(a) True
(b) True
(c) False
(d) True
(e) False
(a) True. For any n × n invertible matrix A, the equation Ax = 0 admits only the trivial solution. This is because if A is invertible, then there exists an inverse matrix A^-1 such that A^-1A = I, where I is the identity matrix. Therefore, if Ax = 0, then A^-1Ax = A^-10, or x = 0. This means that the only solution to the equation is the trivial solution x = 0.
(b) True. For any two matrices A and B of size n × n, (AB)^T = (B^T) (A^T). This is a property of matrix multiplication and transposition, and can be easily verified by performing the operations on the matrices.
(c) False. Let A be a matrix of size n × n. If for two vectors y and z of R^n we have Ay = Az, it does not necessarily mean that y = z. It is possible for two different vectors to produce the same result when multiplied by the same matrix. For example, consider the matrix A = [[1, 0], [0, 1]] and the vectors y = [1, 0] and z = [0, 1]. Both Ay and Az will result in the same vector [1, 1], but y and z are clearly not equal.
(d) True. If A is a matrix of size n × n such that A^3 = I(n), then A is invertible. This is because A^3 = I(n) implies that A^2 = A^-1, meaning that the inverse of A exists and A is invertible.
(e) False. For any two matrices A and B of size n×n such that AB = 0, it is not necessarily true that A = 0 or B = 0. It is possible for two non-zero matrices to multiply to produce the zero matrix. For example, consider the matrices A = [[1, -1], [1, -1]] and B = [[1, 1], [1, 1]]. Both A and B are non-zero matrices, but AB = 0.
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Write an equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4
The equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4 is y = (-3/4)x + 9.
The slope of the given line is -3/4. The desired line will likewise have a slope of -3/4 because it is parallel to this line.
The equation of the line travelling through the point (8,3) with a slope of -3/4 may be found using the point-slope form of a line's equation:
y - y1 = m(x - x1)
where the provided point is (x1, y1), and m is the slope.
When we change the values, we obtain:
y - 3 = (-3/4)(x - 8)
Making the right side simpler:
y - 3 = (-3/4)x + 6
To each sides, add 3:
y = (-3/4)x + 9
Hence, y = (-3/4)x + 9 is the equation of the line going through the point (8,3) that is parallel to the line y=-3/4+4.
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Can someone please tell me what x+
When BD is perpendicular tο AC, the value οf x is fοund tο be 19°.
What is meant by perpendicular lines?
When twο lines crοss at a straight angle οr 90 degrees, perpendicular lines are created. Perpendicularity is the name given tο this characteristic οf lines. A straight line that fοrms a right angle (90 degrees) with anοther line is referred tο as being perpendicular.
In οther wοrds, twο lines are perpendicular tο οne anοther if they cοnnect at a right angle. The term "perpendicular tο all pοints in the plane" οr "perpendicular tο each line it intersects" is used tο describe a line that is perpendicular tο the plane. Perpendicular lines always intersect at 90 degrees but nοt all intersecting lines are perpendicular.
Given a vectοr diagram.
It is given that BD is perpendicular tο AC.
m∠CBE = (5x - 42)°
m∠CBE = (2x - 1)°
Since BD is perpendicular tο AC,
m∠DBC = m∠DBA = 90°
Nοw,
m∠DBC = 90°
m∠CBE + m∠CBE = m∠DBC
Then we can write,
m∠CBE + m∠CBE = 90°
(5x - 42)° + (2x - 1)° = 90°
7x - 43 = 90
7x = 133
x = 133 / 7 = 19°
Therefοre when BD is perpendicular tο AC, the value οf x is fοund tο be 19°.
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i choose 10 consecutive numbers. if i exclude one of the numbers the remaining 9 sum to 2023 which number did i exclude?
The number that was excluded from the 10 consecutive numbers would be = 228.
How to calculate the number that was excluded?Let's take the smallest number of the 10 consecutive number to be = X
Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.
If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:
(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)
Collect the like terms and add up.
= 9x + 36
Recall that the sum of the remaining 9 numbers = 2023.
That is:
= 9X + 36 = 2023
=9x = 1987
x = 221
Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.
If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.
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24kg in the ratio 3 : 5 ?????
Answer: Your welcome!
Step-by-step explanation:
The ratio of 24kg is 3:5, which means 3 parts of 24kg is 3 times the 5th part of 24kg.
Therefore, 3 parts of the 24kg is 18kg and 5 parts of the 24kg is 6kg.
can some body help me
Answer: 9
Step-by-step explanation:
24; can vary by 3.5%
The range of allowable values 24; can vary by 3.5% is 0.9.
What is range?
The difference between the highest and lowest values for a given data set is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.
As a result, the range can also be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.
24 × 3.5% =0.84
so round to nearest tenth is 0.9.
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Complete question:
Find the range of allowable values based on the given information. Round to the nearest tenth.
24; can vary by 3.5%
One year, a company sales increased by 15%. The following year the company's sales increased by 18%. Calculate the overall percentage increase
The overall percentage increase is approximately 35.7%.
What is the overall percentage increase of the company sales?Given that, a company sales increased by 15% in year one and 18% in the following year.
To calculate the overall percentage increase, we need to find the combined effect of the two increases.
One way to do this is to use the formula for compound interest, which is:
A = P(1 + r₁)(1 + r₂)
where:
A = the final amountP = the initial amountr₁ = the first interest rate (as a decimal)r₂ = the second interest rate (as a decimal)In this case, let's assume that the initial sales amount is 100 (you could use any amount as long as you keep it consistent throughout the calculation).
Then, the first year's increase of 15% would result in a new amount of:
100(1 + 0.15) = 115
In the second year, the 18% increase would be applied to this new amount of 115, resulting in:
115(1 + 0.18) = 135.7
Hence, we have an overall increase of:
(135.7 - 100)/100
= 0.357 × 100%
= 35.7%
Therefore, the increase is approximately 35.7 percent.
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar by SSS and the scale factor is 0.625
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔJKT
Let the second triangle be represented as ΔKLS
Now , the measure of side JT = 20
The measure of side JK = 14
The measure of side KS = 32
The measure of side KL = 22.4
The corresponding sides of similar triangles are in the same ratio
So , on simplifying , we get
JT / KS = JK / KL
20 / 32 = 14 / 22.4
On further simplification , we get
0.625 = 0.625
Hence , the triangles are similar
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The Kangaroo Lodge of Madison County has 10 members (A, B, C, D, E, F, G, H, I, and J). The club has five working committees: the Rules Committee (A, C, D, E, I, and I), the Public Relations Committee (B, C, D, H, I, and J), the Guest Speaker Committee (A, D, E, F, and H), the New Year's Eve Party Committee (D, F, G, H, and I), and the Fund Raising Committee (B, D, F, H, and J). (a) Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the members.) (b) Suppose we are interested in knowing which commit- tees have members in common. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the committees.)
Let A, B, C be three sets such that A U B = C & A ∩ B = φ then how do you prove that A = C – B?
When A U B = C & A ∩ B = φ, then A = C - B. The solution has been obtained by using properties of sets.
What is a set?
In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Curly brackets are typically used to represent sets.
We know that
A - B = (A ∪ B) - B
On substituting A U B = C in this, we get
A - B = C - B ...(1)
Similarly,
A - B = A - (A ∩ B)
On substituting A ∩ B = φ in this, we get
A - B = A ...(2)
From (1) and (2), we get
A = C - B
Hence, when A U B = C & A ∩ B = φ, then A = C - B.
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what number is close to 48/100 is it 0 or 1 or 1/2?
Answer:
1/2
Step-by-step explanation:
Our answer options are: 0, 1, 1/2
0 = 0/100
1 = 100/100
1/2 = 50/100
Comparing the 3 options, we see that 1/2 is the closest to 48/100!
So, the answer is 1/2
Find the
1. End behavior
2. X-intercepts
3. Positive/negative
4. Multiplicity
The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.
What is the end behavior and x - intercepts of the functionThe given function is f(x) = -x³ + 2x² + 3
1. End behavior:
As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:
As x approaches negative infinity, f(x) approaches negative infinity.As x approaches positive infinity, f(x) approaches negative infinity.2. X-intercepts:
To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:
-x^3 + 2x^2 + 3 = 0
x^3 - 2x^2 - 3 = 0
Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:
x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)
The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.
3. Positive/negative:
To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:
The leading coefficient of f(x) is negative, so for very large negative or positive values of x, f(x) is negative.The factor -x^3 is negative for negative values of x and positive for positive values of x.The factor 2x^2 is positive for all values of x.The constant term 3 is positive.Putting these together, we can make the following sign chart for f(x):
x f(x)
x < 0 -
0 < x < 3 +
x > 3 -
4. Multiplicity:
The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.
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At the Livingston Zoo's bug exhibit, Marcy watches a millipede crawl for 1 4/8 minutes, stay still for a while, and then crawl for 2 1/8 minutes more. How much total time did Marcy spend watching the millipede crawl?
Marcy spent 2.125 minutes of total time watching the millipede crawl.
How to the total time Marcy spent watching the millipede crawl?To find the total time Marcy spent watching the millipede crawl, we need to add up the time it crawled during the first period and the time it crawled during the second period.
1 4/8 minutes is the same as 1 2/4 minutes, or 1.5 minutes.
2 1/8 minutes is the same as 2.125 minutes.
So the total time the millipede crawled is:
1.5 minutes + 2.125 minutes = 3.625 minutes
Therefore, Marcy spent a total of 3.625 minutes watching the millipede crawl.
We know that Marcy watched the millipede crawl for 1 4/8 minutes, which can be simplified to 1 2/4 minutes, or 1.5 minutes.
Next, the millipede stayed still for a while, and then crawled for 2 1/8 minutes. We can convert 2 1/8 minutes to a decimal by adding the whole number (2) to the fraction (1/8) converted to a decimal (0.125). So:
2 + 0.125 = 2.125 minutes
Marcy spent 2.125 minutes of total time watching the millipede crawl.
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A E G 2. BC AC What is the reason that we can make the statement = 11 AC CD D с a. SAS Similarity Postulate b. Corresponding sides of congruent triangles are congruent C. Corresponding sides of similar triangles are congruent d. Corresponding sides of similar triangles are proportional 3. Complete the following proof of the Pythagorean Theorem, a² + b2 = c2 A -= = As similar triangles have proportional we can write the proportions - = -and - = By the cross- property, = cf and = ce. By the a2 + b2 = cf +ce. allows the equivalent expression, a2 + b2 = By the therefore we can substitute and arrive at the statement a? + b2 = c. Word Bank fue sides á C= B b g b с addition property of equality segment addition postulate cf +e) b2 a2 product angles factoring
The Pythagorean Theorem is proven.
The reason that we can make the statement BC/AC = CD/AC is because corresponding sides of similar triangles are proportional. This is represented by option D. Corresponding sides of similar triangles are proportional.
To complete the proof of the Pythagorean Theorem, a² + b² = c², we can use the following steps:
As similar triangles have proportional sides, we can write the proportions AB/AC = AC/BC and AB/BC = BC/AC.
By the cross-product property, AB * BC = AC * AC and AB * AC = BC * BC.
By the addition property of equality, AB² + BC² = AC² + BC².
By the segment addition postulate, AC + BC = c.
By factoring, (AC + BC)² = c².
By the distributive property, AC² + 2*AC*BC + BC² = c².
By rearranging the terms, AC² + BC² = c² - 2*AC*BC.
By substituting the values of AC and BC from the proportions in step 1, we get a² + b² = c² - 2*a*b.
By simplifying, we get a² + b² = c².
Therefore, the Pythagorean Theorem is proven.
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How is the series 3+5+7+...+51 represented in sigma notation?
Answer:
The third one
Step-by-step explanation:
The only one which gives the last number of the sequence is the third one as subbing in 16 you get 3×16 + 3 = 48 + 3 = 51
6 time the quantity of a number minuse 5 is 90
Answer:
6(x)-5=90
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
Exact Form:
x=95/6
Decimal Form:
x=15.83
Mixed Number Form:
x= 15 5/6
tbh i don't know if this is right
Suppose you deposit $1100 in an account with an annual interest rate of 8 % compounded quarterly: Use the formula 4 = P(1+#)" and round each answer to 2 decimal places, if necessary: Find an equation that gives the amount of money in the account after t years: A(t) Preview Find the amount of money in the account after 8 years After 8 years_ there will be $ in the account: c How many years will it take for the account to contain $2200? It will take years for there to be S2200 in the account: d. If the same account and interest were compounded continuously, how much money would the account contain after 8 years? With continuous compounding interest; there would be in the account after 8 years
a) A(t) = 1100(1 + 0.08/4)^(4t)
b) After 8 years, there will be $2203.99 in the account.
c) It will take approximately 8.03 years for there to be $2200 in the account.
d) With continuous compounding interest, there would be $2219.54 in the account after 8 years.
A(t) = P(1 + r/n)^(nt)
Where:
A(t) = the amount of money in the account after t years
P = the initial deposit
r = the annual interest rate
n = the number of times interest is compounded per year
t = the number of years
Find an equation that gives the amount of money in the account after t years:
A(t) = 1100(1 + 0.08/4)^(4t)
Find the amount of money in the account after 8 years:
A(8) = 1100(1 + 0.08/4)^(4*8)
A(8) = 1100(1.02)^32
A(8) = 2203.99
After 8 years, there will be $2203.99 in the account.
How many years will it take for the account to contain $2200?
2200 = 1100(1 + 0.08/4)^(4t)
2 = (1.02)^4t
log(2) = 4t*log(1.02)
t = log(2)/(4*log(1.02))
t = 8.03
It will take approximately 8.03 years for there to be $2200 in the account.
If the same account and interest were compounded continuously, how much money would the account contain after 8 years?
A(t) = Pe^(rt)
A(8) = 1100*e^(0.08*8)
A(8) = 1100*e^0.64
A(8) = 2219.54
With continuous compounding interest, there would be $2219.54 in the account after 8 years.
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Write an equation in standard form using integers Y= X/5
To write an equation in standard form using integers, we need to eliminate any fractions by multiplying both sides of the equation by the least common multiple of the denominators.
In this case, the denominator is 5. So we can multiply both sides of the equation by 5 to get:-
5Y = X
Now, we can rearrange the equation so that the variables are on the left-hand side and the constants are on the right-hand side, in the form of Ax + By = C.
X - 5Y = 0 (subtracted X from both sides)
Therefore, the equation in standard form using integers is -X - 5Y = 0.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Select the graph that represents the system of equations.
y=−3x−13 y=2x+2
In answering the question above, the solution is As a result, (x,y) = is the system of equations' answer (-3,8).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The equations in the system are:
[tex]y = -3x - 13 \sy = 2x + 2[/tex]
We may put the two equations equal to one another and get x to solve this system:
-3x - 13 = 2x + 2
3x added to both sides results in:
-13 = 5x + 2
By taking 2 away from both sides, we arrive at:
-15 = 5x
When we multiply both sides by 5, we get:
x = -3
We may use either of the original equations to calculate y now that we know x:
y = -3(-3) - 13 = 8
As a result, (x,y) = is the system of equations' answer (-3,8).
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14. Find mMK
16. Find mJPK.
The measures of arcs and segments are
NK = 12, MLK = 41.5 degrees, JK = 24 and JPK = 277 degrees
How to determine the measures of arcs and segmentsLength NK
Given the triangle as the parameter.
Using the Pythagoras theorem, we have
NK = √(KL² - LN²)
So, we have
NK = √(15² - 9²)
Evaluate
NK = 12
The arc measure MK
Here, we start by calculating the central angle MLK
This is done using the following cosine ratio
cos(MLK) = NK/KL
cos(MLK) = 9/12
cos(MLK) = 0.75
Evaluate
MLK = 41.5 degrees
This means that
Arc MK = 41.5 degrees
Length JK
This is calculated as
JK = NK * 2
So, we have
JK = 12 * 2
JK = 24
The arc measure JPK
This is calculated as
JPK = 360 - 2 * MK
So, we have
JPK = 360 - 2 * 41.5 degrees
Evaluate
JPK = 277 degrees
Hence, the arc measure is 277 degrees
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ive been trying to do this since this morning and can't, I need help
a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units'
Given data ,
Let the exponential growth equation be represented as x ( t )
Now , the average percentage change from the year 2000 - 2009 is calculated by
The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )
The total number of years = 9 years
So , the average percentage change = total percentage / number of years
On simplifying , we get
The average percentage change = 12.21 / 9 = 1.35667 %
b)
The population in 2009 was 37,000,000
So , the population growth rate r = 1.35667 %
And , the population in the years 2015 is given by
The number of years n = 6 years
x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶
On simplifying , we get
x ( t ) = 37,000,000 ( 1.013567 )⁶
x ( t ) = 40,115,896
Hence , the population in the year 2015 is 40,115,896
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Please answer this question
160 student tickets were sold.
Describe Equation?Equations are used to model a wide range of phenomena, from physical laws in science to economic models in finance. They are also used in solving problems and making predictions in various fields.
Let's start by setting up a system of equations to represent the given information:
a + s = 200 (equation 1: total number of tickets sold)
7a + 5s - 210 = 870 (equation 2: profit after paying back Mr. Shum's investment)
We can simplify equation 2 by adding 210 to both sides:
7a + 5s = 1080 (equation 3)
Now we can use equation 1 to solve for one variable in terms of the other:
s = 200 - a (equation 4)
Substitute equation 4 into equation 3 and solve for a:
7a + 5(200 - a) = 1080
7a + 1000 - 5a = 1080
2a = 80
a = 40
So 40 adult tickets were sold. We can use equation 4 to find the number of student tickets sold:
s = 200 - a = 200 - 40 = 160
Therefore, 160 student tickets were sold.
To check our answer, we can verify that the total revenue from ticket sales is equal to the initial investment plus the profit:
7(40) + 5(160) = 210 + 870
280 + 800 = 1080
This checks out, so our answer is correct.
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If the nth term of a number sequence is n2-3 find the first 3 terms and the 10th term
[tex]\huge\begin{array}{ccc}a_1=-2\\a_2=1\\a_3=6\\a_{10}=97\end{array}[/tex]
Numerical sequence.
[tex]a_n=n^2-3[/tex]
Find the first 3 terms and the 10th term.
Substitute
n = 1, n = 2, n = 3 and n = 10:
[tex]a_1=1^2-3=1-2=-2\\\\a_2=2^2-3=4-3=1\\\\a_3=3^2-3=9-3=6\\\\a_{10}=10^2-3=100-3=97[/tex]
help me solve this homework
The volume of the triangular prism is 42 in³.
What is a triangular prism?In geometry, a triangular prism is a three-sided polyhedron with a triangle base, a translated copy, and three faces joining equal sides. A right triangular prism is oblique if its sides are not rectangular.
We know that
Volume of Prism (V) = Area of triangle * Height of Prism
Area of triangle = (Base * Height) / 2
Area of triangle = (4 * 3) / 2
Area of triangle = 12 / 2
Area of triangle = 6 in²
Using this, we get
⇒V = 6 * 7
⇒V = 42 in³
Hence, the volume of the triangular prism is 42 in³.
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Since there are multiple questions so the question answered above is attached below
Determine algebraically whether the function is even, odd or neither: g(x) = x/x^2+3
The function [tex]g(x) = \frac{x}{x^2+3}[/tex] is neither even nor odd.
To determine if a function is even, we can use the following test:
f(x) = f(-x)
If this is true, then the function is even.
For the given function, [tex]g(x) = \frac{x}{x^2+3}[/tex], let's plug in -x for x and see if the function is equal to itself:
[tex]g(-x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}[/tex]
As we can see, g(x) does not equal g(-x), so the function is not even.
To determine if a function is odd, we can use the following test:
f(x) = -f(-x)
If this is true, then the function is odd.
For the given function, let's plug in -x for x and see if the function is equal to the negative of itself:
[tex]g(x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}\\\\ -g(-x) = \frac{x}{-x^2+3}[/tex]
As we can see, g(x) does not equal -g(-x), so the function is not odd.
After the algebraic analysis, we can conclude that the function g(x) is neither, i.e., it is neither even nor odd.
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(4,3); y = 3x² - x + 7
Answer:13
Step-by-step explanation:
because when you
Express the difference in median as a multiple of the IRQ for each data set.
IQR difference = 5
What is interquartile range (IQR)?The interquartile range (IQR) is a measure of variability that describes the spread of a set of data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of the data.
The formula for calculating the IQR is:
IQR = Q3 - Q1
The Upper Quartile - Lower Quartile is the definition of the interquartile range.
The answer to the query is
Mount Vernon data set: 55, 60, 65, 70, 75, 80, 85 and 90
Lakewood data set = 65, 70, 75, 80 and 85
Mount Vernon median = 70+75/2 = 77.5
55+60+65+70/4 = 62.5 is the median for the lower half of the collection.
Upper half of set median: 82.5 (75, 80, 85, 90 divided by 4).
Mount Vernon's IQR is 82.5 minus 62.5, or 20.
Likewise, in the instance of Lakewood,
Average: 75
Lower half of the set median equals 65+70/2 = 67.5
Upper half of set median equals 80+85/2 = 82.5
IQR = 82.5 - 67.5 = 15
Hence, IQR difference = 20-15 = 5
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Knowledge Check Subtract. (x+8)/(x+7)-(x-2)/(x) Simplify your answer as much as possible.
The simplified form is 3/(x+7) + 14/(x)(x+7).
What is simplified form of fraction?Simplified form of a fraction is the form of a fraction in which the numerator and denominator are in their lowest form, or the greatest common factor has been taken out of both the numerator and denominator. For example, the fraction 24/36 can be simplified to 2/3.
To subtract the two fractions, we need to find a common denominator. The common denominator of (x+7) and (x) is (x)(x+7). We can then rewrite the two fractions with this common denominator and subtract the numerators:
(x+8)/(x+7) - (x-2)/(x) = (x+8)(x)/(x)(x+7) - (x-2)(x+7)/(x)(x+7)
= (x^2+8x)/(x^2+7x) - (x^2-2x+7x-14)/(x^2+7x)
= (x^2+8x - x^2+2x-7x+14)/(x^2+7x)
= (3x+14)/(x^2+7x)
= 3x/(x^2+7x) + 14/(x^2+7x)
= 3/(x+7) + 14/(x)(x+7)
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Pls give simple working
Answer:
Step-by-step explanation:
sum of all angles in quadrilateral = 360
So, x+48+48+132 =360
x =132
The angle of elevation of the top of the building at a distance of 55 m from its foot on a
horizontal plane is found to be 60°. Find the height of the building rounded to the nearest
tenth of a meter.
The height of the building is _______ meters.
Need help
Let's call the height of the building "h". We can use trigonometry to solve for "h" using the angle of elevation and the horizontal distance from the foot of the building to the point where the angle of elevation is measured.
In this case, we have a right triangle with the height of the building as one leg, the horizontal distance as the adjacent leg, and the angle of elevation as the angle opposite the height. So we can use the tangent function:
tan(60°) = h/55
Solving for "h", we get:
h = 55 tan(60°)
h ≈ 95.1
Rounded to the nearest tenth of a meter, the height of the building is approximately 95.1 meters.