1) The value of AA is [tex]\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right][/tex]. 2) By solving the matrix equation, we got [tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right][/tex]. 3) The value of x and y is -4 and 18
1) A = [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex]
AA = [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex]
AA = [tex]\left[\begin{array}{ccc}(-5)^2&0&0\\0&(-2)^2&0\\0&0&(-4)^2\end{array}\right][/tex]
AA = [tex]\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right][/tex]
2)We are given x₁ - 2x₂ + 3x₃ = 24
-x₁ + 3x₂ - x₃ = -11
2x₁ - 5x₂ + 5x₃ = 24
Now, AX = B
[tex]\left[\begin{array}{ccc}1&-2&3\\-1&3&-1\\2&-5&5\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex]
As, AX = B => X = BA⁻¹ --(1)
Here A⁻¹ = (1/|A|)adjA
Where adjA is Adjoint of matrix A
|A| = 1
AdjA = [tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]
Therefore, A⁻¹ = [tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]
Using (1)
X = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex][tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex][tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right][/tex]
3) [tex]\left[\begin{array}{ccc}x+2&6&-5\\7&2y&2x\\2x+6&6&-5\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2x+6&6&-5\\7&18&-8\\3&-8&11\end{array}\right][/tex]
So, x + 2 = 2x + 6
2x - x = 2 - 6
x = -4
2y = 18
y = 9
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Make a scatter pilot of the data below Speed Stopping (mph) disance 10 88888 20 40 70 12.5 39.5 1140 Use the quadratic regression feature of a graphing calculator to find a quadratic model Round to the hundredths place cy-006²-0312-4
The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.
What do you mean by quadratic regression?An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.
Step 1: Input the data sets into the graphing calculator.
Step 2: Choose "Scatter Plot" from the graphing calculator's interface.
Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.
Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.
Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.
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solve the equation
select the correct answer
a. The solution set is ______
b. The solution set is empty
The solution set of the given equation is; -10
How to find the solution to the equation?The equation is expressed as;
(2x + 5)/2 - 3x/(x - 2) = x
Multiply through by 2(x - 2) to get;
(2x + 5)(x - 2) - 6x = 2x(x - 2)
2x² + 5x - 4x - 10 - 6x = 2x² - 4x
2x² will cancel out to get;
-5x - 10 = -4x
5x - 4x = -10
x = -10
Thus that value of x is the solution
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Use the Venn diagram shown to list the set BUC in roster form?
Answer:
On the Venn diagram, these common elements are located inside the intersection of the three circles representing sets A,B and C . From the figure, we see that 7 and 4 belong to this mutual intersection. So, the roster form of set A∩B∩C A ∩ B ∩ C is given as {4,7}
i hope that help, i am not sure if i am correct
Evaluate the line integral ∫ 4xy dx + 2x 2 − 3xy dy, where C is the arc of the circle x 2 + y 2 = 1, from (1, 0) to (0, 1) in the counterclockwise direction.
Refer to the images attached. Edit: I realized after uploading this answer that the integral in terms of y is MUCH easier, so I attached that as well :) But at least you know it can be done both ways!
Shannon planted t fewer trees than toby. Toby planted 6 trees . Choose the expression that shows how many trees Shannon planted
The expression that presents the number of trees that Shannon planted will be 6 - t.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Shannon planted t fewer trees than toby. Toby planted 6 trees.
Then the number of trees that Shannon planted will be given as,
⇒ 6 - t
The expression that presents the number of trees that Shannon planted will be 6 - t.
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Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution
Use distributive property to remove parentheses
Combining the like terms involving the variable
Subtracting the non-variable from both sides
Isolate the variable.
Yes, these steps are correct for solving a linear equation with one variable.
Variables on the same side: This step involves rearranging the equation so that all the terms with the variable are on one side and all the constant terms are on the other. This is done so that we can isolate the variable and find its value.
Use distributive property to remove parentheses: If there are parentheses in the equation, we can use the distributive property to remove them. For example, if the equation is 3(x + 2) = 9, we can distribute the 3 to get 3x + 6 = 9.
Combining like terms involving the variable: After distributing, we can combine like terms, i.e., terms with the same variable, to get a simplified equation. For example, if the equation is 3x + 2x = 5, we can combine the terms to get 5x = 5.
Subtracting non-variable terms from both sides: If there are any constant terms on the side with the variable, we can subtract them from both sides to isolate the variable even further. For example, if the equation is 5x = 5, we can subtract 5 from both sides to get 0 = 0.
Isolate the variable: The final step is to divide both sides by the coefficient of the variable to find its value. For example, if the equation is 0 = 0, we can divide both sides by 5 to get x = 1.
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a rectangular page is to contain 30 square inches of print hte margins one ach side are 1 inch find the idmensions of hte page such that ht eleast amount of pape ris used
The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.
Now, According to the question:
The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.
A = lw
Here, l represents the length of the page and w represents the width of the page.
Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]
and the page has margins on each side, each having a width of 1in.
We will first set up an equation using the details that we know. We know that the printed area is [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is
[tex]A_p=xy[/tex]
30 = xy
[tex]y = \frac{30}{x}[/tex]
Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2 since we have to consider the margins at the sides. The area of the page is as follows.
A = (x+2)(y + 2)
We can substitute the value of y in terms of x.
A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])
A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4
A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4
A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]
We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.
A'(x) = [tex]2-\frac{60}{x^2}[/tex]
0 = [tex]2-\frac{60}{x^2}[/tex]
[tex]2 =\frac{60}{x^2}[/tex]
[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]
Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.
A"(x) = [tex]\frac{120}{x^3}[/tex]
[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]
[tex]A"(\sqrt{30} )=0.73[/tex]
We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2
x + 2 = √30 + 2
y + 2 = [tex]\frac{30}{x}[/tex] + 2
y +2 = [tex]\frac{30}{\sqrt{30} }[/tex] + 2
y + 2 = [tex]\sqrt{30}+2[/tex]
Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.
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what is oecd?write down 5 research activities related to corporate governance?
Step-by-step explanation:
The Organisation for Economic Co-operation and Development (OECD) is an international organization that aims to promote economic growth and prosperity, as well as to improve social well-being through research and policy analysis.
Five research activities related to corporate governance by OECD are:
Corporate Governance Principles and Guidelines
Board Diversity and Gender Equality
Board Evaluation and Succession Planning
Shareholder Engagement and Activism
Anti-Corruption and Integrity in Corporate Governance.
10 pts!!
Find the equation of a line parallel to y = 2 that contains the point (4, 1). Write the equation in slope-intercept form.
Explanation:
The equation y = 2 is horizontal. Anything parallel to this will also be horizontal. The answer is of the form y = k, where k is some real number. We replace k with 1 since we need the answer to go through (4,1). All points on the answer line have a y coordinate of 1.
The equation y = 1 is the same as y = 0x+1, which shows we have a slope of 0.
The price of a basketball went from $16.75 to $18.50. What is the percent of increase in the price? Round to the nearest tenth.
10.44 Percent of increase in the price of a basketball .
How can I figure out a percentage?A percentage is a number or ratio that is expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to denote it. A percentage is a dimensionless number; there is no specific unit of measurement for it.
By divided the number by the entire value and multiplying the outcome by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
The price of basketball increased = $18.50 -$16.75 = 1.75$
Now the percent of increase in the price= 1.75/16.75×100
= 10.44%
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Mike believes the two triangles are congruent because the corresponding angles are congruent. Is Mike correct? Explain your reasoning. '
Answer:
Mike is incorrect.
Step-by-step explanation:
In this figure, corresponding angles are equal. However there is no guarantee that the corresponding sides are equal. For example, ΔDEF may be ΔABC dilated by a scale factor of 10, say. This means the angles will remain the same but the sides will be different
So Mike is incorrect.
help please i dont understand
Applying the exterior angle theorem, m<JKL = 22 degrees.
How to Apply the Exterior Angle Theorem?According to the exterior angle theorem, the following equation is created to find the value of x:
5x - 3 = x - 1 + 2x + 8
Combine like terms:
5x - 3 = 3x + 7
5x - 3 - 3x = 3x + 7 - 3x
2x - 3 = 7
Add 3 to both sides
2x = 10
x = 5
Find the measure of m<JKL (exterior angle):
m<JKL = 5x - 3
Plug in the value of x:
m<JKL = 5(5) - 3 = 22 degrees.
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For the school dance, Ellie was in charge of making the bubble solution for a bubble maker machine. Ellie mixed 1/2 of a cup of dish soap with 1 1/2 cups of water.
She needed more bubble solution.
To make the new batch of bubble solution, she used exactly 1 cup of water.
Using the same ratio, how many cups of dish soap should Ellie use to make the new batch of bubble solution?
Therefore , the solution of the given problem of ratio comes out to be
x = 13/22 cups of dish soap.
It defines a ratio.A set of equivalent variables "a" and "b" can be defined using the straightforward formula "a / b," where "b" may be bigger than zero. Two ratios are combined to make one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. 3/4 of the group are girls, while 1/4 are boys. Parts can be a division between one or more items, a number, or a portion of the volume of a component.
Here,
Given:
=> 1/2 cup of dish soap
=> 11/2 cups of water
and,
Ratio of dish soap and water is
=> 1/2 : 11/2
=> 1 : 11
After 1 cup addition of water:
=> 11/2 + 1 = 13/2
and
Let x be the new cup of dish soap
So, ratio :
=> x : 13/2 = 1 : 11
=> 2x : 13 = 1:11
=> 13 = 22x
=> x = 13/22
Therefore , the solution of the given problem of ratio comes out to be
x = 13/22 cups of dish soap.
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Rachel purchased a fancy dress for the homecoming dance for $120.00. Since she purchased the dress, the price has increased 20%. What is the new price for the dress?
$120.00 increased by 20% is $144.00
Help fast drew a triangle with sides that measure 3cm, 5 cm, and 5cm. What kind of
Triangle did I draw?
Scalene
OIsosceles
O Equilateral
Answer:
below
Step-by-step explanation:
This is isosceles because you have TWO equal sides
Equilateral has THREE equal sides
1 ten is 10 times as much as
Answer: AS 1
Step-by-step explanation:
What is the best estimation of the equation 7 8 − 6 11 ? Drag the numbers into the boxes. Numbers may be used once, twice, or not at all. 1/42011/21/8 − =
The best estimation of the equation 7/8 − 6/11 is 1/3
How to estimate the equationFrom the question, we have the following parameters that can be used in our computation:
the best estimation of the equation 7 8 − 6 11
Express properly
So, we have
7/8 - 6/11
Take the LCM
This gives
7/8 - 6/11 = (77 - 48)/88
Evaluate the difference
7/8 - 6/11 = 29/88
Approximate
7/8 - 6/11 = 30/90
So, we have
7/8 - 6/11 = 1/3
Hence, the estimate is 1/3
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Jeff is 2 times older than Bob. Peter is 7 years younger than Bob. Write an expression in
simplest form to represent the sum of their ages.
Answer:
4x - 7
Step-by-step explanation:
The x represents Bob's age since, we don't know what it is, I put it as a variable.
2x This represents Jeff who is 2 times Bob's age.
x - 7 Peter is younger than Bob by 7 years so we need to take away 7 from Bob's age
2x + x - 7 + x This would be the expression
4x - 7 Now just combine the like terms. We don't have Bob's age so the expression will stay like this.
Please help me with this question.
The equivalent markup price will be $31.675.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that the cost is $25 and the markup percentage is 26.7%. The markup cost will be calculated as:-
Price = cost x Percentage increase
Price = 25 x 1.267
Price = $31.675
Therefore, the equivalent markup price will be $31.675.
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debra purchased and notebooks. they were 5 dollars each. write an equation to reperents the total cost c that debra paid.
The equation that represents the total cost that Debra paid is: C = 5N
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
Number of notebooks = NCost of each notebook = $5Total cost = ?The function that models the situation is the following:
C = 5N
Where:
Number of notebooks = N
Cost of each notebook = $5
Total cost = C
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Correctly written question:
Debra purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Debra paid.
gina wilson unit 6 homework 4
help with 1,2,3,4,5 and 8
Gina Wilson is an Australian intersex human rights activist. She was the founding president of Intersex Human Rights Australia
Define parallel lines?
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other.In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.Two lines are said to be parallel if either one of the following is satisfied: 1) Corresponding angles are equal. 2) Alternate angles are equal. 3) Interior angles on the same side of the transversal are supplementary.To learn more about parallel lines refers to:
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Following are the different sides of the triangles -
The line segment that divides a triangle in half and connects one vertex to the middle of the other side is known as the median in geometry. There are an equal number of medians at each vertex of a triangle, and they all intersect at the triangle's centroid.
The triangle's three medians are the line segments with endpoints at the triangle's vertices and the midpoint of the opposite side. The point where all medians converge is known as the centroid.
1. The sides are in same ratio,
[tex]\frac{24}{9} = \frac{32}{x}\\[/tex]
⇒ [tex]x = \frac{32 \times 9}{24}[/tex]
⇒ [tex]x = 12[/tex]
2. [tex]\frac{20}{14} = \frac{33}{x}[/tex]
⇒ [tex]x = \frac{33 \times 14}{20}[/tex]
⇒ x = 23.1
3. [tex]\frac{x+ 5}{30} = \frac{16}{20}[/tex]
⇒ [tex]x = \frac{16 \times 30 }{20} - 5\\x = 19[/tex]
4. [tex]\frac{x+8}{2x - 5} = \frac{20}{22.5}[/tex]
⇒ [tex]22.5x + 180 = 40x - 100\\[/tex]
⇒ [tex]17.5 x = 280[/tex]
⇒ [tex]x = 16[/tex]
8. [tex]\frac{33}{41.8} \neq \frac{45}{57}[/tex]
∴ ST is not parallel to PR.
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A triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor. What is the scale factor?
72:1
16:1
128:1
144:1
The solution is Option B.
The scale factor of the translated triangle is S = 16
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the perimeter of the first triangle be P
The value of P = 3 m
Now , the triangle is translated by a scale factor of S
And , the perimeter of the translated triangle = 48 m
So , the scale factor = perimeter of the translated triangle / perimeter of the first triangle
Substituting the values in the equation , we get
The scale factor of the translation S = 48/3
The scale factor of the translation S = 16
Hence , the scale factor is 16
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The scale factor of the triangles will be 16:1. The correct option is B.
What is a scale factor?A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size.
It aids in altering the figure's size but not its shape. The scale factor is defined as the proportion of the new image's size to that of the previous image.
Given that a triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor.
The scale factor will be calculated as:-
Scale factor = 48 / 3
Scale factor = 16: 1
Therefore, the scale factor of the triangles will be 16:1. The correct option is B.
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Scientists are conducting an experiment involving growing cells in a liquid culture. On day 0, there were 1,000 cells in the culture. On day 4, there were 64,000 cells in the culture. Assuming the
number of cells is growing at an exponential rate, how many cells will be in the culture on day 8?
The quantity of cells that will be in the culture on the 8 day assuming the number of cells is growing at an exponential rate would be = 128,000 cells.
What is an exponential rate of growth?An exponential rate of growth is defined as the increase in the population of an object under study over a period of time.
The number of cells the scientist started with = 1,000 cells
The number of cells in 4th day = 64,000
Therefore the rate of growth of cells per day;
= 64000/4
= 16,000
Therefore on the 8th day, the number of cells would be = 8×16000 = 128,000 cells.
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Suppose an investment compounds with an annual interest rate of 7.7%. The equation below models a final balance A given principal
P and time t. Use properties of exponents to approximate the equivalent monthly interest rate. Enter the approximate monthly rate as a percentage rounded to two decimal places.
The monthly rate percentage is given as follows:
r = 0.65%.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.To obtain the monthly interest, we must consider that:
[tex]\left(1 + \frac{r}{12}\right)^{12 \times \frac{1}{12}} = 1.0777[/tex]
Hence the equation is simplified as follows:
r = 0.0777/12
r = 0.0065.
r = 0.65%.
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Two families are taking a trip to the zoo. The Ramones buy 2 adult tickets and 5 child tickets for $50.25, while the Smiths buy 3 adult tickets and 4 child tickets for $53.50. This situation can be represented by the system 2x+5y=50.25
and 3x+4y=53.50
, where x
represents the cost of an adult ticket and y
represents the cost of a child ticket. Solve the system by elimination. What is the cost of each type of ticket to the zoo?
cost of one adult ticket: $
cost of one child ticket: $
Answer:
see below
Step-by-step explanation:
2x+5y=50.25
3x+4y=53.50
use 2nd equation minus first equation to get
x-y=3.25
so x = 3.25+y
substitute x with above equation
2*(3.25+y) +5y =50.25
so 6.5+2y+5y = 50.25
7y = 43.75
y=6.25
x=3.25+y =9.5
El 19.8% de ___ es 720?
Answer:
3,636.36
Step-by-step explanation:
Let x be the number
19.8% de x = 720
19.8% =19.8/100 = 0.198
0.198x = 720
x = 720/0.198 = 3,636.36
What is the missing length?
The base is 18.7 in
Area of shaded region = 152.405 in?
Answer:The missing length can be found using the formula for the area of a triangle, which is:
Area = (base * height) / 2.
We know the base is 18.7 inches and the area of the shaded region is 152.405 in^2.
So, the height can be found using the formula:
152.405 = (18.7 * height) / 2
Solving for height:
height = 2 * 152.405 / 18.7
height = approximately 12.67 inches.
Is negative eight a irrational number
Answer:
No
Step-by-step explanation:
You want to know if -8 is irrational.
Irrational numbersA number is irrational if it has a decimal fraction part that does not terminate and does not repeat.
If you can describe all of the digits of the number explicitly without resort to functions or symbols, the number is not irrational.
-8 is not irrational
Let y have the following probability distribution: 15-X f (x) == (15- , *)* (*)**,x= 0,1,2,--, 15 Find the variance of x (write it up to first decimal place).
The variance of x is 258.2, rounded to the first decimal place.
The variance of a discrete probability distribution with values x and corresponding probabilities f(x) is given by the formula:
Var(x) = Σ[x^2 × f(x) - (Σ[x × f(x)])^2]
To find the variance of x, we need to first find the mean of x, which is given by the formula:
mean(x) = Σ[x × f(x)]
Using the given probability distribution f(x), we can calculate the mean and variance as follows:
mean(x) = Σ[x × f(x)] = 0 × (15!/0!(15-0)!) × (1/5)^0 × (4/5)^(15-0) + 1 × (15!/1!(15-1)!) × (1/5)^1 × (4/5)^(15-1) + 2 × (15!/2!(15-2)!) × (1/5)^2 × (4/5)^(15-2) + ... + 15 × (15!/15!(15-15)!) × (1/5)^15 × (4/5)^(15-15) = 15 × (1/5) = 3
Var(x) = Σ[x^2 × f(x) - (Σ[x × f(x)])^2] = 0^2 × (15!/0!(15-0)!) × (1/5)^0 × (4/5)^(15-0) + 1^2 × (15!/1!(15-1)!) × (1/5)^1 × (4/5)^(15-1) + 2^2 × (15!/2!(15-2)!) × (1/5)^2 × (4/5)^(15-2) + ... + 15^2 × (15!/15!(15-15)!) × (1/5)^15 × (4/5)^(15-15) - (mean(x))^2 = 267.2 - (3)^2 = 267.2 - 9 = 258.2
The variance of x is 258.2, rounded to the first decimal place.
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4. Texas for the last 30 years has manufactured about 31.5 million license plates. The six-digit license plate has been replaced with a seven-digit license plate with the following pattern: L L N – L N N N. There are 3 letters with the restriction of no vowels and 4 numbers between 0-9. How many plate numbers will be assigned? L-Letter, N-Number
6 points
60,761,421
92,610,000
115,316,136
175,316,136
The number of number plates assigned is 40,219,200.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, a seven-digit license plate with the following pattern: L L N – L N N N.
There are 3 letters with the restriction of no vowels and 4 numbers between 0-9.
With no vowels, we have 21.
= 21!/3!(21-3)! + 10!/(10-4)!
= 7980×5040
= 40,219,200
Therefore, the number of number plates assigned is 40,219,200.
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