Probability and likelihood

a team of scientists is studying the animals at a nature reserve. They capture the animals, mark them so they can identify each animal, and then release them back into the park. The table gives the number of animals they’ve identified. Use this information to complete the two tasks that follow.


animal total in park number marked

elk 5,625 225

wolf 928 232

cougar 865 173

bear 1,940 679

mountain goat 328 164

deer 350 105

moose 215 86

part a

what is the probability of the next elk caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.



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part b

describe the likelihood of the next elk caught being unmarked.



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part c

describe a simulation that you can use to model this situation.



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part d

what is the probability of the next wolf caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.



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part e

describe the likelihood of the next wolf caught being unmarked.



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part f

describe a simulation that you can use to model this situation. The simulation should be different from the one in part c.



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part g

in the unit, you found the probability of a compound event by identifying the sample space. However, it is also possible to find the probability of a compound event without finding the sample space. To do this, multiply the probability of the first event by the probability of the second event. For example, the probability of flipping heads twice on a coin is. Using this idea, what is the probability that the next cougar and bear caught will both be unmarked?



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part h

describe the likelihood that the next cougar and bear caught are both unmarked.



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part i

describe a simulation that you can use to model this event.



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part j

using the method described in part g, what is the probability that the next mountain goat, deer, and moose caught are all unmarked?



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part k

describe the likelihood that the next mountain goat, deer, and moose caught are all unmarked.



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part l

describe a simulation that you can use to model this event. Your simulation should be different from the one in part i.



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The area of ΔRST, to the nearest square inch is,

Area = 29,17,735.54 square inches

We have,

In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.

Apply sine rule formula,

sin S / s = sin T / t

sin 8° / 990 = sin 60° / t

0.14 / 990 = 0.87 / t

0.14t = 990 x 0.87

0.14t = 861.3

t = 6,152 inches

Here, ∠R = 180° - (8 + 60)°

∠R = 180 - 68

∠R = 112°

sin S / s = sin R / r

sin 8° / 990 = sin 112° / r

0.14 / 990 = 0.92 / r

0.14r = 0.92 x 990

0.14r = 910.8

r = 910.8 / 0.14

r = 6505 inches

We use the formula

Heron's formula = √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

Solving for s

s = 990 + 6505 + 6,152 /2

s = 6823.5

Solving for the area of the triangle

= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)

= √6823.5 x 5833.5 x 671.5 x 318.5

= 29,17,735.54 square inches

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The answer is "No they are not similar". The correct option is D.

To determine if the two cuboids are similar, we need to check if their corresponding sides are proportional.

If we compare the corresponding sides of the first cuboid and the second cuboid, we get:

6/10 = 0.6

8/12 = 0.666...

6/10 = 0.6

Since these ratios are not equal, the corresponding sides are not proportional, and therefore the two cuboids are not similar.

Therefore, the answer is "No they are not similar".

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The measure of angle m<BEC is 80 degrees

From the information shown, we have that;

m< AD = 120 degrees

m< BC = 80 degrees

To determine the value of m<BEC, we need to know that it is a minor arc in the circle.

Also, a minor arc is described as the shorter arc that connects two endpoints on a circle.

The measure of a minor arc is less than 180° , and  is equal to the measure of the arc's central angle.

We can see than the angle measure of m<BC = m<BEC

Then,

m<BEC = 80 degrees

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The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

We have,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l

where:

a and b are the lengths of the two parallel sides (the bases) of the trapezoid

h is the height of the trapezoid (the perpendicular distance between the two bases)

l is the length of the prism (the distance between the two trapezoidal faces)

Now,

a = 9

b = 12

l = 15

Height h can be calculated using the Pythagorean theorem.

15² = (12 - 9)² + h²

h² = 225 + 9

h² = 234

h = √234

h = 15

Now,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15

V = 2362.5

And,

The surface area (A) of a trapezoidal prism can be calculated using the formula:

A = ph + 2B

where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.

So,

p = 12 + 8 + 12 + 8 = 44

h = 15

B = 12 x 8 = 96

Now,

Total surface area​.
= 44 x 15 + 2 x 96

= 660 + 192

= 852

Thus,

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

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John threw the javelin 3 standard deviations below the mean

An equation is an expression that shows how numbers and variables using mathematical operators.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that John threw 106 feet. The average throw was 130 ft. The standard deviation was 8 feet. Hence:

z = (106 - 130) / 8

z = -3

John threw 3 standard deviations below the mean

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The surface area of the pyramid is 390.8 cm².

The surface area of the triangular pyramid is calculated as follows;

S.A = base area   +  ¹/₂ (perimeter + slant height)

The height of the pyramid is calculated by applying Pythagoras theorem;

h = √ (28²  -  14²)

h = 24.2 cm

Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²

The surface area of the pyramid is calculated as follows;

S.A = 338.8 cm²  + ¹/₂ (76 cm + 28 cm)

S.A = 390.8 cm²

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Answer:

1,425

Step-by-step explanation:

I got this one correct

1. All square, upper triangular matrices are diagonalizable. (TRUE)

2. If a matrix is diagonalizable, then it is invertible. (FALSE)

1. True: All square, upper triangular matrices are diagonalizable.

A square matrix is diagonalizable if it can be transformed into a diagonal matrix by a similarity transformation, which means there exists an invertible matrix P such that P^-1 * A * P is a diagonal matrix. Upper triangular matrices have all their elements below the main diagonal equal to zero.

Since the eigenvalues of an upper triangular matrix are equal to its diagonal elements, we can form a diagonal matrix with these eigenvalues. Since there exists such a diagonal matrix, all square, upper triangular matrices are diagonalizable.

2. False: If a matrix is diagonalizable, it is not necessarily invertible

Diagonalizable matrices can be transformed into a diagonal matrix with the eigenvalues along the main diagonal.

However, invertibility requires that the matrix have a nonzero determinant, which means that all of its eigenvalues must be nonzero.

If a diagonalizable matrix has a zero eigenvalue, its determinant will be zero, and it will not be invertible. Therefore, diagonalizability does not guarantee invertibility.

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Answer:  In order least to greatest, our answer would be-

2.704 ,  2.74  ,  4.2  , 4.27  ,  4.72

.70 is less than .74. In the second set of numbers .2 is less than .27, while they are all less than .72, which gives us the number arrangement above.

I hope this helped & Good Luck!!!

Answer: The answer is 2.704, 2.74, 4.2, 4.27, 4.72

Step-by-step explanation:

According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

Hence, We get;

228 x 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 x 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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Answer:

The equation of a circle with center (a,b) and radius r is given by:

(x - a)² + (y - b)² = r²

Comparing this to the equation x² + y² = 12², we can see that the center of the circle is (0,0) and the radius is 12. Therefore, the radius of the circle is 12 units.

The detail that adds tension to the rising action of the story is when Mother Wolf tells Mowgli that some day he will have to kill Shere Khan.

This statement introduces a sense of conflict and foreshadows a significant challenge that Mowgli must face in the future. The idea of Mowgli, a young boy raised by wolves, confronting and defeating the powerful and dangerous Shere Khan adds suspense to the story, as readers anticipate the eventual showdown between these two characters.

Other details, such as Mowgli growing stronger and learning life lessons, or Mowgli forgetting his mother's advice, are relevant to his character development, but do not contribute as directly to the story's tension. Similarly, Mowgli considering himself a wolf and lacking the ability to speak like a human reflects his unique upbringing, but does not add tension in the same way as the impending confrontation with Shere Khan.

In conclusion, Mother Wolf's warning about Mowgli's future encounter with Shere Khan adds tension to the rising action of the story, as it sets up an exciting and challenging conflict for the protagonist to face, capturing the reader's interest and anticipation.

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Answer:

C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.

The probabilities are given as follows:

a) Square: 1/6.

b) Not the triangle: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The area of the rectangle is given as follows:

A = 12 x 8 = 96.

(area of rectangle, multiply the dimensions).

The areas of each figure are given as follows:

Hence the probability of the square is given as follows:

p = 16/96 = 1/6.

(area of square divided by total area).

The probability that the region is not the triangle is given as follows:

p = (96 - 10)/96

p = 86/96

p = 43/48.

(triangle and not triangle are complementary events).

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If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.

To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.

Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:

tan(5) = 119/x

tan(18) = 119/y

We can solve for x and y by isolating them in each equation:

x = 119/tan(5) ≈ 1343.44 feet

y = 119/tan(18) ≈ 370.79 feet

Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.

We rounded the final answer to the nearest foot, which is 973 feet.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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The value of x in the given circle is 13.9.

Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,

Using the inscribed angle theorem,

It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.

So,

m ∠CFE = arc CE / 2

57 = 10x-25 / 2

10x-25 = 114

10x = 139

x = 13.9

Hence the value of x in the given circle is 13.9.

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The triangle that will always have the same area, no matter how it is drawn, is a right triangle that has two 45° angles. The correct answer is option A

This is because any right triangle with two 45° angles is a special type of triangle called an isosceles right triangle. In an isosceles right triangle, the two legs are congruent, which means they have the same length. Therefore, no matter how the triangle is drawn, its area will always be the same.

To see why this is true, let's use the formula for the area of a right triangle:

Area = (base x height) / 2

In an isosceles right triangle, the base and height are congruent, so we can write:

Area = (leg x leg) / 2

Simplifying this expression, we get:

Area = (leg^2) / 2

Since the legs of an isosceles right triangle are congruent, we can substitute leg for both legs in the formula:

Area = (leg^2) / 2 = (leg x leg) / 2

No matter how the triangle is drawn, the legs will have the same length, so the area of the triangle will always be the same.

Therefore, the correct answer is option A, a right triangle that has two 45° angles.

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The outcome with a frequency closest to its expected frequency is C (3).

In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.

To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.

Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.

Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.

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Answer:

pls mrk me brainliest (⁠・⁠(⁠ｪ⁠)⁠・⁠）

The sculpture was worth £332.80 three years ago when it depreciates by 20% each year

To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.

First, we need to calculate how much the sculpture would be worth after one year of depreciation:

650 - (0.20)(650) = 520

This means that after the first year, the sculpture would be worth £520.

Next, we can calculate the value of the sculpture after the second year of depreciation:

520 - (0.20)(520) = 416

After two years, the sculpture would be worth £416.

Finally, we can calculate the value of the sculpture after the third year of depreciation:

416 - (0.20)(416) = 332.8

Therefore, the sculpture was worth £332.80 three years ago.

To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:

650 = x[tex](1-0.20)^{2}[/tex]

Simplifying this equation, we get:

x = 650 / [tex]0.80^{2}[/tex] = 332.80

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The probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.

Probability refers to the likelihood or chance of an event occurring. In this scenario, we are interested in finding the probability that all four shirts selected from the box of 24 will be regular size.

To determine this probability, we first need to find the total number of ways in which we can select four shirts from the box. This is known as the sample space and can be calculated using the combination formula, which is nCr = n!/(r!(n-r)!). In this case, we have 24 shirts and are selecting four, so the sample space is 24C4 = (24!)/(4!(24-4)!) = 10,626.

Next, we need to find the number of ways in which we can select four regular shirts from the 15 available. This can be calculated using the same combination formula, which is 15C4 = (15!)/(4!(15-4)!) = 1,455.

Finally, we can calculate the probability of selecting all four regular shirts by dividing the number of favorable outcomes (i.e., selecting four regular shirts) by the total number of possible outcomes (i.e., the sample space). So, the probability of selecting all four regular shirts is 1,455/10,626 = 0.1367 or 13.67%.

Therefore, the probability that all four shirts selected from the box of 24 will be regular size is 0.1367 or 13.67%.

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The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84

Also, the number of ways is 30045015

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

¹²C₁₁

The formula for combination is

ⁿCₓ = n!/[(n - x)! * x!]

So, we have

¹²C₁₁ = 12!/[(12 - 11)! * 11!]

Evaluate

¹²C₁₁ = 12

Using the above as a guide, we have the following:

¹²C₁₀ = 12!/[(12 - 10)! * 10!]

¹²C₁₀ = 66

¹²C₅ = 12!/[(12 - 5)! * 5!]

¹²C₅ = 792

¹²C₁ = 12!/[(12 - 1)! * 1!]

¹²C₁ = 12

¹²C₁₂ = 12!/[(12 - 12)! * 12!]

¹²C₁₂ = 1

⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]

⁵C₄ + ⁵C₃ = 15

⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]

⁵C₃/⁵C₂ = 1

4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]

4⁷C₂ = 84

For the number of ways to get people hired, we have

n = 30

x = 10

So, we have

³⁰C₁₀ = 30!/[(30 - 10)! * 10!]

³⁰C₁₀ = 30045015

Hence, the number of ways to get them hired is 30045015 ways

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The coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j

The coordinates of point j' after rotating point jkl 90° clockwise around the origin can be found by applying the following transformation:

j' = (cos(90°) * x - sin(90°) * y, sin(90°) * x + cos(90°) * y)

Since we are rotating 90° clockwise around the origin, we have cos(90°) = 0 and sin(90°) = 1, so the transformation simplifies to:

j' = (0 * x - 1 * y, 1 * x + 0 * y)

j' = (-y, x)

Therefore, the coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j.

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The probability of the normal distribution with given mean and standard deviation representing average content in the selected bottles is smaller than 102.1 mL is equal to 0.9878.

Distribution of the sample means of a normal distribution ,

Mean μ = 101.5 mL

Standard deviationσ = 1.6 mL

sample size n = 36

For normal distribution,

Standard deviation of the sample means is,

σ/√n

= 1.6/√36

= 0.2667 mL

Probability that the average content in the selected bottles is smaller than 102.1 mL,

Standardize the sample mean using the formula,

z = (X- μ) / (σ/√n)

where X is the sample mean.

Substituting the values, we get,

⇒z = (102.1 - 101.5) / (0.2667)

⇒ z = 2.25

Using a standard normal distribution table ,

Probability of a z-score being less than 2.25 is approximately 0.9878.

Therefore, the probability that the average content in the selected bottles is smaller than 102.1 mL is approximately 0.9878.

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Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

a. Relevant parameter: the difference between actual and scheduled arrival time.

Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.

Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

b. Sample mean for Delta Air Lines: -2.31 minutes

Sample mean for United Air Lines: -4.01 minutes

Difference in sample means: -1.70 minutes

c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.

d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider

Delta over United.

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When the price of the new product is $9.25, the demand for the product is 200 units.

The quantity of a specific commodity or service that consumers are willing and able to buy at a specific price and time is referred to as demand. It stands for consumers' willingness and capacity to pay for a good or service.

The demand for a new product at a price of x dollars is denoted by the notation D(x). So, the notation D(9.25) represents the demand for the new product when the price is $9.25. According to the given information, D(9.25) = 200.

Therefore, we can interpret this as: when the price of the new product is $9.25, the demand for the product is 200 units.

D(9.25) = 200

where D(x) represents the demand for the new product when the price is x dollars. We substitute x = 9.25 into the equation to find the demand when the price is $9.25, which is 200 units.

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The statements true of the two-dimensional plane sections that could result from one of these slices made by Misha are B, C, D, E, and F.

A. False. The only two-dimensional plane sections that could result from slicing a cube with a plane are squares or rectangles, but not triangles.

B. True. A plane section that is square could result from one of these slices through the cube.

C. True. A plane section that is rectangular but not square could result from one of these slices through the cube.

D. True. A plane section that is triangular could result from one of these slices through the pyramid.

E. True. A plane section that is square could result from one of these slices through the pyramid.

F. True. A plane section that is rectangular but not square could result from one of these slices through the pyramid.

Therefore, the correct statements are B, C, D, E, and F.

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The union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.

Given that, A={x|x is an odd number greater than 0 and less than 10} and B={2, 3, 4, 5, 6}.

Here, set A={1, 3, 5, 7, 9}

Now, A∪B = {1, 3, 5, 7, 9}∪{2, 3, 4, 5, 6}

= {1, 2, 3, 4, 5, 6, 7, 9}

Therefore, the union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.

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The sine function for the graph is given as follows:

y = sin(3x).

(a one should be placed on the green blank).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

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