almost every year, there is some incidence of volcanic activity on the island of japan. in 2005 there were 5 volcanic episodes, defined as either eruptions or sizable seismic activity. suppose the mean number of episodes is 2.4 per year. let x be the number of episodes in the next two years. an appropriate model to use for x is

Answers

Answer 1

The mean number of volcanic episodes on the island of Japan is 2.4 per year. This means that, on average, we can expect 2-3 volcanic episodes each year. However, in 2005 there were 5 volcanic episodes which were either eruptions or sizable seismic activity.


To predict the number of volcanic episodes in the next two years, we can use the Poisson distribution, which is a commonly used model for predicting the frequency of rare events. The Poisson distribution assumes that the number of events in a fixed period of time is independent and occurs at a constant rate.

Using this model, we can calculate the probability of having different numbers of volcanic episodes in the next two years. For example, the probability of having exactly 2 volcanic episodes in the next two years can be calculated using the formula:

P(X=2) = (e^-4.8 * 4.8^2) / 2!

Where e is the mathematical constant 2.71828, X is the number of volcanic episodes, and 4.8 is the expected number of episodes in two years (2.4 * 2). The result is approximately 0.168, or a 16.8% chance of having exactly 2 episodes in the next two years.

Similarly, we can calculate the probabilities of having more or fewer episodes using the same formula. This can be useful for predicting the likelihood of different scenarios and planning for potential hazards.

In conclusion, the appropriate model to use for predicting the number of volcanic episodes in the next two years is the Poisson distribution. This model assumes that the events are rare, independent, and occur at a constant rate. By using this model, we can calculate the probabilities of different scenarios and plan accordingly.

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Related Questions

Valentina made a scale drawing of a house and its lot. In real life, the porch is 20 feet wide. It is 38 inches wide in the drawing. What is the scale of the drawing?

Answers

Answer:Therefore, the scale of the drawing is 1 inch : 3.166 feet.

Step-by-step explanation:

To find the scale of the drawing, we need to determine the ratio of the size of the porch in the drawing to its actual size.

First, we need to convert 38 inches to feet:

38 inches ÷ 12 inches/foot = 3.1667 feet

Next, we can set up a proportion:

drawing size / actual size = scale factor

Let x be the scale factor. Then:

x / 20 feet = 3.1667 feet / 20 feet

Simplifying the right side:

3.1667 feet / 20 feet = 0.1583

Multiplying both sides by 20 feet:

x = 0.1583 × 20 feet

x = 3.166 feet

Therefore, the scale of the drawing is 1 inch : 3.166 feet.

Can someone give me an answer and show your work on this I don't understand, I'll give brainliest

Answers

Answer: No it is not up to code

Step-by-step explanation:

So we can use trig ratios to solve this:

tan theta = 3.5/40

.: theta = arctan(3.5/40)

theta is about 5

Since 5 > 4.8, these dimensions do not comply with regulation.

Use the formula to find the surface area of the figure. Show your work.

Answers

Answer:

S = 4π(7^2) = 196π square inches

= about 615.75 square inches


Determine the size of the sample space (number of possible outcomes) for the experiment below:

Rolling a fair 6-sided die two
times
The sample space has how many
possible outcomes

Answers

The number of possible outcomes is 36.

Given that a 6-sided die has been rolled twice we need to find the sample space has how many possible outcomes,

Therefore, in one roll there will be 6 outcomes, and when it is rolled twice it will be = 6 × 6 = 36

The sample space =

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There are 36 possibilities for (a,b).

This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.

So, the total number of joint outcomes (a,b) is 6 times 6 which is 36. The set of all possible outcomes for (a,b) is called the sample space of this probability experiment.

Hence the number of possible outcomes is 36.

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question 3 on a railway line, peak ridership occurs between 7:00 am and 5:00 pm. the fairness of a passenger survey could be improved by over-sampling data from which group?

Answers

To improve the fairness of a passenger survey on a railway line, it would be ideal to over-sample data from groups that are less likely to be represented in the regular ridership during peak hours of 7:00 am to 5:00 pm. One such group could be passengers who use the railway line during off-peak hours, such as early mornings or late evenings.

Over-sampling these groups will provide a more comprehensive picture of the ridership patterns and preferences of all passengers, rather than just those who use the railway line during peak hours. This approach will lead to a more accurate assessment of the passenger experience and needs and, therefore, allow for better decision-making when it comes to improving services and amenities.

Other groups that could be over-sampled include passengers with disabilities, seniors, and students who may have different transportation needs and experiences compared to the general ridership. By considering the unique experiences and needs of all passengers, railway companies can work towards creating a more inclusive and accessible transportation system.

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a person wants to enclose a rectangular field with four internal partitions as shown. if there is 19300 feet available for fencing, what dimensions will produce the greatest area? note that the internal partitions also require fencing. The width should be feet and the length should be feet. (Round your answers to two decimal places)

Answers

Answer:

Sure. Here are the steps on how to solve for the dimensions of the rectangular field that will produce the greatest area:

Let x and y be the width and length of the rectangular field, respectively.

The perimeter of the rectangular field is 2x + 4y = 19300 feet.

The area of the rectangular field is xy.

We want to maximize the area, so we need to minimize the perimeter.

We can minimize the perimeter by setting x = y.

Plugging in x = y into the equation 2x + 4y = 19300, we get 4x = 19300.

Solving for x, we get x = 4825 feet.

Since x = y, we know that y = 4825 feet.

Therefore, the dimensions of the rectangular field that will produce the greatest area are 4825 feet by 4825 feet.

To round off your answers to two decimal places, you can use the following formula:

rounded_value = (value * 100) // 100

In this case, the rounded values for x and y are 4825.00 and 4825.00, respectively.

Step-by-step explanation:

Final answer:

The problem is about maximizing the area of a rectangular field given a fixed amount of fencing. Length and width of the rectangle are assumed as x and y, respectively. The total fencing equation is x + 5y = 19300 and the area equation is A=xy. Substituting to get equation in terms of one variable, it turns into a calculus problem to find the dimensions that maximize area.

Explanation:

This particular problem solution requires use of calculus to maximize the total area of a rectangular field, given a fixed fencing limit. We need to maximize the rectangle area with the total fence length being 19300 ft. Here are the steps to create a mathematical model for this problem:

Let's assume the length of the rectangle to be x and width to be y.According to the given problem statement, there would be x length covering the length and 5y covering the width, including the internal partitions.So, the total fencing equation can be written as x + 5y = 19300. The area (A) of the rectangle is x*y. We can substitute y from fencing equation to area equation to solve the problem further in terms of a single variable.

This is a calculus problem where we find the maximum point using the derivative of the area equation. However, the exact dimensions would need further calculations. It's important to note that this task requires comprehensive knowledge of calculus and algebra.

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I've been struggling with this, can someone help me?

Answers

Answer:

(see image for graph)

PLEASE HELP! I have no idea what I'm doing and it's kinda freaking me out ...thanks in advance ​

Answers

All the conic section are,

1) Parabola

2) Hyperbola

3) Ellipse

4) Circle

We have to given that;

We have to find the conic section for each condition.

1) when a plane crosses the generating line at the intersection of a single cone from a double-napped cone.

Then, We get Parabola is formed.

2) We know when a plane intersects on one nape of a double napped cone and then the cross section that is obtained is either a parabola, ellipse or a circle.

But if it passes through both the napes of a double napped cone then the cross-section obtained is a hyperbola.

Hence, the answer is Hyperbola.

3) When, A plane intersects at one cone of a double-napped cone for that the plane is neither parallel to the generating line nor perpendicular to the axis,

Then, Ellipse is formed.

4) When plane intersect at one cone of a double napped cone such that the plane is perpendicular for the generating line.

Then, We get Circle is formed.

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Bookwork code: K81
Calculator
allowed
Second chance! Review your workings and see if you can correct your mistake.
Three angles fit around a point. Two of the angles are 112° and 57°.
a) Work out the size of the third angle.
Give your answer in degrees (°).
b) Which of the words below describes the third angle?
2
Reflex Scroll down Obtuse
Watch video

Answers

A) 112 + 57 = 169
180 - 169 = 11
ANSWER: 11
B) Reflex

the blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and complete 3 rotations every minute. write a sine model, y

Answers

We get the following sine model for the vertical displacement y of a point on the blade at time t: y = 7.5 sin(2π(3t - 1)) + 40. This model gives the height above the ground of a point on the blade at time t, measured in minutes.

Assuming that the blades move in a circular motion, the vertical displacement of a point on a blade can be modeled using a sine function.

Let's start by finding the period of the function, which is the time it takes for the blade to complete one full rotation. Since the blade completes 3 rotations every minute, the period is:

T = 1/3 minutes

Next, we need to find the amplitude of the function, which is half the distance between the highest and lowest points of the blade's path. Since the blade is 15 feet long, the amplitude is:

A = 15/2 = 7.5 feet

Finally, we need to find the vertical displacement of the blade at time t, measured in minutes. Let's assume that t=0 corresponds to a blade pointing directly upwards. As the blade rotates, it moves in a circle with radius 15 feet, centered at a height of 40 feet above the ground. The vertical displacement of the blade is the y-coordinate of the point on the circle at angle θ, where θ is given by:

θ = 2π(3t - 1) (in radians)

This formula gives the angle in radians that the blade has rotated through at time t, taking into account the fact that the blade starts at a random angle at t=0. (The "-1" term ensures that the blade starts at the top at t=0.)

Putting it all together, we get the following sine model for the vertical displacement y of a point on the blade at time t:

y = 7.5 sin(2π(3t - 1)) + 40

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Compare the functions

Answers

The function f(x) and g(x) have the same behavior for all real values except x = -1/4, as f(x) is not defined at x = -1/4.

How to define the domain and range of a function?

The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.

The function f(x) is defined as follows:

f(x) = [(4x + 1)(x - 5)]/(4x + 1).

The denominator cannot be zero, hence the value that is outside the domain is given as follows:

4x + 1 = 0

4x = -1

x = -1/4.

For the other values, the 4x + 1 terms can be simplified, hence f(x) = g(x) = x - 5, meaning that they are equal.

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the distribution of salaries for major league baseball players is strongly skewed right with a mean of 3.3 million dollars and a standard deviation of 1.5 million dollars. a random sample of 40 players is selected, what is the approximate probability the 40 players have a mean salary of at most than 4 million dollars?

Answers

The approximate probability that the 40 players have a mean salary of at most 4 million dollars is approximately 0.9985 or 99.85%.

Given that the sample size is 40, we can use the Central Limit Theorem to approximate the normal distribution of sample means. The mean of the sample means will be the same as the population mean, which is 3.3 million dollars. The standard deviation of the sample means (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, it will be 1.5 million dollars divided by the square root of 40.

Let's calculate the standard error:

Standard Error = 1.5 million dollars / sqrt(40) ≈ 0.237 million dollars.

Now, we want to find the probability that the 40 players have a mean salary of at most 4 million dollars. We can convert this to a standard normal distribution by calculating the z-score:

Z = (X - μ) / SE

where X is the value we want to find the probability for (4 million dollars), μ is the population mean (3.3 million dollars), and SE is the standard error (0.237 million dollars).

Z = (4 - 3.3) / 0.237 ≈ 2.95

To find the probability corresponding to this z-score, we can refer to a standard normal distribution table or use statistical software. Assuming a standard normal distribution, the approximate probability can be found to be about 0.9985.

Therefore, the approximate probability that the 40 players have a mean salary of at most 4 million dollars is approximately 0.9985 or 99.85%.

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Conditional Probability

A bucket contains 60 polygon tiles. Of the tiles, 12 are triangles, 15 are squares, 8 are pentagons, 10 are hexagons, 6 are heptagons, and the rest are octagons. If a tile is chosen at random, find each probability.

Find each probability as a fraction (in simplest form), decimal, and percent.

Answers

The conditional probability is solved and the tiles are chosen

Given data ,

A bucket contains 60 polygon tiles. Of the tiles, 12 are triangles, 15 are squares, 8 are pentagons, 10 are hexagons, 6 are heptagons, and the rest are octagons.

So , Total number of polygon tiles = 60

Number of triangles = 12

Number of squares = 15

Number of pentagons = 8

Number of hexagons = 10

Number of heptagons = 6

Number of octagons = 9

Now , probability of event 1: At least four sides, given that it's not a hexagon

P ( A ) = ( 15 + 8 + 6 + 9 ) / 60

P ( A ) = 0.6333

P ( A ) = 63.33 %

And , Probability: P(not a square | less than 7 sides) P ( B )

P ( B ) = ( 12 + 8 + 10 + 6 ) / 60

P ( B ) = 0.6

P ( B ) = 60 %

Hence , the probabilities are solved

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space inside rectangle with a width of 17 and length of 17

Answers

Answer:

If you're looking for the area of the figure, your answer would be 289.

Step-by-step explanation:

This is because the formula for the area of a rectangle is l x w, so you just multiply 17 x 17.

Hope this helped! :)

Answer: i belive that the answer is 289 because 17x17 is 289

Step-by-step explanation: Hope this helps have a nice day!!!!

I want to know what HP=,KJ=,HJ= and what GK=

Answers

Answer:

HP = 2

HJ = 2.5

HJ = 2.5

GK = √29

Step-by-step explanation:

I assume that HK and GJ are perpendicular, so triangles GPH, GPK, JPH, and JPK are right triangles.

Use the Pythagorean theorem.

a² + b² = c²

(GP)² + (HP)² = (GH)²

5² + (HP)² = (√29)²

25 + (HP)² = 29

(HP)² = 4

HP = 2

(HP)² + (PJ)² = (HJ)²

2² + (1.5)² = (HJ)²

4 + 2.25 = (HJ)²

(HJ)² = 6.25

HJ = 2.5

If GHJK is a kite, then KJ = HJ and GK = GH.

HJ = 2.5

GK = √29

Which of the following expressions can be used to find the area of the polygon? Select all that apply.

An irregular shape that is a rectangle with a piece missing from the upper right corner. The bottom length is twenty feet. The left side width is nine feet. The top length is eighteen feet with a rectangle cut out of the upper right corner. The right side width is six feet.

Answers

Answer: ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle.

Step-by-step explanation:

ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle.

The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100

Answers

Answer:

0.5x(x + 2) = 24

x² + 2x - 48 = 0

x² + (x + 2)² = 100

Step-by-step explanation:

A = bh/2

A = x(x + 2)/2 = 24

0.5x(x + 2) = 24

0.5x² + x = 24

x² + 2x = 48

x² + 2x - 48 = 0

x² + (x + 2)² = 10²

x² + (x + 2)² = 100

a sphere with a diameter of 12 is dilated by a scale factor of 3. find the volume of the sphere upon dilation. answer in terms of pi

Answers

9 pi is the answer but im not sure

. What is the total surface area? 52;4 Record your answer on the grid and fill in the bubbles. Be sure to use correct place value.

Answers

Based on the information, we can infer that the surface area of the rectangular prism is 485.5 in²

How to calculate surface area of rectangular prism?

To calculate the surface area of the rectangular prism we must calculate the area of all the faces of the prism:

7.5 in * 18.5 in = 138.75 in² 4 in * 7.5 in = 30 in² 18.5 in * 4 in = 74 in²

Now we must multiply each result by 2 because each of the faces is repeated 2 times.

138.75 in * 2 = 277.5 in² 30 in * 2 = 60 in² 74 in * 2 = 148 in²

Finally, we must add the values to find the total surface area of the rectangular prism:

277.5 in² + 60 in² + 148 in² = 485.5 in²

Note: This question is incomplete. Here is the complete information.

Attached Image

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the difference between two positive numbers is 9. one number is three times less than four times the other number. what are the two numbers?

Answers

Answer:

See explanation below.

the numbers are 27 and 36

or

the numbers are 4 and 13

Step-by-step explanation:

Let the numbers be x and y.

"the difference between two positive numbers is 9"

y - x = 9

One of your statements is:

"one number is three times less than four times the other"

Are you sure the first word times belongs there?

If so, then the second equation below is correct.

y = 4x/3

y = x + 9

y = 4x/3

4x/3 = x + 9

4x = 3x + 27

x = 27

y = x + 9

y = 27 + 9

y = 36

Answer: the numbers are 27 and 36

If the second statement is really:

"one number is three less than four times the other number"

without the first word "times"

then the second equation is

y = 4x - 3

The equations are:

y - x = 9

y = 4x - 3

4x - 3 - x = 9

3x = 12

x = 4

y - 4 = 9

y = 13

Answer: the numbers are 4 and 13

If Billy had 39 sweets he recieves twice as much and ate 25 what does Billy have now​

Answers

Answer:

53

Step-by-step explanation:

Answer:

Step-by-step explanation:

he had 39 sweets

then he receive 39*2[twice as much as 39] + 39 [the sweet he had before he got more sweet]

39*2=78+39=117-25[the number of sweet he had taken out of the 117 sweets he had before]

117-25=92

Billy has 92 sweets left

Find csc theta. with point (5,8) Answer in the format listed at the bottom of photo.

Answers

Answer:

√89 / 8

Step-by-step explanation:

r = hypotenuse = √(5² + 8²) = √89

csc θ = 1/sin θ

sin θ = opp/hyp = height / √89 = 8/ √89

csc θ = hyp / opp = 1 / (8/ √89) = √89 / 8

If a student is selected at random, what is the probability that they would choose to be playing a videogame? Round To The Nearest Tenth

Answers

The most fun game at the moment seems to be playing a videogame.

If a student is selected randomly from the 59 students who participated in the survey, the probability of choosing a student playing a videogame is 35.6%.

What is the probability?

Probability refers to the chance or likelihood of an expected event, outcome, or success occurring given the possibility of many events, outcomes, or successes.

Probability values are stated as decimals, fractions, or percentages when they lie between 0 and 1.

The number of students going to a party = 6

The number of students playing a videogame = 21

The number of students taking a nap = 11

The number of students drawing a picture = 8

The number of students reading a good book = 7

The number of students playing sports = 6

The total number of student participants in the survey = 59

The probability of choosing a student playing a videogame = 35.6% (21 ÷ 59 × 100)

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If you save 20% of your paycheck each week, how much would you save if you made $224 in a week. How much would you save in a month (4 weeks)?

Answers

If you save 20% of your paycheck each week, you would save $44.80 if you made $224 in a week. In a month (4 weeks), you would save a total of $179.20.

To determine how much you would save each week, you need to multiply your paycheck by the percentage you want to save:

$224 x 20% = $44.80

Therefore, you would save $44.80 each week if you made $224 and saved 20% of your paycheck.

To calculate how much you would save in a month, you need to multiply your weekly savings by the number of weeks in a month:

$44.80 x 4 = $179.20

Therefore, if you made $224 per week and saved 20% of your paycheck, you would save $44.80 each week and a total of $179.20 in a month.

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As indicated in the paycheck number box, this is the 18th paycheck of the year. Determine the current gross pay.

What is the social security tax for his pay period?

What is the year to date social security tax?

What is the Medicare tac for this pay period?

What is the year to date Medicare tax?

What are the union dues for this pay period if it paid weekly?

What is the year to date health insurance contribution if it is paid weekly?

What is the state tax rate?

What is the federal tax rate?





Please help I have finals coming up :(

Answers

The employee's hourly wage, number of hours worked, tax rates, and any Deductions or contributions

To determine the current gross pay, social security tax, year-to-date social security tax, Medicare tax for this pay period, year-to-date Medicare tax, union dues for this pay period, year-to-date health insurance contribution, state tax rate, and federal tax rate, we would need additional information such as the employee's hourly wage, number of hours worked, tax rates, and any deductions or contributions.

The current gross pay can be calculated by multiplying the hourly wage by the number of hours worked. The social security tax and Medicare tax can be calculated based on the employee's gross pay and the respective tax rates set by the government. The year-to-date social security tax and Medicare tax can be calculated by summing up the taxes deducted from each pay period so far in the year.

The union dues and health insurance contributions would depend on the specific terms of the employee's union agreement and health insurance plan. These deductions are typically a fixed amount or a percentage of the employee's gross pay.

The state tax rate and federal tax rate would also vary depending on the employee's income level and the tax brackets set by the state and federal governments. These rates are applied to the employee's taxable income after deducting any allowances or exemptions.

Without specific information about the employee's wages, hours worked, tax rates, deductions, and contributions, it is not possible to provide accurate answers to the questions mentioned. It is recommended to refer to the employee's pay stub or consult with the employer's payroll department for the precise details regarding the mentioned variables.

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at what values of x does f(x)=x^4-8x^2 have a relative minimum

Answers

the function f(x) = x^4 - 8x^2 has a relative minimum at x = 2 and x = -2.

To determine the values of x at which the function f(x) = x^4 - 8x^2 has a relative minimum, we need to find the critical points of the function and then analyze their nature using the second derivative test.

Step 1: Find the derivative of f(x):

f'(x) = 4x^3 - 16x

Step 2: Set the derivative equal to zero to find the critical points:

4x^3 - 16x = 0

Step 3: Factor out common terms and solve for x:

4x(x^2 - 4) = 0

Solving for x, we get:

x = 0 (critical point)

x^2 - 4 = 0

x^2 = 4

x = ±2 (critical points)

Step 4: Analyze the nature of the critical points using the second derivative test:

To apply the second derivative test, we need to find the second derivative of f(x):

f''(x) = 12x^2 - 16

Evaluate f''(x) at each critical point:

f''(0) = 12(0)^2 - 16 = -16

f''(2) = 12(2)^2 - 16 = 44

f''(-2) = 12(-2)^2 - 16 = 44

The second derivative test states that if f''(x) > 0, then the function has a relative minimum at that point. If f''(x) < 0, then the function has a relative maximum.

From the calculations above, we find that f''(2) = 44 > 0 and f''(-2) = 44 > 0. Thus, both x = 2 and x = -2 correspond to relative minimum points.

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pls help , due at 12:00

Answers

The value of x is given as follows:

x = 5.4.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.

For the angle of 60º, we have that:

x is the adjacent side.9.3 is the opposite side.

Hence we apply the tangent ratio to obtain the value of x as follows:

tan(60º) = 9.3/x

x = 9.3/tangent of 60 degrees

x = 5.4.

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5. A basic stereo system costs $189.67. An upgraded
model costs $212.09. How much more does the
upgraded model cost?

Answers

Answer:

 22.42

Step-by-step explanation:

The final price is 212.09.  The original price is 189.67

Subtract the original price from the final price.

212.09

-189.67

---------------

 22.42

Answer:

$22.42

Step-by-step explanation:

To find the increased amount of the model you have to get the difference between the initial cost and the upgraded price.

Initial price = $189.67

Upgraded price = $212.09

Subtract the initial price from the upgraded price.

Increased amount = $212.09 - $189.67

                               = $22.42

q(x)=-7x^3+9x^2-8x+2 (a) Possible number(s) of positive real zeros: & (b) Possible number(s) of negative real zeros:

Answers

Possible number(s) of positive real zeros are 1 or 0 and Possible number(s) of negative real zeros: 2 or any even number

To determine the possible number of positive and negative real zeros of the polynomial q(x) = -7x^3 + 9x^2 - 8x + 2, we can use Descartes' rule of signs.

(a) Possible number(s) of positive real zeros:

For the polynomial q(x), we count the number of sign changes in the coefficients when we write them in descending order:

-7x^3 + 9x^2 - 8x + 2

There is only one sign change, from -8x to +2. Thus, there is exactly 1 positive real zero or none at all.

Possible number(s) of negative real zeros:

To determine the possible number of negative real zeros, we substitute -x into the polynomial:

-7(-x)^3 + 9(-x)^2 - 8(-x) + 2

Simplifying the expression:

7x^3 + 9x^2 + 8x + 2

Again, we count the number of sign changes in the coefficients:

7x^3 + 9x^2 + 8x + 2

There are two sign changes, from 7x^3 to 9x^2 and from 9x^2 to 8x. Thus, there are either 2 negative real zeros or any even number of negative real zeros.

In summary:

(a) Possible number(s) of positive real zeros: 1 or 0

(b) Possible number(s) of negative real zeros: 2 or any even number

To know more about real zeros.

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if 5^n = 8 find 5^2n+3

Answers

Step-by-step explanation:

I assume this is   5^(2n+3)   though it is not actually posted this way

5^(2n + 3 ) = 5^2n * 5^3

                   = (5^n)^2 * 5^3      we know 5^n = 8

                       (8)^2 + 5^3  = 64 + 125 = 189

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