The required confidence interval for the given sample size and sample mean is,
95% confident interval which is true average porosity of the seam lies between 4.49 and 5.20 percent.
98% confident interval which is true average porosity of the other seam lies between 4.10 and 5.02 percent.
Sample size with 95% confidence interval with a width of 0.37 is 16 .
Sample size with 99% confidence interval with a width of 0.21 is 11 .
Sample size 'n' = 19
Confidence interval = 95%
Sample mean = 4.85
True average porosity of a certain seam is , we use the formula,
CI = sample mean ± t(α/2, n-1) ×(standard deviation / √(n))
where t(α/2, n-1) is the critical t-value.
α level (0.05 for a 95% confidence interval)
Degrees of freedom (n-1 = 18).
Plugging in the values, we get,
CI
= 4.85 ± t(0.025, 18) × (0.74 / √(19))
Using a t-table ,
t(0.025, 18) = 2.101.
So the confidence interval is,
CI
= 4.85 ± 2.101 × (0.74 / √(19))
= (4.49, 5.20)
95% confident that the true average porosity of the seam lies between 4.49 and 5.20 percent.
Compute a 98% confidence interval for the true average porosity of another seam .
Sample size = 18
Sample mean = 4.56,
Use the same formula as above but with a different t-value,
CI = 4.56 ± t(0.01, 17) ×(0.74 / √(18))
Using a t-table
t(0.01, 17) = 2.898.
So the confidence interval is,
CI
= 4.56 ± 2.898 × (0.74 / sqrt(18))
= (4.10, 5.02)
98% confident that the true average porosity of the other seam lies between 4.10 and 5.02 percent.
Sample size to obtain a 95% confidence interval with a width of 0.37,
Use the formula,
n = (t(α/2, n-1) × standard deviation / (width / 2))^2
Solving for n, we get,
n = [(t(α/2, n-1) × standard deviation) / (width / 2)]^2
Substituting the given values, we get,
n = [(t(0.025, n-1) × 0.74) / 0.37]^2
Using trial and error or a t-table,
t(0.025, n-1) is approximately 2 for large sample sizes.
So we have,
n = [(2 × 0.74) / 0.37]^2
= 16
A sample size of at least 16 specimens is necessary to obtain a 95% confidence interval with a width of 0.37.
Sample size to estimate the true average porosity to within 0.21 with 99% confidence,
Use the same formula as above but solve for n with the given width and confidence level,
n = [(t(α/2, n-1) ×standard deviation) / (width / 2)]^2
Substituting the given values, we get,
n = [(t(0.005, n-1) × 0.74) / 0.21]^2
Using trial and error or a t-table,
t(0.005, n-1) is approximately 3 for large sample sizes.
So we have
n = [3 × 0.74) / 0.21]^2
= 11.17
≈ 11
Sample size to estimate the true average porosity to within 0.21 with 99% confidence is 11.
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Explain why all of these statements are false: (a) The complete solution to Ax = b is any linear combination of Xp and Xn. (b) The system Ax- b has at most one particular solution. (c) If A is invertible, there is no solution Xn in the nullspace.
These statements are false because (a)False because the complete solution to Ax = b is actually the sum of the particular solution Xp and any linear combination of the solutions in the nullspace Xn. (b) False because if the system Ax = b has a particular solution, it will always have exactly one particular solution. (c) False because if A is invertible, there is indeed a solution Xn in the nullspace, but it is only the trivial solution Xn = 0.
(a) The complete solution to Ax = b is any linear combination of Xp and Xn is false.
Mathematically, the complete solution is given by X = Xp + Xn, not just any linear combination of Xp and Xn.
(b) The system Ax = b has at most one particular solution.
This is due to the fact that the particular solution is the unique point where the affine subspace defined by the system intersects the null space of A.
(c) If A is invertible, there is no solution Xn in the null space.
An invertible matrix has a unique solution for each b, which implies that the null space only contains the zero vector.
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you have a 13 oz. bottle and a 20 oz. bottle, with which you wish to measure exactly 2 oz. however, you have a limited supply of water. if any water enters either bottle and then gets dumped out, it is gone forever. what is the least amount of water you can start with and still complete the task?
The least amount of water required to measure exactly 2 oz is 12 oz. (13 oz + 7 oz - 8 oz = 12 oz).
First, add 13 oz of water to the 20 oz bottle. The combined amount of water will now be 33 oz.
Next, pour water from the 33 oz bottle into the 13 oz bottle until the 13 oz bottle is full to the top.
The remaining amount of water in the 33 oz bottle will be 20 oz.
Now, pour out the water in the 13 oz bottle into the 20 oz bottle.
Now, the 20 oz bottle will have 13 oz of water in it. This leaves the 33 oz bottle with 7 oz of water remaining in it.
Now, pour the remaining 7 oz of water in the 33 oz bottle into the 20 oz bottle.
The 20 oz bottle will now have 20 oz + 7 oz = 27 oz of water in it.
Pour out the water in the 20 oz bottle until the amount of water in it is exactly 2 oz.
Since you started with a combined amount of 33 oz, and the amount of water remaining in the 20 oz bottle is 2 oz, the
amount of water poured out is 33 oz - 2 oz = 31 oz.
Therefore, the least amount of water required to measure exactly 2 oz is 12 oz.
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Darius is building a table. He cuts 12-foot-long boards into sections that are each ¼ foot long. How many sections of the board will Darius have when he is finished cutting?
Answer: 48
Step-by-step explanation: 1/4 goes into 1 four times: 4x12=48
Adrian's recipe for raisin muffins calls for 1 and 3/4 cups raisins for one bunch of muffins. Adrian wants to make two and one half batches of muffins for a bake sale. How many cups of raisins will Adrian use?
Answer: Adrian will need 4 and 1/2 cups of raisins for 2.5 batches of muffins
I need a answer for this
The graph that represents a function is the absolute value graph
Identifying the graph that represents a functionThe vertical line test is a way to determine whether a graph represents a function or not.
To apply the vertical line test, we draw a vertical line through the graph.
If the vertical line intersects the graph at more than one point, then the graph does not represent a function. If the vertical line intersects the graph at only one point, then the graph represents a function.The graph that represents a function using the above as a guide is the absolute value graph in option a
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Can I have some help with math
Answer:
B 1/4
Step-by-step explanation:
Because one coin have 1/2 to land either side, but if it was two coins then is will double it so it will be 1/4.
a machine cuts corks intended for use in wine bottles. it produces corks with diameters that are normal with mean 3.01cm and standard deviation 0.08cm. acceptable corks have diameters between 2.95cm and 3.05cm. a) what % of the corks produced by the machine is acceptable? enter numerical answer b) 80% of all corks produced by the machine have diameters less than: enter numerical answer
The 69.15% of the corks produced by the machine are acceptable. 80% of all corks produced by the machine have diameters less than 3.0772cm.
a) To find the percentage of acceptable corks, we have to calculate the area under the normal distribution curve corks have diameters between the limits of 2.95 cm and 3.05 cm.
Let X be the diameter of the corks produced by the machine. Then X follows a
The corks with diameters that have a normal distribution with mean μ = 3.01 cm
Standard deviation σ = 0.08cm.
Using the standard normal distribution, we can standardize X as follows:
Z = (X - μ) / σ
= (X - 3.01) / 0.08
The probability that Z lies between (2.95 - 3.01) / 0.08 = - 0.75
The probability that Z lies between(3.05 - 3.01) / 0.08 = 0.50.
Using a standard normal table that this probability is approximately 0.6915.
Therefore, the percentage of acceptable corks produced by the machine is 69.15%.
b) To find the diameter D such that 80% of the corks produced by the machine have diameters less than D.
Using the standard normal distribution the Z-score that corresponds to the 80th percentile is:
Z = InvNorm(0.8)
= 0.84
We can then solve for D:
D = μ + Zσ
= 3.01 + 0.84(0.08)
= 3.0772
Therefore, 80% of all corks produced by the machine have diameters less than 3.0772cm.
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yes ik the picture is dark but pls help ike PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
a. Similar
Step-by-step explanation:
The question says the triangles are right triangles, so they can't be obtuse or equilateral.
Since they are both right triangles, they both have a 90° angle. And as stated in the question, they both have a 30° angle. By Angle-Angle (AA) they are similar. But we don't know anything about any sides in either triangle, so we don't know if they are congruent or not. Just we can only know they are similar.
show that p/p²- 7 ÷ p²/p²- 49 can be written in the form a + b/p where a and b are integers
We can simplify the expression as follows:
p/(p² - 7) ÷ p²/(p² - 49)
= p/(p² - 7) * (p² - 49)/p² (by flipping the second fraction and multiplying)
= p(p + 7)(p - 7)/(p² - 7)(p²)
= (p + 7)(p - 7)/(p²)
Now, we can write this expression in the form of a + b/p as follows:
(p + 7)(p - 7)/(p²) = (p² - 49 + 2 * 49p)/(p²)
= 1 - 49/p² + 98/p³
Therefore, we can write the expression as:
p/(p² - 7) ÷ p²/(p² - 49) = (p + 7)(p - 7)/(p²) = 1 - 49/p² + 98/p³
So, we have expressed the given expression in the desired form of a + b/p where a = 1 and b = 0 and they are both integers.
There is a statue that is 12 feet tall. When the sun is really low, it casts a shadow on the ground that is 20 feet long. What is the distance from the top of the statue to the top of the shadow?
Answer
sqrt 544 feet
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
12^2 + 20^2= c^2
144+400=c^2
544=c^2
c= sqrt 544
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Step-by-step explanation:
quit
A triangle has sides with lengths 8, 15, and 17.
Is this a Pythagorean Triple? (yes/no)
With a ratio comparing 8/15, that acute angle should measure between and degrees but closer to degrees.
Answer:
Yes, the triangle with sides 8, 15, and 17 is a Pythagorean triple. This is because 8^2 + 15^2 = 64 + 225 = 289 = 17^2. As for the acute angle between sides 8 and 15, we can use the inverse tangent function to find it. tan(theta) = 8/15 theta = arctan(8/15) Using a calculator, we find that theta ≈ 28.07 degrees. Since we know this is an acute angle, we can conclude that it measures between 0 and 90 degrees, and is closer to 28 degrees than to 62 degrees.
PLEASE HELP!!
- A fisherman is measuring the amount of bait he has remaining, y, in his bucket. He puts 20 pieces of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.
What is the slope for this linear relationship, and what does it mean in this situation?
A) −2; the amount of bait decreases by 2 pieces each hour
B) 2; the amount of bait increases by 2 pieces each hour
C) −20; the amount of bait in the bucket when the fishing trip began
D) 20; the amount of bait in the bucket when the fishing trip began
From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
From the given situation of fisherman , linear relationship is given by
y= 2x +20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
As given in the question,
Number of baits in the bucket of fisherman at the beginning of trip = 20
Amount of bait increases by 2 pieces every hour
Linear relationship is defined as :
'y' represent the total number of bait in the bucket after x hours.
y = 20 + 2x
Compare it with the general equation y =mx + c
Where 'm' is the slope.
Here slope is equal to 2.
According to the situation it means the amount of bait increases by 2 pieces in every hour.
Therefore, From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
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HELPPPPPPPPP PLEASE HURRY !!!!!!!!!!!!!!!!! GIVING 40 POINTS!!!!!!!!!!!!!!!!!!
HELPPPPPPPPPPPPPPPPP
The time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters, and other solutions are below
The height of the cannot at launchTo do this, we find h when t = 0
From the graph, we have
h(0) = 70
So, the height of the cannot at launch is 70 meters
The time to reach the maximum heightFrom the graph, we have the vertex to be
Vertex, (t, h) = (3, 114.1)
So, the time to reach the maximum height is 3 seconds
The maximum heightFrom the graph, we have the vertex to be
Vertex, (t, h) = (3, 114.1)
So, the maximum height is 114.1 meters
How long to land on the groundThis is when h(t) = 0
From the graph, we have
h(7.93) = 0
So, the time spent is 7.93 seconds
The equation if the velocity changesThe given equation is
h(t) = -4.9t^2 + 29.4t + 70
If the initial velocity changes, then the equation becomes
h(t) = -4.9t^2 + 40.5t + 70
The equation if the height of launch is 0The given equation is
h(t) = -4.9t^2 + 29.4t + 70
If the initial height changes, then the equation becomes
h(t) = -4.9t^2 + 29.4t
The time to reach the maximum height and the maximum heightWe have
h(t) = -4.9t^2 + 29.4t
Differentiate and set to 0
-9.8t = -29.4
So, we have
t = 3
Next, we have
h(3) = -4.9 * 3^2 + 29.4 * 3
h(3) = 44.1
So, the time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters
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a bowl contains 10 red balls and 10 blue balls. a woman selects balls at random without looking at them. what is the minimum number of balls she must select to be sure of having at least three blue balls?
The minimum about of balls she should pick is 13.
So, the woman consider all the balls and picks the balls without looking,
To have a clear chance of picking at least 3 blue balls from the bowl she has to first eliminate the possibility of picking red balls.
Therefore,
She first picks 10 balls from the bowl, which gradually eliminates the possibility of picking a red ball.
now, she picks 3 more balls from the rest of the available balls which increases the changes of the balls being blue.
then,
=> 10 + 3 = 13
The minimum about of balls she should pick is 13.
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You and your friends go to Dewar's after the movies. You can order either water or a soda to drir and either a Black & White Sundae, a milkshake, or a banana split.
a. Draw a Tree Diagram to represent the given information
b. What is the probability you choose a water and Black & White Sundae?
c. How many total different combinations could be made with these choice: them?
The probability of choosing water and Black & White Sundae is 1/6.
Define probabilityProbability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
a. Image is attached below.
b. The probability of choosing water and Black & White Sundae is the product of the probabilities of choosing water and Black & White Sundae given that water was chosen. This can be calculated as:
P(Water and B&W Sundae) = P(Water) * P(B&W Sundae | Water)
= 1/2× 1/3
= 1/6
Therefore, the probability of choosing water and Black & White Sundae is 1/6.
c. To calculate the total number of different combinations, we need to multiply the number of drink options by the number of dessert options. Since there are 2 drink options (water and soda) and 3 dessert options (Black & White Sundae, milkshake, and banana split) with 3 different sizes for the milkshake and banana split, we can calculate the total number of different combinations as:
Total combinations = 2×(1 + 3 + 3×3)
= 2 × 13
= 26
Therefore, there are 26 total different combinations.
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7. Michelangelo paints 7/8 of a wall in 1 hour. What part of a wall does Michelangelo paint in 1
minute?
The fraction 7/8 of a wall Michelangelo does paint in 1 minute for the given question.
what is fraction?In mathematics, a fraction is a representation of a part of a whole or a ratio of two quantities. It is typically represented as one number (the numerator) over another number (the denominator), separated by a horizontal line. For example, the fraction 3/4 represents three parts out of a total of four equal parts, or a ratio of three to four.
Fractions can also be represented as decimals or percentages. For instance, the fraction 1/2 is equal to the decimal 0.5 or the percentage 50%. Fractions are used in a variety of mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life, such as in cooking recipes or in measurements of time or distance.
If Michelangelo paints 7/8 of a wall in 1 hour, then he paints (7/8)/1 = 7/8 of a wall in one hour.
So, the answer is 7/8 of a wall.
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I NEED HELP ON THIS ASAP!!!
The perimeter of triangle XYZ with the vertices, X(2, 5), Y(10 9), and Z(6, 1), is approximately 24.07 units.
How to Find the Perimeter of a Triangle?To find the perimeter of the triangle, we need to add up the lengths of all three sides. To do this, we can use the distance formula, which is:
d = √[(x2 - x1)² + (y2 - y1)²]
Using this formula, we can find the length of each side of triangle XYZ:
Side XY:
d = √[(10 - 2)² + (9 - 5)²] = √64 + 16 = √80
Side YZ:
d = √[(6 - 10)² + (1 - 9)²] = √16 + 64 = √80
Side ZX:
d = √[(6 - 2)² + (1 - 5)²] = √16 + 16 = √32
Therefore, the perimeter of triangle XYZ = XY + YZ + ZX = √80 + √80 + √32
Perimeter ≈ 24.07 (rounded to two decimal places)
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solve this system of equations by using the elimination method. 2x+6y=10 -3x+1y=5
PLEASE
Answer:
x = -1
y = 2
Step-by-step explanation:
2x + 6y = 10
-3x + 1y = 5
Time the second equation by -6
2x + 6y = 10
18x - 6y = -30
20x = -20
x = -1
Now put in -1 for x and solve for y
2(-1) + 6y = 10
-2 + 6y = 10
6y = 12
y = 2
Let's Check
2(-1) + 6(2) = 10
-2 + 12 = 10
10 = 10
So, x = -1 and y = 2 is the correct answer.
what percentage of the world's land area has been granted some degree of protection in a park or preserve? view available hint(s)for part a what percentage of the world's land area has been granted some degree of protection in a park or preserve? 100% 90% 15% 1%
The answer to the question, "What percentage of the world's land area has been granted some degree of protection in a park or preserve?" is 15%.
What is a protected area?
A protected area is a defined geographical space, recognised, dedicated and regulated, through legal or other effective means, to achieve the long-term conservation of nature with associated ecosystem services and cultural values.
How does a protected area achieve conservation?
A protected area, by definition, is a place dedicated to the protection and maintenance of biodiversity and other natural and cultural resources of the area. Protected areas often encompass critical habitats, ecosystems, and landscapes. They offer essential ecological, economic, social, and cultural benefits to society.Conservation objectives are reached by restricting, regulating or prohibiting human activities in the protected area. Some common ways in which protected areas achieve conservation goals include:Enforcing regulations, including limits on extractive and polluting activities.Monitoring and managing species, ecosystems and landscapes to ensure their continued viability and integrity.Restoring degraded habitats or managing them for their long-term health and function.
What is a National Park?
A national park is a natural or semi-natural space designated to protect natural and cultural resources. National parks are established by governments to preserve a country's heritage, usually with the aim of promoting recreation and tourism.
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carpetland salespersons average per week in sales. steve contois, the firm's vice president, proposes a compensation plan with new selling incentives. steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. a. develop the appropriate null and alternative hypotheses. : - select your answer - : - select your answer - b. what is the type i error in this situation? in this situation, a type i error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - select your answer - when in fact it does not. what are the consequences of making this error? - select your answer - c. what is the type ii error in this situation? in this situation, a type ii error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - select your answer - when in fact it does not. what are the consequences of making this error?
a. The null hypothesis (H0) states that the average sales per salesperson are not increased by the new remuneration scheme.
The new remuneration scheme raises the average sales per salesperson, contrary hypothesis (H1).
b. a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.
c. a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.
a. The appropriate null and alternative hypotheses are :
Null hypothesis (H0): The new compensation plan does not increase the average sales per salesperson.
Alternative hypothesis (H1): The new compensation plan increases the average sales per salesperson.
b. In this situation, a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.
The consequences of making this error are that the company may adopt the new compensation plan and invest resources into it, without actually benefiting from increased sales.
c. In this situation, a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.
The consequences of making this error are that the company may miss out on an opportunity to increase sales by not implementing the new compensation plan, which could lead to lower profits and reduced competitiveness in the market.
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a smartphone was purposefully dropped from a height of 10 meters to test its durability from external physical impact. it will be damaged 100% of the time, but the damage can occur in different parts of the phone. it has been shown that 76% of the damages occur in the glass screen, while the other 24% occur in the battery. a number of smartphones were tested and the tests were independent. find the probability that the first time you observe a battery damage is during the third trial or later.
Answer:
what the quistion?
Step-by-step explanation:
sry i cant spell
The probability that the first time a battery damage is observed is during the third trial or later is 42.74%.
To solve this problem, we can use the geometric distribution, which models the number of trials until the first success in a sequence of independent trials. In this case, the probability of success is 0.24 (the probability of a battery damage) and the probability of failure is 0.76 (the probability of a glass screen damage).
The probability of observing a battery damage for the first time on the third trial or later can be calculated as the complement of the probability of observing a battery damage on the first or second trial.
The probability of observing a battery damage on the first trial is 0.24, and the probability of observing a battery damage on the second trial is (0.76)(0.24) = 0.1824 (the probability of no battery damage on the first trial times the probability of battery damage on the second trial). Therefore, the probability of observing a battery damage for the first time on the third trial or later is 1 - 0.24 - 0.1824 = 0.5776.
However, the question asks for the probability of observing a battery damage for the first time on the third trial or later, which means we need to take into account the fact that we may have observed a battery damage before the third trial. Therefore, we need to adjust our calculation by subtracting the probability of observing a battery damage for the first time on the first or second trial from our previous result.
The probability of observing a battery damage for the first time on the first or second trial is 0.24 + 0.1824 = 0.4224. Therefore, the probability of observing a battery damage for the first time on the third trial or later is 0.5776 - 0.4224 = 0.1552 or 15.52%.
Therefore, the probability that the first time a battery damage is observed is during the third trial or later is 42.74%
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Express the vector in component form given its magnitude is 41 and direction angle is 220 degrees
Answer:
What I myself would do is plug in the given values, and we get: x = 41 * cos(220 degrees) ≈ -22.59 y = 41 * sin(220 degrees) ≈ -33.73
Therefore, the component form of the vector is (-22.59, -33.73).
Step-by-step explanation:
State different ways to find the measure of a side of triangles.
Pythagorean theorem, trigonometric ratios, Law of sines and Law of cosines are different ways to find the measure of a side of triangles.
There are different ways to find the measure of a side of a triangle;
1.Pythagorean theorem:The theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, we have c²= a² + b².
2.Trigonometric ratios:if we know the measure of one acute angle (other than the right angle) and the length of the adjacent side to that angle, we can use the cosine function to find the length of the hypotenuse, or the sine function to find the length of the opposite side.
3.Law of sines:The law states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles of the triangle. Therefore, if a, b, and c are the lengths of the sides of a triangle and A, B, and C are the measures of the angles opposite those sides, we have a/sin(A) = b/sin(B) = c/sin(C).
4. Law of cosines:The law states that the square of a side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. Therefore, if a, b, and c are the lengths of the sides of a triangle and C is the measure of the included angle between sides a and b, we have c² = a² + b² - 2abcos(C).
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assume two coins, one fair and the other is unfair. you pick one at random, flip it five times, and observe that it comes up as tails all five times. what is the probability that you are flipping the unfair coin?
The probability of flipping the unfair coin given that we observed five tails in a row is approximately 0.9048
Let's define
A: the event of picking the unfair coin
B: the event of getting five tails in a row
We want to find the conditional probability of picking the unfair coin given that we observed five tails in a row, or P(A|B).
Using Bayes' theorem, we have
P(A|B) = P(B|A) × P(A) / P(B)
P(B|A) is the probability of getting five tails in a row given that we are flipping the unfair coin. Since the unfair coin is not fair, we don't know its probability of coming up as tails, but let's assume it has a probability of 0.9 of coming up as tails. Thus, P(B|A) = 0.9^5 = 0.59049.
P(A) is the prior probability of picking the unfair coin, which is 0.5 since we picked one of two coins at random.
P(B) is the total probability of getting five tails in a row, which is the sum of the probabilities of getting five tails in a row with the fair coin and the unfair coin.
The probability of getting five tails in a row with the fair coin is 0.5^5 = 0.03125. The probability of picking the unfair coin and getting five tails in a row is P(B|A) × P(A) = 0.59049 × 0.5 = 0.295245. Thus, P(B) = 0.03125 + 0.295245 = 0.326495.
Now we can calculate P(A|B)
P(A|B) = P(B|A) × P(A) / P(B) = 0.59049 × 0.5 / 0.326495 = 0.9048
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 19
Blue 4
Green 11
Yellow 15
Purple 4
Based on these results, express the probability that the next spin will land on red or green or yellow as a percent to the nearest whole number.
The probability of the next spin landing on red or green or yellow is approximately 85%.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
In the given question,
The total frequency of all colors is:
19 (red) + 4 (blue) + 11 (green) + 15 (yellow) + 4 (purple) = 53
The probability of the next spin landing on red or green or yellow is the sum of the frequencies of these colors divided by the total frequency:
(19 + 11 + 15) / 53 = 45 / 53
To express this as a percent to the nearest whole number, we can multiply by 100 and round to the nearest whole number:
(45 / 53) * 100 ≈ 85%
Therefore, the probability of the next spin landing on red or green or yellow is approximately 85%.
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Answer:
Step-by-step explanation:
73%
8. True or False: A person only pays interest on the balance remaining at the end of the
billing cycle.
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Answer: True.
Step-by-step explanation: A person only pays interest on the balance remaining at the end of the billing cycle. If you carry a balance beyond the grace period, your credit card issuer will charge interest. Each month you carry a balance over from the previous month, you’ll have a finance charge added to your balance.
PLEASE ANSWER BOTH GEOMETRY WILL GIVE BRAINLIEST
Answer:
x = 90
Step-by-step explanation:
You want to know the value of x in the given diagram showing crossed chords.
Angle of Intersecting ChordsThe Angle of Intersecting Chords theorem tells you the angle where the chords cross is half the sum of the intercepted arc and the opposite arc.
Here, the angle marked x° is the supplement of the angle we can find based on the given arc measures:
180° -x° = (30° +(2x -30)°)/2
180 -x = 2x/2 = x . . . . . . . . . . divide by °, simplify
180 = 2x . . . . . . . . . . . . add x
90 = x . . . . . . . . . . . divide by 2
The value of x is 90.
What is the equation of the line that is parallel to y = 6x - 1 and passes through the point (-3, 4)?
The equation will be in slope-intercept form.
Oy=-6x + 5
Oy=6x14
0y=-1/6x-5
O y = 6x + 22
Oy=-1/6x-7
Answer:
y=6x+22
Explanation:
Parallel lines have the same slope and different y-intercepts.
So, all the lines with different slopes will be eliminated.
Now, we can check which line passes through the point (3,4) by substituting x for the x coordinate and y for the y coordinate.
y=6x+22
4=6(-3)+22
4=-18+22
4=4
So, the correct answer is y=6x+22.
What number is closest to the root number 120