there are 5 other numbers on the die in addition to

2 (1, 3, 4, 5, and 6), there are 5 outcomes in which 2 does not appear.

There are six sides to the die, so there are a total of six events that could occur.

The likelihood that the number 2 will not appear on the die is therefore provided by:

Probability is calculated as follows:

=> 5/6 = number of outcomes without 2 out of all possible possibilities.

So, on a typical 6-sided dice, the likelihood that 2 will not occur is 5/6, or roughly 0.8333, or 83.33% (rounded to two decimal places).

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Answer:

x + 4

Step-by-step explanation:

2(–x + 2) + 3x

-2x + 4 + 3x

x + 4

The required square feet of soil that must be turned in the circular garden is 176.625 square feet.

A circular garden is surrounded by a fence that is 47.1 feet long.

That is, circumference of a circle = 2 π r = 2(3.14) r = 6.28r (in feet)

where,  r represents the radius of the circular garden in feet.

Thus,

6.28r = 47.1

⇒ r=7.5 feet

Area of the circular garden is measured by the formula as,

= π r^2  square unit

= (3.14)( 7.5^2) square feet  

= 176.625 square feet

Hence, the required square feet of soil that must be turned in the circular garden is 176.625 square feet.

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Rounding to the nearest hundredth, the arc length of one slice is approximately 53.67 feet.

Arc length is the distance along the curved line or arc of a circle, measured in linear units such as centimeters, feet, or meters. It is calculated as the product of the radius of the circle and the angle subtended by the arc at the center of the circle, expressed in radians.

Here,

Since the circle is divided into eight equal slices, each slice is 360/8 = 45 degrees. The arc length of one slice can be calculated using the formula:

Arc length = (angle/360) x 2πr

where angle is the central angle in degrees, r is the radius of the circle, and π is the constant pi.

In this case, the diameter of the circle is 137 feet, so the radius is half of that, or 68.5 feet.

Substituting the given values into the formula, we get:

Arc length = (45/360) x 2 x 3.14 x 68.5

Arc length = 0.125 x 2 x 3.14 x 68.5

Arc length = 0.785 x 68.5

Arc length = 53.67 feet

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A qualitative variable is a variable that cannot be measured in numerical terms, but rather, is characterized by qualities or attributes that are not numerical. Option A is the correct answer.

Qualitative variables are also called categorical variables because they represent categories or groups. Examples of qualitative variables include gender, nationality, religion, and occupation.

In contrast, quantitative variables can be measured in numerical terms, such as age, height, weight, income, and test scores. Understanding the nature and characteristics of different types of variables is important for selecting appropriate statistical methods and techniques to analyze and interpret data.

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Equation 1: One-step equation

Solve for x: 2x + 5 = 11

Solution:

2x + 5 - 5 = 11 - 5 (Subtract 5 from both sides)

2x = 6 (Simplify)

2x/2 = 6/2 (Divide both sides by 2)

x = 3

Equation 2: One-step equation

Solve for y: 8y - 7 = 23

Solution:

8y - 7 + 7 = 23 + 7 (Add 7 to both sides)

8y = 30 (Simplify)

8y/8 = 30/8 (Divide both sides by 8)

y = 3.75

Equation 3: Equation with fractions

Solve for x: (3/4)x + 1/2 = 7/8

Solution:

(3/4)x + 1/2 - 1/2 = 7/8 - 1/2 (Subtract 1/2 from both sides)

(3/4)x = 3/8 (Simplify)

(3/4)x ÷ (3/4) = 3/8 ÷ (3/4) (Divide both sides by 3/4)

x = 1/2

Equation 4: Equation with fractions

Solve for y: 2/3 - y/4 = 1/6

Solution:

2/3 - y/4 = 1/6

(2/3)x 4/4 - y/4 = 1/6 x 4/4 (Multiply both sides by 4)

8/12 - y/4 = 4/24

8/12 - 3y/12 = 4/24 (Find a common denominator)

5y/12 = 4/24 - 8/12

5y/12 = -4/24 (Simplify)

5y/12 x 24/5 = -4/24 x 24/5 (Multiply both sides by reciprocal of 5/12)

y = -2

Equation 5: Equation with distributive property

Solve for x: 4(x - 3) = 20

Solution:

4(x - 3) = 20

4x - 12 = 20 (Distribute 4)

4x - 12 + 12 = 20 + 12 (Add 12 to both sides)

4x = 32 (Simplify)

4x/4 = 32/4 (Divide both sides by 4)

x = 8

Equation 6: Equation with decimals

Solve for y: 2.5y + 0.75 = 4.25

Solution:

2.5y + 0.75 - 0.75 = 4.25 - 0.75 (Subtract 0.75 from both sides)

2.5y = 3.5 (Simplify)

2.5y/2.5 = 3.5/2.5 (Divide both sides by 2.5)

y = 1.4

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Therefore, the slope of the line represented by this equation is -3.

An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. An equation can also be seen as a balance scale, where both sides of the equation must be equal in order for the equation to be true.

Here,

Now let's look at the given equations:

y=-3x+10

The equation is in slope-intercept form, y=mx+b, where m is the slope of the line. Therefore, the slope of the line represented by this equation is -3. To determine the relationship between this line and line p, we need to know the slope of line p.

y-5=-(2+2)

Simplifying this equation, we get y-5=-4 or y=-4+5 or y=1. This equation represents a horizontal line passing through y=1. A horizontal line has a slope of 0, which is neither parallel nor perpendicular to line p.

-3x+y=1

Rewriting this equation in slope-intercept form, we get y=3x+1. Therefore, the slope of the line represented by this equation is 3. To determine the relationship between this line and line p, we need to know the slope of line p.

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Answer: I think that this question Is biased.

Step-by-step explanation:

It is biased because the mayor might not like having a skate park.

If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.

The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.

We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:

90 pens - 36 red pens = 54 black pens

Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:

36/18 : 54/18

Simplifying further, we get:

2:3

This means that for every 2 red pens, there are 3 black pens in the box.

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The statements about the given quadrilateral are determined as follows:

1. False 2. False 3.True 4.False 5. False 6. False

1.) The quadrilateral is a parallelogram. False

To be a parallelogram, opposite sides must be parallel. We can find the slope of each side:

Slope of JK = (0 - 3) / (2 - (-1)) = -1

Slope of KL = (-6 - 0) / (-1 - 2) = 2

Slope of LM = (-3 - (-6)) / (-4 - (-1)) = 1

Slope of MJ = (3 - (-3)) / (-1 - 2) = 2/3

Since the opposite sides do not have the same slope, the quadrilateral is not a parallelogram.

2.) Both pairs of opposite sides are congruent. False

To be a parallelogram, opposite sides must be congruent. We can use the distance formula to find the length of each side:

Length of JK = √((2 - (-1))² + (0 - 3)²) = √(13)

Length of KL = √((-1 - (-1))² + (-6 - 0)²) = 6

Length of LM = √((-4 - (-1))² + (-3 - (-6))²) = √(13)

Length of MJ = √((-1 - 2)² + (3 - (-3))²) = 6

Since the opposite sides do not have the same length, the quadrilateral does not have congruent opposite sides.

3.) The diagonals bisect each other. True

To check whether the diagonals bisect each other, we can find the midpoint of each diagonal:

Midpoint of JL = ((-1 - 1)/2, (3 - 6)/2) = (-1,-1.5)

Midpoint of KM = ((2 - 4)/2, (0 - 3)/2) = (-1,-1.5)

Since the midpoints of JL and KM are the same point, (-1,-1.5), the diagonals bisect each other.

4.) One pair of opposite sides is parallel. False

As we determined in statement 1, none of the pairs of opposite sides are parallel.

5.) Both pairs of opposite sides are parallel. False

As we determined in statement 1, none of the pairs of opposite sides are parallel.

6.) At least one pair of opposite sides is both parallel and congruent. False

As we determined in statements 1 and 2, none of the pairs of opposite sides are both parallel and congruent.

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Answer: All the faces are rectangular.

Step-by-step explanation: A prism with three rectangular faces is called a rectangular prism. Therefore, the other faces are in the shape of rectangles.

according to the question the probabilities of event can be P(s)= 14/2525, P(C) = 6/2525, P(S and C) = 5/2525, P(S or C) = 3/505

Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.

given,

To solve the problem, we can use the formula:

P(A and B) equals P(A) plus P(B) minus P(A or B)

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A or B) is the probability of either A or B occurring (including the case where both A and B occur).

P(S): the probability that a student writes steak is 14/2525.

P(C): the probability that a student writes chicken is 6/2525.

The likelihood that a student would write steak plus chicken equals 5/2525.A or B. P(A and B) Equals P(A) +P(B), which -P(P(S or C))

P(S or C): the probability that a student writes steak or chicken can be calculated as:

P(S or C) = P(S) + P(C) - P(S and C)

= (14/2525) + (6/2525) - (5/2525)

= 15/2525

= 3/505

Therefore, the answers to the questions are:

P(S) = 14/2525

P(C) = 6/2525

P(S and C) = 5/2525

P(S or C) = 3/505

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The distance between the coordinates A and B is 2 √(10) units.

A mathematical method called the distance formula is used to determine how far apart two points in a coordinate plane are from one another. It can be used with any two points (x1, y1) and (x2, y2) and is based on the Pythagorean theorem.

d = √((x2 - x1)² + (y2 - y1)²)

where d is the separation of the two spots.

To put it another way, we may visualise a right triangle created by the two locations and the horizontal and vertical lengths separating them to get the distance between them. The triangle's hypotenuse, or the distance between its two points, is measured using the distance formula.

The distance formula is given as:

d = √((x2 - x1)² + (y2 - y1)²)

Now, for the given coordinates we have:

d = √((1 - (-5))² + (3 - 1)²)

d = √(6² + 2²)

d = √(40)

d = 2 √(10)

Hence, the distance between A and B is 2 √(10) units.

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As a result, the response is A .The number of dollars it costs to rent the bowling lane for 3 hours.

The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange It is a type of paper money, currency, and monetary unit used in the United States that is equivalent to 100 cents

The total cost (in dollars) for renting a bowling alley for x hours is represented by the function b(x) = 3x + 15.

We change x in the function to 3 to obtain b(3).

B(3) = 3(3) + 15 = 9 + 15 = 24 is the result.

Therefore, b(3) is the amount of money required to rent the bowling alley for three hours.

As a result, the response is A.

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If the orbital period of Saturn is 29.5 years then the distance of Saturn from the sun is 9.5 AU .

The orbital period of a planet is denoted as P.

A planet's distance from the sun in astronomical units is denoted as a.

The relation between orbital period of a planet and it's distance from the sun is given as,

P = a superscript three halves

or, P = a^3/2

The Saturn's orbital period is P= 29.5 years

Thus from the equation showing the relation between orbital period of a planet and it's distance from the sun in AU (astronomical units ) we get,

29.5 =  a^3/2

or, a^3/2 = 29.5

⇒  [tex]\sqrt{a^3}[/tex] = 29.5

Squaring both sides, we get,

⇒  [tex]a^{3}[/tex] = 870.25

⇒ a =  9.5473  

⇒ a = 9.5 (approximately)

Thus, the distance between Saturn and the sun is 9.5 AU (approximately) when the orbital period of Saturn is 29.5 years.

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The measurements of angle 1, angle 2, and angle 3 are 60, 76, and 44 and to verify the solution, we can add up all three angles and check that they add up to 180 degrees.

The given problem involves finding the value of angle 1, given the measurements of angles 2 and 3.

From the problem statement, we can determine that angle 2 is equal to 76 degrees, while angle 3 is equal to 44 degrees.

Using the fact that the sum of angles in a triangle is equal to 180 degrees, we can determine that angle 1 is equal to 180 minus the sum of angles 2 and 3.

angle 2 = 180 - angle TQR

= 180- 104 = 76

angle 3 = 180 - angle PRS

= 180- 136 = 44

Substituting the values of angles 2 and 3, we get the equation 180 - (76 + 44) = 60.

angle 1 = 180- (angle 2 + angle 3)

= 180- (120) = 60.

Therefore, angle 1 is equal to 60 degrees.

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The question is -

Find the measure of angle 1, angle 2, and angle 3.

-13<4x+7 First you have to apply the subtraction property of equality by subtracting 7 from both sides

-20<4x Then, you have to apply the division property of equality by dividing 4 from both sides

-5<x Finally, you'll get that x is greater than -5

The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

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.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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The train will have traveled option (C) 450 km from its starting point after 4 more hours at the same average speed.

The average speed of the train is given by the distance traveled divided by the time taken to travel that distance

average speed = distance ÷ time

Using this formula, we can find the average speed of the train:

average speed = 250 km ÷ 5 h = 50 km/h

Now that we know the average speed of the train, we can use it to calculate how far it will have traveled after another 4 hours:

distance = average speed × time

distance = 50 km/h × 4 h = 200 km

Therefore, the train will have traveled 250 km + 200 km = 450 km from its starting point after 4 more hours at the same average speed.

So, the answer is (C) 450 km.

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The expected count or value is used in the denominator of the formula for the chi-square test statistic.

In a chi-square test, the denominator is the expected frequency or count. Based on a theoretical or null hypothesis, the expected frequency reflects the number of observations that would be expected in each category. The observed-to-expected ratio is calculated using the denominator, which is then used to generate the chi-square statistic.

The total number of cases and controls in each category is the denominator in a chi-square test for independence. The expected frequency is computed by multiplying the row and column totals by the total sample size.

The whole population is the denominator in a chi-square test for goodness of fit, and the expected frequency is determined as the population percentage multiplied by the sample size.

Therefore, the value is used in the denominator of the formula for the chi-square test statistic is called as Expected count.

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The denominator of the formula for the chi-square test statistic is the expected count. The formula for the chi-square test statistic is (observed count - expected count)^2 / expected count, where the expected count is the value that is used in the denominator.

In the context of the chi-square test, the value used in the denominator of the formula for the chi-square test statistic is the "expected count". The chi-square test is used to determine whether there is a significant difference between the observed and expected frequencies in one or more categories.

The formula for calculating the chi-square test statistic is:

Χ² = Σ [(O - E)² / E]

where:
- Χ² is the chi-square test statistic
- O is the observed count for a category
- E is the expected count for that category
- Σ represents the sum over all categories

So, in this formula, you can see that the expected count (E) is used as the denominator.

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The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.

Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.

Then, we have:

x + y = 30 (total number of shots attempted)

Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:

x = 30 - y

Now, we can express Shenille's points in terms of x and y:

Points = 3x + 2y

Substituting x = 30 - y, we get:

Points = 3(30 - y) + 2y

Points = 90 - y

Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.

Total points scored = (0.2x)(3) + (0.3y)(2)

Substituting x = 30 - y, we get:

Total points scored = (0.2(30 - y))(3) + (0.3y)(2

Total points scored = 18 + 0.4y

Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:

y = 30 - x

Substituting this into the equation for total points, we get:

Total points scored = 18 + 0.4(30 - x)

Total points scored = 30 - 0.4x

This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:

Total points scored = 0 + 0.3(30)(2)

Total points scored = 18

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The question is -

In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?

(A) 12

(B) 18

(C) 24

(D) 30

(E) 36

Margin of error is equal to half of this width:

6.544 / 2 = 3.272

In a confidence interval, the margin of error is half of the width of the interval.

So, the width of the confidence interval is:

26.272 - 19.728 = 6.544

Margin of error is equal to half of this width:

6.544 / 2 = 3.272

Rounding to three decimal places, the margin of error is 3.272.

This means that the researchers are 99% confident that the true mean time for the medication to take effect falls between 19.728 and 26.272 minutes.

The margin of error tells us how much we can expect the sample mean (23 minutes) to differ from the true mean. So, we can say with 99% confidence that the true mean time it takes for the medication to take effect is within 3.272 minutes of the sample mean.

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(a) The correct trigonometric ratio to use is the tangent ratio (tan).

(b) The trigonometric equation is tan(17°) = Opposite/Adjacent.

(c) tan(17°) = Opposite/Adjacent

tan(17°) = 150/Adjacent

Adjacent = 150/tan(17°)

Adjacent = 150/0.3045

(2x+y)(4x²-2xy+y²)

Just replace a with 2x and b with y

The player with the highest percentage would be considered the best foul shooter among the group.

To determine which basketball player has the highest percentage in a foul shooting contest, you would need to know the number of foul shots each player attempted and the number of shots they made. The percentage can be calculated by dividing the number of shots made by the number of shots attempted and multiplying by 100.

For example, if Player A attempted 20 foul shots and made 16, their foul shooting percentage would be:

(16/20) x 100 = 80%

You would need to calculate the percentages for each player and compare them to determine who has the highest percentage.

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In a song the twelve days of christmas, my true love gave to me, then total number of possible gifts that my true love give me all together during the twelve days is equal to the 364.

We have There are twelve days of Christmas in a song and my true love gives me presents every day. We have to calculate total number of gifts my true love give me all together during the twelve days. Now, according to the song, on the first day of Christmas my true love gave me: a partridge on a pear tree 1 gift. On the second day of Christmas, my love really gave me: two doves and a gift. cake etc. Mathematically, gifts by true love are written as 1+2+3+... n gifts per day. Number of gifts per day: 1 to 1, 2 to 3, 3 to 6 and 4 to 10. The amount of mis N (N + 1) (N + 2) / 6. Number of parts This form is called tetrahedral number. Change the value N = 12, then N (N + 1) (N + 2) / 6

= 12 × 13 × 14 / 6

= 364

Hence, 364, the total number of gifts, almost one for each day of the year.

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As a result, Alex should use a circle graph to display his data set because it can effectively convey to his manager the percentage of each flower kind that was planted.

To visualise information and data, use a circle graph or pie chart. Typically, a circle graph is used to quickly and proportionately display the findings of an investigation.

A pie chart, often known as a circle chart, is a visual representation of the various values of a given variable or a means to summarise a set of nominal data. This kind of diagram consists of a circle with numerous segments.

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The probability of hitting the bull's-eye all three times when throwing darts can be calculated using the multiplication rule of probability as P(3 hits) = p x p x p = [tex]p^3[/tex],

where p is the probability of hitting the bull's-eye on each throw.

When throwing darts at a dart board, the probability of striking the bull's-eye is affected by many factors, such as the player's skill, the distance from the board, the type of dart used, and so on.

However, assuming that the probability of hitting the bull's-eye is the same for each throw and independent of previous throws;

We can calculate the probability of hitting the bull's-eye all three times using the multiplication rule of probability.

Suppose the probability of hitting the bull's-eye on each throw is p. Then, the probability of missing the bull's-eye on each throw is 1 - p.

The probability of hitting the bull's-eye all three times can be calculated as follows:

P(3 hits) = p x p x p = [tex]p^3[/tex]

For example, if p = 0.05 (or 5%), then the probability of hitting the bull's-eye all three times would be:

P(3 hits) = 0.05 x 0.05 x 0.05 = 0.000125 or 0.0125%

This means that the chance of hitting the bull's-eye all three times is very low, and it would require a lot of skill and luck to achieve such a feat.

However, the probability of hitting the bull's-eye at least once in three throws would be much higher, and it would depend on the player's skill and consistency.

Overall, the probability of hitting the bull's-eye all three times is quite low, and it is more likely that a player will hit it once or twice or miss it altogether.

Nonetheless, the thrill of the game lies in the challenge and the unpredictability of each throw, making darts a popular game of skill and chance.

Learn more about probability

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Answer:

3 and 8

Step-by-step explanation:

Ariana has = $21

Fix cost = $5

Each game ticket costs= $2.

Ticket number=g

Then,

[tex]$5 + 2g \leq 21$\\$$2g \leq 21-5$$\\$$g \leq 8$$[/tex]

then, the solution set is {0,1,2,3,4,5,6,7,8}