Based on the table, a statement which is true is that: C. The table shows a linear relationship, but not a proportional relationship.
What is a proportional relationship?In Mathematics, a proportional relationship simply refers to a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y is the distance measured in miles.x is the time measured in hours.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the distance (miles) and time (hours) on this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16
In conclusion, we can reasonably infer and logically deduce that the table shows a linear relationship because as the time (in hours) increases, the distance (miles) also increases. However, this table does not show a proportional relationship because it has different constant of proportionality.
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problem 1. create two vectors named v and w with the following contents: v : 21,10,32,2,-3,4,5,6,7,4,-22 w : -18,72,11,-9,10,2,34,-5,18,9,2 a) print the length of the vectors b) print all elements of the vectors c) print elements at indices 3 through 7. d) print the sum of the elements in each vector. e) find the mean of each vector. (use r's mean() function) f) sort the vectors in descending order and then print. g) add vectors v and w. h) multiply vectors v and w. i) in vector v select all elements that are greater than zero. j) in vector w select all elements that are less than zero. k) multiply each element of vector v by 6. and then print. l) find maximum and minimum of each vector. m) in each vector, replace all negative values with the average of all numbers in the vector.
Vector v and w have lengths of 11 and contain elements of 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2 respectively. The addition, multiplication, and sorting of both vectors were calculated, as well as the means, maximums, and minimums.
a) The lengths of the vectors v and w are both 11.
b) Vector v contains the elements 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and vector w contains the elements -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2.
c) Elements 3 through 7 of vector v are 2, -3, 4, 5, 6 and elements 3 through 7 of vector w are 10, 2, 34, -5, 18.
d) The sum of the elements in vector v is 60 and the sum of the elements in vector w is 91.
e) The mean of vector v is 5.454545454545455 and the mean of vector w is 8.272727272727273.
f) Vector v is sorted in descending order as 32, 21, 10, 7, 6, 5, 4, 4, 2, -3, -22 and vector w is sorted in descending order as 72, 34, 18, 11, 10, 9, 2, 2, -9, -5.
g) The addition of vectors v and w is 53, 82, 28, 2, 7, 13, 6, 8, -7, 4, -20.
h) The multiplication of vectors v and w is -378, 720, 352, -18.
i) Elements in vector v that are greater than zero are 21, 10, 32, 2, 4, 5, 6, 7, 4.
j) Elements in vector w that are less than zero are -18, -9, -5.
k) Vector v multiplied by 6 is 126, 60, 192, 12, -18, 24, 30, 36, 42, 24, -132.
l) The maximum of vector v is 32 and the minimum of vector v is -22. The maximum of vector w is 72 and the minimum of vector w is -9.
m) In vector v, all negative values are replaced with the average of all numbers in the vector, which is 5.454545454545455. In vector w, all negative values are replaced with the average of all numbers in the vector, which is 8.272727272727273.
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When an economy produces a good where the marginal benefit equals the marginal cost it is
At that level of output and price, profit is maximized when marginal revenue and the marginal cost of production are equal:
MR = *TR/*Q
MC = *C/*Q
Eq. = MR = MC
where, MR = Marginal Revenue
MC = Marginal Cost
* = Change in
TR = Total Revenue
Q = Quantity
C = Cost
The marginal revenue rule states that by selecting the amount at which marginal revenue equals marginal cost, we can maximize the net benefit of any action. The activity's net benefit is maximum at this amount.
The corporation eventually reaches the point at which manufacturing any more units will raise the cost of production per unit, which is known as its optimum production level.
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What are the coordinates of the point on the directed line segment from (−10,−10) to ( − 4 , 2 ) that partitions the segment into a ratio of 5 to 1?
The required point that divides the line into 5:1 is given by (-5,0)
What is the section formula?Let M(x, y) be the point which divides line segment PQ internally in the ratio m : n. PA, MN and QR are drawn perpendicular to x- axis. PS and MB are drawn parallel to x – axis. This is known as section formula.
Given here: A line segment with end points (−10,−10) to ( − 4 , 2 )
Now the coordinates of the point that divides a line in the ratio m:n is given by
x= mx₂+nx₁ /m+n
y=my₂+ny₁/m+n
Thus the co-ordinates are x=5×-4+1×-10 / 5+1
=-30/6
= -5
And y= 5×2+1×-10 / 6
=0
Hence, The required point that divides the line into 5:1 is given by (-5,0)
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PLEASE HELP ITS DUE TODAY AND WOULD GIVE A LOT OF POINTS IF SOMEONE SHOWS THE ANSWER ANY SPAM ANSWERS WILL BE REPORTED!
To find the slope of the line given the points (0,2) and (1,0), we can use the formula: m = (y2 - y1) / (x2 - x1).
m = (0 - 2) / (1 - 0) = -2
Using point-slope form, we can write the equation of the line as:
y - 2 = -2 (x - 0)
y = -2x + 2
To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.
So the linear inequality for the points (0,2) and (1,0) is:
y >= -2x + 2
we are given a classifier that performs classification on r 2 (the space of data points with 2 features (x1, x2)) with the following decision rule: h(x1, x2)
The decision rule given is x1 + x3 – 10 ≥ 0, which can be rearranged to x1 + x3 ≥ 10. This forms a line in the R2 space, and any point on or above this line will be classified as 1, while any point below this line will be classified as 0.
To draw the decision boundary, we can plot the line x1 + x3 = 10 on a graph with the x1 and x3 axes. The region above the line, where x1 + x3 ≥ 10, would be shaded to indicate that it is where the classifier predicts 1.
It is important to note that the classifier predicts 1 if x1 + x3 – 10 ≥ 0, but in the explanation above I have used x1 + x3 = 10 to draw the decision boundary, this is because x1 + x3 – 10 ≥ 0 is equivalent to x1 + x3 ≥ 10.
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X
%
60°
4
Z
30%
Y
Given right triangle XYZ, what is the value of tan(Y)?
02/0
O
O
O
3
√3
2
O2√3
3
The value of tan(Y) = 0.75.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and with the trigonometric functions that describe those relationships.
Since triangle XYZ is a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent to find the value of tan(Y). We can use the Pythagorean theorem to find the lengths of the sides XZ and YZ.
XZ = √(X^2 + Z^2) = √(4^2 + 3^2) = 5
YZ = XZ * sin(Y) = 5 * sin(Y)
Since we know the value of XZ and YZ, we can use the tangent function to find the value of tan(Y):
tan(Y) = YZ / XZ = sin(Y) / cos(Y) = YZ / 5 = 3 / 4 = 0.75
So, the value of tan(Y) = 0.75.
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What is the best name for this shape? Use the drop-down menus to explain your answer. 55° 125° 125° 55° Click the arrows to choose an answer from each menu. The shape has Choose... It has Choose.... It has Choose... The best name for this shape is Choose... angles that are acute and equal. angles that are obtuse and equal. angles that are right angles.
The best name for this shape is rectangle. There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle.
Four names for rectangles: what are they?Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use. This is so that it is clear that a rectangle meets the criteria for each of these other forms, as shown by its definition.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram. Thus, it conforms to all of a parallelogram's characteristics.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram.Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use.To learn more about rectangle refer to:
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What is the value of the expression
10/12 + 3/7
Answer:
= 53/42
Step-by-step explanation:
10/12 is equivalent to: 70/84
3/7 is equivalnt to: 36/84
Then:
10/12 + 3/7 = 70/84 + 36/84
= (70 + 36) / 84
= 106 / 84
= 53 / 42
rhombus is inscribed in rectangle as shown. segments and are parallel to . segments and are parallel to . if and what is the area of rectangle ?
The perimeter of the rectangle WXYZ is 96 cm.
Here we see that
WXYZ is a rectangle (given)
Therefore,
∠WZY = 90 = ∠WZS
Since JS is parallel to PZ and JP is parallel to SZ, we get
JPSZ as a rectangle. Similarly, PKWQ, SYMR, and XQRL are rectangles.
JS = PZ
or, JS = PW + WZ
or, JS = KQ + WZ
or, WZ = JS - KQ
or, WZ = 52 - 25
or, WZ = 27
The side of the rhombus PS is a diagonal of rectangle JSPZ
Therefore length of the diagonal PS = √(JP² + JS²)
= √(52² + 39²)
= 65 cm
Hence for PWKQ,
PK = √(PQ² - KQ²)
= √(65² - 25²)
= 60 cm
For triangles ΔPWQ and ΔSYR,
the corresponding sides are parallel to each other. Hence we can say that
PW/YR = WQ/SY = PQ/RS
Therefore,
60/SY = 65/65 [Since they are the sides of a rhombus]
or, SY = 60 cm
Now, SY = SZ + ZY
or, SY = JP + ZY [Opposite sides of a rectangle are equal]
or, ZY = 60 - 39
or, ZY = 21
Hence the perimeter of WXYZ
2(length + width)
= 2(27 + 21)
= 96 cm
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Complete Question
Rhombus PQRS is inscribed in a rectangle JKLM, as shown. Segments PZ and XR are parallel to JM. Segments QW and YS are parallel to JK. If JP = 39 cm, JS = 52 cm, and KQ = 25 cm, what is the perimeter of rectangle WXYZ?
Type the correct answer in each box. Lmk!
There were 0-5 Listeners when the song was released.
The approximate number of listeners who had heard the song after the hour 5 was 15- below 50
The number of listeners was about 29,458 after hour 5842.62/
How can I explain?Alternative forms
Y= 4,637(1.26)ˣ
292131/50,5842,31/50,5.84262 =10³
5842.62
Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.
Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.
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two rooms in a tiny house share a wall the area of the living room is 54. The area of the bedroom is 42. the expression 54+42 represents the total area in square feet. Write and equivalent express to represent the total area as a product using the GCF as one of those factors
54+42=_(_+7)
If two rooms in a tiny house share a wall the area of the living room is 54. The expression to represent the total area as a product using the GCF as one of those factors is: 6×3+ 6× 8 and 6(3 + 8).
How to find the total area?Living room area = 54 square feet
Area of the bedroom = 42 square feet
Total area of the two rooms = 54 + 42
Total area of the two rooms = 66 square feet
So, the expressions that represent the total area of the two rooms is: 6×3+ 6× 8 and 6(3 + 8).
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Answer:
54+42=6(9+7)
Step-by-step explanation:
How many pounds of chamomile tea that costs $18.10 per pound must be mixed with 12 lb of orange tea that costs
$ 12.22 per pound to make a mixture that costs $14.74 per pound?
lb
9 pounds of Chamomile tea needed to make a mixture that costs $14.74 per pound
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
let:
x pounds of Chamomile tea needed
Therefore,
18.10X + 12.22(12) = 14.74(12 + x)
18.10X + 146.64 = 176.88 + 14.74x
3.36X = 30.24
X = 9 pounds
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Let y = πx + π. For what value of x is y = π^3?
The value of the variable x = π³ - π/π
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.
These algebraic expressions are also comprised of arithmetic operations, such as;
DivisionMultiplicationSubtractionFloor divisionAdditionBracketParenthesesFrom the information, we have that;
y = π³
y = πx + π
Substitute the values, we get;
π³ = πx + π
collect like terms
π³ - π = πx
Divide both sides by the coefficient of x
x = π³ - π/π
Thus, the value is x = π³ - π/π
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6. Insert < >, or = to make the sentence true. (1 point)
3/4 ? 4/7
O>
O<
O=
Answer:
3/4 > 4/7
Step-by-step explanation:
1. Find the LCM of 4 and 7, which is 28
2. Take 3/4 and multiply the numerator and the denominator by 7 (because 7x4=28)
You will end up with 21/28
3. Take 4/7 and multiply the numerator and the denominator by 4 (because 4x7=28)
You will end up with 16/28
Now that the denominators are the same, the fraction with the bigger numerator is the greater fraction. Therefore, 3/4 is the greater than 4/7.
is the linear relationship represented by the table a proportional relationship?
Tickets
Cost
0
$0
The linear relationship
the point (0, 0)
2
$14.50
Choose
4
$29
6
$43.50
a proportional relationship because the ratios between each pair of values are equivalent and the graph
Choose...
through
The linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).
What is proportional relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".
We are given points as (2,14.5), (4,29), (6,43.5) and the origin (0,0).
We know that in a proportional relationship the ratios are equal i.e.
[tex]\frac{y_{1} }{x_{1}} = \frac{y_{2} }{x_{2} } = \frac{y_{n} }{x_{n} }[/tex]
So,
⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25
Since, the ratios are same, therefore the linear relationship is a proportional relationship.
The graph of the given situation has been plotted and it can be seen that the graph passes through the origin i.e. (0,0)
Hence, the linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).
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Find the smallest value of m such that the product of 189m is a perfect square
Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
-5x + -4 + 1 - 4x
show your work to combine "like terms"
Answer:
-9x + -3
Step-by-step explanation:
1. Primeiro, vamos penteinar SO prazoos que possuem um mesmamã variável, ou seja, -5x e -4x:
-5x - 4x
2. Agora, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, 1 e -4:
-5x - 4x + 1 -
4 3. Por fim, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, -4 e 1:
-5x - 4x + -4 + 1
Find the difference in the given lengths of the polygons. (7x + 2) units (6x - 5) units
By solving a subtraction, we can write the difference between the lengths as:
|x + 7|
How to find the difference between the lengths?Here we want to find the difference between the two lenghts below:
L₁ = (7x + 2)
L₂ = (6x - 5)
The difference between these can be written as the absolute value of the subtraction, then we will get:
| L₁ - L₂|
We use the absolute value because we don't know which one is the larger value.
Replacing the expressions we will get:
| (7x + 2) - (6x - 5)|
|7x + 2 - 6x + 5|
| x + 7|
That is the difference.
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Complete the following table.
Population Growth Rate, k Doubling Time, T Country A 1.3% per year
Country B. 30 years
Population Growth Rate, k Doubling Time,
T
Country A
1.3% per year
years
Country B [% per year
30 years
(Round doubling time to the nearest whole number and round growth rate to the nearest tenth.)
The numbers that correctly complete this table are 53.83 years and 2.12%
How to calculate the doubling time using the population growth?The formula that can be used is:
Doubling time = 70 (constant)/ population growth
Doubling time =70 / 1.3
Doubling time = 53.84 years
How to calculate the population growth using the doubling time?The same formula can be applied:
33 = 70 (constant)/ population growth
population growth = 70 /33
population growth = 2.12 %
Based on this, the correct numbers to complete the table are 53.83 years and 2.12%.
Note: Here is the missing table:
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How do you know when an expressionis in its simplest form?
Answer:
Uma expressão está e sua forma mais simples quando não há mais nenhuma simplificação possível. Isso significa que não há mais nenhum termo que possa ser combinado ou cancelado, e que todos os termos estão na sua forma mais simples. Além disso, todos os fatores e expoentes devem estar na sua forma mais simples.
Help with this equation
Translations between points B and B' and points S and S' are result of using translation vector T(x, y) = (- 3, - 1).
How to determine the translation formula behind two-point transformation
In this problem we find the case of two points being translated by rigid transformation formula. Translations are defined by following equations:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.First, derive translation vector from translation formula:
T(x, y) = B'(x, y) - B(x, y)
T(x, y) = (- 9, - 2) - (- 6, - 1)
T(x, y) = (- 3, - 1)
Second, check that point S' is the image of point S:
S'(x, y) = S(x, y) + T(x, y)
S'(x, y) = (5, 1) + (- 3, - 1)
S'(x, y) = (2, 0)
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Match the given differential equation with one or more of the solutions. (Select all that apply.) xy' = 4y y = 4x y = 0 y =4 Y = 4x4
The solutions that match the given differential equation are a)y=0 and b)y=2x.
The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.
In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.
Therefore, the general solution to this differential equation is y = c1 + c2x.
y=0 is a solution of the differential equation since it satisfies the equation when plugged in.
y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.
y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.
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A recent study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty- two hundred study? Florida residents were surveyed, Which of the following is the sample used in tho a) all Florida residents b) the 4200 Florida residents surveyed c) all Florida residents who lived along the beaches d) the Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters
The sample used in the study is b) the 4200 Florida residents surveyed. surveyed. To obtain the answer following steps are :
1. Read the question and identify the key words: sample, Florida residents, 4200
2. Consider the given options and eliminate those that don't match
3. Based on the given information and the options, the answer is b) the 4200 Florida residents surveyed.
This is because the sample used in the study was the 4200 Florida residents who were surveyed, and this sample was used to estimate the proportion of all Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters.
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based on the information in the table, what quantity of reserves would the federal reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.
Now, According to the question:
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
We know that:
Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).
The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.
It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.
So the answer is $0.30 billion + $0.36 billion = $0.66 billion.
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The given question is incomplete, complete question is :
Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
I dont understand this
Find the measure of a single exterior angle of the regular polygon shown below. If necessary, round to the nearest tenth.
The measure of an exterior angle of the regular polygon shown in the figure is 60°.
What are exterior angle?The angle between a side of a polygon and an extended adjacent side is called its exterior angle.
Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,
We know that, the sum of interior angles of regular hexagon is 720°
Therefore, one interior angle = 720 / 6 = 120°
If we extend a side of the hexagon, (refer to figure attached in solution)
Then, the interior angle and an exterior angle "A" will make a linear pair,
Therefore,
120° + A = 180°
A = 60°
Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.
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Refer to the following distribution of commissions:Monthly Commissions Class Frequencies$600 up to $800 3800 up to 1,000 71,000 up to 1,200 111,200 up to 1,400 121,400 up to 1,600 401,600 up to 1,800 241,800 up to 2,000 92,000 up to 2,200 4For the preceding distribution, what is the midpoint of the class with the greatest frequency?O 1,500O 1,700O The midpoint cannot be determined.O 1,400
From the given table the greatest frequency is 40,
midpoint of greatest frequency =$2100.
Relative frequency is also referred to as the empirical probability, which is calculated by the division of each frequency by the total number of frequency in the sample.
We can answer the question creating the following table:
Class Frequency Rel. Frequency
$600-$800 3 3/120=0.025
$800-$1000 7 7/120=0.059
$1000-$1200 11 11/120=0.092
$1200-$1400 22 22/120=0.183
$1400-$1600 40 40/120=0.333
$1600-$1800 24 24/120=0.2
$1800-$2000 9 9/120=0.075
$2000-$2200 4 4/120=0.033
Total 120 1
From the above table the greatest frequency is 40,
midpoint of greatest frequency =$2100.
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Determine whether the statement below is true or false. Justify the answer. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. A. The statement is true. Each elementary row operation replaces a system with an equivalent system B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system. C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.
Elementary row operations are always applied to an augmented matrix after the solution has been found. So the option D is correct.
Elementary row operations:
1. It is possible to convert a system of linear equations into an equivalent system, or into a new system of equations that has the same solutions as the original system, using these straightforward techniques.
2. In order to convert a matrix to row echelon form, Gaussian elimination is used.
3. Simple row operations on an augmented matrix never alter the underlying linear system's solution set.
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solve: a + 1/10 = 5/10.
Answer:
5/10 - 1/10 = 4/10
a = 4/10
4/10 + 1/10 = 5/10
Step-by-step explanation:
Hope it helps! =D
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function:
y = (pie)x Power Function
y = xy Exponential Function
y = x2(2-x3) Polynomial (degree of 2)
y = tan t â cos t Trigonometric
y = s / 1+s Algebraic Function
y = sqrt(x3 â 1) / 1+ 3sqrt(x) Root Function
Not sure on these. Thanks!
A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.
The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.
Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.
Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.
Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.
Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.
Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.
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