Answers
x is 6 and y is 0 are the only solutions to the given pair of linear equations.
What are the linear equations?It is possible to write the given pair as x-3y 6=0. and 2x−3y−12=0
Here, a 1 = 1, b 1 = 3, c 1 = 6, and a 2 = 2, b 2 = 3, c 2 = 12, and eq2 a 2.
a1 = 2
b1 , b2
b 1 = −6
3 = −2 1
therefore a 2
a 1= b 2 b 1.
The given pair of equations is therefore consistent.
In order to solve them graphically, we've
Take x-3y=6=0, x=0y=2, and x=3y=1 into consideration.
Draw a line to connect the points.
Think about 2x3y12=0 x=0y=4 x=3y=2.
Create a line connecting the two points.
x=6 and y=0 are the only solutions to the given pair of linear equations.
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Related Questions
Use technology to find the surface area S of the surface generated when the plane curve defined by the equations æ(t) = = -6e-t, y(t) = 7e-t, on the interval 1
Answers
The surface area S is given by the definite integral of the function :
|r(t) X r'(t)| over the interval [1], which can be approximated by numerical integration methods.
To find the surface area of the surface generated by the given equations, we need to first find the cross-sectional area of the surface at every point of t and then integrate it over the interval. To do this, we need to find the vector r(t) = (x(t),y(t)) and its derivative r'(t) = (x'(t),y'(t)) which gives the tangent vector to the curve at t. The cross-sectional area of the surface at t is given by the magnitude of the vector cross product of the vectors r(t) and r'(t) and is written as |r(t) X r'(t)|. Then the surface area S is given by the definite integral of this cross-sectional area over the interval [1].
The definite integral can be solved analytically or numerically, however, the final answer would be the integration of the function |r(t) X r'(t)| over the interval [1], which is not possible to solve analytically, so we use numerical integration methods.
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There were seven serving lines at the
annual pancake breakfast. The total
number of people served at each of
the seven lines were 126, 118, 127, 134,
98, 132, and 121. What was the median
number of people served?
Answers
Answer: 126
Step-by-step explanation: Given that the median is the middle number in a sorted, ascending, or descending list of numbers and can be more descriptive of that data set than the average. We know that we need to put the numbers in order from greatest to least or least to greatest first.
Step 1: Ordering the numbers (from least to greatest)
98,118,121,126,127,132,134
Step 2: Finding the value in the middle
98,118,121, 126 ,127,132,134
We now know that 126 is the median number of people served.
Answer: 126 is the median number of people served.
Step-by-step explanation:
The median is found by arranging the data points in a set from lowest to greatest. Once this is done, if there are an odd number of data points, simply find the number in the middle. If there is an even number, find the average of the two middle numbers. Here, you would arrange the numbers as such, 98,118,121,126,127,132,134. Once this is done, since there are seven lines (an odd number of data points, therefore), figure out which number is in the middle, and here it is 126. Hence, the median is 126 (people)
let x and y be identically independent random variables such that the moment generating function x y is X+Y isφX+Y(t)=e2t+0.24.2t+0.09e2tFind P(X0)
.
Answers
The probability of X being greater than 0 is 1.
P(X>0)=1-P(X≤0)
=1-φX+Y(-∞)=1-e^(-2*(-∞))-0.24*2*(-∞)-0.09*e^(-2*(-∞))
=1-0-0-0=1
Since x and y are identically independent random variables, P(X>0)=1-P(X≤0).
The moment generating function of x+y is given as φX+Y(t)=e2t+0.24.2t+0.09e2t.
To find P(X>0), we need to calculate P(X≤0). This can be done by putting t=-∞ in the moment generating function.
Therefore, P(X>0)=1-φX+Y(-∞)=1-e^(-2*(-∞))-0.24*2*(-∞)-0.09*e^(-2*(-∞))=1-0-0-0=1
The probability of X being greater than 0 is 1.
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find the standard deviation of the data below
16,10,5,7,13
Answers
The standard deviation for the given data, can be found to be 3. 97
How to find the standard deviation ?To find the standard deviation, you first need to find the mean of the data as:
= Sum of the numbers / Sample number
= ( 16 + 10 + 5 + 7 + 13 ) / 5
= 51 / 5
= 10. 2
The variance can then be found from this data, the mean, and a variance calculator to be 15.76.
The standard deviation is:
= √ 15.76
= 3. 97
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What is the answer for these expressions
Answers
Answer:
a.7a-ab+b
=7×3-3×5+5
=21-15+5
=11
b.10a÷(2b)
=10×3÷(2×5)
=30÷10
=3
C.4ab-6b+5a
=4×3×5-6×5+5×3
=60-30+15
=45
*Mark me brainliest
List all the vertices, edges, and faces in the figure below.
Answers
The 3 dimensional figure has 6 vertices , 9 edges and 5 faces.
What Are Vertices, Faces And Edges?Vertices in shapes are the points where two or more line segments or edges meet (like a corner). Edges are the line segments that join one vertex to another and are also where the shape’s faces meet. Faces are the flat surface of a solid shape.
Given here: A figure with 3 rectangular faces and 2 triangular faces.
We know, Vertices are the corners of the three-dimensional shape, where the edges meet. Faces are flat surfaces and edges are the lines where two faces meet.
The vertices of the figure are A,B,C,D,E,F And edges as AB,BC,CF,FA,EB,DC,AE,FD,ED
And the faces are as follows
rectangular faces- AFDE, ABCF, EDCB
Triangular faces- EAB, DFC
Hence, The 3 dimensional figure has 6 vertices , 9 edges and 5 faces.
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hite at
Examine the linear graph. Determine
the y-intercept and write it as an
ordered pair.
180-
160-
140-
120-
100-
80
60
40-
20
-10%
(42, 148)
10 20 30 40 50 60 70
Answers
The y-intercept of the given line is 100.
What is the y-intercept?
The y-intercept is the point at which the line crosses the y-axis, which occurs when x = 0. To find the y-intercept, we can plug in x = 0 into the equation of the line.
We can write the equation of the line in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope m using the point slope formula:
m = (y2 - y1) / (x2 - x1) = (148-100)/(42-0) = 48/42 = 4/3
Now we can substitute the point (0,100) into the equation of the line:
y = (4/3)x + b
100 = (4/3) * 0 + b
b = 100
So the y-intercept is (0,100)
Hence, the y-intercept of the given line is 100.
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A project should take no more than 60 hours. If John can spare 7.5 hours per day to work on the project, what is the maximum number of days it will take him to finish
Answers
Answer:
8 days
Step-by-step explanation:
We know
A project should take no more than 60 hours, which means the number of hours should [tex]\leq[/tex] 60 hours.
John can spare 7.5 hours per day to work on the project.
Let x represent the number of days; we have the equation
7.5x [tex]\leq[/tex] 60
x [tex]\leq[/tex] 8
So, the maximum number of days it will take him to finish is 8 days.
2a^(3) -4a^( 2)-6a-1-4a^( 3)+6a^( 2)-11a-3
Answers
This equation can be resolved by simplifying it appropriately. Solve it by combining like terms.
To solve this problem
2a^(3) -4a^( 2)-6a-1-4a^( 3)+6a^( 2)-11a-3
Firstly, take away the ones that are 1 and 3 from it.
2a^(3) -4a^( 2)-6a-4a^( 3)+6a^( 2)-11a-4
Then combine like terms
2a^(3) -4a^( 2)-6a-4a^( 3)+6a^( 2)-11a-4
-2a^(3) -4a^( 2)-6a+6a^( 2)-11a-4
Then mix related terms owing a^(2)
-2a^(3) -4a^( 2)-6a+6a^( 2)-11a-4
-2a^(3) +2a^( 2)-6a-11a-4
Combine like terms having ( a )
-2a^(3) +2a^( 2)-6a-11a-4
-2a^(3) +2a^( 2)-17a-4
Consequently, the answer to this issue is
-2a^(3) +2a^( 2)-17a-4
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1. Talk about the time and hours
you spend watching television
and on the internet.
2. How many hours do you spend
alone with yourself?
3. What is the value of time?
Answers
I spend around 0 hours watching television( as I don't have a T.V.) and around 2-3 hours on internet.
Around 1-2 hours I am all by myself.
As one of the famous quote says-" Time is nothing but a stubborn illusion." but the very importance of time is a topic that we cannot even fathom to compare it. It's not something we can buy, not something we can control but a process that decays everything. Since we humans live for a very short amount of time, we should use it more wisely than money.
I spend around 0 hours watching television( as I don't have a T.V.) and around 2-3 hours on internet and Around 1-2 hours I am all by myself.
Why is time so important?Our lives are significantly influenced by time. We gain the good habit of structuring and organizing our day-to-day activities with time. You can acquire knowledge and experience over time if you better appreciate time. Because you can't change the passage of time, it is the most valuable resource.
How are hours written in time?The minutes are represented by a two-digit number that ranges from 00 to 59, and the hour is represented by a two-digit number that ranges from 00 to 23 (or 24). The hour and the minute are separated by a colon: 00:15
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greatest common factor of 12 and 60
Answers
Answer:
12
Step-by-step explanation:
There are 6 common factors of 12 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 60 is 12.
Factor this:
(will mark the brainliest
Answers
Answer: [tex]a^{n}(n^{2}+n+1)[/tex]
Step-by-step explanation:
Since the equation a^n+a^n+1+a^n+2
= a^n+n*a^n+n^2*a^n
= a^n*(n^2+n+1)
Answer:
[tex] {a}^{n} ( {a}^{2} + a + 1)[/tex]
Step-by-step explanation:
Remember exponent product rule: [tex]a^{n+m}=a^n*a^m[/tex]
Rewritten: [tex]{a}^{n} + ( {a}^{n}* {a}^{1}) + ({a}^{n} * {a}^{2})[/tex]
factor the common factor [tex] {a}^{n} [/tex] to get
[tex] {a}^{n} (1 + a + {a}^{2} )[/tex]
reorder from highest exponent to get answer.
consider the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1). the fourth vertex lies above the point (0,0) at height 1. see the picture below a tetrahedron as described in the problem setup an integral the represents the volume of the tetrahedron then evaluate it.
Answers
The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The integral that represents the volume of the tetrahedron is given by:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$$
Evaluating the integral, we get:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx = \int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx = \int_0^1 \frac{1}{2} (1-x)^2\,dx = \frac{1}{6}$$
Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
We first set up the integral that represents the volume of the tetrahedron. The integral is a triple integral, so it can be written as $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$. This integral is the volume of a 3-dimensional region enclosed by the limits $x \in [0,1]$, $y \in [0,1-x]$, and $z \in [0,1-x-y]$. This region is exactly the same as the volume of the tetrahedron because it is the same 3-dimensional region.
Next, we evaluate the integral. First, we integrate with respect to $z$, which gives us $\int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx$. Then, we integrate with respect to $y$, which gives us $\int_0^1 \frac{1}{2} (1-x)^2\,dx$. Finally, we integrate with respect to $x$, which gives us $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
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ASAP: ANSWER
Can someone solve the question in the picture?
Answers
The statements that complete the proof are:
QS || RT and ∠R ≅ ∠T∠Q ≅ ∠TΔQST ≅ ΔQSTΔQTS ≅ ΔTQR∠QTS ≅ ∠TQRHow to complete the statements in the proofFrom the question, we have the following parameters that can be used in our computation:
The incomplete two-column proof
Given that
QS || RT and ∠R ≅ ∠T
We have
∠Q ≅ ∠T because alternate inerior angles are equal
By the reflexive property, we have
ΔQST ≅ ΔQST
This implies that
ΔQTS ≅ ΔTQR
Lastly, we have: ∠QTS ≅ ∠TQR
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a right triangle is given. the first side has length 9. the second side has length x. the third side of length 15 is opposite the right angle. g
Answers
The second side of triangle has the length is 12cm.
What is the Pythagorean theorem theory?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides.Pythagoras discovered that the square of the hypotenuse is equal to the sum of the squares of the other two sides for a right angle triangle with one of the angles being 90 degrees: a2+b2=c2.A, B, and C are the three positive integers, and the Pythagorean triples are written as a2+b2 = c2. These triples are shown as (a,b,c). Here, the right-angled triangle's base, hypotenuse, and perpendicular are denoted by letters a, b, and c, respectively. The most popular and diminutive triplets include (3,4,5).Given data :
We know that,
BY p Pythagorean theorem,
a² + b² = c²
9² + b² = 15²
b² = 15² - 9²
b² = 144
b = 12
Therefore,
The second side means the hypotenuse is equal to 12cm.
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what is the radius,diameter, ad circumference of the area of a circle that is 2289.1ft squared long
Answers
For the given Circumference, the radius of the circle is 364.50 feet, and diameter is 729 feet.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
How do you figure out a circle's radius and area?A circle's circumference is equal to two times its radius or diameter, where r is the radius and d is the diameter. Where r is the circle's radius, the area of a circle is equal to πr2
The Circumference of the circle is 2289.1 sq. feet,
Circumference = 2πr
2289.1 = 2 π r
⇒ 2289.1 = 2 × 3.14 × r
⇒ r = 2289.1 / 6.28
⇒ r = 364.50
We know, Diameter = 2 × Radius
⇒ Diameter = 2 × 364.50 = 729
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Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answers
Answer:
2x+3y=1470
Step-by-step explanation:
Karl was attempting to calculate economic figures. He found the following equation to be true:fp-w=10000If f=5 and w=5+125i, what is p?
Answers
The value of p = (125i + 10005)/5
=> p = 25i + 2001
Now, According to the question:
Let's know:
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Karl was attempting to calculate economic figures.
The given equation is:
fp - w = 10000
f = 5 and w = 5 + 125i
To solve for the value of p.
(-125i - 5) + 5 p = 10000
Add 5 + 125i to both sides:
5 p + ((-125 i - 5) + 125 i + 5) = 125 i + 5 + 10000
(-125 i - 5) + (125 i + 5) = 0:
5 p = 10000 + 5 + 125 i
10000 + 5 + 125 i = (10000 + 5) + 125 i = 10005 + 125 i:
5 p = 125 i + 10005
Divide both sides of 5 p = 125 i + 10005 by 5:
(5 p)/5 = (125 i + 10005)/5
p = (125i + 10005)/5
Hence, The value of p = (125i + 10005)/5.
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5/6-(-4/9) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
1 [tex]\frac{15}{18}[/tex]
Step-by-step explanation:
Re-write the problem:
5x3 -4 x 2 15 -8
—————— = —- —- =
6x 3 9 x 2 18 18
15 - -8
——— = 1 [tex]\frac{15}{18}[/tex]
18
What is the area of this trapezoid in [tex]\ in2[/tex]
Answers
The area of trapezoid having side lengths of 14 inches & 8 inches and height 12 inches is, 132 In.²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
A trapezoid,
segment lengths,
AB = 8 in.
BE = 12 in.
DF = 3 in.
FE = 8 in.
EC = 3 in.
Total length of side 1 = AB = 8 in.
Total length of side 1 = DF + FE + EC
= 3 + 8 + 3
= 14 in.
Height = 12 in.
Area of trapezoid = 1/2(Sum of sides) x distance between them
= 1/2(8 + 14) x 12
= 132 In.²
Hence, the area is 132 In.²
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The heights (in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed below.
Heights (inches) 59.4 61.2 62.1 64.7 60.1 58.3 64.6 63.7 66.1
Weights (pounds) 87 94 93 119 96 90 123 98 139
a. Find the coefficient of variation in heights.
b. Find the coefficient of variation in weights.
c. Compare the variation in heights to the variation in weights of thirteen-year-old girls.
Answers
The coefficient of variation in heights is 0.0432 (the or) 4.32 %.
The coefficient of variation in weights is 0.1733 (or) 17.33 %.
Variation in heights is less than variation in weights of thirteen-year-old girls.
For given Height data
Mean for heights will be sum of all the heights divided by total number of heights.
= [tex]\frac{59.4 +61.2+ 62.1 +64.7 +60.1 +58.3 +64.6 +63.7 +66.1}{9}[/tex]
= 62.2444
Standard Deviation for heights
When we have n number of observations and the observations are
[tex]\mathrm{x}_1, \mathrm{x}_2, \ldots \ldots \mathrm{x}_n[/tex], then the mean deviation of the value from the mean is determined as [tex]$$\sum_{i=1}^n\left(x_i-\bar{x}\right)^2$$[/tex]
=2.6908
(a) coefficient of variation in heights:
Standard deviation is the positive coefficient of the variance.
[tex]=\frac{\text { Standard Deviation }}{\text { Mean }}[/tex]
[tex]=\frac{2.6908}{62.2444}[/tex]
= 0.0432 (or) 4.32 %
(b) Coefficient of variation in weights is:
[tex]=\frac{\text { S.D }}{\text { mean }}[/tex]
[tex]=\frac{18.0831}{104.3333}[/tex]
= 0.1733 or 17.33 %
(c) Coefficient of variation in heights is 0.0432 (or) 4.32 %
Coefficient of variation in weights is 0.1733 or 17.33 %
0.0432 (or) 4.32 % < 0.1733 or 17.33 %
Variation in heights < Variation in weights.
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melissa is younger than natalie and is older and shorter than jason. natalie is taller and younger than ken, but ken is taller than jason. list the ages of the four people in order, starting with the oldest. list the heights of the four people in order, starting with the tallest.
Answers
Ages in order starting with the oldest : ken , natalie , melissa , jason.
Heights in order starting with the tallest : natalie, ken , jason , melissa.
by descending order.
From the information given in the question :
natalie (N) is older than melissa (M)
melissa (M) is older than jason (J)
ken (K) is older than natalie (N)
So , similarly ken is the oldest among those 4. and then order follows as natalie older than melissa older than jason.
K>N>M>J
jason (J) is taller than melissa (M)
natali (N) is taller than ken (K)
ken (K) is taller than jason (J)
So, similarly natali is the tallest among all 4, and then order follows as
ken taller than jason taller than melissa.
N>K>J>M
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Vita wants to center a towel bar on her door that is 27 inches wide.
end of the door is 9 inches. Write and solve an equation to find the length
She determines that the distance from each end of the towel bar to the
of the towel bar.
Answers
The length of the towel bar is 9.5 inches.
How to solve the equation?Length is used to measure distance, In the International System of Quantities, a quantity with the distance dimension is referred to as length. The majority of measurement systems select a base unit for length from which all other units are derived. The metre serves as the International System of Units' fundamental unit of length.
Suppose, the length of the towel bar is x inches
The distance from each end of the towel bar to the end of the door is 9
inches. So, the total width of the door will be:[(x+(9*2)]=(x+18) inches
Given that, the width of the door is 27 inches 27.5 So, the equation will be.
x+18=27.5
x=27.5-18=9.5
Thus, the length of the towel bar will be 9.5 inches.
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which of the following is the taylor series centered at \(\displaystyle 0\) for \(\displaystyle e^x\)?
Answers
ex=1+x2+x3/2!+x4/3! is the Taylor series centered.
The function itself evaluated at a = 0 as well as the first three derivatives are therefore required to determine the first four terms using this formula (because the 0t h derivative equals the function itself).
The fourth derivative can be used to determine the next term as the fourth derivative is required to obtain four non-zero terms using this function and the 0th term is zero. This is likely why the first four derivatives were chosen.
f(0)=0(e0)=0
ex=1+x+x2/2!+x3/3!
ex=x(1+x+x2/2!+x3/3!)
ex=1+x2+x3/2!+x4/3!
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square root equation need answer asap
Answers
Step 1: rewrite
Step 2 : remove radicals
Step 3: simplify each side
Step-by-Step Explanation
[tex]5 = \sqrt{r - 3} \\ = > (5) ^{2} = {( \sqrt{r - 3)} }^{2} \\ = > 25 = r - 3 \\ = > r = 25 + 3 = 28[/tex]
Answer
r = 28
Hope it helps.
If you have any query, feel free to ask.
from the given diagram, we can deduce that large nn models are always better than traditional learning algorithms. true/false?
Answers
False. While large neural networks (NNs) can often outperform traditional learning algorithms in certain tasks, this is not always the case.
The performance of a large NN depends on the size of its training dataset, the type of problem it is being used to solve, the amount of data preprocessing and feature engineering that has been done, the size of the network, the type of optimisation algorithm being used, and the quality of the hyperparameters used. There is no single formula or calculation that can be used to determine which type of algorithm will be better than another.
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ake a look at the following set of the average hours of work per week for two groups of adolescents and compute the more appropriate average score.
Child Group 1 Group 2
1 Lots Little
2 Little Somewhat
3 Somewhat Somewhat
4 Little Little
5 Little Somewhat
6 Little Lots
7 Little Lots
8 Little Somewhat
9 Somewhat Somewhat
10 Lots Somewhat
Answers
The more appropriate average score for the two groups of adolescents is 1.83.
The appropriate average score for the two groups of adolescents can be computed using the following formula: (Group1 score + Group2 score) / 2.
For example, in the first row, the Group 1 score is "Lots" and the Group 2 score is "Little". The average score for this row would be (3 + 1) / 2 = 2.
In the second row, the Group 1 score is "Little" and the Group 2 score is "Somewhat". The average score for this row would be (1 + 2) / 2 = 1.5.
Similarly, for the remaining 8 rows, the average scores can be calculated as follows:
Row 3: (1 + 2) / 2 = 1.5
Row 4: (1 + 1) / 2 = 1
Row 5: (1 + 2) / 2 = 1.5
Row 6: (1 + 3) / 2 = 2
Row 7: (1 + 3) / 2 = 2
Row 8: (1 + 2) / 2 = 1.5
Row 9: (1 + 2) / 2 = 1.5
Row 10: (3 + 2) / 2 = 2.5
Therefore, the more appropriate average score for the two groups of adolescents is 1.83.
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please help asap!
Find/create a problem that can be modeled and solved using Systems of Linear Equations and then solve it by using GRAPHING.
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The problem that can be solved is 2x + 3y = 5 and x + y = 2 & the solution to th system is (1, 1)
How to determine the problemFrom the question, we are to
Create a problem that can be modeled and solved using systems of linear equations
A problem that can be solved using graph is as follows:
2x + 3y = 5
x + y = 2
Next, we plot and attach the graph
The point of intersection on the graph is the solution
This means that the solution is (1. 1)
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show that the medians of the triangle with (non-colinear) vertices (a1, a2, a3) intersect at a1 a2 a3 3
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The medians of a triangle connect the midpoints of each side and intersect at the centroid of the triangle.
Medians of a triangle are lines that connect the midpoints of each side of the triangle to the opposite vertex. This means that they divide the triangle into two halves, each with an area that is equal to half of the area of the entire triangle. The medians of a triangle with vertices (a1, a2, a3) intersect at a point known as the centroid of the triangle, which is located at the intersection of the three medians. The centroid can be found by taking the average of the three vertices, or by finding the intersection of the three medians. The centroid is the point at which the three medians of the triangle intersect and is the center of gravity for the triangle. In other words, it is the point that all three medians will intersect at.
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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)f(x, y) = y2 − x2; 1/4x2 + y2 = 64
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The maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.
What are Lagrange multipliers?
Lagrange's multiplier is a mathematical technique used to find the maximum or minimum value of a function subject to certain constraints. It is named after Joseph-Louis Lagrange, who first introduced the method in the 18th century.
To use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y^2 - x^2 subject to the constraint 1/4x^2 + y^2 = 64, we need to first set up the Lagrange function:
L(x, y, λ) = y^2 - x^2 + λ(1/4x^2 + y^2 - 64)
We then find the partial derivatives of L with respect to x, y and λ:
∂L/∂x = -2x + λ(1/2x) = 0
∂L/∂y = 2y + λ(y) = 0
∂L/∂λ = 1/4x^2 + y^2 - 64 = 0
Solving these equations, we find the following solutions:
x = 0, y = 0, λ = -8
x = 8√2, y = 8√2, λ = 4
x = -8√2, y = -8√2, λ = 4
Now, we need to check these solutions to see if they satisfy the constraint 1/4x^2 + y^2 = 64. Only the first solution x = 0, y = 0 satisfies the constraint.
Hence, the maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.
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