Can please someone help me asap? It’s due tomorrow. I will give brainliest if it’s all correct.

Please do part a, b, and c

The cost of the shirt, in dollars, after the 30% discount is $17.50.

What is discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.

If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:

30% of $25 = 0.30 x $25 = $7.50

The discount amount is $7.50, so the new price of the shirt after the discount is:

$25 - $7.50 = $17.50

Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.

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Tyler will need to score an 85 on Test 6 to finish the year with an average score of 75.

To calculate the score that Tyler needs to get on Test 6 to achieve an average score of 75, we need to use the following formula

(average score) = (total points earned / total number of tests)

Let's assume that Tyler has taken five tests so far, and his total points earned are X. Also, let's assume that Test 6 is worth Y points.

Therefore, the equation becomes:

75 = (X + Y) / 6

Multiplying both sides by 6, we get:

X + Y = 450

Now, let's say Tyler's scores on his first five tests are as follows

Test 1: 65, Test 2: 72, Test 3: 70, Test 4: 78 and Test 5: 80

To find out how many points Tyler has earned so far (X), we simply add up his scores on the first five tests

X = 65 + 72 + 70 + 78 + 80

X = 365

Substituting this value of X in the equation we derived earlier, we get

365 + Y = 450

Solving for Y, we get:

Y = 85

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The trigonometric ratios with respect to the angle C are:

sin(C) = 15/17, cos(C) = 8/17, tan(C) = 15/8, cosec(C) = 17/15, sec(C) = 17/8, cot(C) = 8/15

Trigonometric ratios are ratios of the sides of a right triangle used to calculate angles and side lengths.

The three main ratios are sine, cosine, and tangent, which are defined as the ratios of the opposite, adjacent, and hypotenuse sides.

Using the right triangle ABC, we can find the trigonometric ratios with respect to angle C:

sin(C) = opposite/hypotenuse = AB/AC = 15/17

cos(C) = adjacent/hypotenuse = BC/AC = 8/17

tan(C) = opposite/adjacent = AB/BC = 15/8

cosec(C) = 1/sin(C) = AC/AB = 17/15

sec(C) = 1/cos(C) = AC/BC = 17/8

cot(C) = 1/tan(C) = BC/AB = 8/15

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The angle G is (1/18) th {or (20/360)th } fraction of complete circle.

The angle G is measured to be 20°.

We know, the total angle of a complete circle is 360°.

Thus, by simple fraction we can say,

The angle G fraction of complete circle is = 20° / 360°

Simplifying we get, the angle G fraction of complete circle is = 1/18

Hence the angle G is (1/18 )th fraction of a complete circle.

In mathematical term, fractions are defined as a part of the whole. In other words, fraction is referred to the ratio of the value observing to the whole set of values.

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The area within the floor plan that Mutt can roam is determined as 37.7 m².

The total possible area that Mutt can roam is calculated as follows;

A = πr²

where;

A = π (6 m)²

A = 113.1 m²

The area outside the 120⁰ is calculated as follows;

θ = 360 - 120

θ = 240⁰

A = 240⁰/360 x 113.1 m²

A = 75.4 m²

The area that Mutt can roam is calculated as follows;

A = 113.1 m² - 75.4 m²

A = 37.7 m²

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The type of sampling the principal can use is systematic sampling.

Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in a university, you could survey a sample of 50 students.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval.

Therefore , with the definition of systematic sampling, it is best for the principal to use a method of systematic sampling for the procedure.

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Step-by-step explanation:

Each term goes UP by 4 from the one before it

 common difference,   d = 4

The expression simplified is 5³ = 125

Remember that in products the exponents add up and in quotients the exponents are reduced.

Then we can write the numeartor as:

5⁻³*5⁸ = 5⁻³⁺⁸ = 5⁵

Now the quotient becomes:

5⁵/5² = 5⁵⁻² = 5³

That is the expression simplified.

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Answer: A

Step-by-step explanation:

As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar

Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. To put it another way, profit is what is left over after all costs have been subtracted from revenue1.

For instance, if a business sells widgets for $100 apiece and the cost of production is $50 each widget, the profit would be $50. The business would make $10,000 in total income and incur $5,000 in total costs if it sold 100 widgets. There would be $5,000 in total profit.

Using the given equation y=-2x²+145x1051 we can utilise the procedures below to get the greatest profit the corporation may make:

1. Using the equation x = -b/2a, where a = -2 and b = 145, determine the x-coordinate of the parabola's vertex.

2. To determine the highest possible value of y, substitute this x value into the equation.

These actions result in:

x = -b/2a = -145/(2×(-2)) = 36.25

When we enter this x value into the equation, we obtain:

y = -2(36.25)² + 145(36.25) - 1051 ≈ $1,292

As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar.

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Answer:

Step-by-step explanation:

[tex]\sqrt{40}[/tex] = [tex]\sqrt{4}[/tex] x [tex]\sqrt{10}[/tex] = [tex]2\sqrt{10[/tex]

[tex]\frac{20}{2\sqrt{10} }[/tex] = [tex]\frac{10}{\sqrt{10} }[/tex]

[tex]\frac{10}{\sqrt{10} } * \frac{\sqrt{10} }{\sqrt{10} } = \frac{10\sqrt{10} }{10} = \sqrt{10} }[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{2} }{2}[/tex]

From the above since [tex]\frac{20}{\sqrt{40} }[/tex]   is not equal to  [tex]\frac{1}{\sqrt{2} }[/tex] it implies that they are not the same

Answer: H(t) = -16t^2 + vt + h

Step-by-step explanation:

The equation that models the height of a ball hit straight up in the air from a certain height from the ground is given by:

H(t) = -16t^2 + vt + h

where H(t) is the height of the ball at time t, v is the initial velocity of the ball, and h is the initial height of the ball.

The equation you provided is incomplete. Could you please check and provide me with the correct equation so that I can help you better?

The null hypothesis for this test is that the 2 groups will not differ in terms of their suggested sentences.

The null hypothesis is a statement that there is no difference between the two populations or variables being tested.

It can be thought of as the "default" position, which assumes that any observed difference is due to chance.

The null hypothesis is usually written in a way that it can be tested and rejected or not rejected through statistical analysis.

The null hypothesis for this test is that the two groups will not differ in terms of their suggested sentences.

This means that any difference between the groups in their suggested sentences is due to chance and not a difference in the population or variables being tested.

This hypothesis can be tested and rejected or not rejected through statistical analysis.

If the two groups do differ in their suggested sentences then the null hypothesis will be rejected and it will be concluded that the difference is not due to chance but rather due to a difference in the population or variables being tested.

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Answer:

Jar 2 has the greatest unit price. B is correct.

Step-by-step explanation:

Jar 1: $1.60/16 oz = 10¢/ounce

Jar 2: $2.40/20 oz = 12¢/ounce

Jar 3: $2.64/24 oz = 11¢/ounce

Jar 4: $2.88/32 oz = 9¢/ounce

Jar 2 has the greatest unit price, so the correct answer is B.

The coordinates for PLUTO are P(3,2), L(5, -2), U(1, -6), T-3, -2) and O(-1, 1)

When a figure is rotated 90 degrees clockwise about the origin, its new coordinates are found by switching the x and y values of each point and then negating the new x value. This means that if a point had coordinates (x, y) in the original figure, its new coordinates in the rotated figure would be (-y, x).

Using this information, we can find the coordinates of each vertex of PLUTO by working backwards from the coordinates of the vertices of P'L'U'T'O'. For example, the coordinates of P can be found by negating the y-coordinate of P' and switching the x and y values. Applying this formula to P'(2,-3) gives us P(3,2).

Similarly, the coordinates of L can be found by negating the y-coordinate of L' and switching the x and y values. Applying this formula to L'(-2,-5) gives us L(5,-2).

Then for the other coordinates are calculated based on then we get the following,

U'(-6,-1) is U(1, -6)

T'(-2,3) is (-3, -2)

and O'(1,1) is (-1, 1).

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If we shuffle a deck of cards ,turn over first card, then

(a) "Sample-Space" of this experiment is set of all 52 cards.

(b) Number of outcomes in event that the first card is a heart is 13 .

Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.

In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).

So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".

Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.

In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).

Therefore, there are 13 outcomes in the event .

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The given question is incomplete, the complete question is

Shuffle a deck of cards and turn over the first card.

(a) What is the sample space of this experiment?

(b) How many outcomes are in the event that the first card is a heart?

Welch's two-sample t-test indicates that the average of Load Return's population is significantly greater than the average of No Load Return's population, with a large effect size.

The null hypothesis (H0) that the two population means are equal is rejected as the p-value (0.005) is less than the chosen significance level (α=0.05). This indicates that the chance of a Type 1 error is small, and the alternative hypothesis (H1) that the average of Load Return's population is greater than the average of No Load Return's population is supported.

The test statistic (T=-2.646) falls outside the 95% critical value accepted range, which further supports the rejection of H0. The effect size (0.68) is considered large, indicating that the difference between the two population means is substantial.

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Complete Question:

use the 60 mutual funds in the table below to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)

Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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a. The dimensions that maximize the area of the pen are 33 meters by 100 meters.

b. The dimensions of each rectangular pen that minimize the amount of fence used are 10sqrt(2) meters by 10sqrt(2) meters.

a. To maximize the area of the rectangular pen, we need to find the dimensions that use up all 200 meters of fencing, except for the side that is against the barn. Let the length of the pen be x and the width be y. Then we have:

Perimeter of the pen = 2x + y = 200 - x (since one side is against the barn)

Simplifying this equation, we get:

3x + y = 200

Area of the pen = xy

Now we can express y in terms of x using the equation above:

y = 200 - 3x

Substituting this into the expression for area, we get:

A(x) = x(200 - 3x) = 200x - 3x^2

To maximize the area, we need to find the value of x that makes A(x) as large as possible. We can do this by taking the derivative of A(x) with respect to x and setting it equal to 0:

A'(x) = 200 - 6x

200 - 6x = 0

x = 33.33

Since we can't have a fractional length, we choose x = 33 meters (rounded to the nearest meter). Then y = 200 - 3x = 100 meters.

b. Let the dimensions of each rectangular pen be x and y. Then we have:

Area of each pen = xy = 100

Perimeter of each pen = 2x + 2y

We want to minimize the amount of fence used, which is equal to the total perimeter of all four pens. So, we need to find the dimensions that minimize the total perimeter subject to the constraint that the area of each pen is 100. We can use Lagrange multipliers to solve this problem:

L(x, y, λ) = 2x + 2y + λ(xy - 100)

Taking the partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2 + λy = 0

∂L/∂y = 2 + λx = 0

∂L/∂λ = xy - 100 = 0

Solving these equations simultaneously, we get:

x = y = sqrt(200/λ)

xy = 100

Substituting the first equation into the second equation, we get:

sqrt(200/λ)^2 = 100

λ = 2

Substituting λ = 2 back into the first equation, we get:

x = y = sqrt(200/λ) = 10sqrt(2)

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The length of AC using the laws of sines is 29.5 inches

We can use the law of sines to solve this problem.

The law of sines states that in any triangle ∆ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

In this case, we know that m<A = 33°, m<C = 58°, and AB = 25 in.

We need to find AC, which is opposite to angle A.

Let's use the law of sines to solve for AC:

AC/sin(B) = AB/sin(C)

Where

B = 180 - 33 - 58

B = 89

So, we have

AC/sin(89°) = 25/sin(58°)

This gives

AC = 29.5 in. (rounded to the nearest tenth)

Therefore, the answer is 29.5 inches

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Answer:

B

B

A

B

D

C

Step-by-step explanation:

5. B

65 = teachers

15 = principal

65/80 = 81.25

If there's is a total of 900 people, find 81.25 (number of teachers)

=731.25

=731

6. B

The best graphical representation for the teacher's data would be a histogram. A histogram is a graph that displays the distribution of continuous data, such as the number of students who prefer a particular subject. It shows the frequency of each interval, or bin, of values.

A stem-and-leaf plot is typically used for small datasets and displays each data point. A circle graph, also known as a pie chart, is used to show how different parts make up a whole and is not appropriate for showing the distribution of preferences among the students. A box plot, also known as a box-and-whisker plot, is used to display the distribution of data, but it may not be as useful for showing the specific frequencies of each preference as a histogram would be.

7) A

There's an image for it I attached

8) B

The correct circle graph that represents the data in the table is option B) circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

In the given table, the number of visitors for each type of transportation is given. To create a circle graph, we need to convert the given numbers to percentages. Then, we can use these percentages to determine the angle of each section in the circle graph.

Using the given numbers, we can calculate the percentage of visitors for each transportation type as follows:

Walk: (120/300) x 100 = 40%

Bicycle: (24/300) x 100 = 8%

Car Service: (45/300) x 100 = 15%

Bus: (30/300) x 100 = 10%

Subway: (81/300) x 100 = 27%

Option B) correctly represents these percentages in a circle graph.

9) D

The best prediction about the scoops of ice cream the college will need is option D) The college will have about 1,440 students who prefer ice cream.

To make this prediction, we need to use the information given in the table and assume that the entire student body has the same preferences as the sample of 225 students.

According to the table, 81 out of 225 students prefer ice cream.

To estimate the number of students who prefer ice cream in the entire student body of 4,000 students, we can use proportions.

81/225 = x/4000

Multiplying both sides by 4000, we get:x = 81/225 x 4000 = 1,440

Therefore, the college will have about 1,440 students who prefer ice cream, and they will need to prepare that many scoops.

10) C

The drive-thru that typically has more wait time is option C) Super Fast Food, because it has a larger median.

The median is the middle value when a set of data is arranged in order. In this case, the median wait time for Super Fast Food is 12 minutes, and the median wait time for Burger Quick is 15.5 minutes.

This means that half of the customers at Super Fast Food waited less than 12 minutes, while half of the customers at Burger Quick waited less than 15.5 minutes.

Therefore, the wait time at Super Fast Food is typically shorter than at Burger Quick.

The mean, on the other hand, is influenced by outliers or extreme values, and it is not as robust a measure of central tendency as the median. Therefore, we cannot determine which drive-thru typically has more wait time based on the mean alone.

Iam do not understand what do you mean 1335690964225753897426908224 1335690964225753897426908224 88 9 109 250 10 10 XL 220 10 10 30 250 30 30 30 400

The appropriate correlational technique when the underlying distribution of interval scores is violently skewed would be:

b. Spearman's rank correlation coefficient

When the distribution of interval scores is violently skewed, meaning that the data is not normally distributed and may have extreme values or significant departures from normality, Pearson's correlation coefficient (option a) may not be appropriate as it assumes a linear relationship between variables and normality of data.

Instead, Spearman's rank correlation coefficient (option b) is a more appropriate choice. Spearman's rank correlation coefficient is a non-parametric method that does not assume normality of data and is based on the ranks of data rather than the actual values. It measures the strength and direction of monotonic association between variables, making it suitable for data that may not meet the assumptions of Pearson's correlation coefficient.

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Complete Question

When the underlying distribution of interval scores is violently skewed, the appropriate correlational technique should be:

a. Pearson's correlation coefficient

b. Spearman's rank correlation coefficient

c. Kendall's tau

d. Point-biserial correlation coefficient

e. Phi coefficient

The appropriate correlational technique when the underlying distribution of interval scores is violently skewed depends on the type of data and the research question, and may include non-parametric tests such as Spearman's rank correlation coefficient.

When the underlying distribution of interval scores is violently skewed, the appropriate correlational technique depends on the type of data and the research question.

If the data is bivariate (two variables) and both variables are continuous, then the appropriate correlational technique would be Spearman's rank correlation coefficient, which is a non-parametric test that measures the strength and direction of the association between two variables.

Spearman's rank correlation coefficient is used when the data is not normally distributed or when the relationship between the variables is not linear.

On the other hand, if one or both of the variables are dichotomous or categorical, then a different correlational technique may be more appropriate.

For example, if one variable is dichotomous and the other is continuous, a point-biserial correlation coefficient may be used.

If both variables are categorical, a chi-square test of independence or Cramer's V may be used.

It is important to note that the appropriateness of a particular correlational technique depends on the specific characteristics of the data and research question.

Therefore, it is recommended to consult with a statistician or data analyst to determine the most appropriate technique for a particular study.

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The method that uses an arithmetic mean to forecast the next period is "moving averages".

The method that uses an arithmetic mean to forecast the next period is the "moving averages" method.

In this method, the average of the past observations is calculated, and this average is used as the forecast for the next period.

The number of past observations used in the calculation of the moving average depends on the specific variant of the method being used.

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The probability of selecting two marbles with the same color is approximately 0.27 or 27%.

To work out the likelihood that the two marbles drawn have similar variety, we can utilize the accompanying advances:

In the first place, we compute the likelihood of drawing a red marble on the principal pick: 12/24 = 1/2.

On the off chance that the main marble drawn is red, there will be 11 red marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more red marble on the subsequent pick is 11/23.

Likewise, in the event that the principal marble drawn is blue, there will be 4 blue marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more blue marble on the subsequent pick is 4/23.

Furthermore, on the off chance that the main marble drawn is yellow, there will be 6 yellow marbles left taken care of, out of a sum of 23 marbles. So the likelihood of drawing one more yellow marble on the subsequent pick is 6/23.

To get the complete likelihood of drawing two marbles of similar variety, we want to add the probabilities of every one of these cases:

(1/2) x (11/23) + (5/24) x (4/23) + (7/24) x (6/23) = 55/138 or roughly 0.398 or 39.8%.

In this way, the likelihood of drawing two marbles of a similar variety is roughly 39.8%.

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The inference engine in an expert system will use both forward and backward chaining as needed to manipulate the rules and make decisions based on the available data and the desired outcome.

To address your question concisely:
The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the Inference Engine.
An expert system is composed of three primary components: the Knowledge Base, the Inference Engine, and the User Interface.

The Knowledge Base contains the domain-specific facts and rules that the system relies on to solve problems.

The User Interface facilitates communication between the user and the system.
The Inference Engine is responsible for reasoning and drawing conclusions based on the knowledge stored in the Knowledge Base.

It applies logical techniques such as forward and backward chaining to manipulate and evaluate rules.
In forward chaining, the Inference Engine begins with the available data and applies rules to deduce new information or conclusions.

This approach is data-driven, as it starts with facts and moves towards conclusions.
In backward chaining, the Inference Engine starts with a goal or hypothesis and works backward to find supporting evidence or facts.

This approach is goal-driven, as it begins with a desired conclusion and looks for rules that can lead to it.
By employing both forward and backward chaining, the Inference Engine is able to effectively analyze and manipulate rules to provide accurate and reliable solutions to problems within the domain of the expert system.

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By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.

The inference engine component of an expert system uses forward and backward chaining to manipulate a series of rules. Forward chaining involves starting with initial data and applying rules to draw a conclusion, while backward chaining involves starting with a goal and working backward to find the necessary data and rules to reach that goal.

By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.

The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the "inference engine". The inference engine applies logical reasoning to deduce new information based on the provided facts and rules in the knowledge base, ultimately assisting in problem-solving and decision-making processes.

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Use an independent samples t-test to compare annual household income between homeowners and renters, considering within-group variability and determining statistical significance.

To look at the distinction in the normal yearly family pay between the people who own their own homes and the individuals who lease, a suitable factual test to utilize would be an autonomous examples t-test.

This test is utilized to think about the method for two autonomous gatherings, for this situation, the gathering of property holders and the gathering of tenants.

As the family pay is estimated on a proportion scale, the t-test can be utilized to decide whether there is a huge distinction in the method for the two gatherings, considering the changeability inside each gathering.

The consequences of the t-test will give a p-esteem, which can be utilized to decide the factual meaning of any distinctions tracked down between the two gatherings.

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Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

The probability of getting 1, 2, or 3 at the most 9 times after rolling a fair die 12 times is given by 0.9807.

Probability that 1, 2, or 3 is rolled at most 9 times,

Consider all the possible outcomes of rolling a fair die 12 times.

Count the number of outcomes where 1, 2, or 3 is rolled at most 9 times.

Use the complementary probability,

Probability that 1, 2, or 3 is rolled more than 9 times,

Then subtract that probability from 1 .

Let X be the number of times 1, 2, or 3 is rolled in 12 rolls.

Then X follows a binomial distribution with n=12 and p=1/2,

Since there are 3 favorable outcomes out of 6 possible outcomes on each roll.

The probability that 1, 2, or 3 is rolled more than 9 times can be calculated as follows,

P(X > 9) = P(X = 10) + P(X = 11) + P(X = 12)

= (¹²C₁₀) (1/2)^10 (1/2)^2 + (¹²C₁₁) (1/2)^11 (1/2)^1 + (¹²C₁₂) (1/2)^12 (1/2)^0

= 66/2^12 + 12/2^12 + 1/2^12

= 79/2^12

Probability that 1, 2, or 3 is rolled at most 9 times is,

P(X ≤ 9)

= 1 - P(X > 9)

= 1 - 79/2^12

= 4017/2^12

Rounding this to four decimal places gives,

P(X ≤ 9) ≈ 0.9807

Therefore, the probability that 1, 2, or 3 is rolled at most 9 times is approximately 0.9807.

Learn more about probability here

brainly.com/question/11075616

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