If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
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The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
If you add two positive numbers together, which of the following is true about the result?
Answer:
If you add two positive numbers together you will get a positive.
Step-by-step explanation:
9. The linear regression equation is = 34.38x - 91.75. Use the equation to predict how far this
4.38x-91-75 Use
person will travel after 10 hours of driving.
The answer of the given question based on the linear regression is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
What is Distance?Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.
Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.
Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.
What is Distance?The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.
The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is
y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.
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The complete question is,
The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.
solve the system 2 -1 5 -2 with -2 -1 . give your solution in real form. , . an ellipse with counterclockwise orientation 1. describe the trajectory.
The solution of the system 2 -1 5 with -2 -1 in real form is (x, y) = (7/4, 7/2).
To solve the system with the given coefficients, first, let's rewrite it as a linear system of equations:
2x - y = 5
-2x - y = -2
Now, let's solve this system step-by-step:
Step 1: Solve for y in the first equation:
y = 2x - 5
Step 2: Substitute the expression for y from Step 1 into the second equation:
-2x - (2x - 5) = -2
Step 3: Simplify and solve for x:
-2x - 2x + 5 = -2
-4x = -7
x = 7/4
Step 4: Substitute the value of x back into the expression for y:
y = 2(7/4) - 5
y = 7/2
The solution in real form is (x, y) = (7/4, 7/2).
Regarding the ellipse with counterclockwise orientation, the trajectory can be described as a smooth, closed curve in the shape of an ellipse. The ellipse will have a major and minor axis, with the points on the ellipse moving continuously in a counterclockwise direction along the curve.
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9 N = 480 ´ 109
(a) Write N as a number in standard form.
(1)
(b) Write N as a product of powers of its prime factors.
Show your working clearly.
(3)
(c) Find the largest factor of N that is an odd number.
Answer:
(a) To write 9 N as a number in standard form, we need to express it as a number between 1 and 10 multiplied by a power of 10. To do this, we can divide 9 N by 10 until we get a number between 1 and 10:
9 N = 480 × 10^9
9 N ÷ 10 = 48 × 10^9
9 N ÷ 10^2 = 4.8 × 10^9
9 N ÷ 10^3 = 0.48 × 10^9
9 N ÷ 10^4 = 0.048 × 10^9
9 N ÷ 10^5 = 0.0048 × 10^9
Therefore, 9 N = 4.8 × 10^10.
(b) To write N as a product of powers of its prime factors, we can first factorize N:
480 × 10^9 = 2^5 × 3 × 5 × 10^9
Then, we can express 10^9 as 2^9 × 5^9 and substitute it in the factorization:
2^5 × 3 × 5 × 2^9 × 5^9 = 2^14 × 3 × 5^10
Therefore, N = 2^14 × 3 × 5^10.
(c) To find the largest factor of N that is an odd number, we need to remove all factors of 2 from the factorization of N. We can do this by dividing N by 2 as many times as possible:
N = 2^14 × 3 × 5^10
N ÷ 2 = 2^13 × 3 × 5^10
N ÷ 2^2 = 2^12 × 3 × 5^10
N ÷ 2^3 = 2^11 × 3 × 5^10
N ÷ 2^4 = 2^10 × 3 × 5^10
N ÷ 2^5 = 2^9 × 3 × 5^10
N ÷ 2^6 = 2^8 × 3 × 5^10
N ÷ 2^7 = 2^7 × 3 × 5^10
N ÷ 2^8 = 2^6 × 3 × 5^10
N ÷ 2^9 = 2^5 × 3 × 5^10
N ÷ 2^10 = 2^4 × 3 × 5^10
N ÷ 2^11 = 2^3 × 3 × 5^10
N ÷ 2^12 = 2^2 × 3 × 5^10
N ÷ 2^13 = 2 × 3 × 5^10
N ÷ 2^14 = 3 × 5^10
Therefore, the largest factor of N that is an odd number is 3 × 5^10.
The rate of the jetstream is 300 mph traveling with the jetstream an airplane can fly 3000 miles in the same amount of time as it takes to fly 1000 miles against the jetstream. What is the airplanes, average rate in calm air?
The airplane's average rate in calm air is 600 mph.
What is an average?
In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics
Let's denote the airplane's average rate in calm air by x mph.
When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:
3000 / (x + 300) = 1000 / (x - 300)
We can cross-multiply to simplify:
3000(x - 300) = 1000(x + 300)
Expanding the brackets gives:
3000x - 900000 = 1000x + 300000
Simplifying and rearranging terms gives:
2000x = 1200000
x = 600
Therefore, the airplane's average rate in calm air is 600 mph.
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combined with a high tide on september 16, 2020 by how many feet did that storm surge submerge the lowest parts of pensacola beach? enter a number (no words) in the blank.
The steps to find the depth through which the storm submerges the lowest parts of the Pensacola Beach is given below.
How to solve for the feet that the storm submerges?As it has been given in the question, Pensacola beach is located 5-10 feet above sea level.
The ocean water rises upto 5.5 feet during a storm
Hence you need to add up the height of the highest tide on 16 September to 5.5 feet.
If the combined height of the highest tide and the storm tide is greater than 10 feet, then the whole Pensacola beach submerges.
You just subtract the combined height of the storm and the highest tide from the height of the beach.
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Portions of Pensacola Beach, a coastal community built on a barrier island, are located at 3 - 10 feet above sea level.
Hurricane Sally, which struck Pensacola on September 16, 2020 and brought a 5.5 foot storm.
Combined with a high tide on September 16,202, by how many feet did that storm surge submerge the lowest parts of Pensacola Beach? (Hint: use the information in question and change the date on the tidal chart to September 16, 2020) Now, compare your answers above, and think about how the type (pattern) and size of the tides differ for these two locations
after a (not very successful) trick or treating round, candice has 12 tootsie rolls and 10 twizzlers in her pillow case. her mother asks her to share the loot with her three younger brothers. (a) how many different ways can she do this?
Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.
(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:
*****|**********|***|****
The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:
C(27, 3) = 27! / (3! * 24!) = 2925
(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:
C(16, 3) = 560 for the Tootsie rolls
C(10, 3) = 120 for the Twizzlers
To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:
560 * 120 = 67200
Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.
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Complete question:
After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.
(A) How many different ways can she do this?
(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?
a newsletter publisher believes that under 69% 69 % of their readers own a rolls royce. is there sufficient evidence at the 0.10 0.10 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69
A newsletter publisher believes that under 69% of their readers own a Rolls Royce.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.
Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.
Null Hypothesis (H0): p ≤ 0.69
Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.
Alternative Hypothesis (H1): p > 0.69
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Find the x-intercept of 3 tan(3x) over the interval (pi/6,3pi/6)
Express your answer in terms of pi.
The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
What is function ?
A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.
Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).
Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.
To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.
Let's first simplify the function:
3 tan(3x) = 0
tan(3x) = 0
We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:
tan(3x) = 0 --> 3x = nπ for n ∈ ℤ
Now we solve for x:
3x = nπ
x = nπ/3
Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:
π/6 < x < 3π/6
π/6 < nπ/3 < 3π/6
1/2 < n < 3/2
So the values of x that satisfy the given condition are:
x = π/3 and x = 2π/3
Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
Expressed in terms of π, the x-intercepts are:
π/3π and 2π/3π, which simplify to:
x = 1/3 and x = 2/3.
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The polynomial has been factored completely. What are the zeros of the function?
x2-2x-48-(x+6)(x-8)
x=6 and x=8
x=-6 and x=8
x = 6 and x = -8
x = -6 and x = -8
The zeroes of the factored polynomial as required to be determined in the task content are: x = -6 and x = 8.
What are the zeroes of the factorised polynomial?It follows from the task content that the zeroes of the completely factorised polynomial are to be determined.
Since the given polynomial is; x² - 2x - 48 which has been factorised completely to; (x + 6) (x - 8).
Ultimately, the zeroes of the Polynomial are as follows;
x + 6 = 0; x = -6.
and
x - 8 = 0; x = 8.
Conclusively, the zeroes of the polynomial are; x = -6 and x = 8.
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a dependent variable that maintains constant measurements throughout an experiment will be depicted by a
A dependent variable that maintains constant measurements throughout an experiment will be depicted by a straight, horizontal line in a graph.
In an experiment, the dependent variable is the variable being measured, and it is expected to change in response to changes in the independent variable. However, if the dependent variable remains constant throughout the experiment, it indicates that it is not affected by the independent variable.
When such a situation arises, the data points for the dependent variable will be located at the same level or value, resulting in a horizontal line in the graph.
This straight, horizontal line represents the constant measurements of the dependent variable, and it can provide valuable insights into the nature of the relationship between the independent variable and the dependent variable.
A dependent variable that maintains constant measurements throughout an experiment may indicate a flaw in the experimental design, such as an incorrect assumption about the nature of the relationship between the independent variable and the dependent variable, or an uncontrolled confounding variable.
Therefore, it is important to carefully analyze the data and the experimental design to identify and address any potential issues.
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Compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only 1 inch.
HINT: The cones are similar
the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.
the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:
V₁ = (1/3)π[tex]r^2[/tex]h
If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:
V₂ = (1/3)π[tex]r^2[/tex](h-1)
To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:
V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h
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< Back to task
In the quadrilateral below, angles DAB and BCD are the same size.
What is the size of angle DAB?
D
228
34° -B
Answer >
The size of angle DAB in the quadrilateral is 49°.
How to find the size of angle DAB?The sum of the interior angles of a quadrilateral is 360°. We can say:
∠A + ∠B + ∠C + ∠D = 360°
∠A + 34° + ∠C + 228° = 360°
∠A + ∠C + 262° = 360°
∠A + ∠C = 360 - 262
∠A + ∠C = 98
Since angles DAB and BCD are the same size. This implies ∠A = ∠C. Thus:
∠A + ∠A = 98
2∠A = 98
∠A = 98/2
∠A = 49°
Therefore, the size of angle DAB is 49°.
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Complete Question
Check the attached image
Write the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
y = -5x² + 5 is the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
We know that the vertex of the parabola is (0, 5), which means that the equation for the parabola has the form:
y = a(x - 0)² + 5
where 'a' is a constant that determines the shape of the parabola. Since the parabola passes through the point (1, 0), we can substitute these values into the equation and solve for 'a':
0 = a(1 - 0)² + 5
0 = a + 5
a = -5
Therefore, the equation of the parabola is: y = -5x² + 5
This equation represents a parabola that opens downwards (since the coefficient of x² is negative), has a vertex at (0, 5), and passes through the point (1, 0).
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Find the value of x.
In the figure of circle provided. the value of x is
161 degreesHow to find the value of xIn a circle, equal chords subtends equal arc length.
In the problem it was given that:
chord SU is equal to chord ST hence we have that
x + x + 38 = 360 (angle in a circle)
collecting like terms
2x + 38 = 360
2x = 360 - 38
2x = 322
Isolating x by dividing both sides by 2
2x / 2 = 322 / 2
x = 161
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Elyse has a gift card to a local movie theater. the graph shows the amount of money remaining on her gift card based on the number of movies she has seen.
a. write an equation to represent the situation.
b. interpret the slope and y-intercept in the context of the situation.
a. The equation to represent the situation is y = -12x + 120, where x is the number of movies and y is the amount of money remaining on the gift card.
What is money?Money is a medium of exchange that is widely accepted as a way to pay for goods and services or to settle debts. Money also serves as a store of value, providing a way for people to save for the future. Money is generally created through government-backed fiat currencies, such as the U.S. dollar, which are issued and regulated by central banks. Money can also be created in the form of crypto-currencies, such as Bitcoin, which are not issued by any single government or central bank. Money is essential for economic growth and stability, as it allows for efficient exchanges of goods and services. Money can also be a source of financial security, providing people with a way to manage their finances and plan for the future.
b. The slope of -12 indicates that for every movie that Elyse sees, she will spend $12 from her gift card. The y-intercept of 120 indicates that if Elyse has not seen any movies, she will have $120 remaining on her gift card.
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The situation is,
a) The line equation is [tex]y = -3x - 6[/tex]
b) The line's y-intercept is -6, which indicates that when the amount of movies x = 0 , the amount on gift y = -6
c) The slope of the line is -3, indicating that as the number of movies x increases, the rate of change of the amount on the gift is declining.
What is an Equation of a line?a). The equation provides the line's slope.
Slope,
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Changing the numbers indicated in the slope equation,
Slope,
[tex]m=\frac{(6-12)}{(4-2)}[/tex]
Slope m = -6/2
Slope m = -3
The slope is -3
The equation of the line is,
[tex]y - y_1 = m ( x - x_1 )[/tex]
Substitute the given values in the equation,
[tex]y - 12 = -3 ( x - 2 )[/tex]
Simplify the equation,
[tex]y - 12 = -3x + 6[/tex]
Adding 12 on both sides
[tex]y = -3x - 6[/tex]
The equation of line is [tex]y = -3x - 6[/tex]
b). The y-intercept of the equation of line [tex]y = -3x - 6[/tex] is [tex]-6[/tex], when [tex]x=0[/tex]
c). The slope of the line [tex]y = -3x - 6[/tex] is [tex]m = -3[/tex] and the value is decreasing
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The completr question and graph attached below,
c. What is the slope, and what does it mean in the context of the situation?
we learned in exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. we now consider a random sample of fifty 18-20 year olds. a) how many people would you expect to have consumed alcoholic beverages? do not round your answer.
Rounding off the value of X to the nearest whole number, we get that approximately 35 people would be expected to have consumed alcoholic beverages among 50 randomly selected 18-20 year-olds.
In exercise 3.25, it was learned that about 69.7% of 18-20 year-olds consumed alcoholic beverages in 2008.
Now, consider a random sample of fifty 18-20 year-olds.
It is required to calculate the number of people who would be expected to have consumed alcoholic beverages.
Let X be the number of people who have consumed alcoholic beverages out of 50 randomly selected 18-20 year-olds.
Let p be the proportion of 18-20 year-olds who consumed alcoholic beverages in 2008.
Therefore, the sample proportion is given as \hat{p}
Hence, p=0.69 \hat{p}=X/50
Now, by the properties of the sample proportion, E(\hat{p})=p
Therefore,
E(\hat{p})=E(X/50)
Thus, p=E(X/50) Or, X=50p
Substituting the value of p, we have
X=50(0.697)=34.85
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what moves beyond excel graphs and charts into sophisticated analysis techniques such as controls, instruments, maps, time-series graphs, and more?
Answer:
Data Visualization Tools
Step-by-step explanation:
(HELP PLS)
Milwaukee's average high temperature in the summer is four
degrees lower than other cities in its same latitude.
Which option best describes the reason for that change?
OSioux Falls is near mountains.
O Milwaukee is beside a lake.
OSioux Falls is closer to a desert.
O Milwaukee has more mountains.
We can claim that after answering the above question, the As a result, equation the correct answer is "Milwaukee is near a lake."
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."
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in practice, the most frequently encountered hypothesis test about a population variance is a .
In practice, the most frequently encountered hypothesis test about a population variance is an F-test.
In statistics, hypothesis tests provide us with a tool to evaluate evidence about a population. Hypothesis testing is a crucial part of statistical inference, in which an analyst tests hypotheses using statistical methods such as t-tests, chi-squared tests, and analysis of variance (ANOVA).
In practice, the most commonly used hypothesis test for population variance is the F-test. This test can be used to test the null hypothesis that two population variances are equal. F-tests have a wide range of uses, including in quality control, financial analysis, engineering, and more. The F-test statistic is calculated by dividing the sample variance of one sample by the sample variance of another sample. The F-test requires that the data come from populations that follow normal distributions, and it is sensitive to outliers in the data.
Therefore, in practice, the most frequently encountered hypothesis test about a population variance is an F-test.
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.
in a survey, 69% of americans said they own an answering machine. if 15 americans are selected at random, find the probability that exactly 7 own an answering machine. round your answer to three decimal places.
Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.
To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.
In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:
P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)
Using a calculator or statistical software, we can evaluate this expression to find:
P(X = 7) ≈ 0.170
This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.
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if 10 friends are going to occupy 10 seats in shuttle on the way to the airport, how many different ways can they arrange themselves in the shuttle? provide your answer below:
If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.
Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.
Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800
Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.
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i need help ASAP
Calculate the amount of interest on $2,000.00 for 4 years, compounding daily at 2.25 % APR.
From the Monthly Interest Table use $1.094171 in interest for each $1.00 invested
A $2,088.34
B $2188.34
C $2,288.34
D $2,388.34
Answer:
Step-by-step explanation:
First, we need to calculate the annual interest rate from the given APR.
APR = 2.25%
Daily interest rate = 2.25% / 365 = 0.00616438
Now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = time in years
In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.
A = 2000(1 + 0.00616438/365)^(365*4)
A = 2000(1.00616438)^1460
A = $2,388.34 (rounded to the nearest cent)
Therefore, the answer is option D) $2,388.34.
Complete the table
Original Price
Percent of Discount
15%
Sale Price
$146.54
The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.
What does a maths percent mean?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.
What does the word "percentage" actually mean?Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.
[tex]w-[0.15]=146.54[/tex]
so [tex]w-85p=146.54[/tex]
[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.
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in 2005 the population of a district was 35,700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function?
The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.
The formula for the continuous exponential growth is given by the formula:
P = Pe^(rt)
where,P is the population in the future.
P0 is the initial population.
t is the time.
r is the continuous interest rate expressed as a decimal.
e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.
Therefore, t = 25.We will now use the formula:
P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.
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Answer: I got 97,042.7
Step-by-step explanation:
solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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2x + y = -7
3x = 6 + 4y
x = ?
y = ?
2x + y = -7
y= -7-2x
put this value in 2nd equation
3x=6+4(-7-2x)
3x=6-28-8x
11x= -22
x= -2
y= -7-2(-2)
y= -7+4
y= -3
You are offered a job that pays $34,000 during the first year, with an annual increase of 6% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.06 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
Pls help answer with good detailed explanation
math help needed detailed explanation
The percentage of 8th graders who send more than 50 texts is 56.15%
How to find the percentage?Here we want to find the percentage of eight grades who send more than 50 texts, and to get that we need to use the values in the table.
The formula for that percentage is:
P = 100%*(number that send more than 50 texts)/(total number)
On the table we can see that the total number of 8th gradesr is 130, and the number that send more than 50 messages is 73, then the percentage is:
P = 100%*(73/130)
P = 56.15%
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