Relative value is the opposite of absolute value. while absolute cost examines the cost of an asset or organisation with out evaluating it to any others, relative fee is primarily based on the value of similar assets or businesses.
Relative value is a technique of determining an asset's worth that takes into account the value of similar belongings. that is in contrast with absolute price, which seems most effective at an asset's intrinsic value and does not evaluate it to other assets. Absolute change refers to the easy difference inside the indicator over two intervals in time, i.e. Relative change expresses the absolute exchange as a percentage of the price of the indicator in the earlier length. A relative maximum or minimum happens at turning factors at the curve wherein because the absolute minimal and most are the proper values over the entire area of the function. In different words the absolute minimum and most are bounded by means of the area of the function.
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The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = − 2 . The y -intercept is y = − 1.8 .
Answer:
[tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]
Step-by-step explanation:
Multiplicity is basically how much of a factor of a polynomial appears. In this case, if we disregard the y-intercept, we can show a multiplicity of 2 at x = 3 and a multiplicity of 1 at x=-2 with [tex]y=(x-3)^2(x+2)[/tex].
Of course, there will need to be a scale factor for the function so that the y-intercept will be at y = -1.8, so we can solve the following:
[tex]-1.8=a(0-3)^2(0+2)\\-1.8=a(3)^2(2)\\-1.8=a(9)(2)\\-1.8=18a\\-0.1=a[/tex]
Thus, we can write the function as [tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]. See below for a visual.
suppose you roll two six-sided dice. let the macrostate s of the two dice be the sum of their top faces.
The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.
The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.
It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.
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Which of the following tables represents a relation that is a function? x y 2 −5 2 −3 2 0 2 3 2 5 x y −3 0 −1 3 0 4 3 0 4 3 x y −4 2 −3 2 0 −2 0 2 4 2 x y −4 −2 −3 4 −1 −1 −1 2 3 −3
The tables represents a relation that is a function will be table number 3. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The number of value of the variable 'y' mush be one for a given value of 'x'. Then the relation will be a function.
If the number of value of the variable 'y' is 2 or more than two. Then the relation will not be a function.
Let's check the third option. Then we have
x y
−3 0
−1 3
0 4
3 0
4 3
The tables represents a relation that is a function will be table number 3. Then the correct option is C.
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Auberon swam 52 meters in five minutes at this rate how many meters would he swim in 10 minutes 12 minutes
If Auberon swim 52 meters in five minutes then at this rate the number of meters would he swim in 10 minutes & 12 minutes are respectively,
104 meters & 124.8 meters
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Since Auberon swim 52 meters in 5 minutes,
you can find his average rate of swimming by dividing the distance by the time:
Rate = 52 meters / 5 minutes
= 10.4 meters per minute
To find the distance he would swim in 10 minutes, you can multiply his average rate by the time:
Distance in 10 minutes = 10.4 meters per minute x 10 minutes
= 104 meters
To find the distance he would swim in 12 minutes, you can multiply his average rate by the time:
Distance in 12 minutes = 10.4 meters per minute x 12 minutes
= 124.8 meters
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ABC ∼ DEF. The area of DEF is given. Find the area of ABC.
Check the picture below.
[tex]\cfrac{12^2}{48^2}=\cfrac{A}{960}\implies \implies \cfrac{144}{2304}=\cfrac{A}{960}\implies \cfrac{1}{16}=\cfrac{A}{960} \\\\\\ 960=16A\implies \cfrac{960}{16}=A\implies \boxed{60=A}[/tex]
Ko Tapu is a vertical limestone rock located off the coast of
Thailand. Peter sets up a camera in a boat to shoot some
footage of the top of Ko Tapu. The horizontal distance from
the camera to a point at the base of the rock is 135 feet, and
the vertical distance from the point at the base of the rock to
a point at the top of the rock is 66 feet, as shown in the
figure.
135 ft
What is the measure of the angle of elevation, to the nearest
degree, that Peter should set the camera so he can video the
top of the rock?
Answer: The angle of elevation that Peter should set the camera to is 35.3°, rounded to the nearest degree (35°).
Step-by-step explanation: To find the angle of elevation, we can use the tangent function. Let's call the angle of elevation "x". Then:
tan(x) = 66/135
We can find the value of x using the inverse tangent (arctan) function:
x = arctan(66/135)
Finally, we can convert the result from radians to degrees:
x = arctan(66/135) * 180/π
x = 35.3° (rounded to nearest degree)
Prove: If two angles are supplementary, then one of the angles must be obtuse.
Which image provides a counterexample to this statement?
O A.
0 в.
о с.
O D.
A
A
A
В
M
M
M
B
В
B
В
B
м с
M
с
Option D is the counterexample of this given statement.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. For example, angle 110° and angle 70° are supplementary angles because the sum of 110° and 70° is equal to 180°.
Given a statement, If two angles are supplementary, then one of the angles must be obtuse.
In A, ∠BMC is an obtuse angle.
In B, ∠AMB is an obtuse angle
In C, ∠AMB is an obtuse angle.
But in D, there are two right angles. { two right angles are supplementary. }
Therefore, Option D is the counterexample of this given statement.
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National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:
Month Sales
(000)Units
Feb. 19
Mar. 18
Apr. 12
May. 20
Jun. 17
Jul. 21
Aug. 21
Forecast September sales volume using each of the following
(1) A linear trend equation.(Round your intermediate calculations and final answer to 2 decimal places.)
Yt thousands
(2) A five-month moving average. (Round your answer to 2 decimal places.
Moving average thousands
(3) Exponential smoothing with a smoothing constant equal to .40, assuming a March forecast of 19(000). (Round your intermediate forecast values and final answer to 2 decimal places)
Forecast thousands
(4) The naive approach
Naive approach thousands
(5) A weighted average using .50 for August, .20 for July, and .30 for June. (Round your answer to 2 decimal places.
Weighted average thousands
The forecasts for September sales volume using a linear trend equation, a five-month moving average, exponential smoothing with a smoothing constant of 0.40, the naive approach, and a weighted average are 17.86, 18.60, 18.72, 21.00, and 19.60 thousands, respectively.
1. A linear trend equation:
This is a method of extrapolating future values from existing data by fitting a linear line to the data points by calculating the slope and y-intercept of the line. To calculate the trend equation, we use the formula Yt = mXt + b, where Yt is the forecasted value, m is the slope of the line, Xt is the independent variable, and b is the intercept. We can calculate m and b by using the formula m = (n∑XY - (∑X)(∑Y)) / (n∑X2 - (∑X)2) and b = (∑Y - m(∑X)) / n. To calculate the forecast for September, we substitute the September value with the 7th month value and solve the equation. Y7 = mX7 + b. Therefore, the forecast for September is 17.86 thousands.
2. A five-month moving average:
This is a method of smoothing data points by taking the average of the preceding five data points and using this average value as the forecast. To calculate the five-month moving average, we use the formula Yt = (Yt-1 + Yt-2 + Yt-3 + Yt-4 + Yt-5) / 5. Therefore, the forecast for September is 18.60 thousands.
3. Exponential smoothing with a smoothing constant equal to .40, assuming a March forecast of 19(000):
This is a method of forecasting future values by using a weighted average of the past data points and the previous forecast. To calculate the forecast, we use the formula Yt = αYt-1 + (1-α)Ft-1, where Yt is the forecasted value, α is the smoothing constant, Yt-1 is the previous data point, and Ft-1 is the previous forecast. Therefore, the forecast for September is 18.72 thousands.
4. The naive approach:
This is a method of forecasting future values by simply taking the most recent data point as the forecast. Therefore, the forecast for September is 21.00 thousands.
5. A weighted average using .50 for August, .20 for July, and .30 for June:
This is a method of forecasting future values by taking a weighted average of the past data points. To calculate the forecast, we use the formula Yt = (0.5Yt-1 + 0.2Yt-2 + 0.3Yt-3) / (0.5 + 0.2 + 0.3). Therefore, the forecast for September is 19.60 thousands.
The forecasts for September sales volume using a linear trend equation, a five-month moving average, exponential smoothing with a smoothing constant of 0.40, the naive approach, and a weighted average are 17.86, 18.60, 18.72, 21.00, and 19.60 thousands, respectively.
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6TH GRADE MATH!!! Please Help me I'm stuck on this (worth 20 points!) Pleasee Help!!!! MARKING BRAINLIST!
A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 20 square feet. If she added another rectangular piece with vertices located at (−18, 13), (−14, 13), (−18, 5), and (−14, 5), what is the total area of the garden?
640 ft2
320 ft2
52 ft2
32 ft2
The total area of the garden is given as follows:
52 ft².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For the new rectangle, the dimensions are given as follows:
l = 18 - 14 = 4.w = 13 - 5 = 8.Hence the area of the new part is of:
A = 4 x 8
A = 32 ft².
Considering the previous part of 20 ft², the total area is given as follows:
32 + 20 = 52 ft².
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A vehicle's distance d in miles is given by the function d(r,t)=r⋅t, in which r is the rate in miles per hour and t is the time in hours. What happens to the value of d if the rate is tripled and the time increases by 3 hours?
If the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 12.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The original distance, d(r,t), can be expressed as d(r,t) = rt.
Value of d if the rate is tripled and the time increases by 3 hours
The new distance, d(3r,t + 3), can be expressed as d(3r,t + 3) = 3r(t + 3).
The new distance d(3r,t + 3) = 3r(t + 3)
= 3rt + 3(3r)
= 3rt +9r
= 3d(r,t) + 9r
Therefore, if the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 3 + 9 = 12.
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on the last three physics exams a student scored 90.87. and 89. what score just the student earn on the next exam to have an average 90?
Answer: 94
Step-by-step explanation:
First 3 exams are: 90, 87 & 89.
And since the average should be 90 after the 4th exam, we know the sum of the previous ones will be 90 x 4 = 360.
So,
90+87+89+n = 360
=> n = 94.
claim: if x is even then 9x 5 is odd. prove the claim for all x < 0, using the smallest counterexample method.
The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.
The smallest counterexample method is used to prove that a claim is false by providing an example that does not follow the claim. To prove the claim that if x is even then 9x 5 is odd, for all x < 0, we can use the smallest counterexample method by finding the smallest value of x that would disprove the claim.
Let x = -2, then 9(-2) - 5 = -17. Since -17 is even, it does not follow the claim that if x is even then 9x - 5 is odd, thus disproving the claim for all x < 0.
To explain this with formula and calculation, let x = -2, then 9x - 5 = 9(-2) - 5 = -17. Since -17 is even, the claim that if x is even then 9x - 5 is odd is false. Therefore, the claim is false for all x < 0.
The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.
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will give brainliest
could someone help me? im stuck, not the best with matrices/matrix.
The order of the matrix is
C. 5 x 3What is order of a matrix?The order of a matrix is the number of rows and columns it has.
It is represented as "m x n",
where
m is the number of rows and
n is the number of columns.
For example, a matrix with 3 rows and 4 columns has an order of 3 x 4.
In the problem, the matrix has 5 rows and 3 columns and hence the order is 5 x 3
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Use the point on the unit circle to find the value of the three trigonometric functions below.
sin t=
tan t=
sec t=
The value of trigonometric equations from the unit circle is
sin t = 1/2
cos t = √3/2
tan t = ( 1 / √3 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the point on the unit circle be represented as P ( √3/2 , 1/2 )
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
( √3/2 )² + ( 1/2 )² = 1
4/3 + 1/4 = 4/4 = 1
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Substituting the values in the equation , we get
cos t = √3/2
sin t = 1/2
tan t = sin t / cost
On simplifying the equation , we get
tan t = ( 1 / √3 )
Hence , the equations are solved
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Need Help For Parts B and C, chart is below
For the function f(x) = x, we know f(4) = 2 and f(9)=3.
a. Use linear interpolation to find [tex]\sqrt{5}[/tex].
Answer: [tex]\sqrt{5} = 2.2[/tex]
b. Use the table of square roots in the back of the text to find the error to 3 decimal places
c. What is the percentage error? (Recall that percentage error is 100∗error/(exact answer). )
The error to 3 decimal place is 0.036
The percentage error is solved to be 1.61%
How to find the errorThe error is calculated using the formula
= Approximate value – Exact Value
where
the approximate value = 2.2
Exact value from the table = 2.236
error = 2.2 - 2.236
error= -0.036
The percentage error
=(Approximate value – Exact Value) / Exact value * 100
= 0.036 / 2.236 * 100
= 0.0161 * 100
= 1.61%
The percentage error is 1.61%
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Solve the system by substitution
Y= 8
-3x-y=1
Answer:
x = -3
Step-by-step explanation:
-3x - 8 = 1
-3x = 9
3x = -9
x = -9/3
x = -3
Worth 25 points! Pls show work on both questions inside of the picture.
The area of the composite figure is 54 inches².
The perimeter of the figure is 35 inches.
How to find the area and perimeter of a composite figure?A composite figures is a figure with 2 or more 2 dimensional figures. The composite figure can be divided into three shapes.
Let's find the area of the composite figure as follows:]
area of the composite figure = area of the trapezium + area of the square + area of the rectangle
area of the trapezium = 1 / 2 (a + b)h
area of the trapezium = 1 / 2 (5 + 8)4
area of the trapezium = 1 / 2 × 4 × 13
area of the trapezium = 52 / 2
area of the trapezium = 26 inches²
Therefore,
area of the square = 4² = 16 inches²
area of the rectangle = 4 × 3 = 12 inches²
Therefore,
area of the composite figure = 12 + 16 + 26
area of the composite figure = 54 inches²
Let's find the perimeter of the composite figure as follows:
perimeter of the composite figure = 12 + 7 + 4 + 3 + 5 + 4
perimeter of the composite figure = 35 inches
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select all the rates that are unit rates 2/4/5 3/4/1 3:4 9/1 10:1
From the given rates, the unit rates are as follows 9/1 and 10:1. That is option D and E.
What is a unit rate?A unit rate of a measurement of the distance of a traveling vehicle or of a moving object is the rate for per one of the value of interest.
A unit rate can only be two figures that shows the relationship that exists between them and a whole value.
Therefore the given rates that shows unit rate are 9/1 and 10:1
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you are opening a t-shirt store. you can have long sleeves or short sleeves, three different colors, five different designs, and four different sizes. how many different shirts can you make? leave answer as a whole number, do not include decimals. answer: 120
There are 120 different shirts you can make from different combinations of sleeves, colors, and sizes.
To find the number of different shirts that can be made, use the fundamental counting principle wherein we multiply the number of options for each characteristic:
Long sleeves or short sleeves: 2 options
Three different colors: 3 options
Five different designs: 5 options
Four different sizes: 4 options
2 x 3 x 5 x 4 = 120
Therefore, the total number of different shirts that can be made is 120.
This calculation assumes that all of the characteristics are independent and can be combined in any way, which means that each shirt can have a unique combination of long/short sleeves, color, design, and size.
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If the arc measures of MN=87, what is the measure of
The required measure of the angle ∠MON is given as 87°.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO, so the measure of the section is equal to MON i.e.
∠MON = 87°
Thus, the required measure of the angle ∠MON is given as 87°.
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Let u = [0 26 8] and A = [5 -3 1 -3 7 1]. Is u in the plane in R^3 spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced row echelon form of the augmented matrix is which is an inconsistent system.
B. No, the reduced row echelon form of the augmented matrix is which is an inconsistent system. In this case, the vector u is [0 26 8] and the matrix A is [5 -3 1; -3 7 1].
To check if u is in the plane spanned by the columns of A, we can form the augmented matrix by appending u to A, and attempt to reduce it to the reduced row echelon form.
If the resulting augmented matrix is an inconsistent system (i.e. the last row has a non-zero coefficient in the last column and a zero in the right-hand side), then u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.
In this case, the reduced row echelon form of the augmented matrix is an inconsistent system, which means that u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.
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Let p, q, r be logical statements. Use truth tables to determine whether the following statements are tautologies.
a. [(p ^ q) -> r] <-> [p -> (q -> r)]
b. [(p Ë… q) ^ (~ q)] -> p
Truth tables are utilized to decide redundancies by assessing reality an incentive for every single imaginable mix. Both [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions.
a. We should assemble reality table for [(p ^ q) - > r] <-> [p - > (q - > r)].
p | q | r | (p ^ q) - > r | p - > (q - > r) | [(p ^ q) - > r] <-> [p - > (q - > r)]
T | T | T | T | T | T, T | T | F | F | F | F, T | F | T | T | T | T, T | F | F | T | T | T,
F | T | T | T | T | T, F | T | F | T | T | T, F | F | T | T | T | T, F | F | F | T | T | T
Since every one of the qualities in the last segment are "T", the assertion [(p ^ q) - > r] <-> [p - > (q - > r)] is a redundancy.
b. We should construct reality table for [(p ∧ q) ^ (~q)] - > p.
p | q | ~q | (p ∧ q) ^ (~q) | [(p ∧ q) ^ (~q)] - > p
T | T | F | F | T, T | F | T | T | T, F | T | F | F | T, F | F | T | F | T
Since every one of the qualities in the last section are "T", the assertion [(p ∧ q) ^ (~q)] - > p is a repetition.
A repetition is a coherent explanation that is in every case valid, no matter what reality values doled out to its singular parts. To decide whether an assertion is a repetition, we can utilize a reality table which records generally potential blends of truth values for the parts and assesses reality worth of the whole assertion. In the event that reality worth of the assertion is generally "Valid" for every conceivable mix, then, at that point, the assertion is a redundancy. In the models given, the two explanations [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions through truth tables.
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In triangle BCD below, H is the circumcenter. Given BD= 80 and HB=50, find the segments below. Round to tenths if necessary.
The length of EH is determined as 10.72.
What is the length EH?The length of EH can be determined if the length of the each side is properly identified as shown below.
In the given figure, H is the circumcenter of triangle BCD,
BD = 80HB = 50BC = 18HD = 14Triangle BHD is isosceles, therefore BH = HD
Point E is midpoint of BC, therefore BE = ¹/₂ of BC
Using Pythagorean, calculated the value of EH as follows;
EH = √ (BH² - BE²)
EH = √ ( 14² - ( 18 /2) ² )
EH = √ ( 196 - 81 )
EH = √115 = 10.72
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The side length of BE is 40 units
How to determine the side length of BEFrom the question, we have the following parameters that can be used in our computation:
H is the circumcenter.
BD= 80 and HB=50
Using the above as a guide, we have the following:
BE = 1/2 * BD
Substitute the known values in the above equation, so, we have the following representation
BE = 1/2 * 80
Evaluate
BE = 40 units
Hence, the side length of BE is 40 units
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y = 3x + 2
y = 4x-5
I need help showing work pls
The option C.(1, -1) is correct. The solution for the system of equations y = -3x + 2 and y = 4x - 5 is x = 1 and y = -1.
How to evaluate for the solutions of the equationsWe shall write the equations as:
y = -3x + 2...(1)
y = 4x - 5...(2)
to get the value of x, we evaluate as follows:
4x - 5 = -3x + 2
4x + 3x = 5 + 2 {collect like terms}
7x = 7
x = 7/7 {divide through by 7}
x = 1
put the value 1 for x in equation (1) we have;
y = -3(1) + 2
y = -3 + 2
y = -1.
Therefore, the solution for the system of equations y = -3x + 2 and y = 4x - 5 is x = 1 and y = -1.
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Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression. Write the algebraic expression that Danielle should write. Type your expression with no spaces.
The algebraic expression that Danielle should write is 2x - 4
How to determine the algebraic expression that Danielle should writeFrom the question, we have the following parameters that can be used in our computation:
4 less than twice a number
Represent the number with x
So, we have the following representation
4 less than twice x
Twice x means 2x
So, we have
4 less than 2x
Less than here means minut
So, we have the following representation
2x - 4
Hence, the expression is 2x - 4
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Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing
formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total
area answer)
The area of the given figure is 43.3 units².
What is trapezium?A trapezium is a quadrilateral with four sides where two sides are parallel to each other.
We have,
The figure has two shapes:
Trapezium and a semicircle.
Now,
We will consider one box as one unit.
Trapezium:
Height = 6 units
Parallel sides = 8 units and 5 units
Area = 1/2 x height x (sum of the parallel sides)
Area = 1/2 x 6 x (8 + 5)
Area = 3 x 13
Area = 39 units²
Semicircle:
Diamter = 6 units
Radius = 3 units
Area = 1/2 x πr²
Area = 1/2 x 3.14 x 3²
Area = 4.3 units²
Now,
Area of the figure.
= 39 + 4.3
= 43.3 units²
Thus,
The area is 43.3 units².
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how many different linear arrangements are there of the letters a, b, c, d, e, f for which (a) a and b are next to each other? (b) a is before b? (c) a is before b and b is before c?
Answer:
the total number of arrangement is six
Step-by-step explanation:
Part (a) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other.
Suppose A and B are together and form a group, then no. of groups are .
These groups can be arranged in
A and B can be arranged in .
Therefore, the possible no. of arrangements are .
Part (b) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B.
Total no. of arrangements with six letters
The no. of arrangements in which A is before B
Therefore, the possible no. of arrangements are .
Part (c) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and B is before C.
Total no. of arrangements with six letters
A, B and C can be arranged in
Out of these 6 arrangements, there is only one arrangement in which A is before B and B is before C.
So, the possible no. of ways =
Therefore, the possible no. of arrangements are .
Part (d) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and C is before D.
The no. of arrangements in which A is before B
Out of these arrangements, half will be with C before D and half will be with D before C.
Therefore, the possible no. of arrangements are .
Part (e) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other and C and D are also next to each other.
If A and B form one group and C and D from another group then there are groups and these groups can be arranged in
A and B can be arranged in
Similarly, C and D can be arranged in
Therefore, the possible no. of arrangements are .
Part (f) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that E is not last in line.
The no. of arrangements in which the position of E is fixed at last
The no. of arrangements in which the position of E is not fixed
Therefore, the possible no. of arrangements are
find the values for: - m train (number of training examples) - m test (number of test examples) - num px (
m_train = train_set_x_orig.shape[0], m_test = test_set_x_orig.shape[0], num_px = train_set_x_orig.shape[1] can be used to obtain the values for m_train, m_test, and num_px respectively.
The information provided is related to a machine learning problem where a dataset is split into two parts: training set and test set. The training set is used to train a machine learning model, while the test set is used to evaluate the performance of the model.
The training set is represented as a numpy array named "train_set_x_orig" with shape (m_train, num_px, num_px, 3). The first dimension of the array, m_train, represents the number of training examples. The next two dimensions, num_px, represent the height and width of each training image, and the last dimension, 3, represents the RGB color channels of each pixel in the image.
To access the value of m_train, the following code can be used: m_train = train_set_x_orig.shape[0]
Similarly, the values for m_test and num_px can be obtained by accessing the corresponding test set arrays using the numpy array method "shape".
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The complete question is:
Find the values for: - m_train (number of training examples) - m_test (number of test examples) - num_px (= height = width of a training image) Remember that train_set_x_orig is a numpy-array of shape (m_train, num_px, num_px, 3). For example, you can get to m_train by writing train_set_x_orig.shape[0].
An editor has a stack of k documents to review. The order in which the doc- uments are reviewed is random with each ordering being equally likely. Of the k documents to review, two are named "Relaxation Through Mathematics" and "The Joy of Calculus." Give an expression for each of the probabilities below as a function of k. Simplify your final expression as much as possible so that your answer does not include any expressions in the form () (a) What is the probability that "Relaxation Through Mathematics" is first to review? (b) What is the probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack?
The probability that "Relaxation Through Mathematics" is first to review is 1/k, and the probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)).
A) The probability that "Relaxation Through Mathematics" is first to review is 1/k. This is because there are k documents to review, and the order in which they are reviewed is random with each ordering being equally likely. Therefore, the probability that any given document is chosen first is 1/k.
B) The probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)). This is because there are k documents to review, and the probability that the first document is "Relaxation Through Mathematics" is 1/k. Then, since there are k-1 documents remaining in the stack, the probability that the second document is "The Joy of Calculus" is 1/(k-1). Therefore, the probability that both documents are next to each other is (1/k)*(1/(k-1)).
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You are thinking of using a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect the distribution of the population is not normal and may be moderately skewed. Which of the following statements is correct?A. You should not use the t procedure because the population does not have a normal distribution.B. You may use the t procedure, but you should probably only claim the significance level is 0.10.C. You may use the t procedure, provided your sample size is large, say at least fifty.D. You may not use the t procedure. t procedures are robust to nonnormality for confidence intervals but not for tests of hypotheses
The correct statement is: C. You may use the t procedure, provided your sample size is large, say at least fifty.
A t-test is a statistical test used to determine whether two sets of data are significantly different from one another. When the population standard deviation is unknown and the sample size is small, a t-test is usually used. The normality assumption is not crucial for the validity of a t-test, as long as the sample size is large enough (typically over 30). However, the more the sample deviates from normality, the more likely it is that the t-test will produce incorrect results. To deal with non-normal data, the t-test is robust, meaning it is not highly sensitive to deviations from normality, when the sample size is large enough.
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