2x-6+4=14 valor de X
Answers
Explanation:
2x-6+4=14
-4 -4
2x-6=10
+6 +6
2x=16
/2 /2
X=8
Related Questions
if (5,b-7) lies on x axis, then b=?
Answers
Solving a simple linear equation we can see that the value of b is 7.
How to get the value of b?Here we have the point (5, b - 7) and we want to find the value of b such that the point lies on the x-axis.
Remember that a point lies on the x-axis only if the y-value is zero, so we need to solve the linear equation:
b - 7 = 0
Adding 7 in both sides we get:
b - 7+ 7 = 0 + 7
b = 7
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The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature of -20°C. After 1 hour, the temperature of the ice-cream base has decreased to 58°C. Use Newton's law of cooling to formulate and solve the initial-value problem to determine the temperature of the ice cream 2 hours after it was placed in the freezer. Round your answer to two decimal places.
Answers
The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
From Newton's law of cooling, we have that
\(T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}\)
Where
\((t) = \ time\)
\(T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)\)
\(T_{s} = Surrounding \ temperature\)
\(T_{0} = Initial \ temperature \ of \ the \ body\)
\(k = constant\)
From the question,
\(T_{0} = 86 ^{o}C\)
\(T_{s} = -20 ^{o}C\)
∴ \(T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C\)
\(T_{0} - T_{s} = 106^{o} C\)
Therefore, the equation \(T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}\) becomes
\(T_{(t)}=-20+106 e^{kt}\)
Also, from the question
After 1 hour, the temperature of the ice-cream base has decreased to 58°C.
That is,
At time \(t = 1 \ hour\), \(T_{(t)} = 58^{o}C\)
Then, we can write that
\(T_{(1)}=58 = -20+106 e^{k(1)}\)
Then, we get
\(58 = -20+106 e^{k(1)}\)
Now, solve for \(k\)
First collect like terms
\(58 +20 = 106 e^{k}\)
\(78 =106 e^{k}\)
Then,
\(e^{k} = \frac{78}{106}\)
\(e^{k} = 0.735849\)
Now, take the natural log of both sides
\(ln(e^{k}) =ln( 0.735849)\)
\(k = -0.30673\)
This is the value of the constant \(k\)
Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at \(t = 2 \ hours\)
From
\(T_{(t)}=-20+106 e^{kt}\)
Then
\(T_{(2)}=-20+106 e^{(-0.30673 \times 2)}\)
\(T_{(2)}=-20+106 e^{-0.61346}\)
\(T_{(2)}=-20+106\times 0.5414741237\)
\(T_{(2)}=-20+57.396257\)
\(T_{(2)}=37.396257 \ ^{o}C\)
\(T_{(2)} \approxeq 37.40 \ ^{o}C\)
Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
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the person above me i correct
a banana bread recipe needs a 2/3 cup of sugar and 1 1/2 cups of flour and some other ingredients. a)  how much sugar and flour are needed to make half the amount in the recipe? b) how many total cups of sugar and flour do you have? answer as a mixed number.
Answers
Answer:
1/3 cup of sugar and 1/4 cup of flour
What is the solution to 4
O a>-21-
O a<-21-
O a> 21/1/
O a<21/1/2
Mark this and return
a>-162
C
Save and Exit
Next
Submit
TIME
01
Answers
The solution to 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.
What is inequality?Inequality is the unequal distribution of opportunities, resources, or rights among people or groups. It can be found in wealth, income, health, education, access to services and resources, and legal rights. Inequality is a social phenomenon that affects people differently depending on race, gender, age, or background. Inequality can be a result of unequal access to resources, differences in power dynamics, or the unequal distribution of resources among people or groups. It can lead to disparities in health, education, and economic outcomes for those who experience it. Inequality can be addressed through policies that promote equity and inclusion, such as targeted education initiatives and access to employment opportunities.
The reason this is happening is because when solving inequalities, we must isolate the variable on one side of the inequality sign. In this case, we can do this by adding 162 to both sides of the inequality. This will move the -21 to the other side and the result is a>-162.
In order to ensure that the solution is correct, it is important to check the answer by substituting a value larger than -162 into the inequality. If the value satisfies the inequality, then the solution is correct.
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The sοlutiοn tο 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.
What is inequality?Inequality is the unequal distributiοn οf οppοrtunities, resοurces, οr rights amοng peοple οr grοups. It can be fοund in wealth, incοme, health, educatiοn, access tο services and resοurces, and legal rights. Inequality is a sοcial phenοmenοn that affects peοple differently depending οn race, gender, age, οr backgrοund. Inequality can be a result οf unequal access tο resοurces, differences in pοwer dynamics, οr the unequal distributiοn οf resοurces amοng peοple οr grοups. It can lead tο disparities in health, educatiοn, and ecοnοmic οutcοmes fοr thοse whο experience it. Inequality can be addressed thrοugh pοlicies that prοmοte equity and inclusiοn, such as targeted educatiοn initiatives and access tο emplοyment οppοrtunities.
The reasοn this is happening is because when sοlving inequalities, we must isοlate the variable οn οne side οf the inequality sign. In this case, we can dο this by adding 162 tο bοth sides οf the inequality. This will mοve the -21 tο the οther side and the result is a>-162.
In οrder tο ensure that the sοlutiοn is cοrrect, it is impοrtant tο check the answer by substituting a value larger than -162 intο the inequality. If the value satisfies the inequality, then the sοlutiοn is cοrrect.
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Complete question:
What is the solution to 3/4a>-16?
a>-21 1/3
a<-21 1/3
a>21 1/3
a<21 1/3
Solve the following inequality algebraically.
-4|2-x| 1 <-35
Answers
Answer:
x<-27/4
Step-by-step explanation:
−4(2−x)1<−35
Multiply −4 and 1 to get −4.
−4(2−x) <−35
Use the distributive property to multiply −4 by 2−x.
−8+4x<−35
Add 8 to both sides.
4x<−35+8
Add −35 and 8 to get −27.
4x<−27
Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.
GIVING 100 POINTS ...Pls provide an expatiation on what I did wrong. Thank you
Answers
(
x
0
,
y
0
)
, is: (−0)2 + (−0)2 = 2
(
x
−
x
0
)
2
+
(
y
−
y
0
)
2
=
r
2
.
If the circle is centered on the origin, this becomes the familiar equation: x^2+y^2=r^2 .
Since a diameter is two radii, r= 5 units in your question.
So, the net result with 0 = −4
x
0
=
−
4
, and 0 = 9
y
0
=
9
, is:
( + 4)2 + ( − 9)2 = 52 = 25(1) (1) (x + 4
)
2
+ (y − 9
)
2
=
5
2
= 25
Often we see other forms of the same equation, say, with y as a function of x,
= ±25 − ( +4)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√+9= 9 ± 25 − (2 + 8 + 16)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√= 9 ± 9 − 8 −2‾‾‾‾‾‾‾‾‾‾‾‾‾√ y = ±
25
−
(
x
+
4
)
2
+9 = 9 ±
25
−
(
x
2
+
8
x
+
16
)
= 9 ±
9
−
8
x
−
x
2
.
In other coordinate systems, for example, polar coordinates, the equation depends on other variables, related to x and y in some way, so the equation may look quite different.
To see results in polar form we need to substitute expressions in the new variables in place of the original x and y. So, = ⋅cos ; = ⋅sin
x
=
ρ
⋅
cos
θ
;
y
=
ρ
⋅
sin
θ
, and equation (1) becomes(⋅cos + 4)2 + (⋅sin − 9)2 = 25 (ρ⋅cos
θ
+ 4
)
2
+ (ρ⋅sin
θ
− 9
)
2
= 25
This quickly becomes messy when we try solving for one of the new variables. I won’t bother you with too much trig., but, one possible version of our equation becomes: = 9sin−4cos ± 9 − 72cossin − 47cos2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
ρ
=
9
sin
θ
−
4
cos
θ
±
9
−
72
cos
θ
sin
θ
−
47
cos
2
θ
Now, if we encountered these equations in the wild, we may clearly see some similarities. They all involve squares and square-roots. The numbers nine and four float around through them, etc. But, would we see that they define the same geometric object?
the answer is
(x+4)^2 + (y–9)^2 = 25
a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set
A. 27
B. 17
C. 3
D. 41
In which of these cases should the mean be used?
A. When the data is left-skewed
B. When the data is symmetric
C. When the data is right-skewed
D. When the data has extreme values
Answers
To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).
We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:
IQR = Q3 - Q1 = 17 - 9 = 8
To identify outliers, we can use the following rule:
- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
Using this rule, we can evaluate each data point:
A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).
C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.
D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
Therefore, the outliers in the data set are A (27) and D (41).
As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.
Therefore, the correct option would be B. When the data is symmetric.
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Which congruence criteria can be used directly from the information about triangles HIJ and MNO to prove
A. HL CONGRUENCE
B. AAS CONGRUENCE
C. ASA CONGRUENCE
D. SAS CONGRUENCE
Answers
Answer:
Step-by-step explanation:
(C). ASA postulate of congruence.
Without doing math you can easily identify the congruence criteria by looking at the given.
It reads :
SIDE HI is congruent to SIDE NO (S)
ANGLE N is congruent to ANGLE H (A)
ANGLE H is congruent to ANGLE O (A)
Since we have two angles and one side, it brings us to the answer AAS.
compute the fundamental group of the "solid torus" S1 x B2 and the product space S1 x S2.
Answers
The fundamental group of the solid torus S^1 x B^2 is isomorphic to the fundamental group of the circle, denoted as π1(S^1). The circle S^1 is a 1-dimensional manifold, and its fundamental group is the group of integers, denoted as Z.
So, the fundamental group of the solid torus S^1 x B^2 is π1(S^1 x B^2) ≅ Z.
Now, let's consider the product space S^1 x S^2. The fundamental group of S^1 is Z, as mentioned earlier. The fundamental group of the 2-dimensional sphere S^2 is trivial, which means it is the identity element, denoted as {e}.
The fundamental group of the product space S^1 x S^2 is given by the direct product of the fundamental groups of S^1 and S^2. Therefore, π1(S^1 x S^2) ≅ Z x {e} ≅ Z.
In summary:
The fundamental group of the solid torus S^1 x B^2 is isomorphic to the group of integers, Z.
The fundamental group of the product space S^1 x S^2 is also isomorphic to the group of integers, Z.
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Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answers
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)
Three answer choices have the same quotient as 4.55 ÷ 0.7. Which one does NOT
Answers
Answer:
Answer: 455 / 7
Step-by-step explanation: Three answer choices have the same quotient as 4.55 ÷ 0.7. Which one does NOT?
answer choices
455 ÷ 70
455 ÷ 7
45.5 ÷ 7
4.55 ÷ 0.70
The number resulting from the division of one number by another is regarded as quotient. For example, The quotient of 12 divided by 4 is 3.
And so, the first, third and last options on expansion by division all yield the same results in decimals (6.5) as that in the question (4.55 / 0.7 = 6.5) which is an indication that they have the same quotient.
Only the second option does not do so. 455 / 70 = 65
Find the coordinates of the vertex of the following parabola algebraically. Write your
answer as an (x, y) point.
y=x²-8x + 24
Answers
Answer:
\((4,8)\)
Step-by-step explanation:
\(y=x^2-8x+24 \\ \\ y=(x^2-8x+16)+24-16 \\ \\ y=(x-4)^2+8\)
So, the vertex is \((4,8)\).
Looking north, two skyscrapers are sighted from the viewing deck of the Empire State Building at 1250 feet up. One skyscraper is sighted at a 20° angle of depression and a second skyscraper is sighted at a 30° angle of depression. How far apart are the two skyscrapers to the nearest foot?
Answers
Answer:
Step-by-step explanation:
The angle of depression is the angle between the line of sight and a vertical line.
The distance between the two skyscrapers is 1269ft
I've added as an attachment, a figure that illustrates the scenario
First, we calculate distance AB using the following tangent ratio
\(\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}\)
So, we have:
\(\mathbf{\tan(60) = \frac{AB}{1250}}\)
Make AB the subject
\(\mathbf{AB = 1250 \times \tan(60)}\)
Next, we calculate distance AC using the following tangent ratio
\(\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}\)
So, we have:
\(\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}\)
\(\mathbf{\tan(70) = \frac{AB + BC}{1250}}\)
Make AB + BC, the subject
\(\mathbf{AB + BC = 1250 \times \tan(70)}\)
Make BC the subject
\(\mathbf{BC = 1250 \times \tan(70) - AB}\)
Substitute \(\mathbf{AB = 1250 \times \tan(60)}\)
\(\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}\)
\(\mathbf{BC = 1269}\)
Hence, the distance between the two skyscrapers is 1269ft
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Please show your work
Answers
Answer:
2=40 3=140 4=40
Step-by-step explanation:
the center line is equal to 180 degrees so if angle 1 is 140, 180-140=40 angle 2=40
angle 2 and 4 and the same by some process (its been awhile since geometry to remember exact terms)
angle 1 and 3 are the same (same reason)
Answer:
<2 is 40°, <3 is 140°, <4 is 40°
Step-by-step explanation:
Angle 1 and angle 3 are equal because of the vertical angles theorem. Angle 2 is supplementary to angle 3(<3 = 140°), so 180 - 140 = 40°. <2 and <4 are equal because of the vertical angles theorem.
Select all the sets to which the following number belongs: 11NaturalO WholeIntegerO RationalIrrationalReal
Answers
natural numbers, whole numbers, integer, rational number and real numbers
Explanation:\(11\text{ can be written as }\frac{11}{1}\)Natural numbers starts from 1 to positive infinity. 11 is between 1 and positive infinity. Hence, it is a natural number
Whole numbers start from 0 to positive infinity. 11 is between 0 and positive infinity. Hence, it is a whole number
Integer consists of natural numbers, 0 and the negative of the natural numbers (...-2, -1, 0, 1, 2....)
11 is between these sets of numbers. Hence it is an integer
Rational numbers are numbers that can be written as a fraction.
11 can be written as a fraction. Hence, it is a rational number
Irrational numbers cannot be written as a fraction. So this option is wrong
Real numbers consists of natural numbers, whole numbers, integers and rational numbers.
Since 11 fall in one of these, it is also a real number
The sets to which the following number 11 belongs to are natural numbers, whole numbers, integer, rational number and real numbers
In the model ln(Yi) = β0 + β1 * Xi + ui, the elasticity of Y with respect to X is ...
Answers
In the model ln(Yi) = β0 + β1 * Xi + ui, the elasticity of Y with respect to X is equal to β1.
The model is given in a logarithmic form: ln(Yi) = β0 + β1 * Xi + ui.
Elasticity measures the percentage change in one variable (Y) in response to a 1% change in another variable (X).
In a semi-logarithmic model like this, the coefficient of the independent variable (β1) directly represents the elasticity of Y with respect to X.
Therefore, the elasticity of Y with respect to X is β1.
Keep in mind that this result holds true for a semi-logarithmic model, where the dependent variable (Y) is in its natural logarithmic form, and the independent variable (X) is in its original form.
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How do you do exponents
Answers
Which is the range for the function shown in the graph below?
All real numbers for
x
All real numbers for
y
x≤
2
y≥
3
Answers
The range of the function shown in the graph is the set of all real numbers for y.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
The set of input values in the function is called domain and the set of output values are called range of the function.
So the range of the function will be the set of y values.
From the graph, it is clear that, the curve is passing corresponding to every y value.
In other words, if we draw a horizontal lines from curve, all the y values are touching the curve.
So the range is the set of all real numbers.
Hence the range is all the real numbers for y.
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A ______________ is a relation that assigns exactly one output value to one input value
Answers
Answer:
A __function__ is a relation that assigns exactly one output value to one input value.
Step-by-step explanation:
Answer:
A function is a relation that assigns exactly one output value to one input value.
Please help I don’t understand this
Answers
The graph of the square root function can be seen on the image at the end.
How to graph the square root function?Here we want to graph the square root function:
f(x) = -√-x
Tograph it, we need to evaluate it in some values of x and find some points.
Remember that the argument can only be positive numbers or 0.
So we start with x = 0.
f(0) = -√-0 = -√0 = 0
So we have the point (0, 0)
When x = -1
f(-1) = -√-(-1) = -√1 = -1
So we have the point (-1, -1)
when x = -4
f(-4) = -√-(-4) = -√4 = -2
So we have the point (-4, -4)
And so on, when you have enough points, just graph them and connect them with a curve.
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Four different linear functions are represented below.Part A: Which function has the graph with a y-intercept closest to 0? Part B: which function has the graph with the greatest y-intercept?Part C: which functions have graphs with slopes less than 4? Check all that apply
Answers
We have here four linear functions, and we have to compare the slopes of them as well as their y-intercept. For this, it is important to remember the general equation for the line in the slope-intercept form:
\(y=mx+b\)Where
• m is the slope of the line
,• b is the y-intercept of the line (0, b)
The y-intercept is the point where the line passes through the y-axis, and at this point, we have that x = 0.
Finding the slopes and the y-intercept for the four functionsFunction 1We have in this case that the function passes through the points:
• (0, 5), (1, 1)
We can find the equation of this line using the two-point form of the line equation:
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)Using the points above, we can label them as follows:
• (0, 5) ---> x1 = 0, y1 = 5
,• (1, 1) ---> x2 = 1, y2 = 1
Then we have:
\(\begin{gathered} y-5_{}=\frac{1_{}-5}{1-0_{}}(x-0_{}) \\ y-5=-\frac{4}{1}x \\ y-5=-4x \\ y=-4x+5 \end{gathered}\)Therefore, the slope for this line is m = -4, and the y-intercept is (0, 5).
Function 2For Function 2 we need to do the same procedure as before. We have to select two points of the function to find its equation:
We can select the following points: (0, 1), (1, 6).
Then we can proceed as we did in the previous part:
• (0, 1) ---> x1 = 0, y1 = 1
,• (1, 6) ---> x2 = 1, y2 = 6
\(\begin{gathered} y-1_{}=\frac{6_{}-1_{}}{1-0_{}}(x-0) \\ y-1=5x \\ y=5x+1 \end{gathered}\)Therefore, the slope in Function 2 is 5, m = 5, and the y-intercept is (0, 1).
Function 3We can see that Function 3 has already its line equation in slope-intercept form:
\(y=-x-2\)Then the slope for Function 3 is m = -1, and its y-intercept is (0, -2).
FunctionFrom the question, we have:
Rewrite, using the distributive
property.
16b-8b = ([?]-8)b = [?]b
![Rewrite, using the distributiveproperty.16b-8b = ([?]-8)b = [?]b](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9Tmzv11947B9UtnbF6DBvWJp63YQcon7.png)
Answers
Answer:
8b
Step-by-step explanation:
You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:
\(\displaystyle{16b-8b=\left(16-8\right)b}\)
Then evaluate and simplify:
\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)
Factor 5x2-5x - 60.
5(x + 3)(x-4)
5(x - 3)(x + 4)
5(x-4)(x + 3)
Answers
Answer:
5(x−4) (x+3)
Check image for explanation
What is the place value of 432?.
Answers
Place value of 432 is 400 +30+02 .
What is place value?
In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.
Main body:
The place value of a digit will increase by 10 times as we move left on the place worth chart and reduces by ten times as we tend to move right.
The place of digit 4 will be hundreds.
The place of digit 3 will be tens.
The place of digit 2 will be ones.
Hence place value of 432 is 400 +30+02 .
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The radius of a circle is 18 in. Find its circumference in terms of π
Answers
The circumference of the circle with a radius of 18 inches is 36π inches.
To find the circumference of a circle, you can use the formula C = 2πr, where C represents the circumference and r is the radius. Given that the radius of the circle is 18 inches, we can substitute this value into the formula to calculate the circumference.
C = 2π(18)
C = 36π
This means that if you were to measure around the outer edge of the circle, it would be approximately 113.04 inches (since π is approximately 3.14159).
It's important to note that the value of π is an irrational number, meaning it cannot be expressed as a finite decimal or a fraction. Therefore, it is commonly represented by the Greek letter π.
In practical terms, when working with circles and calculations involving circumference, it is generally more accurate and precise to keep π in the formula rather than using an approximation.
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Which of the following lists is in the correct order from smallest to largest? -13, -19, -21, -24 11, -12, 15, -19 -7, -3, 6, 2 -19, -14, 5, 11
Answers
Answer:
-24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15
Step-by-step explanation:
Hey there!
To put the numbers in least to greatest form, you need to put the biggest numbers with a - sign in front of it
This means negative
Negative means below zero
Then after putting the big negative numbers, you put positive numbers going from smallest to largest
So the numbers in least to greatest is -24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15
In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) invertible matrix P such that P^-1 AP is diagonal. A = [1 2 3 2]
Answers
The given matrix A is a 2x2 matrix.
First, we find the characteristic polynomial by taking the determinant of the matrix A minus λ times the identity matrix I:
|A - λI| =
|1-λ 2 |
| 3 2-λ| = (1-λ)(2-λ) - 2(3) = λ^2 - 3λ - 4
Thus, the characteristic polynomial of A is λ^2 - 3λ - 4.
Next, we find the eigenvalues of A by solving the characteristic polynomial:
λ^2 - 3λ - 4 = 0
(λ - 4)(λ + 1) = 0
Thus, the eigenvalues of A are λ1 = 4 and λ2 = -1.
To find the eigenvectors, we solve the system of linear equations (A - λI)x = 0 for each eigenvalue.
For λ1 = 4, we have:
(1-4)x1 + 2x2 = 0
3x1 - 2x2 = 0
Solving this system, we get the eigenvector x1 = [2, 3] (or any non-zero scalar multiple of it).
For λ2 = -1, we have:
(1+1)x1 + 2x2 = 0
3x1 + 2+1x2 = 0
Solving this system, we get the eigenvector x2 = [-1, 3] (or any non-zero scalar multiple of it).
To find an invertible matrix P such that P^-1 AP is diagonal, we construct the matrix P using the eigenvectors x1 and x2 as its columns. That is,
P = [2 -1; 3 3]
We can verify that P is invertible by calculating its determinant:
|P| = (2)(3) - (-1)(3) = 9
Since |P| is non-zero, P is invertible.
Then, we calculate P^-1:
P^-1 = (1/9)[3 1; -3 2]
Finally, we can check that P^-1 AP is diagonal:
P^-1 AP = (1/9)[3 1; -3 2][1 2; 3 2][2 -1; 3 3]
= (1/9)[12 0; 0 -1][2 -1; 3 3]
= [8/3 -4/3; -3 1]
Thus, we have found the characteristic polynomial, eigenvalues, eigenvectors, and invertible matrix P such that P^-1 AP is diagonal.
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if y1, y2,..., yn denote a random sample from an exponential distribution with mean β, show that f (y | β) is in the exponential family and that y is sufficient for β.
Answers
y is sufficient for β
The probability density function (pdf) of an exponential distribution with mean β is given by:
f(y | β) = (1/β)exp(-y/β), for y ≥ 0
To show that f(y | β) is in the exponential family, we need to write it in the form:
f(y | β) = h(y)exp{θT(y) - A(θ)}
where h(y), θ, and A(θ) are functions that depend only on y, θ, and do not depend on β.
First, we can rewrite the pdf as:
f(y | β) = (1/β)exp(-y/β)
= (1/β)exp{(-1/β)y}
= (1/β)exp{(-1/β)yx}
where x = 1.
Next, we can identify the functions h(y), θ, and A(θ):
h(y) = 1
θ = -1/β
A(θ) = -log(-θ)
= -log(1/β)
= log(β)
Substituting these values, we get:
f(y | β) = exp{(-1/β)y}exp{-log(β)}
= exp{(-1/β)y - log(β)}
Therefore, f(y | β) is in the exponential family.
To show that y is sufficient for β, we can use the factorization theorem.
The joint pdf of the sample y1, y2, ..., yn is:
f(y1, y2, ..., yn | β) = (1/β)^n exp{- (y1 + y2 + ... + yn)/β}
= (1/β)^n exp{-n(ybar)/β}
where ybar is the sample mean.
Using the factorization theorem, we can write:
f(y1, y2, ..., yn | β) = h(y)g(T(y), β)
where T(y) = ∑ yi and h(y) does not depend on β.
Therefore, y is sufficient for β.
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Given △FGH ~ △LMN, select all the statements that are true. (will give brainliest
Answers
Answer:
Your answers are the first option, your third option, and your last option. I just finished taking the quiz. I hope this helps!
What is the greatest common factor between 18 and 30 and 54
Answers
The greatest common factor (GCF) of 18, 30, and 54 is 6.
The greatest number that divides two or more numbers without leaving a residue is known as the GCF.
The prime factorization approach is the most effective way to resolve this issue.
Using this technique, you will first determine the largest common factor amongst each number's prime factors.
The prime factorization of 18 is 2 x 3 x 3.
The prime factorization of 30 is 2 x 3 x 5. The prime factorization of 54 is 2 x 3 x 3 x 3.
The largest common factor amongst all of them is 6, which is the GCF.
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