The fraction that is most often used to approximate pi is 22/7
What fraction is most often used to approximate pi?The fraction 22/7 is often used to approximate pi. This is because 22/7 is a common fraction that is close to the decimal approximation of pi, which is 3.14159265359...
While pi is an irrational number that cannot be expressed as a finite decimal or fraction, 22/7 is a commonly used approximation that is easy to remember and gives a reasonable estimate of pi to two decimal places.
However, it is important to note that there are other fractions that can be used to approximate pi with greater accuracy, such as 355/113, which is accurate to six decimal places.
Nonetheless, 22/7 remains a popular approximation of pi in various contexts, from mathematics and engineering to everyday life.
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1.2: Entrance Fees
A state park charges an entrance fee based on the number of people in a vehicle. A car
containing 2 people is charged $14, a car containing 4 people is charged $20, and a van
containing 8 people is charged $32.
1. How much do you think a bus containing 30 people would be charged?
2. If a bus is charged $122, how many people do you think it contains?
3. What rule do you think the state park uses to decide the entrance fee for a vehicle?
The fixed fee of $6 covers the cost of the vehicle, and the fee of $4 per person covers the cost of maintaining the park facilities and services.
What is function?In mathematics, a function is a rule that assigns a unique output for each input in a specified set. It is often denoted by an equation or formula, and it describes the relationship between the inputs (independent variables) and the outputs (dependent variables). The set of all possible inputs is called the domain, and the set of all possible outputs is called the range. Functions are used in many areas of mathematics, as well as in science, engineering, and other fields to model real-world phenomena and to solve problems.
Here,
1. To estimate how much a bus containing 30 people would be charged, we can look for a pattern in the given examples. We notice that the fee increases as the number of people in the vehicle increases. Also, the fee for a car containing 2 people is $14, which can be seen as a fixed fee. Therefore, we can assume that the fee for a vehicle containing n people is of the form f(n) = a + bn, where a is the fixed fee and b is the fee per person. Using the information given, we can set up two equations:
f(2) = 14, which gives a + 2b = 14
f(4) = 20, which gives a + 4b = 20
Solving these equations, we get a = 6 and b = 4. Therefore, the rule for the entrance fee is f(n) = 6 + 4n. Substituting n = 30, we get f(30) = $126.
2. To estimate how many people a bus contains if it is charged $122, we can use the same rule that we derived in part 1: f(n) = 6 + 4n. Setting f(n) = 122, we get 6 + 4n = 122, which gives n = 29. Therefore, we can estimate that the bus contains 29 people.
3. Based on the given examples and our analysis in parts 1 and 2, we can infer that the state park uses a linear rule to decide the entrance fee for a vehicle. Specifically, the rule is f(n) = 6 + 4n, where n is the number of people in the vehicle.
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what is the probability that either elsa or scott is president and the other is vice president? write your answer as a reduced fraction
The probability of Jose being the president and Ellen being the vice president in a committee of eight people choosing leaders at random is 1/56.
The probability of Jose being chosen as the president and Ellen being chosen as the vice president is:
P(Jose as president and Ellen as vice president) = P(Jose as president) * P(Ellen as vice president | Jose as president)
Since the assignments are made at random and there are no restrictions on who can be chosen for each position, the probability of Jose being chosen as president is 1/8, and the probability of Ellen being chosen as vice president, given that Jose is president, is 1/7 (since there are 7 remaining people who can be chosen for the position of secretary).
Therefore,
P(Jose as president and Ellen as vice president) = (1/8) * (1/7) = 1/56
So the probability that Jose is president and Ellen is vice president is 1/56.
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_____The given question is incomplete, the complete question is given below:
A committee of eight people must choose a president, a vice president, and a secretary.
Two of the committee members are Ellen and Jose. Assume the assignments are made at random. What is the probability that Jose is president and Ellen is vice president?
A Texile factory uses a 43 liter bucket of dye per 1 roll of fabric that is 1,067 feet long. If the factory has 4 buckets of dye, can it dye 5 rolls of fabric?
Given data in the problem is,
—-> 43 litre bucket of dye per 1 roll
-—> In feet, it is 1067 feet long
If 4 buckets of dye, can it dye 5 rolls of fabric
The factory has 172 liters of dye available.
What is mean by liters?Liters is a unit of volume in the International System of Units (SI). It is commonly used to measure the volume of liquids, gases, and solids that can be poured or contained in a container. One liter is equivalent to 1000 cubic centimeters (cc) or milliliters (ml), and it is roughly equal to 1.057 quarts or 0.264 gallons.
In the given question,
First, we need to find out how much dye is needed for one roll of fabric. We know that 43 liters of dye are needed for 1 roll of fabric that is 1,067 feet long.
Therefore, we can say that:
1 roll of fabric = 43 liters
To find out how much dye is needed for 5 rolls of fabric, we can multiply both sides of this equation by 5:
5 rolls of fabric = 5 × 43 liters
1,067 feet = 215 liters
1,067 feet
So, 5 rolls of fabric would require 215 liters of dye.
Next, we need to check if the 4 buckets of dye are enough to dye 5 rolls of fabric. Each bucket contains 43 liters of dye, so 4 buckets would contain:
4 buckets of dye = 4 × 43 liters
= 172 liters
Therefore, the factory has 172 liters of dye available.
Since 215 liters of dye are required for 5 rolls of fabric, and the factory has only 172 liters of dye available, it cannot dye 5 rolls of fabric with the given amount of dye.
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Please help. Susie ran a race. She ran 5 miles an hour and the race took her T hours to complete how long was the race and write your answer as an expression.
Answer:
The expression you use to find the amount of miles would be 5xT=X miles.
or 5t
Students rented buses and vans to go attend the southwood staff/ student hockey game. There were 8 vans and 12 buses for 360 students
a) write an equation to describe this relationship
b) if there were 12 students per van, how many students fit in each bus?
Therefore, each bus can hold 22 students if there were 12 students per van.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are symbols that can represent different values. Solving an equation means finding the value or values of the variable(s) that make the equation true.
Here,
a) Let V be the number of vans and B be the number of buses. We know that there were 8 vans and 12 buses, so we can write:
V + B = 20 (the total number of vehicles)
We also know that there were 360 students in total. If we assume that each van can hold 12 students, and each bus can hold some number of students, we can write:
12V + bB = 360 (the total number of students)
where b is the number of students that each bus can hold.
b) We can use the equation we derived in part a) and substitute V = 8 to solve for B:
V + B = 20
8 + B = 20
B = 12
So there were 12 buses in total. We can then use the equation 12V + bB = 360 and substitute V = 8 and B = 12 to solve for b:
12V + bB = 360
12(8) + b(12) = 360
96 + 12b = 360
12b = 264
b = 22
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Create a proportion from each set of numbers ONLY use 4 numbers from each set:
1) 66, 99, 8, 11, 6, 88
2) 45, 14, 25, 35, 19, 10
3) 5, 48, 12, 18, 1, 4
4) 9, 45, 13, 75, 25, 5
5) 72, 9, 84, 12, 6, 54
Help please i need this answered fast
Dale
rapide
veloce
The scale factor of the two rectangles show a common ratio of 4/5
What is scale factor?A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.
When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.
A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.
The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.
In the given figure;
12/15 = 36/45
Let's find the ratio here;
4/5 =4/5
The scale factor is 4/5
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A 9.6 8.4 7.2 6.0 4.8 3.6 2.4 1.2 0 1 2 3 4 5 6 7 8 9 10 X The equation of the line of best fit for the nine points is determined. Then, three more points are added to the scatter plot, but the equation of the original line of best fit remains unchanged. Which three ordered pairs are most likely the added data points?
A (4,4), (5,5), (6,6)
B (4,10),(4,11),(4,12)
C (8,9),(8,10),(8,11)
D(10,10),(10,11),(10,12)
I need an answer asap
The answer option to the above question is The 3 ordered pairs are B, (4,10),(4,11),(4,12).
What is an equation?In this context, the word "equation" refers to the equation of the line that best fits a certain set of data points. A straight line that most accurately depicts the trend or pattern in a collection of data points is called the line of best fit. Predictions or estimations for additional data points that might not be a part of the initial set can be made using the equation of the line of best fit.
According to the given information:
To determine which three ordered pairs are most likely the added data points, we need to consider the slope and y-intercept of the original line of best fit. Since the equation of the line of best fit remains unchanged, the new points must lie on the original line.
The original line of best fit can be determined using a linear regression algorithm. However, we can estimate the slope and y-intercept of the line by simply finding the coordinates of two points on the line.
We can use the first and last points in the original set of data to estimate the slope and y-intercept. Using these points, we find that the equation of the line of best fit is:
y = -0.84x + 10.8
Now we can check which of the given sets of points lie on this line:
A: (4,4), (5,5), (6,6)
For (4,4), y = -0.84(4) + 10.8 = 7.56, which is not equal to 4. So (4,4) is not on the line.
Similarly, (5,5) and (6,6) are not on the line.
Therefore, A is not the correct answer.
B: (4,10),(4,11),(4,12)
For (4,10), y = -0.84(4) + 10.8 = 7.56, which is equal to 10. So (4,10) is on the line.
Similarly, (4,11) and (4,12) are also on the line.
Therefore, B is a possible answer.
C: (8,9),(8,10),(8,11)
For (8,9), y = -0.84(8) + 10.8 = 4.32, which is not equal to 9. So (8,9) is not on the line.
Similarly, (8,10) and (8,11) are not on the line.
Therefore, C is not the correct answer.
D: (10,10),(10,11),(10,12)
For (10,10), y = -0.84(10) + 10.8 = 3.96, which is not equal to 10. So (10,10) is not on the line.
Similarly, (10,11) and (10,12) are not on the line.
Therefore, D is not the correct answer.
Therefore, the answer is B, (4,10),(4,11),(4,12).
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Determine the surface area of the trapezoidal prism to nearest whole number (no unit is required)
We can conclude after answering the provided question that As a result, rectangle the surface area of the trapezoidal prism is 180 to the nearest whole number.
What is rectangle?In Euclidean geometry, a rectangle is a triangular prism with four slight angles. It can also be described as a basic rule hexagon or one in which all of the angles are equal. A whole other option for the parallelogram is a straight angle. Four of something like the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "vector graphics rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel sizes of its two sides.
Two trapezoidal faces and four rectangular faces comprise the trapezoidal prism.
To begin, we can use the formula to calculate the area of one of the trapezoidal faces:
Trapezoid area = (1/2) x (sum of parallel sides) x (height)
Area of trapezoidal face = (1/2) x (7 + 10) x 4 = 34
7 x 4 = 28 area of rectangular face
The total area of the rectangular faces is: because there are four rectangular faces
Total rectangular face area = 4 x 28 = 112
Total surface area equals the sum of the areas of trapezoidal and rectangular faces.
Surface area total = 68 + 112 = 180
As a result, the surface area of the trapezoidal prism is 180 to the nearest whole number.
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medical care and compensation costs for workers injured on the job vary a lot and are strongly skewed as a whole. the national academy of social insurance reports that the mean worker's compensation claim cost in a year is $439 per insured worker, with standard deviation $20,000. the law of large numbers says that
The law of large numbers says that as a company insures more and more workers chosen at random, the average costs get closer to $439. So, the answer is option B.
As a company insures more and more workers chosen at random, the average cost gets closer to $439.
The law of large numbers states that as the sample size increases, the sample mean gets closer to the population mean. In this case, the population mean is the mean worker's compensation claim cost of $439 per insured worker.
As the company insures more and more workers chosen at random, the sample size increases, and the sample mean of the worker's compensation claim cost will converge to the population mean of $439.
The law of large numbers does not guarantee that an insurance company can get an average workers' compensation cost lower than the mean by insuring a large number of people. The option B is correct.
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--The given question is incomplete, the complete question is given below
"Medical care and compensation costs for workers injured on the job vary a lot and are strongly skewed as a whole. The National Academy of Social Insurance reports that the mean worker's compensation claim cost in a year is = $439 per insured μworker, with standard deviation = $20,000. The law of large numbers says that σ(choose the correct option)
A) an insurance company can get an average workers’ compensation cost lower than the mean by insuring a large number of people.
B) as a company insures more and more workers chosen at random, the average costs gets closer to $439"--
the sum that shows how many concert tickets were sold if 100 was sold last week and 2/5 of the remaining tickets were sold thus week
The sum that shows how many concert tickets were sold using the given parameters is: ²/₅x + 60
How to solve Algebraic expressions?Algebraic expressions are defined as the simple idea of expressing numbers with the aid of letters or alphabets without even specifying their actual values.
Let the total number of tickets available for sale be denoted as x.
We are told that 100 tickets were sold last week. Thus:
Amount of tickets left unsold = (x - 100)
We are now told that 2/5 of the remaining tickets were sold this week. Thus:
Number of tickets sold this week = ²/₅(x - 100)
Thus:
Total Number of Tickets sold = 100 + ²/₅(x - 100)
= 100 + ²/₅x - 40
= ²/₅x + 60
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The total weight of 5 bags of rice is 32.4 kg. If the average weight of 2 bags of rice is 8.16 kg, what is the average weight of the other 3 bags of rice?
We can start by using the formula for calculating the average:
Average = Total sum / Number of items
Let x be the average weight of the other 3 bags of rice. Then we can set up the following equation:
(2 bags weight + 3 bags weight) / 5 bags = Total weight / Number of bags
Substituting the given values, we get:
(2 x 8.16 kg + 3 bags weight) / 5 bags = 32.4 kg / 5 bags
Simplifying and solving for 3 bags weight, we get:
3 bags weight = (32.4 kg / 5 bags) x 5 - 2 x 8.16 kg
3 bags weight = 16.2 kg - 16.32 kg
3 bags weight = -0.12 kg
This means that the total weight of the other 3 bags is negative, which is not possible. Therefore, we have made an error in our calculations.
We can check our work by solving for the average weight of all 5 bags using the formula:
Average = Total sum / Number of items
Substituting the given values, we get:
Average = 32.4 kg / 5 bags
Average = 6.48 kg per bag
Therefore, the average weight of the other 3 bags of rice is:
Average = (Total weight - 2 x 8.16 kg) / 3 bags
Average = (32.4 kg - 16.32 kg) / 3 bags
Average = 16.08 kg / 3 bags
Average = 5.36 kg per bag
Therefore, the average weight of the other 3 bags of rice is 5.36 kg.
5.36kg.
I hope my answer helped you.
RobertOnBrainly
A line has a slope of -5 and passes through the point (1,-9) write its form in slope intercept form
Answer:
[tex]y = - 5x - 4[/tex]
Step-by-step explanation:
[tex] - 9 = - 5(1) + b[/tex]
[tex] - 9 = - 5 + b[/tex]
[tex]b = - 4[/tex]
[tex]y = - 5x - 4[/tex]
which of the following distributions have a sufficient estimator? (a). bernoulli. (b). poisson. (c). exponential. (d). none of the above or more than one answer.
A sufficient estimator is the distributions of exponential.The correct answer to this question is (c) exponential.
What is an estimator?An estimator is a rule or procedure that is used to determine an estimate of a parameter based on observed data. A statistic is used to estimate a parameter, and it is computed from the observed data. An estimator is a random variable that computes a statistic from the data.
The following distributions have a sufficient estimator:
Poisson Distribution with parameters λ and x is a Poisson distribution.
The rate of the occurrence is λ.
Exponential Distribution with parameters λ and x is an exponential distribution.
The mean waiting time is 1/λ.
Bernoulli The Bernoulli distribution is not sufficient for an estimator, but the binomial distribution, which generalizes the Bernoulli distribution, is. In the context of the binomial distribution, p is a parameter Exponential
The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, such as the amount of time until the next vehicle arrives at a traffic intersection or the amount of time a particular component lasts in a manufacturing process.
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Lisa has 3 ribbons she won at the track meet over the weekend. A 1st place ribbon, a 2nd ribbon, and a 3rd place ribbon. The 2nd place ribbon is 4/5 of the length of the 1st place ribbon. The 2nd place ribbon is 1/2 the length of the 3rd place ribbon. The length of the 3rd place ribbon is 90 centimeters longer than the 1st place ribbon. How long is the 2nd place ribbon?
Answer:
20cm
Step-by-step explanation:
90cm ÷ 1/2 the length 90 = 20cm
Sam has $150. She used 40% to buy a dog. How much did the dog cost?
Answer:
Step-by-step explanation:
60$. (((150 * 40 and divide by 100)))
Step-by-step explanation:
She used 40% of $150 :
40% * $150 = .40 * 150 = $ 60 for the pup-a-roo.
15 points to answer please help I don't get it....
Answer:
a) y = -2.812x + 97.554
b) the correlation coefficient is about -0.97, which is a strong linear fit.
Step-by-step explanation:
you need a graphing calculator for linear regression, but desmos works fine :)
plugging in all the values into a table and letting the calculator do the work :D (attatched image)
the equation: y = -2.812x + 97.554
next, (also in the screenshot) the r-value, or the correlation coefficient, is about -0.97, and we want this to be as close to 1 or -1 as possible to get a perfect linear regression.
this is pretty close to -1, so i'd say that the linear fit is strong :)
A financial investment broker earns 4% on each customer dollar invested. If he broker invests $50,000, what is the commission on the investment? pls hurry it is my hW
A financial investment broker earns 4% on each customer dollar invested. If the broker invests $50,000, the commission on the investment is $2,000.
The commission earned by the broker on the investment will be equal to 4% of the total investment amount.
So, the commission earned by the broker on investing $50,000 will be:
Commission = 4% of $50,000
Commission = (4/100) x $50,000
Commission = 4 x $500
Commission = $2,000
Therefore, the commission earned by the broker on investing $50,000 will be $2,000.
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help on the question in the image
Answer:
Q and R
Step-by-step explanation:
Assume N || M Select all true statements.
Answer:
Step-by-step explanation:
when i got it it was d
Ok I really do not know what this is
The total area of the rectangle and square joined together is 27 cm².
What is the area of the geometry?First, let's find the area of the rectangle. The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width.
In this case, the length of the rectangle is 6 cm and the width is equal to the length of the square, which is also 3 cm. So, the area of the rectangle is:
A = 6 cm x 3 cm
A = 18 cm^2
Now let's find the area of the square. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side.
In this case, the length of the side of the square is also 3 cm. So, the area of the square is:
A = 3 cm x 3 cm
A = 9 cm^2
To find the total area of the rectangle and square joined together, we simply add the two areas together:
Total area = area of rectangle + area of square
Total area = 18 cm^2 + 9 cm^2
Total area = 27 cm^2
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The diameter,D , of a sphere is 11.2 cm . Calculate the sphere's volume V, . Use the value for 3.14 ,pie and round your answer to the nearest tenth. (Do not round any intermediate computations.) will give brainliest.
735.24563 is the the sphere's volume V.
What does sphere refer to?
The shape and symmetry of a sphere are both round. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. On the basis of its radius, it has a surface area and a volume.
There are no faces, corners, or edges on it. the collection of all locations in three dimensions that are the same distance from a specific point (the centre) is known as the radius, or the outcome of rotating a circle around one of its diameters. The elements and characteristics of a sphere are comparable to those of a circle.
D = 11.2
r = 11.2/2 = 5.6
the sphere's volume = 4/3 πr³
= 4/3 * 3.14 * (5.6)³
= 735.24563
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(5) A light pole of height 8 metres gives a shade on the ground of length 5 metres, then the measure of the elevation angle of the sun at that moment to the nearest degree equals .....
The measure of the angle of elevation is 58°( nearest degree)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The height of the pole will represent the opposite to the angle of elevation and the length of the shade will be the adjascent to the angle of elevation.
Represent the angle of elevation by x
Tan x = opp/adj
Tan x = 8/5
Tan x = 1.6
x = tan^-1(1.6)
x = 58° ( nearest degree)
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North America has an area of 9,365,000 square miles, which is about 136% the area of South America. How many times greater is an area of North America than South America? Write your answer as a decimal in as a mixed number.
I remember doing this but I don’t seem to remember
Use the discriminant to describe the roots of each equation. Then select the best description. x2 - 4x + 4 = 0
non-real roots
double root
real and rational roots
real and irrational roots
The best description of the roots of the equation [tex]x^2 - 4x + 4 = 0[/tex] is that it has two equal or identical real roots.
What are the identical real roots?Identical real roots are solutions to a quadratic equation in which both roots have the same value. In other words, if a quadratic equation has identical real roots, it means that there is only one solution to the equation, and that solution is repeated twice.
To use the discriminant to describe the roots of equation [tex]x^2 - 4x + 4 = 0[/tex] we need to first identify the coefficients of the quadratic equation:
[tex]a = 1\\b = -4\\c = 4[/tex]
The discriminant is given by the expression [tex]b^2 - 4ac[/tex]. Substituting the values of a, b, and c, we get:
[tex]b^2 - 4ac\\ = (-4)^2 - 4(1)(4)\\ = 16 - 16 = 0[/tex]
Since the discriminant is equal to zero, this tells us that the quadratic equation has two equal roots. In other words, the equation has a single root with a multiplicity of two.
The best description of the roots of equation x^2 - 4x + 4 = 0 is that it has two equal or identical real roots.
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What is the critical value t* for constructing a 99% confidence interval
for a mean with 11 degrees of freedom?
The critical value t for constructing a 99% confidence interval for a with 11 degrees of freedom is approximately 3.106.
What is t-distribution table?A t-distribution table is a table of values that shows the critical values for the t-distribution, which is a probability distribution used in statistics.
The table is typically organized by degrees of freedom and the level of significance (α) for a two-tailed test.
To find the critical value t* for a 99% confidence interval for a mean with 11 degrees of freedom, we can use a t-distribution table or a calculator.
Using a t-distribution table, we can find the critical value that corresponds to a 99% confidence level and 11 degrees of freedom.
The table shows that the critical value is approximately 3.106.
Alternatively, we can use a calculator that has a t-distribution function.
For example, using the function (0.005, 11) in Microsoft Excel will give us the same result of approximately 3.106.
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The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 30 times the sine of the quantity pi over 20 times t end quantity plus 15 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?
Answer:
40 seconds
Step-by-step explanation:
You have a Ferris wheel such that the height of a rider is modeled by d=30sin(πt/20)+15, and you want to know the time it takes for one revolution.
PeriodicityThe sine function has a period of 2π. The value of the function when the argument is 2π is the same as when it is zero. The period is the time difference between those argument values. Since the argument is 0 when t=0, we only need to find the value of t that makes the argument 2π:
2π = πt/20
40 = t . . . . . . . multiply by 20/π
The Ferris wheel makes one revolution in 40 seconds.
Kierra conducts a survey in her neighborhood to find out how many males and females attend summer camp. part of her survey results are shown Enter values in the blanks to complete the table for Kierra's survey results.
The full scope of her survey or the methodology she used to collect her data.
According to Kierra's survey results, it seems that the number of females attending summer camp is slightly higher than the number of males. To complete the table for her survey results, we can use the following information:
- In the "Gender" column, we can write "Male" and "Female" to represent the two categories Kierra surveyed.
- In the "Number of Participants" column, we can fill in the values that Kierra collected from her neighborhood.
For example, if she surveyed 100 people and found that 40 of them were males attending summer camp, we can write "40" in the row for "Male" under the "Number of Participants" column.
- We can then add up the values in each row to find the total number of participants in each category. For example, if Kierra found that 60 females attended summer camp, we can write "60" in the row for "Female" under the "Total" column.
| Gender | Number of Participants | Total |
|--------|----------------------|-------|
| Male | 40 | 100 |
| Female | 60 | 100 |
It's important to note that this is only a small part of Kierra's survey results, and we don't know the full scope of her survey or the methodology she used to collect her data.
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Deena and Jackson tossed two coins at the same time. In five tosses, Deena got heads on both coins three times. In 50 tosses, Jackson got heads on both coins 12 times. What does this illustrate about theoretical and experimental probability that both tossed coins will be heads?
Experimental probability approaches theoretical probability when the sample size is large.
Experimental probability is not affected by sample size.
Smaller groups give more accurate results.
Larger groups have greater chance for error.
Answer:
experimental probability approaches theoretical probability when the sample size is large.
Step-by-step explanation:
This illustrates that experimental probability approaches theoretical probability when the sample size is large. As the number of tosses increases, the experimental probability of both coins being heads for both Deena and Jackson approaches the theoretical probability of 1/4 (since the probability of getting heads on a single coin toss is 1/2, and the probability of getting heads on two coin tosses is (1/2) * (1/2) = 1/4). This is because the law of large numbers states that as the sample size increases, the experimental probability approaches the theoretical probability. Therefore, the more tosses that are performed, the closer the experimental probability will be to the theoretical probability.
Circle T is shown where points Q and S are on the circle and ZQTS = 75°.
O
T
75°
S
The ratio of the central angle, ZQTS, to the whole circle is [DROP DOWN 1].
QS represents [DROP DOWN 2] of the circle's circumference.
which is approximately 3.864 times the length of QS.the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
What is angle?An angle is a measure of the amount of turn between two lines or rays that meet at a common point, known as the vertex of the angle. The angle is typically measured in degrees or radians. In a Euclidean plane, an angle can range from 0 degrees (corresponding to two lines that are parallel to each other) to 180 degrees (corresponding to two lines that form a straight line). An angle greater than 180 degrees is called a reflex angle. Angles are used in many areas of mathematics and physics, such as geometry, trigonometry, and calculus, as well as in real-world applications such as navigation, architecture, and engineering.
by the question.
The ratio of the central angle ZQTS to the whole circle is 1/12, or 0.0833 (rounded to four decimal places). This is because there are 360 degrees in a circle, and 75 is 1/12 of 360.
QS represents 1/4 of the circle's circumference. This is because the central angle ZQTS is 75 degrees, which is 1/3 of a right angle (90 degrees). An inscribed angle that intercepts the same arc as a 1/3 angle will have twice the measure of the 1/3 angle, or 150 degrees. Thus, angle QTS is 150 degrees. Angle QOS is also 150 degrees, since it intercepts the same arc as QTS. Therefore, angle QOT is 60 degrees, since the angles in triangle QOT add up to 180 degrees. Since triangle QOT is an equilateral triangle, QT and QS are equal in length, and angle QTS is 75 degrees, we can use the sine function to find the length of QS. The sine of 75 degrees is approximately 0.966, so QS represents approximately 0.966 times the circumference of the circle. Since QS represents 1/4 of the circumference, the circumference of the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
To learn more about circumference:
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