The fundamental period of [n] is N=72
(a) z(t) = 0 is a constant signal, which means it does not vary with time. A constant signal is not periodic because it does not repeat over time. Therefore, z(t) = 0 is not periodic.
(b) [n] = 1 sin[n] + 4 cos[-] 72- is a discrete-time signal, which means it is defined only at integer values of n. To determine whether it is periodic, we need to check whether there exists a positive integer N such that [n] = [n+N] for all integer values of n.
Using trigonometric identities, we can simplify [n] as follows:
[n] = 1 sin[n] + 4 cos[-] 72-
= 2 sin[36-] cos[-] 36- + 2 cos[36-] sin[n]
Next, we can rewrite [n+N] using the same trigonometric identities:
[n+N] = 2 sin[36-] cos[-] 36- + 2 cos[36-] sin[n+N]
For [n] to be periodic with period N, [n] must be equal to [n+N] for all integer values of n. This means that the two expressions above must be equal for all n, which in turn means that sin[n] must be equal to sin[n+N] and cos[n] must be equal to cos[n+N] for all n.
Since sin and cos are periodic with period 2π, this condition is satisfied if and only if N is a multiple of 72, which is the least common multiple of 36 and 72. Therefore, the fundamental period of [n] is N=72.
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Two histograms showing the number of hours students in the jazz band practiced in a week are shown. The sample
mean of Group 1's data is 2.57. The sample mean of Group 2's data is 3.337.
Which statement about the two histograms is true?
Graph 1 has a larger sample standard deviation than Graph 2.
Graph 2 has a larger sample standard deviation than Graph 1.
Both graphs have the same sample standard deviation.
The relationship of the sample standard deviations cannot be determined.
Answer:
The Answer Is B "Graph 2 has a larger sample standard deviation than Graph 1"
Step-by-step explanation:
Because the message in the text said the mean of Group 1's data is 2.57 while the sample mean of Group 2's data is 3.337 and from what I understand. 3.337 is a lot more than 2.57
Answer:
(b) Graph 2 has a larger sample standard deviation than Graph 1
Step-by-step explanation:
Given the two histograms of hours practiced, you want to know the relationship between the sample standard deviations of the two data sets.
Standard deviationThe standard deviation is a measure of data variability. It will tend to be larger for less-symmetrical data distributions, and for those that are skewed one way or another.
The data of Graph 2 is less symmetrical than that of Graph 1, so we expect its standard deviation to be higher. A computation of the standard deviation confirms this.
Graph 1 standard deviation: about 1.40
Graph 2 standard deviation: about 1.53
Graph 2 has a larger sample standard deviation than Graph 1, choice B.
__
Additional comment
In the computation, the first list (L1) is the set of data values. The second list, {2, 3, 4, ...} for example, is their relative frequencies—the heights of the bars in the histogram.
The given mean values seem to show that each bar is represented by its midpoint value, 0.5 for the first bar, for example. For the purpose of the standard deviation calculation, we don't need to make that adjustment.
<95141404393>
Express the numbers on the graph as an inequality, set notation, and interval notation
The inequality is -2 < x ≤ 1 and the interval notation is ( -2 , 1 ]
Given data ,
Let the inequality be represented as A
Now , the value of A is
-2 < x ≤ 1
And , Interval notation: (-2, 1]
In interval notation, the parentheses "(" and ")" represent open intervals, which means the endpoints are not included, and the square bracket "]" represents a closed interval, which means the endpoint is included.
And , Set-builder notation: {x | -2 < x ≤ 1}
In set-builder notation, the vertical bar "|" is read as "such that," and the inequality -2 < x ≤ 1 describes the set of all values of x that satisfy this condition.
Hence , the inequality is -2 < x ≤ 1
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xamine the given statement, then identify whether the statement is a null hypothesis, an alternative hypothesis, or neither. the mean income of workers who have majored in history is less than $25,000.
The given statement, "The mean income of workers who have majored in history is less than $25,000," is an alternative hypothesis.
An alternative hypothesis is a statement that is tested against the null hypothesis, which generally claims no relationship or effect. In this case, the null hypothesis would be, "The mean income of workers who have majored in history is greater than or equal to $25,000."
We must first comprehend the idea of null and alternative hypotheses in hypothesis testing before we can comprehend why the above statement is an alternate hypothesis.
When doing a hypothesis test, we begin with a null hypothesis, which is a claim that there is no connection between the variables under investigation.
The null hypothesis in this situation would be "The mean income of workers with history majors is greater than or equal to $25,000."
On the other side, the competing hypothesis asserts that the median income of people who majored in history is less than $25,000.
The supplied claim, "The mean income of workers who majored in history is less than $25,000," is, therefore, a counterclaim.
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HELP ME!!!!!!!! LEAP PRACTICE!!!!!!!! (MATH)!!!!!!!
Answer:I can't see the question
Step-by-step explanation:
What is the nth term of 5. 5 7 2008. 5 10 11. 5
Therefore, the nth term of the sequence is approximately 29.94.
Assuming that the sequence is formed by alternating between adding 1.5 and multiplying by a constant factor, the nth term can be calculated using the following formula:
nth term = [tex]5.5 * c^{((n-1)//2}) + 1.5 * ((n-1) % 2)[/tex]
Here "//" represents integer division, "%" represents the modulo operator, and c is the constant factor that multiplies each term.
Assuming that the constant factor is 1.5 and the sequence starts with the first term being 5.5, the first few terms of the sequence would be:
5.5, 7, 10.5, 16, 24.5, 37, 55.5, 83, 124.5, ...
Using the formula above, we can find the nth term for any given value of n. For example, the 10th term would be:
nth term = 5.5 * [tex]1.5^4[/tex]+ 1.5 * 1
= 5.5 * 5.0625 + 1.5
= 29.9375
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Correct Question:
What is the nth term of 5.5 7 2008.510 11.5.
How do you distribute an exponent (X-2y)2
for each of the following linear operators t on a vector space v and ordered bases {3, compute [t),e, and determine whether f3 is a basis consisting of eigenvectors of t.
Given a linear operator T on a vector space V and an ordered basis {3}, we need to compute the matrix representation [T] with respect to this basis. Once we have the matrix [T], we can find its eigenvectors and eigenvalues
To address your question, we first need to understand the concepts involved:
1. A linear operator (T) is a function that maps a vector space V to itself, while preserving the structure of the space.
2. An ordered basis is a linearly independent set of vectors that spans the vector space V.
3. [T] is the matrix representation of the linear operator T with respect to the ordered basis.
4. Eigenvectors are non-zero vectors that satisfy the equation T(v) = λv, where λ is a scalar called an eigenvalue.
. If the eigenvectors of T form a basis for the vector space V (i.e., they are linearly independent and span the space), then we can say that F3 is a basis consisting of eigenvectors of T.
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Find the largest number of 2 digits which is a perfect square
81 is the largest number of two-digit which is a perfect square.
Perfect squares are those integers that result from multiplying any number by itself.
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are the numbers.
Therefore, there exist 17 two-digit numbers whose digit sums are squares.
The greatest number among those that form a perfect square must be found.
We are aware that the initial number of perfect squares is 100. Furthermore, it is a perfect square of 10.
The number whose square will appear is obviously going to be fewer than 10 today.
The square of 9, which is written as 9²=81, is the first number before 10, so let's start there.
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Quasilinearization Method
Q10-) Give some examples for the maximal solution and minimal
solution of first order IVP.
The Quasilinearization Method is a technique used to approximate solutions for nonlinear differential equations by linearizing them iteratively. It is particularly helpful when solving first-order IVPs.
A maximal solution to a first-order IVP is a solution that exists on the largest possible interval, while a minimal solution exists on the smallest possible interval.
Example 1:
Consider the first-order IVP: dy/dt = y^2, y(0) = 1.
Maximal solution: The maximal solution to this IVP is y(t) = 1/(1 - t) on the interval (-∞, 1).
Minimal solution: The minimal solution is the same as the maximal solution for this example, as there are no other solutions that exist on a smaller interval.
Example 2:
Consider the first-order IVP: dy/dx = x + y, y(0) = 0.
Maximal solution: The maximal solution to this IVP is y(x) = -x + e^x - 1 on the interval (-∞, +∞).
Minimal solution: The minimal solution is the same as the maximal solution for this example since there are no other solutions that exist on a smaller interval.
In both examples, the Quasilinearization Method can be applied to linearize the differential equations and approximate the solutions. The maximal and minimal solutions represent the largest and smallest possible intervals where the solutions are valid.
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QUESTION 2When drawing up a timetable, the following principles must bekept in mind, or taken into consideration:a. Educators should be efficiently deployed, and teaching loadss should be balanced across the timetable.b. The capacity of the building will determine whether thelearners move from classroom to classroom, or whether the educatorsmove or both groups move.c. It should allow for non-teaching timed. Educators should be timetabled to teach the learning areas orsubjects in which they are trainede. Balance: practical subjects or double periods should notfollow too closely upon teach other2.1 Reflect on the school timetable you followed during teachingpractice and elaborate on the above-mentioned points with the aidof one practical example for each.
Educational psychology provides teachers with research-based principles to guide their teaching.
When teachers go through educational psychology, they are taught on ways to improve their teaching.
These ways will be based on research overtime that have proved efficient in helping students learn from teachers.
Some of these include empowering school social and cultural structures, minimizing bias, implementing an equity pedagogy, the method of knowledge creation, and integrating content (Banks, 1995a).
The main goal of multicultural education is to reduce barriers to educational opportunity and success for students from different cultural backgrounds. The principle that all pupils, regardless of culture, deserve educational equity serves as its cornerstone.
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The radius of a circle is 9 miles. What is the area of a sector bounded by a 180° arc? 180° Give the exact answer in simplest form. JT Submit r=9 mi 00 square miles
The area of sector that is bounded by the 180° sector arc, obtained from the formula for the area of circle is 40.5·π square miles
What is the formula for finding the area of a circle?The area of a circle can be obtained from the product of the pi and the square of the radius of the circle.
Mathematically, the area of a circle = π × (Radius)²
The length of the radius of the circle = 9 miles
The angle bounded by the sector = 180°
The area bounded by the sector is therefore;
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A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade.
The purchasing manager is depending on the Belt's effort requiring that the average cost of an internal critical raw material component be less than or equal to $3,600 in order to stay within budget.
Using a sample of 42 first article components, a Mean of the new product upgrade price of $3,200 and a Standard Deviation of $180 was estimated.
Based on the data provided, the Z value for the data assuming a Normal Distribution is?
Response:
5.42
4.30
2.22
1.11
Based on the data provided and assuming a Normal Distribution, the Z-value is 2.22.
To determine the Z value for the data assuming a Normal Distribution, we will use the following formula:
Z = (X - μ) / σ
Where:
Z = Z value
X = average cost of internal critical raw material component (which should be less than or equal to $3,600)
μ = mean of the new product upgrade price ($3,200)
σ = standard deviation ($180)
First, we need to determine the difference between the desired average cost and the mean:
Difference = $3,600 - $3,200 = $400
Next, we will divide the difference by the standard deviation:
Z = $400÷$180 ≈ 2.22
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WRITE Describe how to add and subtract polynomials using both the vertical and horizontal methods.
To add polynomials in a horizontal method, combine coefficients
polynomials in standard form
For the vertical method, write the
✓align like terms in columns, and combine like terms. To subtract
of the polynomial that is being subtracted,
polynomials in a horizontal method, find the additive inverse
and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms in
columns, and subtract by adding the additive identity
To add polynomials in a horizontal method, combine like terms. For the vertical method, write the polynomials in standard form and align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the negative (opposite) of the polynomial that is being subtracted and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms, and subtract by adding the negative (opposite).
What is the polynomials about?To add polynomials vertically, one need to write them in standard form and align like terms in the columns. Combine like terms and add them to the polynomial.
Therefore, note that Polynomials are seen as expressions with variables and coefficients. Combine or subtract like terms when adding or subtracting them.
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WRITE Describe how to add and subtract polynomials using both the vertical and horizontal methods.
To add polynomials in a horizontal method, combine ----- For the vertical method, write the polynomials in -------- align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the ------ of the polynomial that is being and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms and and subtract by adding the -------
out of a group of 100 people what is the probability that there exactly 10 days with exactly 3 birthdays
The probability of there being exactly 10 days with exactly 3 birthdays out of a group of 100 people is extremely low, approximately 4.63 x [tex]10^{-37}[/tex]
To answer this question, we need to use the concept of probability. The probability of an event happening is the number of desired outcomes divided by the total number of possible outcomes.
In this case, the desired outcome is that there are exactly 10 days with exactly 3 birthdays. To calculate this probability, we need to consider the total number of ways that 100 people can be distributed across 365 days.
There are a total of [tex]365^{100}[/tex] possible ways to distribute birthdays. However, not all of these possibilities are valid because we are looking for exactly 10 days with exactly 3 birthdays.
We can use the formula for combinations to calculate the number of ways that 10 days can be selected out of 365. This is given by:
C(365, 10) = 3.535 x [tex]10^{21}[/tex]
For each of these combinations, we need to calculate the number of ways that exactly 3 people can be assigned to each of the 10 days. This is given by:
[tex]C(100, 3)^{10}[/tex] = 7.917 x [tex]10^{61}[/tex]
The total number of valid outcomes is the product of these two values:
3.535 x [tex]10^{21}[/tex] x 7.917 x [tex]10^{61}[/tex] = 2.798 x [tex]10^{83}[/tex]
The probability of the desired outcome is then:
Desired outcomes / Total outcomes = [tex]2.798 * 10^{83} / 365^{100}[/tex] = 4.63 x[tex]10^{-37}[/tex]
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To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not lonner than 122 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?
The inequality that can be used to represent the lengths of the glass that will fit in the frame is 12 < x ≤ 122
How to determine the inequality can be used to represent the lengths of the glass that will fit in the frameWe are given that the length, x, of a piece of glass must be longer than 12 cm but not longer than 122 cm in order to fit in an existing frame.
This can be represented mathematically using the inequality 12 < x ≤ 122
Therefore, the inequality that can be used to represent the lengths of the glass that will fit in the frame is 12 < x ≤ 122
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What value is a discontinuity of x squared plus 7 x plus 1, all over x squared plus 2 x minus 15?
NEED HELP FAST
At x equals -5 and x equals 3 our function is discontinuous.
We have been given a rational function:
f(x) = [tex]\frac{x^{2}+7x+1 }{x^{2} +2x-15}[/tex]
We are asked to find the points at which our function is discontinuous.
A rational function is discontinuous when the function is undefined or the denominator is zero.
Let us find what values of x will make our denominator zero.
[tex]x^{2} +2x-15=0[/tex]
We will use factoring to find the zeros of x. By splitting the middle term we will get,
[tex]x^{2} + 5x - 3x -15=0\\\\x(x+5)-3(x+5)=0[/tex]
(x +5)(x - 3) = 0
x = -5 and x = 3
Therefore, at x equals -5 and x equals 3 our function is discontinuous.
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The 22 students in Mrs. Aire's class, each purchased balloons to decorate for a party in the gym. Each student paid $3.80. About how much money did the students spend?
Answer:
$83.60
Step-by-step explanation:
22 x $3.80 = $83.60
When do we use n, p and q? When we are testing a proportion, a
mean (average), or both?
Explain.
When testing a proportion, we use p and q to represent the proportion of success and failure, respectively.
For example, if we are testing the proportion of students who passed a test, we would use p to represent the proportion who passed and q to represent the proportion who did not pass.
When testing a mean (average), we use n to represent the sample size. For example, if we are testing the average height of a sample of individuals, we would use n to represent the number of individuals in the sample.
In some cases, we may use all three terms when testing both a proportion and a mean. For example, if we are testing the proportion of students who passed a test and the average score of those who passed, we would use p and q to represent the proportion of success and failure, and n to represent the sample size of those who passed. We would also use the mean to represent the average score of those who passed.
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Let X is a random variable with probability density function f(x) = {3x? for 0
The variance of X is 3/80.
Given the probability density function of X,
f(x) = {3x² for 0 < x < 1
{0 otherwise
We can use this to answer the following:
(a) Find P(X < 0.5)
To find P(X < 0.5), we need to integrate the density function from 0 to 0.5:
P(X < 0.5) = ∫[0,0.5] f(x) dx
= ∫[0,0.5] 3x² dx
= [x³]₀.₃
= 0.125
(b) Find the cumulative distribution function of X, F(x)
The cumulative distribution function (CDF) of X is given by:
F(x) = P(X ≤ x) = ∫[0,x] f(t) dt
If x ≤ 0, then F(x) = 0. If 0 < x ≤ 1, then
F(x) = ∫[0,x] f(t) dt
= ∫[0,x] 3t² dt
= [t³]₀.ₓ
= x³
If x > 1, then F(x) = 1. So, the CDF of X is:
F(x) = {0 if x ≤ 0
{x³ if 0 < x ≤ 1
{1 if x > 1
(c) Find the expected value of X, E(X)
The expected value of X is given by:
E(X) = ∫[−∞,∞] x f(x) dx
Since the density function f(x) is zero outside the interval [0,1], we can restrict the integration to this interval:
E(X) = ∫[0,1] x f(x) dx
= ∫[0,1] 3x³ dx
= [3/4 x⁴]₀.₁
= 3/4 * 1⁴ - 0
= 3/4
Therefore, the expected value of X is 3/4.
(d) Find the variance of X, Var(X)
The variance of X is given by:
Var(X) = E(X²) - [E(X)]²
We have already found E(X) in part (c). To find E(X²), we integrate x² times the density function:
E(X²) = ∫[0,1] x² f(x) dx
= ∫[0,1] 3x⁴ dx
= [3/5 x⁵]₀.₁
= 3/5 * 1⁵ - 0
= 3/5
Substituting into the formula for variance:
Var(X) = E(X²) - [E(X)]²
= 3/5 - (3/4)²
= 3/5 - 9/16
= 3/80
Therefore, the variance of X is 3/80.
Complete question: Let X be a random variable defined by the density function
[tex]$$f(x)=\left\{\begin{array}{cl}3 x^2 & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array}\right.$$[/tex]
Find
(a)[tex]$E(X)$[/tex]
(b) [tex]$E(3 X-2)$[/tex]
(c) [tex]$E\left(X^2\right)$[/tex]
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Use the figure to find the Surface Area.
32 sq. units
64 sq. units
85 1/3 sq. units
The surface area of the sphere is 64π square units.
Option B is the correct answer.
We have,
Surface area of a sphere = 4πr² ______(1)
Now,
Radius = 4 units
Substituting in (1)
The surface area of a sphere
= 4πr²
= 4 x π x 4²
= 4π x 16
= 64π square units
Thus,
The surface area of the sphere is 64π square units.
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. Divide
6x³+x²+7x+9
2x+1
The polynomial long division of 6x³+x²+7x+9 by 2x+1 gives a quotient of 3x² - x + 4
Dividing using polynomial long divisionFrom the question, we have the following parameters that can be used in our computation:
6x³+x²+7x+9 by 2x+1
Using the polynomial long division setup, we have
2x + 1 | 6x³ + x² + 7x + 9
Evaluating the division, we have
3x² - x + 4
2x + 1 | 6x³ + x² + 7x + 9
6x³ + 3x²
---------------------------------------
-2x² + 7x + 9
-2x² - x
---------------------------------------
8x + 9
8x + 4
---------------------------------------
5
Hence, the quotient is 3x² - x + 4
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Construct a confidence interval for assuming that each sample is from a normal population (a) -26,0 = 3, n=15, 90 percentage confidence (Round your answers to 2 decimal places.)
The 90% confidence interval for the population mean is (-9.05, 15.05).
To construct a confidence interval for a population mean with a known standard deviation when the sample size is less than 30, we use the formula:
CI = x ± z*(σ/√n)
where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.
Given the information provided, we have:
x = 3
σ = 26
n = 15
The desired confidence level is 90%, which corresponds to a z-score of 1.645 (from the standard normal distribution table)
Substituting these values into the formula, we get:
CI = 3 ± 1.645*(26/√15)
CI = 3 ± 12.05
Therefore, the 90% confidence interval for the population mean is (-9.05, 15.05).
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An object in the shape of a rectangular prism has a length of 7 inches, a width of 6 inches, and a height of 4 inches. The object's density is 10.6 grams per cubic centimeter. Find the mass of the object to the nearest gram.
The mass of the object to the nearest gram is 29223 grams.
We have,
The volume of the rectangular prism.
V = length x width x height
Substituting the given values, we get:
V = 7 x 6 x 4 = 168 cubic inches
We need to convert the volume to cubic centimeters since the density is given in grams per cubic centimeter.
There are 2.54 centimeters in an inch, so:
V = 168 cubic inches x (2.54 cm/in)³
V = 2755.392 cubic centimeters
Now we can find the mass of the object.
mass = density x volume
Substituting the given density and calculated volume, we get:
mass = 10.6 g/cm³ x 2755.392 cm³
mass = 29223.1232 grams
Rounding to the nearest gram, we get:
mass = 29223 grams
Therefore,
The mass of the object to the nearest gram is 29223 grams.
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Write an exponential decay function to the model the situation compare the average rates of change over the given intervals
Initial value:58
Decay factor:0. 9
1
To write an exponential decay function to the given model and we compare the average rate of changes over the given intervals. Then the average rate of change comes out to be, for situation 1 is-4.065 and situation 2 is -2.667.
It is given that,
Initial value: 50
Decay factor: 0.9
1 ≤ x ≤ 4 and
5 ≤ x ≤ 8
x = 1
f(x) = 50(0.9)¹
f(x) = 45
x = 4
f(x) = 50(0.9)¹
f(x) = 32.805
Now, the average rate of change for situation 1 where x = 1 and x = 4
= (32.805 - 45) / (4 - 1)
= -4.065
average rate of change for situation 2 where x = 5 and x = 8
= (50(0.9)⁵ - 50(0.9)⁸) / (5 - 8)
= 8.0011 / -3
= -2.667
Thus, the average rate of change for situation 1 is-4.065 and situation 2 is -2.667.
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Note that the full question is:
Write an exponential decay function to the model the situation compare the average rates of change over the given intervals
Initial value: 50
Decay factor: 0.9
1 ≤ x ≤ 4 and
5 ≤ x ≤ 8
(-76.25 Points] DETAILS BBBASICSTATSACC 8.1.018.MI. MY NOTES ASK YOUR TEACHER What price do farmers get for their watermelon crops? In the third week of July, a random sample of 42 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that o is known to be $1.92 per 100 pounds. (a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) lower limit क upper limit $ margin of error (6) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.25 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.) farming regions (c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop in dollars). What is the margin of error (in dollars)? Hint: 1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.) Tower limit S 6 upper limit margin of error S
Answer:
I'm not quite sure if you are joking or not, but here is your answer:
(a) The point estimate for the population mean price (per 100 pounds) is x = $6.88. The standard deviation is known to be σ = $1.92. The sample size is n = 42. For a 90% confidence interval, the critical value is 1.645 (obtained from a t-distribution table with 41 degrees of freedom). The margin of error is:
Margin of error = Critical value x Standard error
Standard error = Standard deviation / sqrt(sample size) = 1.92 / sqrt(42) = 0.2968
Margin of error = 1.645 x 0.2968 = 0.4882 ≈ 0.49
The lower limit of the confidence interval is:
Lower limit = Point estimate - Margin of error = 6.88 - 0.49 = $6.39
The upper limit of the confidence interval is:
Upper limit = Point estimate + Margin of error = 6.88 + 0.49 = $7.37
Therefore, the 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop is $6.39 to $7.37. The margin of error is $0.49.
(b) The maximal error of estimate is E = 0.25. The confidence level is 90%. The standard deviation is known to be σ = $1.92. We need to find the sample size (n) that satisfies the following formula:
Margin of error = Critical value x Standard error
Standard error = Standard deviation / sqrt(sample size)
For a 90% confidence interval, the critical value is 1.645. Substituting the known values and solving for n, we get:
0.25 = 1.645 x (1.92 / sqrt(n))
sqrt(n) = (1.645 x 1.92) / 0.25
n = [(1.645 x 1.92) / 0.25]^2
n ≈ 113
Therefore, a sample size of 113 farming regions is necessary for a 90% confidence level with maximal error of estimate E = 0.25 for the mean price per 100 pounds of watermelon.
(c) The farm brings 15 tons of watermelon to market, which is equivalent to 30,000 pounds (since 1 ton = 2,000 pounds). The point estimate for the population mean cash value of this crop is unknown. We can use the confidence interval obtained in part (a) to estimate this interval. Multiplying the lower and upper limits by 300 (since 300 pounds of watermelon correspond to $6.88), we get:
Lower limit = 6.39 x 300 = $1917
Upper limit = 7.37 x 300 = $2211
Therefore, the 90% confidence interval for the population mean cash value of this crop is $1917 to $2211. The margin of error is:
Margin of error = (Upper limit - Lower limit) / 2 = (2211 - 1917) / 2 = $147
5. A woman pays $2.78 for some bananas and eggs. If each banana costs $0.69 and each egg costs $0.35, how many eggs and how many bananas did the woman buy
If a woman pays $2.78 for some bananas and eggs. If each banana costs $0.69 and each egg costs $0.35, then she bought 4 bananas and 6 eggs.
Let's assume the woman bought x bananas and y eggs.
According to the problem, each banana costs $0.69 and each egg costs $0.35.
So the cost of x bananas would be 0.69x and the cost of y eggs would be 0.35y.
The total cost of the bananas and eggs is given as $2.78. So we can write the equation:
0.69x + 0.35y = 2.78
Now we need to solve for x and y.
We can start by multiplying the entire equation by 100 to get rid of the decimals:
69x + 35y = 278
We can also simplify the equation by dividing both sides by 1 (which doesn't change the equation):
69x/1 + 35y/1 = 278/1
Now we can use a system of equations to solve for x and y.
Let's solve for y in terms of x by isolating y on one side of the equation:
35y = 278 - 69x
y = (278 - 69x)/35
Now we can substitute this expression for y into the original equation:
0.69x + 0.35((278 - 69x)/35) = 2.78
Simplifying this equation, we get:
0.69x + 8 - 2x = 2.78
Solving for x, we get:
0.69x - 2x = 2.78 - 8
-1.31x = -5.22
x = 4
So the woman bought 4 bananas.
Now we can substitute this value for x into the expression we derived for y:
y = (278 - 69(4))/35
y = 6
So the woman bought 6 eggs.
Therefore, the woman bought 4 bananas and 6 eggs.
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Here are the scores of 13 students on an algebra test.
65, 72, 73, 73, 77, 80, 81, 82, 83, 85, 86, 90, 91
Notice that the scores are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Answer:
Q1=65
Range= 65-91= 26
Median= 81
Mode= 73
Median=953 ( if your confused on how to get mode juts add all the scores of the 13 students and then divided by the 13 students so 65,+ 72,+ 73+, 73, +77, +80, +81, +82, +83, +85,+ 86,+ 90,+ 91+÷13=953)
Q2=91
Short Questions: Answer the following questions. Justify your answer mathematically.
a. (6 pnts) Write the negation of the following statement: ∀x ∃y,y > x.
b. (6 pnts) Write the negation of following statement: There exists an integer n such that 2n2 −5n + 2 = 0.
c. (6 pnts) Prove or disprove: ∃x ∀y,(y > x) ⇒ (y > 6).
d. (6 pnts) Prove or disprove: If n is a real number, then either n > 7 or n ≤ 9.
e. (12 pnts) Prove by contraposition: if the product of two integers is odd then both of the integers must be odd.
A. The negation of the given statement is "There exists an x such that for all y, y is not greater than x".
B. The negation of the given statement is "For all integers n, 2n² - 5n + 2 is not equal to 0".
E. the statement is true by contraposition.
What are integers?Integers are a type of number that includes all positive whole numbers (1, 2, 3, ...), zero (0), and negative whole numbers (-1, -2, -3, ...). In mathematical notation, the set of integers is denoted by the symbol Z.
a. The given statement is ∀x ∃y, y > x. Its negation is ¬(∀x ∃y, y > x), which is equivalent to ∃x ¬(∃y, y > x). By De Morgan's law, we can simplify this as ∃x ∀y, ¬(y > x). Therefore, the negation of the given statement is "There exists an x such that for all y, y is not greater than x".
b. The given statement is ∃n ∈ Z, 2n² − 5n + 2 = 0. Its negation is ¬(∃n ∈ Z, 2n² − 5n + 2 = 0), which is equivalent to ∀n ∈ Z, 2n² − 5n + 2 ≠ 0. Therefore, the negation of the given statement is "For all integers n, 2n² - 5n + 2 is not equal to 0".
c. To disprove the statement, we need to find a counterexample where the statement is false. Let x = 10. Then, for any y greater than 10, y is also greater than 6. Therefore, the statement is true for this choice of x, and hence the statement is true.
d. To prove the statement, we can use proof by contradiction. Assume that there exists a real number n such that n ≤ 7 and n > 9. This is a contradiction, and hence our assumption must be false. Therefore, the statement "If n is a real number, then either n > 7 or n ≤ 9" is true.
e. To prove by contraposition, we need to show that if one of the integers is even, then the product of the integers is even. Let's assume that one of the integers is even, say a = 2k. Then, the other integer can be odd or even, but in either case, the product of the integers will be even. Therefore, the statement is true by contraposition.
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Assume that the situation can be expressed as a linear cost function. find the cost function
fixed cost is $300; 40 items cost $2,300 to produce
The linear cost function is C(x)=????
C(x) is the linear cost function: C(x) = $50x + $300
Where x denotes the number of things manufactured.
What is function?A function connects an input with an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input. The standard manner of writing a function is f(x) "f(x) =... "
To find the linear cost function, we need to determine the slope of the cost function and the value of the y-intercept.
Given that 40 items cost $2,300 to produce, we can use this information to find the slope:
Slope = (Change in cost) / (Change in quantity)
Slope = (Total cost for 40 items - Fixed cost) / (40 items - 0 items)
Slope = ($2,300 - $300) / (40 - 0)
Slope = $2,000 / 40
Slope = $50 per item
The fixed cost of $300 represents the y-intercept of the cost function.
Therefore, the linear cost function C(x) is:
C(x) = $50x + $300
Where x represents the number of items produced.
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In a carnival game, players get 5 chances to
throw a basketball through a hoop. The dot
plot shows the number of baskets made by
20 different players.
Answer:
140
Step-by-step explanation:
7/20 = 0.35 = 35% of the 20 players made all five baskets.
If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.
35% of 400 = 0.35*400 = 140
We expect about 140 people will make all five baskets.
Note how 140/400 = 0.35 = 35%
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Through another alternative method, we can solve like this
7/20 = x/400
7*400 = 20*x ... cross multiply
2800 = 20x
20x = 2800
x = 2800/20 ... dividing both sides by 20
x = 140 which is the same result as before
it's going to be 150 baskets made