So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
This is how we can compute the inverse of a matrix using the row reduction method.
To compute \(A^{-1}\) using the row reduction method, we need to first set up an augmented matrix with \(A\) on the left and the identity matrix on the right. Then, we will use elementary row operations to reduce the left side of the matrix to the identity matrix, which will result in the inverse of \(A\) on the right side. Here are the steps:
1. Set up the augmented matrix:
\[\left[\begin{array}{ccc|ccc}
a_{11} & a_{12} & a_{13} & 1 & 0 & 0 \\
a_{21} & a_{22} & a_{23} & 0 & 1 & 0 \\
a_{31} & a_{32} & a_{33} & 0 & 0 & 1 \\
\end{array}\right]\]
2. Use elementary row operations to reduce the left side of the matrix to the identity matrix. For example, we can use the following operations:
- Multiply the first row by a constant to make the first element 1
- Subtract a multiple of the first row from the second and third rows to make the first element of those rows 0
- Repeat these steps for the second and third columns until the left side of the matrix is the identity matrix
3. Once the left side of the matrix is the identity matrix, the right side of the matrix will be the inverse of \(A\):
\[\left[\begin{array}{ccc|ccc}
1 & 0 & 0 & a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
0 & 1 & 0 & a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
0 & 0 & 1 & a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
This is how we can compute the inverse of a matrix using the row reduction method.
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13 A box is in the shape of a cuboid 32 cm by 20 cm by 8 cm.
Box
32 cm
Sam has 75 bricks.
Each brick is a cube of side length 4 cm.
Can Sam fit all 75 bricks into the box?
You must show how you get your answer.
8 cm
20 cm
Brick
4 cm
Answer:
Yes.
Step-by-step explanation:
Volume of box:
32 × 20 × 8 = 5,120 cubic centimeters
Volume of each brick:
4^3 = 64 cubic centimeters
5,120 ÷ 64 = 80 bricks
So Sam can fit all 75 bricks into the box.
Identifying solutions to a linear equation in one variable: Two -... For each value of y, determine whether it is a solution to 40=5-7y.
The only value of y that is a solution to the equation 40=5-7y is y=-5.
To identify solutions to a linear equation in one variable, we can plug in the given values of y and see if the equation is true.
For the first value of y, let's plug in y=1:
40=5-7(1)
40=5-7
40=-2
This equation is not true, so y=1 is not a solution to the equation.
Now let's try y=2:
40=5-7(2)
40=5-14
40=-9
This equation is also not true, so y=2 is not a solution to the equation.
Finally, let's try y=-5:
40=5-7(-5)
40=5+35
40=40
This equation is true, so y=-5 is a solution to the equation.
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Identify the terms, the degree of each term and the degree of the polynomial. Then identify the leading term, th leading coefficient, and the constant term. -6r^(10)-11r^(3)+7r^(2)+3r-5
The leading term is -6r10; its coefficient is -6. The leading coefficient is -6. The constant term is -5.
What is leading term?Leading term is the term with the highest degree within an expression. It is the most important term and is used to determine the overall behaviour of a function.
The terms, degrees, and coefficients of the given polynomial are as follows:
-6r10: term, 10th degree, coefficient -6-11r3: term, 3rd degree, coefficient -117r2: term, 2nd degree, coefficient 73r: term, 1st degree, coefficient 3-5: term, 0th degree, coefficient -5To know more about leading term click on below link:
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simplify long division
The long division process is explained below.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
While doing long division method, you have to follow certain steps.
Consider an example 259 ÷ 9.
259 is the dividend, 9 is the divisor.
First consider the first digit of the dividend, which is 2. But 2 is not greater than or equal to 9.
So take the next digit also and so consider the first two digits.
The first two digits of the dividend is 25.
25 is not a multiple of 9.
The number which is a multiple of 9 nearer to but less than 25 is 18.
18 = 2 × 9.
Write 2 in the quotient and subtract 25 - 18 = 7
Now 7 is less than 9. So bring down the next (third) digit of the dividend, which is 9.
So the number we get is 79.
Again 79 is not a multiple of 9. The nearest lesser multiple of 9 is 72.
72 = 9 × 8
So write 8 in the quotient.
Remainder is 79 - 72 = 7
So we get the quotient as 28 and the remainder is 7.
Hence the simplification of the long division is explained.
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Please help I don’t understand slope at all
Answer:
Step-by-step explanation:
Dang, they made this a little harder. Now we need to actually calculate a slope. Good thing is, it's relatively easy. Slope is basically the rate of change, or the rise of the function over the run, which is shown as:
Δy/Δx
We can use two points to find the slope. I will use (2,795) and (4,1525)
(y1 - y2) / (x2 - x1)
(1525 - 795) / (4 - 2)
730 / 2
365
This is our slope, 365x.
Now we need the y-intercept, which is where the line hits the y-axis. It seems to be at 100, so the new equation is:
y = 365x + 100
If we want to know how many followers Lauren will have in 2018, we just use 7 for x years after 2011, since 2018 is 7 after 2011.
y = 365(7) + 100
y = 2555 + 100
y = 2655
Lauren has 2655 followers in 2018.
Station 6-
The x-intercept tells us when the depth below the sea level is 0 feet.
The y-intercept tells us the starting depth when the time is 0.
The meaning of the slope being -10x is that the depth below the sea level decreases 10 feet per minute. Hope this helps, and sorry for seeing this late!
Harvey asked some of his friends how old they
were. His results are shown in the table below.
What was the median age?
Age (years)
11
12
13
14
15
16
Frequency
2
5
4
3
2
4
Answer 13
Step-by-step explanation:Place all numbers in order from youngest to oldest. and the one in the middle is the median
Answer:13
Step-by-step explanation:
An engineer is hired to design a bridge to carry traffic across the river. Her first problem is to determine the distance from point A to point B. To do so, she starts at point A and measures a distance of 250 m in a direction at a right angle to the segment AB. At point C, she uses her transit to find the angle ACB which measures 49°52'. How long should the bridge be?
An engineer is hired to design a bridge to carry traffic across the river. The length of the bridge is 324.35 meters.
To find the distance from point A to point B, we can use the Law of Sines. This states that the ratio of the length of a side of a triangle to the sine of the opposite angle is equal for all sides and angles of the triangle. In this case, we have:
AC/ sin(B) = AB/ sin(C)
We can plug in the given values and solve for AB:
250 m/ sin(49°52') = AB/ sin(90°)
Simplifying and rearranging, we get:
AB = (250 m * sin(90°))/ sin(49°52')
Using a calculator, we find that sin(90°) = 1 and sin(49°52') ≈ 0.7705. Plugging these values back into the equation, we get:
AB = (250 m * 1)/ 0.7705
AB ≈ 324.35 m
Therefore, the distance from point A to point B, and the length of the bridge, should be approximately 324.35 meters.
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The ordered pair (- 2, - 7.5) represents the location of point P. The ordered pair (4, 3) represents the location of point Q. What is the rate of change of with respect to for this function?
The rate of change of with respect to for this function is 1.75.
What is the rate of change of with respect to for this function?From the question, we have the following parameters that can be used in our computation:
P = (-2, -7.5)
Q = (4, 3)
Using the two given points, we can find the slope of the line passing through them using the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-2, -7.5) and (x2, y2) = (4, 3)
slope = (3 - (-7.5)) / (4 - (-2))
= 10.5 / 6
= 1.75
Hence, the rate of change (i.e., the slope) of the line passing through points P and Q is 1.75.
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Show that the set is linearly dependet by finding a nontrival linear combination of vectors in the set whose sum is the zero vector. (use s1, s2, s3 resepectively for the vectors in the set)
S={(5,4),(−1,1),(2,0)}
(0,0)= Express the vector s1 in the set as a linear combination of the vectors s2 and s3. s1=
The vector s₁ in the set can be expressed as a linear combination of the vectors s₂ and s₃:
s₁ = (-4/3)s₂ + (1/3)s₃
How to express that the vector S₁ is a linear combination of the vectors S₂ and S₃?The set S = {(5,4),(−1,1),(2,0)} is linearly dependent if there exists a nontrivial linear combination of the vectors in the set whose sum is the zero vector. In other words, if there exists scalars a, b, and c such that:
a(5,4) + b(−1,1) + c(2,0) = (0,0)
Expanding the above equation gives us:
(5a - b + 2c, 4a + b) = (0,0)
This implies that:
5a - b + 2c = 0
4a + b = 0
Solving the above system of equations gives us:
a = 1/3, b = -4/3, c = 1/3
Therefore, the nontrivial linear combination of the vectors in the set whose sum is the zero vector is:
(1/3)(5,4) + (-4/3)(−1,1) + (1/3)(2,0) = (0,0)
To express the vector s₁ in the set as a linear combination of the vectors s₂ and s₃, we can use the above solution and write:
s₁ = (-4/3)s₂ + (1/3)s₃
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.
Describe how to find the product of the two terms 3x²y^5 and 4x³y^7
Answer:
see explanation
Step-by-step explanation:
using the property of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
given
3x²[tex]y^{5}[/tex] × 4x³[tex]y^{7}[/tex] ( separate like parts in the product )
= 3 × 4 × x² × x³ × [tex]y^{5}[/tex] × [tex]y^{7}[/tex]
= 12 × [tex]x^{(2+3)}[/tex] × [tex]y^{(5+7)}[/tex]
= 12[tex]x^{5}[/tex][tex]y^{12}[/tex]
List all the possible rational roots of x^4 - 2x^3 -6x^2 + 22x - 15 = 0
The possible rational roots are:
±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2
What are Functions?A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.
To list all the possible rational roots of x⁴ - 2x³ -6x² + 22x - 15 = 0, we need to find all the factors of the constant term -15 (in this case, they are 1, -1, 3, -3, 5, -5, 15, and -15) and all the factors of the leading coefficient 1 (in this case, they are 1 and -1). Then, we form all possible fractions of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Therefore, the possible rational roots are:
±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2
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A tent shaped like a triangular prism with the dimensions shown. If the volume of the tent is 12.6 cubic meters, what is the center height, h, of the tent
The base is 2.8m the height that connects the 2 bases is 4.5m
The center height of the tent is 1.57 meters.
What is Triangle?Triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. Triangles come in a variety of forms, including equilateral, isosceles and scalene. The sum of the three interior angles of a triangle is always 180°, making it one of the few geometric shapes whose angles add up to a fixed number. Triangles are the strongest shape, making them ideal for construction and engineering projects.
Using the formula for the volume of a triangular prism, V = B x H x L, we can determine the center height, h, of the tent:
V = B x H x L
12.6 = 2.8 x H x 4.5
H = 12.6 ÷ (2.8 x 4.5)
H = 1.57 meters
Therefore, the center height of the tent is 1.57 meters.
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What is the root word for these words anthropology judge psychology people economy mind democracy man judicious law. My mom can close this so anwser soon people
The correct match of each root word with its meaning are :
(i) Anthropology⇔(d) man
(ii) Psychology⇔(c) mind
(iii) Economy⇔(e) law
(iv) Democracy⇔(b) people
(v) Judicious⇔(a) judge
The term (i) Anthropology is related to (d) man because,
The term "Anthropology" is called the study of human-societies and cultures and their development.
The term (ii) Psychology is related to (c) mind ,
The term "Psychology" is defined as the scientific-study of behavior and mental processes of mind;
The term (iii) Economy is related to (e) law,
The Economy can be termed as the social science that deals with the production, distribution, and consumption of goods and services and their management.
The economy and practices of commerce are governed by certain laws or principles. So, the best option to match economy is law.
The term (iv) Democracy is related to (b) people ,
Democracy is defined as system of government by the whole population or all the eligible members of a state, typically through elected representatives.
The term (v) Judicious is related to (a) judge,
The word "judge" is a derived from the word "judicious", which means, showing and using sound judgement.
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The given question is incomplete, the complete question is
Match the below root of each word to its meaning.
(i) Anthropology (a) judge
(ii) Psychology (b) people
(iii) Economy (c) mind
(iv) Democracy (d) man
(v) Judicious (e) law
A true bank shot will create two similar right triangles. Determine the measures of the triangles you estimated using the GeoGebra applet. Are they similar?
Answer: The two triangles created by the bank shot are similar.
Step-by-step explanation: The measures of the triangles are as follows:
Triangle 1:
Angle A = 53.14 degrees, Angle B = 36.86 degrees, Angle C = 90 degrees
Triangle 2:
Angle A = 53.14 degrees, Angle B = 36.86 degrees, Angle C = 90 degrees
Yes, the two triangles are similar.
orm the operation in the parentheses. (3)/(8)-:((7)/(12)+(3)/(8))=(3)/(8)-:((14)/(24)+(9)/(24))
To solve this problem, we first need to find a common denominator for the fractions in the parentheses.
The common denominator for 12 and 8 is 24, so we can rewrite the fractions as (14/24) and (9/24). Then, we can add these fractions together to get (14/24) + (9/24) = (23/24). Next, we can subtract this fraction from (3/8) by finding a common denominator for 8 and 24, which is 24. We can rewrite (3/8) as (9/24) and then subtract (23/24) from it to get (9/24) - (23/24) = (-14/24). Finally, we can simplify this fraction to get (-7/12).
So, the final answer is:
(3/8) - ((7/12) + (3/8)) = (3/8) - ((14/24) + (9/24)) = (9/24) - (23/24) = (-14/24) = (-7/12)
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Math part 4 question 9
Answer: All questions and answers from the Mathematics Part I (solutions) Book of Class 9 Math Chapter 4 are provided here for you for free.
Step-by-step explanation:
EASY 7TH-GRADE MATH NEED HELP NOW!!!!
-3/4(5p-12)+2(8-1/4p)
Answer:
-17p+100
______
4
Step-by-step explanation: combine multiplied terms into a single fraction. distribute. combine multiplied terms into a single fraction. find a common denominator. combine fractions with a common denominator. multiply the numbers.Rearrange terms.Combine multiplied terms into a single fraction.Cancel terms that are in both the numerator and denominator.Find common denominator.Combine fractions with common denominator.Distribute.Add the numbers.Combine like terms
Your retirement account earns 7%, compounded quarterly. How much must the account contain when you retire if you want to withdraw $4000 at the end of each quarter for 30 years? ANSWER: _______dollars Round your final answer to the nearest cent. Note: This is almost identical to example 3 (only the payment amount is different), so check out the example 3 video if you need help.
__________
Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.
To find the amount that the retirement account must contain when you retire, we can use the formula for the future value of an annuity due:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n) * (1 + r/n)
Where FV is the future value, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, PMT = $4000, r = 0.07, n = 4 (since the account is compounded quarterly), and t = 30.
Plugging these values into the formula, we get:
FV = 4000 * [(1 + 0.07/4)^(4*30) - 1] / (0.07/4) * (1 + 0.07/4)
FV = 4000 * [(1.0175)^120 - 1] / (0.0175) * (1.0175)
FV = 4000 * 11.9478 / 0.0175 * 1.0175
FV = $2,758,686.58
Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.
Round your final answer to the nearest cent, the retirement account must contain $2,758,686.58.
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Pls help guys I give brainliest
Use the equation to finish the table by finding the x- and y-coordinates. Plot the points and graph the line. Show your work.
We can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.
Describe Graph?Graphs are used to help people understand and interpret information in a way that is easy to see and analyze. There are many different types of graphs, each with its own characteristics and applications.
Some common types of graphs include:
Line graph: A line graph displays data as a series of points connected by lines, typically used to show trends or changes over time.
Bar graph: A bar graph displays data as bars of different heights, typically used to compare values or quantities.
Pie chart: A pie chart displays data as a circle divided into slices, typically used to show proportions or percentages.
To find the y-coordinate for each x-coordinate, we can substitute each value of x into the equation y = (1/2)x + 4 and simplify:
When x = -2:
y = (1/2)(-2) + 4
y = -1 + 4
y = 3
So, the point (-2, 3) is on the line.
When x = 0:
y = (1/2)(0) + 4
y = 0 + 4
y = 4
So, the point (0, 4) is on the line.
We can complete the table as follows:
x y = (1/2)x + 4 y
-2 y = (1/2)(-2) + 4 3
0 y = (1/2)(0) + 4 4
To graph the line, we can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.
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Which linear equation best represents a trend line for the data in the scatter plot?
It's important to evaluate the fit of the equation to the data before making any predictions or decisions based on it.
To determine the linear equation that best represents the trend line for a given scatter plot, we need to find the line of best fit. The line of best fit is a straight line that represents the general trend of the data and can be used to make predictions or estimates based on the data.
One way to find the line of best fit is by using the method of least squares. This involves finding the line that minimizes the sum of the squared differences between each data point and the line itself.
Once we have the line of best fit, we can express it as a linear equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To determine the linear equation that best represents the trend line for a given scatter plot, we would need to perform the following steps:
Plot the scatter plot of the given data points.
Visually inspect the scatter plot to see if there appears to be a linear relationship between the variables.
Calculate the line of best fit using the method of least squares.
Express the line of best fit as a linear equation of the form y = mx + b.
Use the equation to make predictions or estimates based on the data.
It's important to note that the linear equation that best represents the trend line for a scatter plot may not always be a good predictor of the data, especially if the data is not linear or if there are outliers present.
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Solve:-2x +3y =
If x=2 and y=-3
hi
im pretty sure that this is the answer
hope this helps
good luck;)
Suppose a novel infectious disease reaches the portland-metro area. This disease takes 9 days to recover from, and has a basic reproduction number of R0=4.5. Suppose the disease is 0.3% fatal. We'll model the disease outbreak with an SIR model.
i) Find a value for N, the total population of the portland-metro area.
ii) Determine the values of a and b, the constants for the SIR model.
iii) Suppose on day 0, there are 5 cases of the disease. If 15% of the initial population has immunity to the disease, determine the initial values S(0), I(0) and R(0).
iv) Solve the SIR model numerically, over a time interval that shows the whole course of the disease outbreak. Create a graph showing S, I and R vs time. The remaining questions can all be answered by reading and interpreting the graph:
v) How many people ultimately will be infected?
vi) How many will die from the disease?
vii) When is the peak of the outbreak?
viii) When is the outbreak is over?
ix) For this disease, what is the herd immunity threshold? Find the time at which the number of R individuals reaches the herd immunity threshold.
x) How many people die of the disease, after the herd immunity threshold is reached?
The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.
i) The total population of the Portland-metro area, N, can be determined by looking up the population of the city, county, and other areas that make up the metro area.
ii) To determine the values of a and b, we need to look at the basic reproduction number, R0. For an SIR model, the constant a is equal to the basic reproduction number (R0=4.5), and the constant b is equal to (a/N).
iii) To determine the initial values S(0), I(0) and R(0), we can use the equation S(0)=N-5-0.15N, I(0)=5, and R(0)=0.15N.
iv) To solve the SIR model numerically, we need to create a differential equation for each variable (S, I, and R) and use numerical integration to solve the system. Then, a graph can be created to show the values of S, I, and R over time.
v) From the graph, we can see that the total number of people infected is equal to the peak of the I(t) curve.
vi) The total number of people that die from the disease is equal to the peak of the R(t) curve.
vii) The peak of the outbreak is at the time when the I(t) curve has its highest value.
viii) The outbreak is over when the I(t) curve reaches 0.
ix) The herd immunity threshold is reached when the R(t) curve reaches a value equal to the basic reproduction number (R0).
x) The total number of people that die of the disease after the herd immunity threshold is reached can be determined by looking at the value of the R(t) curve after it reaches the herd immunity threshold.
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what are the outlier in this data
The data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.
What is outlier of data?An outlier is a data point that is significantly different from other data points in a data set. Outliers can occur due to errors in data collection or measurement, or they can be legitimate data points that are simply far outside the range of the other data. In statistical analysis, it is important to identify outliers and decide whether to remove them from the data set or keep them and analyse them separately.
There are several methods for identifying outliers, including graphical methods and statistical methods such as the use of z-scores or the interquartile range.
To identify outliers in this data, we can start by calculating some basic statistical measures such as the mean and standard deviation.
The mean of the given data is:
(1.11 + 1.13 + 1.40 + 1.32 + 1.14 + 1.28 + 1.13 + 1.8 + 1.10 + 1.20) / 10 = 1.304
The standard deviation of this data is:
sqrt(((1.11 - 1.304)² + (1.13 - 1.304)² + (1.40 - 1.304)² + (1.32 - 1.304)² + (1.14 - 1.304)² + (1.28 - 1.304)² + (1.13 - 1.304)² + (1.8 - 1.304)² + (1.10 - 1.304)² + (1.20 - 1.304)^2) / 9) = 0.247
One common rule of thumb for identifying outliers is to consider any data point that falls more than 2 or 3 standard deviations from the mean to be an outlier. Using this rule, we can identify any values that fall outside the range:
1.304 - 2 * 0.247 = 0.81
1.304 + 2 * 0.247 = 1.798
1.304 - 3 * 0.247 = 0.563
1.304 + 3 * 0.247 = 2.045
Based on this rule, we can see that the data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.
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Lee measures a box and finds the length is inches, the width is 15 inches, and the height is 13 inches. What is the volume of the box?
1,852.5 cubic inches
1,267.5 cubic inches
37.5 cubic inches
922 cubic inches
Answer:
I think the question is incomplete
Mike constructed a kite by attaching two congruent triangles as shown in the diagram below.
Which equation can Mike use to determine the amount of material, in square inches, needed to create the kite?
F. A=[12(12)(8)]⋅2
G.A=[12(6)(8)]⋅2
H.A=[(12)(4)]⋅2
J.A=[(6)(10)]⋅2
The amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.
What is area of an isosceles triangle?Either of a triangle's two sides that are equal in length is said to be isosceles. This characteristic equates to the triangle's two angles being equal. Two of the sides and two of the angles of an isosceles triangle are equal. An isosceles triangle has three sides that are all the same length, have the same angles, and meet at symmetrical corners. Two right-angle triangles are produced if a perpendicular line is traced from the junction of two equal sides to the base of the unequal side.
The area of the triangle is given as:
A = 1/2(b)(h)
Here, the base = 6 and height = 8 in.
Thus, the area of the triangle is:
A = 1/2(6)(8)
The figure consists of 2 similar triangles. So, the area of the second triangle is added to get the final area.
A = [1/2(6)(8)].2
Hence, the amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.
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Watch help video Factor the expression completely. 2x-5x^(2) Answer: Subnit Answer
The answer is x(2-5x).
In factorization, you just need to identify the common factors and accordingly solve as per your requirement!
To factor the expression 2x-5x^(2) completely, we need to find the greatest common factor (GCF) of the two terms and factor it out. The GCF of 2x and 5x^(2) is x. So we can factor it out of the expression:
2x-5x^(2) = x(2-5x)
Now, the expression is factored in completely. The final answer is:
x(2-5x)
Therefore, factoring the expression 2x-5x^(2) gives the answer x(2-5x).
I hope this helps! Let me know if you have any further questions.
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True / False, please give me the explanation and reason
1. If in the year 2000 the price index is 120 and the value of the price index in 2001 is 125, it implies that there was a 5% increase in the price level in 2001.
2. The weighted aggregate price index assigns a lower weight to the items that are sold in higher quantities.
1). The statement " If in the year 2000 the price index is 120 and the value of the price index in 2001 is 125, it implies that there was a 5% increase in the price level in 2001." is true. Percentage change = (New price index - Old price index) / Old price index x 100, Plugging in the values from the question:Percentage change = (125 - 120) / 120 x 100 = 4.17%. Therefore, there was a 4.17% increase in the price level in 2001. 2). The statement " The weighted aggregate price index assigns a lower weight to the items that are sold in higher quantities." is False. This is false because these items have a greater impact on the overall price level
The price index measures the change in prices of a basket of goods and services from one period to another. In this case, the price index in 2000 is 120 and the price index in 2001 is 125. To calculate the percentage change in the price level, you can use the formula:
The weighted aggregate price index assigns a higher weight to the items that are sold in higher quantities. This is false because these items have a greater impact on the overall price level. For example, if the price of a popular item, such as gasoline, increases, it will have a greater impact on the overall price level than if the price of a less popular item, such as a luxury car, increases.
Therefore, the weighted aggregate price index assigns a higher weight to the items that are sold in higher quantities to accurately reflect their impact on the overall price level.
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(a) How many ways can 8 people be arranged on 8 chairs in a row?
(b) How many ways can 8 people be seated around a circular table? (Note that rotating the chairs around the table does not change the seating) (c) Let {P.P2, P3, ...Ps} be eight people. How many committees can be selected from the people if ps has to be the chair of the committee (and so a member of the committee)?
There would be 40,320 ways can 8 people be arranged on 8 chairs in a row. There are 5,040 ways can 8 people be seated around a circular table. There are 128 committees can be selected from the people if ps has to be the chair of the committee
(a) The number of ways that 8 people can be arranged on 8 chairs in a row is 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320. This is because there are 8 choices for the first chair, 7 choices for the second chair, and so on until there is only one choice for the last chair.
(b) The number of ways that 8 people can be seated around a circular table is (8-1)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040. This is because we can fix one person in one seat and then there are 7 choices for the next seat, 6 choices for the next seat, and so on until there is only one choice for the last seat.
(c) The number of committees that can be selected from the 8 people if Ps has to be the chair of the committee is 2^(8-1) = 2⁷ = 128. This is because there are 7 people left to choose from and each person can either be on the committee or not on the committee, which gives us 2 choices for each person.
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Assume binomial distribution where n = 3 and p = 0.6. Determine
the mean and standard deviation of the distribution.
The mean and the standard deviation of the binomial variable are given as follows:
Mean of 1.8.Standard deviation of 0.8485.What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula(PMF) is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for n and p in this problem are given as follows:
n = 3, p = 0.6.
The mean of the binomial distribution is given by the following equation:
E(X) = np.
Hence:
E(X) = 3 x 0.6
E(X) = 1.8.
The standard deviation of the binomial distribution is given by the following equation:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
Hence:
[tex]\sqrt{V(X)} = \sqrt{3 \times 0.6 \times 0.4}[/tex]
[tex]\sqrt{V(X)} = 0.8485[/tex]
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