Systematic sampling and cluster sampling are examples of probability sampling methods used in human research. These methods are employed to ensure that each participant in the population has a known, non-zero chance of being selected, which helps in obtaining representative samples and drawing more accurate conclusions.
Systematic sampling and cluster sampling are both examples of probability sampling methods used in human research.
Probability sampling methods involve randomly selecting participants from a larger population, giving each individual an equal chance of being selected.
Systematic sampling involves selecting every nth participant from a list of the population, while cluster sampling involves dividing the population into clusters or groups and then randomly selecting entire clusters to include in the study.
These methods are considered to be more representative and unbiased than non-probability sampling methods, which do not involve random selection and may not accurately reflect the characteristics of the population.
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approximately how many times larger is 4.2 x 10-¹ than 1.4 x 10-5?
C) 3 x 104
B) 3.3 x 103
A) 3 x 10-4
D) 3.3 × 10-3
4.2 x 10-¹ is approximately 3 x 10^4 times larger than 1.4 x 10-5.
A straight line of the form ŷ=a+bx is fitted to the 5 data points (1,0), (0,3), (3,1), (2,-3), and (4,2) by the method of least squares. What is the value of b?
The value of b is -0.45.
Calculate the mean of x and y values.
The mean of x values is: [tex]x=\frac{(1 + 0 + 3 + 2 + 4)}{5} =2[/tex]
The mean of y values is: [tex]y =\frac{ (0 + 3 + 1 - 3 + 2)}{5} =0.6[/tex]
Calculate the sample covariance between x and y values.
The sample covariance between x and y is: [tex]s_{xy} =[/tex] Σ [tex]\frac{[(xi - x)(yi - y)]}{(n-1)}[/tex]
where Σ denotes the sum of, xi and yi are the i-th values of x and y, respectively, and n is the sample size.
[tex]s_{xy} = \frac{ [(1 - 2)(0 - 0.6) + (0 - 2)(3 - 0.6) + (3 - 2)(1 - 0.6) + (2 - 2)(-3 - 0.6) + (4 - 2)(2 - 0.6)]}{(5 - 1)}[/tex]
[tex]s_{xy} = -1.8[/tex]
Calculate the sample variance of x values.
The sample variance of x is:
[tex]s_{x^{2} } =[/tex] Σ [tex]\frac{(xi - x)^2}{(n-1)}[/tex]
[tex]s_{x^{2} } =\frac{[(1 - 2)^2 + (0 - 2)^2 + (3 - 2)^2 + (2 - 2)^2 + (4 - 2)^2] }{(5 - 1)}[/tex]
[tex]s_{x^{2} } = 4[/tex]
Calculate the value of b.
The value of b is given by:
[tex]b = \frac{s_{xy} }{s_{x^{2} } }[/tex]
[tex]b = \frac{-1.8}{4}[/tex]
[tex]b = - 0.45[/tex]
Therefore, the value of b in the equation of a straight line that is fitted to the 5 data points by the method of least squares is -0.45.
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The accompanying table shows the average yearly balance in a savings account what is the average rate of change in dollars per year from 10 to 30 years
0 380
10 562.49
20 832.63
30 1232.49
40 1824.39
50 2700.54
(1)33.5
(2)0.0298
(3)46.41
(4)42.06
The average rate of change in dollars per year from 10 to 30 years is: 1. 33.5.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(t) over the interval [10, 30]:
a = 10; f(a) = 562.49
b = 30; f(b) = 1232.49
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (1232.49 - 562.49)/(30 - 10)
Average rate of change = 670/20
Average rate of change = 33.5.
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Which expression gives the area vector for a patch on the left face?
The expression that gives the area vector for a patch on the left face can be found using the cross product of the edge vectors on that face. In order to obtain the area vector, we need:
1. Identify the left face of the object.
2. Determine two edge vectors on the left face by subtracting the coordinates of their corresponding points. Let these edge vectors be A and B.
3. Calculate the cross product of vectors A and B, denoted as A x B. This will give you the area vector for the patch on the left face.
4. If needed, calculate the magnitude of the area vector to obtain the area of the patch.
By using the cross product of the edge vectors, you can find the area vector for a patch on the left face of an object. The cross product results in a vector that is perpendicular to the plane of the two input vectors, and its magnitude represents the area of the parallelogram formed by the two vectors. This area vector is useful in various applications, such as calculating surface integrals and determining the orientation of a face in 3D space.
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How many times larger is 9 x 105 than 5 x 103?
1.8
18
180
1,800
The number of times by which 9 × 10⁵ is larger than 5 × 10³ as required to be determined is; 180.
How larger is 9 × 10⁵ compared to 5 × 10³?It follows from the task content that the number 9 × 10⁵ is to be compared to 5 × 10³ and determine how larger it is.
On this note, to determine how large 9 × 10⁵ is compared to 5 × 10³; we have that;
(9 × 10⁵) / (5 × 10³)
= (9/5) × (10⁵/10³)
= 1.8 × 100
= 180.
Consequently, the correct answer as required is 180.
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Answer: 180
Step-by-step explanation:
try it and find out........ because it is right -.-
7. In the diagram below of parallelogram ABCD, AFGB, CF bisects angle DCB, DG bisects angle ADC, and CF and
DG intersect at E.
If m/B= 75°, then the measure of angle EFA is
The value of the angle m∠EFA is: 127.5°
How to find the angle of the parallelogram?A parallelogram is defined as a quadrilateral that has its opposite sides parallel and equal to each other. It has its interior opposite angles equal. Also, the angles on the same side of the transversal sum up to 180 degrees or are supplementary to each other.
Since the figure is a parallelogram, it means that:
DC║AB
Thus:
m∠B = 75°
m∠DCB = 180° - 75°
m∠DCB = 105°
CF bisects ∠DCB
Thus:
m∠DCF = m∠FCB = ¹/₂ * 105° = 52.5°
Thus:
m∠EFA = 180° - 52.5°
m∠EFA = 127.5°
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m∠EFG=30 and EF=4 units, find the length of arc EG. Round to the nearest hundredth.
The length of the arc with a central angle of 30 degrees and radius 4 inches is 2.09 units
Finding the length of the arcFrom the question, we have the following parameters that can be used in our computation:
central angle = 30 degrees
Radius = 4 units
Using the above as a guide, we have the following:
Length of arc = central angle/360 * 2 * 3.14 * Radius
Substitute the known values in the above equation, so, we have the following representation
Length of arc = 30/360 * 2 * 3.14 * 4
Evaluate
Length of arc = 2.09
Hence, the length of the arc is 2.09 units
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After substituting that coordinate, what is the flux dΦ through the patch in terms of dA?
After substituting the given coordinate in the flux equation, the resulting flux dΦ through the patch can be expressed in terms of dA as dΦ = E⋅dA⋅cosθ
Here, E represents the electric field intensity, dA is the area of the patch, and cosθ is the angle between the normal vector of the patch and the electric field lines passing through it.The term dA represents the differential area of the patch and is used to calculate the total flux through the entire surface by integrating over the entire area. This integration process adds up the contributions of all the small patches of the surface.
Therefore, the flux through any small patch of the surface can be calculated using the above equation by substituting the appropriate values of E, dA, and cosθ. This formula is particularly useful in calculating the flux through curved surfaces or irregularly shaped patches.In summary, after substituting the given coordinate, the flux dΦ through the patch can be expressed in terms of dA using the formula dΦ = E⋅dA⋅cosθ, which helps in determining the total flux through the entire surface.
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Help me, please answer all numbers this
Read the following questions from Consumer Skills CS What's The Catch Be A Savvy.
Here is how Samuel described the concept to Frank: We are all set! You can rent an item like this big screen TV for a small monthly payment, in this case, $134.28, and at the end of the rental period you own the item. If you can't make the payment, well, you just turn it back in with no questions asked. Oh, and there's no credit check. So, just think -- you can walk away with this $3,000 TV set for a little over one hundred dollars a month. What a deal! What is there not to like?
Answer this:
Review the advertisement to answer these questions:
11. A. How much would Frank pay for the TV if he had money saved to pay for it today?
B. How many months would Frank have to make payments in order to own the TV?
C. he made all the monthly payments, how much would Frank pay over the course of the rental period? How does this amount compare to the cash price?
12. List any concerns that you think that Frank might have about this "deal!
13. Rent-to-own centers are a multi-billion dollar business. Why do you think their approach is so popular?
14. Extra Credit. While this isn't technically a loan, it might be fun to figure out what the implied interest on this rental arrangement is.
A. Go to this Rent-To-Own Model (TV) spreadsheet'.
B. Make a copy of the spreadsheet
C. Enter Interest Rate guesses in cell B6.
D. Keep guessing until you can get cell F31 as close to zero as possible (+/- $100 is Ok)
E. What is the implied interest rate?
a. $3,000
b. < than 22 months
c. $3,222.72
How much would Frank pay for the TV?From the quote that says "So, just think -- you can walk away with this $3,000 TV set for a little over one hundred dollars a month', we can deduce from it that the company original price for the TV is $3,000. Hence, Frank will need to pay $3,000 for the TV if he had money saved to pay for it today.
How many months to make monthly payments?Monthly payment for the TV credit = $134
The Original TV cost = $3000.
The number of months to make monthly payments will be more than:
= $3,000 / $134
= 22.3880597015
= 22 months.
How much would Frank pay over the course of the rental period?If we assume a rental period of 24 months, Frank would pay a total of:
= 24 month x $134.28
= $3,222.72
So, this is more than the cash price of $3,000.
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138. Copy List with Random Pointer
A linked list is given such that each node contains an additional random pointer which could point to any node in the list or null.
Return a deep copy of the list.
After creating all the new nodes, we can traverse the original list again and set the random pointers of each new node based on the mapping stored in the hash map. Finally, we can return the head of the new list.
This problem requires creating a deep copy of a linked list that contains an additional random pointer for each node.
The random pointer can point to any node in the list or be null.
To solve this problem, we need to traverse the original linked list and create a new node for each node in the original list. The new node should have the same value as the original node and a null random pointer. We can store a mapping between the original node and the new node in a hash map.
After creating all the new nodes, we can traverse the original list again and set the random pointers of each new node based on the mapping stored in the hash map. Finally, we can return the head of the new list.
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A cleaning company models its profits on the graph.
p(t)
Profit ($ thousands)
250-
200
150-
100
50
0 1 2 3 4
6 7 8
Time (years)
Which equation best models the situation?
9 10
t
The equation of the scatter plot is given by the curve fitting of parabola equation y = -3.54x² + 41.7x + 73
Given data ,
Let the cleaning company models its profits be plotted on the graph
where the points are given by
A ( 1 , 100 ) , B ( 2 , 175 ) , C ( 3 , 150 ) , D ( 3 , 175 ) , E ( 5 , 175 ) , F ( 6 , 225 ) , G ( 7 , 175 ) , H ( 8 , 200 ) , I ( 9 , 150 )
Using the curve fitting model , we can plot the graph as
y = -3.54x² + 41.7x + 73
Hence , the equation of graph is y = -3.54x² + 41.7x + 73
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The complete question is attached below :
A cleaning company models its profits on the graph.
p(t)
Profit ($ thousands)
For P = {9, 12, 13, 15}, Q= {2, 7, 11}, and R= {4, 7, 8, 11}, find PU (QU R). Select the correct choice below and fill in the answer box within your choice. A. PU(QU R) = { } (Use a comma to separate answers as needed.) B. PU ( QU R) is the empty set.
The answer is A. PU(QU R) = {2, 4, 7, 8, 9, 11, 12, 13, 15}.
To find PU (QU R), we first need to find QU R, which means we need to take the union of Q and R and then find the union of that set with P.
Q U R = {2, 4, 7, 8, 11}
PU(QU R) = P U (Q U R) = {9, 12, 13, 15} U {2, 4, 7, 8, 11} = {2, 4, 7, 8, 9, 11, 12, 13, 15}
Therefore, the answer is A. PU(QU R) = {2, 4, 7, 8, 9, 11, 12, 13, 15}.
Note that the order of the sets does not matter when taking the union, and any repeated elements are counted only once in the final set.
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How do I solve this ????
The solution to the inequality is 2x + y < 7 and the graph is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
2x + y < 7
On simplifying the equation , we get
Let the point be P ( 2 , 3 )
2 ( 2 ) + 3 < 7
4 + 3 < 7
7 is not less than 7
So , it is not a solution to the inequality
Hence , the equation is 2x + y < 7
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True or False
(8,8) = (9-1,6+3)
This is a false statement because y-coordinates are different.
How to find the given statement is true or false?
In mathematics, an ordered pair is a pair of elements, usually written in the form (x,y), where x and y are two values that are related in some way. In the case of (8,8), this represents an ordered pair where the value of x is 8 and the value of y is 8.
On the other hand, (9-1, 6+3) can be simplified using basic arithmetic operations. We first evaluate the expressions inside the parentheses, 9-1 and 6+3, which give us 8 and 9 respectively. Then we combine them into an ordered pair to get (8,9).
When we compare the two ordered pairs, we can see that the x-coordinates are the same, but the y-coordinates are different. Therefore, (8,8) is not equal to (9-1,6+3) and the statement "True or False(8,8) = (9-1,6+3)" is false.
Let's evaluate each side of the equation separately:
(8,8) represents an ordered pair with 8 as the x-coordinate and 8 as the y-coordinate.
(9-1, 6+3) evaluates to (8,9), since 9-1 = 8 and 6+3 = 9.
So we have:
(8,8) = (8,9)
This is a false statement, since the y-coordinates are different. Therefore, the answer is False.
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Which of the following intervals corresponds to the smallest area under a Normal curve?
a. Q1 to Q3
b. μ to μ + 3σ
c. Q1 to μ + 2σ
d. μ - σ to Q3
The interval that corresponds to the smallest area under a Normal curve is option D, μ - σ to Q3. This is because it covers only one standard deviation below the mean (μ - σ) and a smaller portion of the upper tail (up to Q3) compared to the other options. Smaller intervals generally correspond to smaller areas under the curve.
The interval that corresponds to the smallest area under a Normal curve is option D, μ - σ to Q3. This is because it covers only one standard deviation below the mean (μ - σ) and a smaller portion of the upper tail (up to Q3) compared to the other options. Smaller intervals generally correspond to smaller areas under the curve. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal.
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The diameter of a circle is 12 cm. Find its circumference in pi
Answer:
12π
Step-by-step explanation:
We Know
Circumference of a circle = d x π
d = 12 cm
Find its circumference in pi.
Let's solve
12 x π = 12π
So, the circumference of the circle is 12π
Answer:
C=12π
C≈37.69911 cm
Step-by-step explanation:
d=2r, with d being diameter and r being the radius.
C=2πr, with C being the circumference and r being the radius.
Therefore, C=πd.
C=πd
C=π(12)
C=12π
C≈37.69911 cm
Hope this helps and good luck on your homework!
You’re in a math class of 16 students (including yourself). Your teacher has a bag of 16 chocolate bars, and says “This morning, I had exactly one golden ticket. There’s an 80% chance I put it in one of these bars, and a 20% chance I threw it away.”
She then passes the bag around, and everyone takes a bar at random. You keep your bar closed while each of the other students in the class opens theirs and discovers no golden ticket inside.
What are the chances your bar has the golden ticket in it?
Please enter your answer as a percent from 0 to 100 without the % symbol, and round to the nearest integer. E.g. if your answer is 55.37%, please enter it as 55.
The chances of your bar having the golden ticket are still 80%.
The chances of your bar having the golden ticket in it are still 80%.
Even though the other students have opened their bars and found no golden ticket, the probability of the golden ticket being in the remaining bar has not changed.
The fact that the other students opened their bars and found nothing does not affect the probability of your bar containing the golden ticket.
Therefore, the chances of your bar having the golden ticket are still 80%.
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what is the value of a in the question below?
Answer:
a= 5.7
Step-by-step explanation:
Ok, when solving problems like this, it is important to do it step by step to minimize any mistakes.
Original Equation:
[tex]\frac{10a}{3} -1.5=17.5[/tex]
Then we add 1.5 to both sides
[tex]\frac{10a}{3} -1.5+1.5=17.5+1.5[/tex]
Simplify:
[tex]\frac{10a}{3}=19[/tex]
Multiply both sides by 3 to get rid of the denominator in the left side.
[tex]\frac{10a}{3} *3 = 19*3[/tex]
Simplify:
[tex]10a=57[/tex]
Divide both sides by 10 to isolate a
[tex]a = 5.7[/tex]
We can check our answer by plugging our value into the original equation!
Original equation:
[tex]\frac{10a}{3}-1.5=17.5[/tex]
New equation:
[tex]\frac{10(5.7)}{3}-1.5=17.5[/tex]
Multiply the numerator:
[tex]\frac{57}{3}-1.5=17.5[/tex]
Divide the fraction:
[tex]19-1.5= 17.5[/tex]
Subtract:
[tex]17.5=17.5[/tex]
as you can see, the values on both sides of the equation match.
So, a = 5.7
Question content area top
Part 1
An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69. 0 in and a standard deviation of 2. 8 in. Complete parts (a) through (d)
The probability that he can fit without bending is 0.9938.
We have,
Mean = 69
standard Deviation = 2.8
So, The probability that he can fit without bending is
z= (x - [tex]\mu[/tex]) / [tex]\sigma[/tex]
z = (76 - 69)/2.8
z = 2.5
z = 2.5
and, P- value for 2.5 = 0.9938.
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__________ is the IV and ____________ is the DV.
a. Gender: GSR
b. GSR: gender
c. Gender : Time
d. Breast feeding: GSR
Gender is the independent variable (IV) and Galvanic Skin Response (GSR) is the dependent variable (DV). This means that you are investigating how differences in gender might affect the GSR.
So, the correct is A. Gender: GSR
What's meant by Gender and GSRGender, as the IV, refers to the classification of individuals as male, female, or other, while GSR, as the DV, is a physiological measure of emotional arousal, often used in psychological research.
By examining the relationship between these two variables, you aim to determine whether variations in gender have any impact on GSR levels.
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Which of these tables represents a function?
X
-1
-2
0
W.
y
15
6
15
6
X y
0
4
15
6
0
-2
X.
6
-1
X
4 0
-1
6
6
>
Y.
-2
-2
15
X
6
4
0
15 -1
3
N
Z.
y
-2
The table that represents a function is the table in which each value of x is mapped to a single value of y.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.More can be learned about relations and functions at https://brainly.com/question/12463448
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In order to test the effects of the 1988 heat wave on worker productivity, 48 machinists were randomly assigned to two groups of 24 machinists each. Each group was tested at a different room temperature (cool and hot) using dependent measures of number of parts produced and accuracy. What type of design does this study represent
The dependent measures of the study were the number of parts produced and accuracy, which were used to assess the effects of the 1988 heat wave on worker productivity.
Based on the information provided, the study described represents a between-subjects design.
This is because the 48 machinists were randomly assigned to two different groups, with one group being tested at a cool room temperature and the other group being tested at a hot room temperature.
Each group was then measured using dependent measures of number of parts produced and accuracy.
A between-subjects design is a type of experimental design where different groups of participants are assigned to different conditions or treatments, and the outcomes are compared between these groups.
In this case, the two groups of machinists were assigned to different room temperatures and their productivity and accuracy were measured.
The use of dependent measures also suggests that this study was experimental in nature, meaning that the researchers were manipulating the independent variable (room temperature) in order to see how it affected the dependent variables (number of parts produced and accuracy).
Overall, this study used a between-subjects experimental design to test the effects of the 1988 heat wave on worker productivity, by randomly assigning machinists to different room temperatures and measuring their productivity and accuracy using dependent measures.
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a glass jar contains 7 Red 5 green 10 blue and 3 yellow marbles if three marbles are chosen at random from the jar without replacement what is the probability of choosing a red marble into blue marbles
The probability of choosing a red marble followed by two blue marbles from the jar is 0.137 or approximately 13.7%.
The probability of choosing a red marble followed by two blue marbles from a jar containing 7 red, 5 green, 10 blue, and 3 yellow marbles.
To solve this problem, we need to first calculate the total number of possible ways to choose three marbles from the jar.
This is given by the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of marbles in the jar, and r is the number of marbles we want to choose.
Using this formula, we can find that the total number of ways to choose three marbles from the jar is:
nCr = 25! / (3!22!) = 2300
Next, we need to calculate the number of ways to choose a red marble followed by two blue marbles.
We can do this by using the multiplication principle of counting:
Number of ways to choose a red marble = 7
Number of ways to choose two blue marbles = 10C2 = 45
Total number of ways to choose a red marble followed by two blue marbles = 7 * 45 = 315
Finally, we can calculate the probability of choosing a red marble followed by two blue marbles by dividing the number of ways to choose a red marble followed by two blue marbles by the total number of possible ways to choose three marbles from the jar:
P(red, blue, blue) = 315 / 2300 = 0.137
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y=x^2+x-30 find the zeros
Answer:
x = 5 or -6
Step-by-step explanation:
We can find the zeros of the function:
[tex]y=x^2+x-30[/tex]
by setting y to 0, then solving for x.
To do this, we need to factor the right side of the equation.
[tex]0=x^2+x-30[/tex]
[tex]0=(x + 6)(x - 5)[/tex]
We can see that (x + 6) and (x - 5) are the two parts of this factorization because 6 and -5 add to 1 (which is the coefficient of the middle term), and they multiply to -30 (the constant term).
From this factored form, we can split the equation into two because we know that:
IF [tex]ab = 0[/tex],
THEN [tex]a=0[/tex] OR [tex]b=0[/tex]
So, we can solve for x in the following two equations:
[tex]x + 6 = 0[/tex] [tex]x - 5 = 0[/tex]
[tex]\boxed{x = -6}[/tex] OR [tex]\boxed{x = 5}[/tex]
__
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Derive the statements as corollaries of Theorems 4.3.1, 4.3.2.
*Theorem 4.3.1 = Every integer is a rational number.
**Theorem 4.3.2 = The sum of any two rational numbers is rational.
For any rational numbers r and s, 2r + 3s is rational.
For any rational numbers r and s, 2r + 3s is rational. This is a corollary of Theorem 4.3.2.
Since r and s are rational numbers, they can be expressed as a ratio of integers:
r = a/b
s = c/d
where a, b, c, and d are integers and d and b are nonzero.
Then,
2r + 3s = 2(a/b) + 3(c/d)
= (2ad + 3bc)/(bd)
Since the product and sum of any two integers is also an integer, we know that 2ad and 3bc are integers. Thus, the numerator is the sum of two integers, which means it is also an integer. The denominator is the product of two nonzero integers, which means it is also nonzero. Therefore, 2r + 3s is a ratio of integers, and hence it is a rational number.
Therefore, for any rational numbers r and s, 2r + 3s is rational. This is a corollary of Theorem 4.3.2.
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Help me please I'll give brainliest. And PLEASE put all three answers.
Answer: you have to multiply by ft2 x 250 = the answer is 23.22576 divide by 1.45161 and this is your real answer = 89.16
Step-by-step explanation: you have to do what i told you to do above of me
Answer: 24 - Rectangle 1
Step-by-step explanation:
The two Rectangle 1's are the top and bottom rectangles. To find the area of a rectangle, you have to multiply length x width. You know that the bottom rectangle is identical to the top rectangle, so by solving for the bottom rectangle, we solve for the top!
The length of this rectangle at the bottom is 8, and the width is 3. 8 x 3 = 24. The area of the bottom and top rectangles (1) are 24.
The question wants you to multiply one rectangle with an area of 24 feet squared by 2, because there are two of the same rectangles (top and bottom). 24 x 2 = 42. The total area of the top and bottom rectangles is 42 square feet.
You can do the same with the other rectangles. Using length x width = area, you can then multiply that times two to get the area of two of the same rectangles. Here's one more example from the problem:
The largest rectangle from the rectangular prism is facing the front, the other is facing the back. The length of these two rectangles is 15, the width is 8.
length x width = area
15 x 8 = area
120 square feet = area
Now, multiply that by 2 and you get the area of both of the same rectangles. 240 square feet.
Now we have Rectangle 1 (x2) = 42, and another Rectangle (2 or 3) (x2) = 240. Now, all you have to do is find the area of the rectangle with the length of 15 and the width of three and multiply it by two to find the areas of all the triangles. Then, save all three answers: 42, 240, and the other answer. Then, add 42, 240, and the other answer together to get the Total Surface Area. Good luck!
Donald has $200 in savings account that earns 5% interest per year.the interest is not compounded. How much will he have in total in 1 year?
Donald will have $210 at the end of the year
Given that the principal amount Donald is having at the start of the year is $200 and the rate of interest per annum is 5%.
Since the interest is not compounded, at the end of the year the amount of interest he will be earning = 0.05 x 200 = $10 (since interest is not compounded)
From, the above analysis, Donald is earning $10 of interest per annum from $200.
Now, Total money Donald will be having in 1 year = principal amount + interest earned money = $200 + $10 = $210
From the above solution, we can conclude that Donals is having $210 in total for one year.
To know more about the calculation of Interest,
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10 increased by the product of a number and 7 is greater than -24. Use the variable b for the unknown number.
The solution for the inequality is b > -34/7.
Inequality refers to the phenomenon of unequal and/or unjust distribution of resources and opportunities among members of a given society.
The inequality can be expressed as:
10 + 7b > -24
To solve for b, we need to isolate the variable b. We can do this by subtracting 10 from both sides of the inequality:
10 + 7b - 10 > -24 - 10
This simplifies to:
7b > -34
Finally, we divide both sides of the inequality by 7 to solve for b:
(7b) / 7 > (-34) / 7
b > -34/7
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what would you have to know about the solution set of a homogeneous system of 18 linear equations in 20 variables in order to know that every associated nonhomogeneous equation has a solution
The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.
To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.
This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.
If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.
However,
We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.
This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.
If it is, then the nonhomogeneous equation has a solution.
So, in summary, to know that every associated nonhomogeneous equation has a solution.
We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.
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Help please (Image attached)
The value of the infinite series as n tends to 0 is: 0
How to estimate infinite series?Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.
From the infinite series, we want to find the value of the series as n tends to 0.
We are given the series as:
x/2ˣ
At x = 0, we have:
0/2⁰ = 0/1 = 0
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