Answer:
irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of√2. A counterpart problem in measurement would be to find the length of the diagonal of a square whose side is one unit long; there is no subdivision of the unit length that will divide evenly into the length of the diagonal
Answer:
Step-by-step explanation:
a real number that cannot be written as a simple fraction: 1.5 is rational, but π is irrational. Irrational means not Rational
Test the hypothesis using the? P-value approach. Be sure to verify the requirements of the test.
Upper H 0 : p equals 0.65 versus Upper H 1 : p less than 0.65
n equals 150 comma x equals 87 comma alpha equals 0.05
With a sample size of 150 and a sample proportion of 0.58, the test statistic is -3.01. The p-value is approximately 0.0027, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the true proportion is less than 0.65.
To test the hypothesis using the P-value approach, we can follow these steps:
Step 1: Verify the requirements of the test.
Random sample: Not given explicitly, but we assume that the sample is a simple random sample.
Independence: The sample size is less than 10% of the population size, so we can assume independence.
Sample size: n = 150 >= 10 successes and n(1-p) = 150(0.35) = 52.5 >= 10 failures. Hence, the sample size is large enough.
Success-failure condition: Both np = 150(0.65) = 97.5 and n(1-p) = 150(0.35) = 52.5 are greater than 10.
All the requirements are satisfied.
Step 2: State the null and alternative hypotheses.
Upper H0: p = 0.65 (null hypothesis)
Upper H1: p < 0.65 (alternative hypothesis)
Step 3: Calculate the test statistic.
The test statistic for a one-tailed lower-tailed test is z = (x - np) / sqrt(np(1-p)/n), where x is the number of successes in the sample, n is the sample size, p is the hypothesized proportion under the null hypothesis, and np and n(1-p) are the expected number of successes and failures under the null hypothesis.
Substituting the given values, we get z = (87 - 97.5) / sqrt(97.5(0.35)/150) = -2.62 (rounded to two decimal places).
Step 4: Calculate the P-value.
The P-value is the probability of getting a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true.
Since this is a lower-tailed test, the P-value is the area to the left of the observed test statistic in the standard normal distribution.
Using a calculator or a table, we find P(z < -2.62) = 0.0044 (rounded to four decimal places).
Step 5: Make a decision and interpret the results.
The P-value (0.0044) is less than the significance level (0.05), so we reject the null hypothesis.
There is sufficient evidence to conclude that the true proportion of successes is less than 0.65 at the 0.05 level of significance.
In other words, there is evidence to support the alternative hypothesis that the proportion of successes is less than 0.65.
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organizations that build __________ information systems create systems that are paramount to business success.
A. collaborative
B. office
C. networked
D. strategic
E. none of these information systems
Organizations that build strategic information systems create systems that are paramount to business success. The correct option is(D).
Strategic information systems are those that support the long-term goals and objectives of an organization, aligning the use of technology with the strategic direction of the business. These systems provide a competitive advantage by enabling the organization to achieve its strategic goals and objectives more efficiently and effectively.
They typically involve the integration of different types of information systems, such as transaction processing systems, decision support systems, and executive information systems, to support the decision-making process at all levels of the organization.
By building strategic information systems, organizations can improve their overall performance, enhance their operational efficiency, and gain a competitive advantage in the marketplace.
Such systems can help organizations to better understand their customers, identify new market opportunities, improve supply chain management, and optimize business processes.
In today's rapidly changing business environment, strategic information systems are essential for organizations to remain competitive and achieve long-term success.
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HELP ASAP/ An international data plan charges $10.00 for 4GB of data. Anything over 4GB is priced at $2.50 per GB. Which equation can be used to find y, the total cost of the international plan, if x represents the number of GB over 4?
The equation is y = 2.50x + 10.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: An international data plan charges $10.00 for 4GB of data. Anything over 4GB is priced at $2.50 per GB.
We have to find the equation that can be used to find y, the total cost of the international plan, if x represents the number of GB over 4.
Let the total cost of the international plan = y
x be the cost of the plan for over 4 GB.
Fixed charge for 4 GB = $10
Now y = 2.50x + 10
Hence, the equation is y = 2.50x + 10.
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What is the image point of (6, 2) after a translation right 3 units and down 5 units?
Answer:
(9,-3)
Step-by-step explanation:
Given the vectors:
x1 =x2 =x3 =
What is the dimension of Span(x1,x2, x3)?
Please give a detailed proof of solution. Thank you!
The dimension of Span(x1, x2, x3) is zero.
How to find the dimension of Span?The dimension of the span of a set of vectors is the number of vectors in a basis for that span. A basis is a linearly independent subset of vectors that span the same space as the original set.
In this case, we have:
x1 = x2 = x3 = [0, 0, 0]
Since all three vectors are identical and equal to the zero vector, any linear combination of them will also be the zero vector. That is:
c1x1 + c2x2 + c3x3 = (c1 + c2 + c3)[0, 0, 0] = [0, 0, 0]
Therefore, the set {x1, x2, x3} is linearly dependent and does not form a basis for the span of these vectors.
In fact, the span of these vectors consists only of the zero vector.
So, the dimension of Span(x1, x2, x3) is zero, since there are no linearly independent vectors in this span.
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the probability that a patient recovers from a stomach disease is .8. suppose 20 people are known to have contracted this disease. what is the probabi
We can use the binomial distribution formula to find the probability of how many people will recover from the stomach disease out of the 20 people who have contracted it.
The probability that a patient recovers from a stomach disease is .8, and we know that 20 people have contracted this disease. To find the probability of how many of these 20 people will recover, we can use the binomial distribution formula.
The binomial distribution formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where X is the number of successes, k is the specific number of successes we want to find, n is the total number of trials, p is the probability of success, and (n choose k) represents the number of combinations of n items taken k at a time.
In this case, we want to find the probability that out of the 20 people with the disease, k of them will recover. We can set n = 20, p = 0.8, and k can range from 0 to 20.
To find the probability that exactly 10 people will recover, we plug in n = 20, p = 0.8, and k = 10 into the formula: P(X=10) = (20 choose 10) * 0.8^10 * (1-0.8)^(20-10) = 0.0687, or approximately 6.87%.
To find the probability that at least 15 people will recover, we need to add up the probabilities of 15, 16, 17, 18, 19, and 20 people recovering. We can use a calculator or a table to find each individual probability and add them up. The total probability is approximately 0.9894, or 98.94%.
Overall, we can use the binomial distribution formula to find the probability of how many people will recover from the stomach disease out of the 20 people who have contracted it.
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The recursive rule for a sequence is shown.
a^n=a^n-1+5
a1 = 12
Write the explicit rule in simplified form for the sequence.
a^n =
Considering the recursive rule, the explicit rule for the arithmetic sequence is given by aₙ = 12 + 5(n - 1).
What is arithmetic progression?
An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. The n-ary sum of AP is the sum (addition) of the first n terms of the arithmetic sequence.
This means that n is twice the value of the first term ("a") and the product of the difference between the second term and the first term ("d", also called the tolerance), plus the sum of (n-1). It is equal to the value divided by a factor. where n is the number of terms to add.
The nth term of an arithmetic sequence is given by:
aₙ = a₁ + (n- 1)d
the first term is = 12
the common difference is d = 5
thus, the explicit formula is given by
aₙ = 12 + 5(n - 1)
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finf an angle berween 0 and 360 that is cotrmiinal with given angle? exmple
To find an angle that is coterminal with a given angle between 0 and 360 degrees, you can add or subtract multiples of 360 degrees until you reach an angle that falls within the desired range. For example, if the given angle is 45 degrees, you can add 360 degrees to get 405 degrees, which is coterminal with 45 degrees. Alternatively, you can subtract 360 degrees to get -315 degrees, which is also coterminal with 45 degrees when you add 360 degrees to it to bring it back into the range of 0 to 360 degrees.
Hi! To find an angle between 0 and 360 degrees that is coterminal with a given angle, you can use the following steps:
1. Determine the given angle (e.g., the example angle).
2. Add or subtract multiples of 360 degrees until the resulting angle falls within the desired range (between 0 and 360 degrees).
For example, if the given angle is -45 degrees:
-45 + 360 = 315 degrees
Now the coterminal angle is 315 degrees, which is between 0 and 360 degrees.
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a car started out from memphis toward little rock at the rate of 60 km/hr. a second car left from the same point 2 hours later and drove along the same route at 75 km/hr. how long did it take the second car to overtake the first car?
According to the distance, it took the second car 8 hours to overtake the first car.
Let's assume that the distance between Memphis and Little Rock is D kilometers, and let's call the time it takes the second car to overtake the first car T hours. We can use the following formula to calculate the distance traveled by each car:
Distance = Speed x Time
For the first car, we can say that it traveled for T + 2 hours (because it started two hours earlier) at a speed of 60 km/hr:
Distance1 = 60 x (T + 2)
For the second car, we can say that it traveled for T hours at a speed of 75 km/hr:
Distance2 = 75 x T
Since they meet at some point on the route, we can say that Distance1 = Distance2, which means that:
60 x (T + 2) = 75 x T
Simplifying this equation, we get:
60T + 120 = 75T
120 = 15T
T = 8
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Given that sin theta = 7/25 and cos theta < 0, determine the values of the sine and cosine functions for 2theta.
The values of the sine and cosine functions for 2θ are:
sin(2θ) = -336/625
cos(2θ) = 527/625
We have,
We can determine the values of the sine and cosine functions for 2θ using the double-angle formulas:
sin(2θ) = 2sin θ cos θ
cos(2θ) = cos²θ - sin²θ
Given sin θ = 7/25, we can use the Pythagorean identity
sin²θ + cos²θ = 1 to find cos θ:
sin²θ + cos²θ = 1
(7/25)² + cos²θ = 1
49/625 + cos²θ = 1
cos²θ = 1 - 49/625
cos²θ = 576/625
cos θ = -24/25
Now, we can find sin(2θ) and cos(2θ) using the double-angle formulas:
sin(2θ) = 2sin θ cos θ
= 2 * (7/25) * (-24/25)
= -336/625
cos(2θ) = cos²θ - sin²θ
= (-24/25)² - (7/25)²
= 576/625 - 49/625
= 527/625
Therefore,
The values of the sine and cosine functions for 2θ are:
sin(2θ) = -336/625
cos(2θ) = 527/625
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find the quadratic equation whose roots are 1/2 and -1/3
[tex]\begin{cases} x = \cfrac{1}{2} \implies 2x=1&\implies 2x-1=0\\[1em] x = -\cfrac{1}{3}\implies 3x=-1&\implies 3x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 2x -1 )( 3x +1 ) = \stackrel{0}{y}}\hspace{3em}\stackrel{\textit{now, we're assuming that}}{a=1}\qquad 1( 2x -1 )( 3x +1 ) =y \\\\\\ \stackrel{ F~O~I~L }{( 2x -1 )( 3x +1 )} =y\implies \boxed{6x^2-x-1=y}[/tex]
factor out the GCF from the polynomial?
The GCF, when factored out from the polynomial would be 5x^3(5x^3 + x + 2).
How to factor the GCF ?To factor the greatest common factor (GCF) out of the polynomial 25x^6 + 5x^4 + 10x^3, we first need to identify the GCF of the coefficients and the variables.
Coefficients: 25, 5, 10
The GCF of 25, 5, and 10 is 5.
Variables: x^6, x^4, x^3
The GCF of x^6, x^4, and x^3 is x^3 since it is the lowest power of x.
Now, we can factor the GCF (5x^3) out of the polynomial:
5x^3(5x^3 + x + 2)
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The full question is:
Factor the GCF out of the polynomial below:
25x^6 + 5x^ 4 + 10x^3
If C is any piecewise-smooth simple closed plane curve and f and g are differentiable functions, show that integral_c f(x) dx + g(y)dy - 0.
If C is "piecewise-smooth" simple closed "plane-curve" and "f" and "g" are "differentiable-functions", then the process to show that ∫c [f(x) dx + g(y) dy] is explained below.
The "Green's-Theorem" is defined as a fundamental result in vector calculus that relates "line-integral" of a vector field around a closed curve in plane to a "double-integral" of curl of vector field over region enclosed by curve.
To prove that ∫c [f(x) dx + g(y) dy] = 0 for any piecewise-smooth simple closed plane curve C and differentiable functions f(x) and g(y), we use Green's theorem.
Green's theorem states that for a two-dimensional vector field F = (P, Q) and a simple closed curve C in the plane oriented counterclockwise, we have:
⇒ ∫c F · dr = ∬R (∂Q/∂x - ∂P/∂y) dA
where "dr" is an infinitesimal displacement along the curve C, and "dA" is an infinitesimal area element in "region-R" enclosed by "curve-C".
Let F = (f(x), g(y)) be the vector field defined by the given functions f(x) and g(y).
Then, we have:
⇒ P = f(x)
⇒ Q = g(y)
Taking the partial derivatives,
We get,
⇒ ∂P/∂y = 0
⇒ ∂Q/∂x = 0
Substituting these values into Green's theorem,
We get,
⇒ ∫c F · dr = ∬R (∂Q/∂x - ∂P/∂y) dA
⇒ ∫c (f(x) dx + g(y) dy) = 0
Therefore, it is proved that ∫c [f(x) dx + g(y) dy] = 0.
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if a group is abelian, what does this tell us about normality of the subgroups? why?
If a group is abelian, then all of its subgroups are normal.
This is because, in an abelian group, the order of multiplication of elements does not matter.
Therefore, if we take an element from a subgroup and conjugate it with an element outside of the subgroup, the result will still be in the subgroup.
Thus, the subgroup is normal.
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Estimate the solution to the system of equations. You can use the interactive graph below to find the solution.
Choice A: x= -1 2/5, y= 1 3/5
Choice B: x= -2 2/5, y= 1 3/5
Choice C: x= -1 2/5, y= 2 3/5
Choice D: x= -2 2/5, y= 2 3/5
The solution of the system of equations is given by the intersection of the two lines, we can see that the correct option is A.
x = -(1 + 2/5), y = (1 +3/5)
How to solve a system of equations graphically?To solve a system of equations graphically, we need to graph both equations of the system in the same coordinate axis and then find the point where the graphs intercept.
Here the system of equations is:
-3x + 3y = 9
2x - 7y = -14
The graph of the system can be seen in the image at the end, there we can see that the two lines intersect at the point (-1.4, 1.6). so that is the solution.
The best estimation from the given ones is:
x = -(1 + 2/5), y = (1 +3/5)
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Kinsey is making candles by melting wax. Some of the candles are in the shape of a sphere with a radius of 2 inches.
What is the volume, in cubic inches, of one spherical candle? Use 3.14 for π Round your answer to the nearest hundredth
The volume of one spherical candle is approximately 33.51 cubic inches.
What is meant by volume?
Volume refers to the amount of space occupied by an object or substance. It is typically measured in cubic units such as litres, cubic meters, or gallons.
What is meant by spherical?
Spherical refers to any object or geometry that is based on or resembles a sphere, which is a three-dimensional shape with all points on its surface equidistant from its centre.
According to the given information
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Substituting r = 2 into the formula, we get:
V = (4/3)π(2)³
V = (4/3)π(8)
V = (32/3)π
V ≈ 33.51 cubic inches (rounded to the nearest hundredth)
Therefore, the volume of one spherical candle is approximately 33.51 cubic inches.
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Explain why a point on the boundary should not be used as a test point.
Answer: A test point on the boundary does not show which half–plane contains the points that make the inequality true.
Step-by-step explanation:
Which of the linear equations represents the graphed line?
The linear equations that represents the graphed line is y = (2/3)x + 1
How to find the linear equations that represents a graphed line?The general form of linear equations is given by:
y = mx + c
where m is the slope and c is the y-intercept
The given graph passes through points (0, 1) and (6, 5). Thus, we can say:
c = 1
By definition, slope is given by:
m = (y2 - y1)/(x2 - x1)
where x1 = 0, y1 = 1 and x2 = 6, y2 = 5
m = (5 - 1)/(6 - 0)
m = 4/6
m = 2/3
Substitute m and c into y = mx + c:
y = (2/3)x + 1
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Use the image to determine the line of reflection.
Graph of polygon ABCDE with point E at 5 comma negative 1. A second polygon A prime B prime C prime D prime E prime with E prime at 5 comma negative 5.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 6
Reflection across y = −3
Therefore , the solution of the given problem of coordinates comes out to be "Reflection across x = 5" is the right response.
What exactly is coordinate plane mean?A parameter can accurately detect position using a variety of attributes or coordinates when used in conjunction with specific other algebra elements on this location, such as Euclidean space. When travelling in reflected space, coordinates, which look as groups of numbers, can be used to pinpoint specific locations or objects. Finding an object over both surfaces can be done using the y & x measurements.
Here,
We must consider the relative positions of the corresponding points in each polygon in order to identify the line of reflection between polygons ABCDE and A' B' C' D' E'.
As a result, the line of reflection has to be horizontal and equally spaced from E and E'.
The line of reflection must be the vertical line that crosses x = 5 because both E and E' have x-coordinates of 5.
In light of this, the reflection must cross the line x = 5.
The closest choice, "Reflection across x = 6," is not the right response because the line of reflection is not x = 6.
"Reflection across x = 5" is the right response.
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Plot the complex number on the complex plane and write it in polar form and in exponential form. 10 + 10 i
To plot the complex number 10 + 10i on the complex plane, we can think of it as a point in Cartesian coordinates (x,y), where the x-coordinate is the real part and the y-coordinate is the imaginary part. In this case, we have x = 10 and y = 10, so we can plot the point (10, 10) in the complex plane.
To write this complex number in polar form, we can use the formula r = |z| = sqrt(x^2 + y^2) to find the modulus (or magnitude) of the complex number. In this case, we have r = sqrt(10^2 + 10^2) = sqrt(200) = 10*sqrt(2).
Next, we can use the formula theta = atan2(y,x) to find the argument (or angle) of the complex number in radians. Note that the atan2 function takes both the y and x coordinates as arguments, and returns an angle in the range [-pi, pi]. In this case, we have theta = atan2(10,10) = pi/4.
Therefore, the polar form of the complex number 10 + 10i is z = 10*sqrt(2) * (cos(pi/4) + i*sin(pi/4)).
To write this complex number in exponential form, we can use Euler's formula e^(ix) = cos(x) + i*sin(x). In this case, we have x = pi/4, so we can write:
10 + 10i = 10*sqrt(2) * (cos(pi/4) + i*sin(pi/4))
= 10*sqrt(2) * e^(i*pi/4)
Therefore, the exponential form of the complex number 10 + 10i is z = 10*sqrt(2) * e^(i*pi/4).
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The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated? Pedestrian Intoxicated?
Yes No
Yes 54 83
No 246 603
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
Question #2
The table summarizes results from 978 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated? Pedestrian Intoxicated?
Yes No
Yes 45 76
No 260 597
If two different pedestrian deaths are randomly selected, find the probability that they both involved pedestrians that were intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = Incorrect%
The total number of pedestrian deaths is 986. From the table, we see that 603 of these deaths were caused by a sober driver and a sober pedestrian, and 83 were caused by a sober driver and an intoxicated pedestrian. Therefore, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is:
(603 + 83)/986 = 0.7134
Rounded to one decimal place, this is 71.3%.
The total number of pedestrian deaths is 978. From the table, we see that 76 deaths were caused by a sober driver and a sober pedestrian, and 45 deaths were caused by an intoxicated driver and a sober pedestrian. To find the probability that two different pedestrian deaths involve intoxicated pedestrians, we need to calculate the probability of choosing two intoxicated pedestrians out of the remaining 857 (after the first death is chosen). This is:
(83/857) x (82/856) = 0.0092
Multiplying by 100 and rounding to one decimal place, the probability is 0.9%. Therefore, the answer is:
prob = 0.9%
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What is y=4x-1 and 2x+y=23 as an ordered pair
Answer:
x,y=(4, 15)
Step-by-step explanation:
We need to substitute the value of y=4x-1 and plug it into the equation 2x+y=23.
By this we get:
2x+4x-1=23
6x-1=23
6x=24
x=4
We can now solve for y using the given value of x.
2x+y=23
2×4+y=23
8+y=23
y=23-8
y=15
Hope this helps!
Answer:
x,y=(4, 15)
Step-by-step explanation:
We need to substitute the value of y=4x-1 and plug it into the equation 2x+y=23.
By this we get:
2x+4x-1=23
6x-1=23
6x=24
x=4
We can now solve for y using the given value of x.
2x+y=23
2×4+y=23
8+y=23
y=23-8
y=15
Step-by-step explanation:
Anyone know what it is?
if 0 < a < b, show that i) a < âab < b
Given that 0 < a < b, we need to show that a < √ab < b.
i) To show a < √ab, we know that 0 < a, and since a < b, both a and b are positive numbers. Multiplying two positive numbers gives us another positive number, so ab > 0. Taking the square root of a positive number gives a value greater than the original number. Therefore, √ab > √a² or √ab > a.
ii) To show √ab < b, we already know a < b. Since both a and b are positive numbers, ab < b². Taking the square root of both sides gives us √ab < √b², which simplifies to √ab < b.
So, a < √ab < b is proven true.
To show that 0 < a < b, i) a < âab < b, we can start by multiplying both sides of the inequality a < b by â, which is greater than 0 since a and b are positive numbers.
This gives us:
âa < âb
Next, we can add âab to both sides of the inequality, which gives us:
âa + âab < âb + âab
Simplifying this expression, we get:
âa(1+b) < b(1+âa)
Dividing both sides by (1+b)(1+âa), we obtain:
âa < b
Therefore, we have shown that 0 < a < b, and combining this with the inequality âa < âab < âb from above, we can conclude that:
a < âab < b
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a = {a, b, c, d} x = {1, 2, 3, 4} the function f:a→x is defined as f = {(a, 4), (b, 1), (c, 4), (d, 4)} select the set corresponding to the range of f. O (1.4) O [1, 2, 3, 4) O {1} O [0]
The range of a function is the set of all output values. In this case, the function f maps each element of the set a to a specific element in the set x.
The range of f is therefore the set of all possible output values, which are 1, 4. So, the set corresponding to the range of f is option O [1, 2, 3, 4). The range of a function is the set of all possible output values. In this case, the function f is defined as f = {(a, 4), (b, 1), (c, 4), (d, 4)}. The output values are 4, 1, 4, and 4. So, the range of f is the set of unique output values: {1, 4}.
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let x be a random variable with probability density function f(x) = 0 c(1 – x^2) −1 < x < 1 0 otherwise
a. what is the value of c? b. what is the cumulative distribution function of x?
c. What is E(X)? d. What is Var(X)?
a. The value of c is 1/2.
b. The cumulative distribution function of x is [tex]F(x) = 0 for x < -1, F(x) = (1/2) + (1/2)x - (1/2)x^3 for -1 ≤ x ≤ 1, and F(x) = 1 for x > 1.[/tex]
c. E(X) = 0. d. Var(X) = 1/3.
a. To find the value of c, we need to use the fact that the total area under the density function must be equal to 1:
Integral from -1 to 1 of f(x) dx = 1
Using the given formula for f(x), we get:
Integral from -1 to 1 of c[tex](1 - x^2)^-1[/tex] dx = 1
Taking the integral of [tex](1 - x^2)^-1[/tex] with respect to x, we get:
[tex]-ln|1 - x^2|[/tex] from -1 to 1
Substituting the limits and equating to 1, we get:
-ln(1 - 1) + ln(1 - (-1)) = 1
ln(2) = 1
Therefore, c = 1/ln(2).
b. The cumulative distribution function (CDF) of x is given by:
F(x) = Integral from -∞ to x of f(t) dt
For x < -1, F(x) = 0 since the density function is 0 in this region.
For -1 ≤ x < 1, we have:
F(x) = Integral from -1 to x of [tex]c(1 - t^2)^-1 dt[/tex]
Using substitution u = [tex]1 - t^2, du/dt = -2t[/tex], we can rewrite this as:
F(x) = Integral from 0 to [tex]1-x^2 of c u^-1 (du/(-2t))[/tex]
= (-1/2) c ln|u| from [tex]0 to 1-x^2[/tex]
= (-1/2) c ln[tex](1/(1-x^2))[/tex]
= (1/2) ln(1/[tex](1-x^2))[/tex]
For x ≥ 1, F(x) = 1 since the density function is 0 in this region.
c. To find E(X), we need to take the expected value of X:
E(X) = Integral from -∞ to ∞ of x f(x) dx
For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.
For -1 ≤ x ≤ 1, we have:
E(X) = Integral from -[tex]1 to 1 of x c(1 - x^2)^-1 dx[/tex]
Using substitution u = 1 - x^2, du/dx = -2x, we can rewrite this as:
E(X) = Integral from 0 to 1 of [tex](1 - u) c u^-1 (-du/(2x))[/tex]
= (-c/2) Integral from 0 to 1 of[tex](1 - u) u^-1 du[/tex]
= (-c/2) ln(u) from 0 to 1
= (-c/2) ln(1/1)
= 0
Therefore, E(X) = 0.
d. To find Var(X), we first need to find [tex]E(X^2):[/tex]
E(X^2) = Integral from -∞ to ∞ of[tex]x^2 f(x) dx[/tex]
For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.
For -1 ≤ x ≤ 1, we have:
E[tex](X^2)[/tex]= Integral from -[tex]1 to 1 of x^2 c(1 - x^2)^-1 dx[/tex]
Using substitution u = [tex]1 - x^2, du/dx = -2x[/tex], we can rewrite this as:
E[tex](X^2)[/tex] = Integral from 0 to [tex]1 of (1 - u) c u^-1 (-du/(2x))[/tex]
= (-c/2) Integral
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determine whether s is a basis for p3. s = {3 − 4t2 t3, −4 t2, 3t t3, 5t}
we have found constants c1, c2, c3, and c4 such that f(t) can be expressed as a linear combination of the polynomials in s.
To determine whether s is a basis for p3, we need to check whether the polynomials in s are linearly independent and span p3.
First, we check for linear independence by setting up the equation:
c1(3 − 4t2 t3) + c2(−4 t2) + c3(3t t3) + c4(5t) = 0
where c1, c2, c3, c4 are constants. This equation must hold true for all values of t in order for the polynomials in s to be linearly independent.
Simplifying the equation and grouping like terms, we get:
(3c1 + 3c3)t3 + (-4c1 - 4c2)t2 + (3c3)t + (5c4) = 0
Since this equation must hold for all values of t, each coefficient must be equal to zero. Solving for c1, c2, c3, and c4, we get:
c1 = 0
c2 = 0
c3 = 0
c4 = 0
Therefore, the polynomials in s are linearly independent.
Next, we need to check if the polynomials in s span p3. This means that any polynomial in p3 can be expressed as a linear combination of the polynomials in s.
Let f(t) = at3 + bt2 + ct + d be an arbitrary polynomial in p3.
We need to find constants c1, c2, c3, c4 such that:
c1(3 − 4t2 t3) + c2(−4 t2) + c3(3t t3) + c4(5t) = at3 + bt2 + ct + d
Equating the coefficients of like terms, we get the following system of equations:
3c1 = a
-4c1 - 4c2 = b
3c3 = c
5c4 = d
Solving for c1, c2, c3, and c4, we get:
c1 = a/3
c2 = (-4a-3b)/12
c3 = c/3
c4 = d/5
Therefore, we have found constants c1, c2, c3, and c4 such that f(t) can be expressed as a linear combination of the polynomials in s.
Since the polynomials in s are linearly independent and span p3, we can conclude that s is a basis for p3.
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Which of the following is a correct Internet citation?
A. "Butterfly Gardens in the Tri-State Area," Smith, Melanie P., <
http://www.sciencefoundations.org/butterfly>.
B. Butterfly Gardens in the Tri-State Area:
www.sciencefoundations.org/butterfly, Accessed: May 25, 2011;
Smith, Melanie P.
C. Smith, Melanie P., May 25, 2011: Butterfly Gardens in the Tri-State
Area. Internet: .
OD. http://www.sciencefoundations.org/butterfly; Accessed: May 25,
2011. Butterfly Gardens in the Tri-State Area, Smith, Melanie P.
Assume that the numbers of a data set are arranged in ascending order. Which statement about the third quartile is true?
75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
In any data set, if arranged in ascending order, the mid value gives the median.
If there are even number of entries, the middle value of the mid two entries average would be the median.
I quartile is the entry below which 25% of the entries lie and III quartile is one above which 25% of the entries will lie
Hence out of 4 options given
the last one is the correct answer
75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
Complete Question-
Assume that the numbers of a data set are arranged in ascending order. Which statement about the third quartile is true?
A. All of the numbers lie below the third quartile.
B. 50% of the numbers lie below or on the third quartile, and the remaining 50% lie above it.
C. 25% of the numbers lie below or on the third quartile, and the remaining 75% lie above it.
D. 75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
Given the following syllogism,
No satyrs are goats.
All satyrs are animals.
Some animals are not goats.
1. This argument and fallacy are:
2. Construct a Venn Diagram
Statement 1- No satyrs are goats.
Statement 2- All satyrs are animals.
What is venn diagram?A representation of logical or mathematical sets as closed curves or circles within a rectangle (the universal set), with the crossings of the circles denoting the elements that are shared by all the sets. is called venn diagram.
As some animals are satyrs, and satyrs cannot be goats, this implies that not all animals are goats. Therefore, if statements 1 and 2 are accurate, then assertion 3 must also be accurate.
However, the mythological divinity known as the Satyr is really shown as a human with certain animal parts, making the premise false. However, phrase 1 and 2 logically imply sentence 3.
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Venn diagram attached below,
