let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be 0 ≤ h ≤ 3
If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.
Let m is a vector space over a field F, a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .
L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)
L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)
A subset h⊆ m which satisfy (1) and (2) is a subspace of v
Dimension of Vector space and a subspace :
According to linear algebra theorem,
The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .
If m is spanned then here, dim m = 3
h ⊆ subs m <===> dim h < dim m
If h is subspace of m and dim m = 3 then,
dim h = h with 0≤ h ≤3
If h is zero, the dimension of improper subspace , h = {0}
If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,
Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3
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max is a function that expects two int parameters and returns the value of the larger one.
Two variables , population1 and population2, have already been defined and associated with intvalues.
Write an expression (not a statement!) whose value is the larger of population1 andpopulation2 by calling max.
max(population1, population2)
The larger of population1 and population2 by calling max.
max(population1, population2)
Since the function max returns a large integer among two integers, max(population1,population2) will give us the large one among population1 and population2. Now if we compare that value with population2 using another max, then that will provide us with the large among maximum (population1,population2) i.e it will be the largest among these three variables.
Therefore the required expression will be:
max(population1,population2).
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In parallelogram ABCD below, find the value of y.
The value of y shown in the parallelogram given in question is 7.
What is parallelogram?
In Euclidean geometry, a parallelogram is an easy quadrilateral with two sets of parallel sides. The confronting\opposed sides and the opposing angles of a parallelogram are of equal length. To show the congruence of opposed sides and opposite angles, the Euclidean parallel postulate or one of its equivalent formulations must be utilized because both criteria follow directly from this postulate.
To find the value of y we need to use one the property of the parallelogram.
It is property of the parallelogram that it's diagonals bisects each other.
So,
In the given figure,
4y-7 = y + 14
3y = 21
y = 21/3
y = 7
Therefore, the value of y is 7.
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since nobody seems to be answering my last questions, does my answer look correct?
Answer: Correct, 4.4 is the answer when rounded, but to be more exact, it would be 4.420
Step-by-step explanation:
The only discrepancy is the rounding, the rest of the work is correct. It is subjective to the teacher whether the answer is sufficient or not, but you did a great job otherwise. If your teacher does want preciseness, however, I would not round to 4.5, it would be more accurate as 4.44 when setting up your equation.
Which formula decribe the following geometric equence? Remember that n repreent the term number. 2, 6, 18, 54,. An = 3 · 2 n - 1
an = 3 2( n - 1)
an = 2 3( n - 1)
an = 2 · 3 n - 1
For the given geometric progression, the nth term of the given GP is [tex]A_n=2.3^{n-1}[/tex].
Option (C) is correct.
What is the Geometric Progression?
Geometric Progression (GP) is a type of sequence in mathematics in which each succeeding term is produced by multiplying each preceding term by a fixed number known as a common ratio. This progression is also known as a pattern-following geometric sequence of numbers.
The given sequence is 2, 6, 18, 54
here the first term(a) = 2 and the common ratio(r) = 6/2 =3
Then by using the formula for the nth term of a GP, we get
[tex]A_n=ar^{n-1}\\\\A_n=2.3^{n-1}[/tex]
Hence the nth term of the given GP is [tex]A_n=2.3^{n-1}[/tex].
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the radius of a circle is increasing at a constant rate of 5 meters per second. at the instant when the radius of the circle is 1010 meters, what is the rate of change of the area? round your answer to three decimal places.
the radius of a circle is increasing at a constant rate of 5 meters per second, so the rate of change of the area is [tex]100\pi m/sec^{2}[/tex]
How is the rate of change calculated?Divide the y-value change by the x-value change to determine the rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
Suppose the radius of circle be r.
now, [tex]\frac{dr}{dt} = 5 m/sec[/tex]
And, area of circle is [tex]\pi r^{2}[/tex]
[tex]\frac{dA}{dy} = 2\pi r\frac{dr}{dt},[/tex] differentiate both sides with respect to t,
[tex]\frac{dA}{dt} |_{r=10} = 2\pi (10)(5)[/tex]
= [tex]100\pi m/sec^{2}[/tex]
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a firm has two plants(x and y) producing the same product which sells for $12 each. fixed costs are $5,000/year at plant x and $7,000/year at plant y and variable costs are $3.00/unit and $2.00/unit for x and y, respectively. the total profit at x and y are equal when the volume of each plant(units) is: group of answer choices 1,500 2,000 500 none of the above 1,000
A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
To solve the problem, first translate the given problem into equations.
The formula for profit is:
profit = revenue from sales - total cost
total cost = fixed cost + variable cost
revenue = selling price x number of units sold
Let:
x = the number of units sold in plant X
y = the number of units sold in plant Y
From the problem, we can conclude:
Profit X = profit Y
x = y
Profit X = 12x - (5000 + 3x) (equation 1)
Profit Y = 12 y - (7000 + 2y) (equation 2)
Substitute y = x into equation 2
Profit Y = 12 x - (7000 + 2x)
Hence,
12x - (5000 + 3x) = 12 x - (7000 + 2x)
3x - 2x = 7000 - 5000
x = 2,000
Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
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A sales position needs to be filled. There are two candidates available. The first candidate has 10 years of experience and can sell 10 units a week making a $3,000 profit per week for the company. He is asking for $80,000 salary. The second candidate has one year of experience and can sell eight units a week making a $2,400 profit for the company. He is asking for $45,000 salary. What candidate would make the company the most money their first year of employment?.
The candidate that would make the company the most money in their first year of employment is Candidate B
Which candidate would make more money?The amount of profit that a candidate can make for the company is:
= ( Number of weeks in year x Profit per week ) - Salary for the year
We shall assume 48 working weeks in a year.
The amount of money made by Candidate A would be:
= ( 48 x 3, 000 ) - 80, 000
= $64, 000
The amount of money made by Candidate B is:
= ( 48 x 2, 400 ) - 45, 000
= $70, 200
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A urvey of 100 tudent wa taken concerning their knowledge of foreign
language. The reult were a follow: How many tudent do NOT know any of
the three language?
30 know French
19 know German
16 know Spanih
2 know both French and Spanih
12 know both French and German
7 know both German and Spanih
8 Know all three language
There are 48 such students who did not know any of the three languages.
Given,
Since we have given that
Number of students were taken for survey n(U)= 100
Number of students who know French n(F) = 30
Number of students who know German n(G) = 19
Number of students who know Russian n(R) = 16
Number of students who know both French and Russian n(F∩ R) = 11
Number of students who know both German and French n(G ∩ F) = 12
Number of students who know both Russian and German n(R ∩ G) = 6
Number of students who know all three languages = 4
So, n(F∪G∪R)=n(F)+n(G)+n(R)-n(F∩G)-n(F∩R)-n(G∩R)+n(F∩G∩R)
n(F∪G∪R)=30+19+16-12-11-6+4
n(F∪G∪R)=52
So, the number of students who do not know any of the three languages is
[tex]n ( F ∩ G ∩ R )' = n (U) - n ( F ∩ G ∩ R )\\n ( F ∩ G ∩ R )' = 100- 52\\\\n ( F ∩ G ∩ R )' = 48[/tex]
Hence, there are 48 such students who did not know any of the three languages.
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Suppose the length of the tube used in our experiment is 4 m and a tuning fork of frequency 321 hz is used in air where the speed of sound is 342. 4 m/s? (give your answers as integers. For this question, the length of the tube is of the entire plastic cylinder, and not the adjustable length of the air column). How many resonances will be observed?.
9.028 many resonances will be observed when a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s.
Given that,
When a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s, how long is the tube utilized in our experiment, 4 m?
We have to find what many of resonances will be seen.
We know that,
The length of the tube is Lₙ=4 m
Frequency is ν = 321 hz
Speed of sound is v = 342 m/s
We know that,
ν=vλ
321=342λ
λ=321/342
λ=0.938
Now,
Lₙ=(2n+1/4)λ
4=(2n+1/4)0.938
n=8.028
We get,
N=n+1=8.028+1=9.028
Therefore, 9.028 many resonances will be observed when a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s.
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5x-4y=9
X+7=-6
Solve by substituting
Answer: x= -13
y= -18.5
When you plug these into the first equation, you will find the answer of 9.
Hope this helps.
Hoodies at Old Navy are sold at a 30% markup during the month of September. If the original price of a hoodie is $23.00, what is the amount of the markup?
By working with the given percentage, we can see that the amount of the markup is $6.90
What is the amount of the markup?
Suppose that the original price is P, and we have a markup (in percentage form) of X, then the amount of the markup is:
M = P*(X/100%)
Here we know that the original price of a hoodie is P = $23.00, while the percentage of the markup is 30%.
Then the amount of the markup in these hoodies is:
M = $23.00*(30%/100%)
M = $23.00*0.3
M = $6.90
The amount of the markup is $6.90
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What is a parent in a graph?.
The parent graph is the graph of a relatively simple function.
Graph:
Graph refers the diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we need to define the parent in a graph.
Parent function refers the simplest form of a given family of functions.
Here by transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.
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Determine the slope and y-intercept of the graph below.
Answer:
y-intercept: -3
slope: 3
Step-by-step explanation:
Slope can be found by using rise/run
The equation: y = 3x - 3
A block of mass m=2.50kg is pushed a distance d=2.20m along a frictionless, horizontal table by a constant applied force of magnitude F=16.0N directed at an angle θ=25.0 below the horizontal as shown in above figure. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block.
a.) W=31.9J
b.) Normal force=0
c.) Gravitational force = 0
We apply the definition of "work by a constant force" in the first three part and in the fourth part, we total the results. The work performed by the overall (net) force is equal to the sum of the separate forces' respective amounts of work.
Work by a constant force is defined as W=FΔrcosθ.
Work, in general, is the result of force and the displacement it produces. W = FX is the formula used to express how much work a force has produced. Here, x is the body's displacement as a result of the force F. The dot product informs us that only the force that causes displacement is taken into account when calculating the work done.
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Solve for x. Round to the nearest tenth?
Check the picture below.
[tex]\cos(63^o)=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{16}}\implies 16\cos(63^o)=x\implies 7.3\approx x[/tex]
Make sure your calculator is in Degree mode.
pope john paul ii's 1979 visit to this eastern bloc nation, his homeland, drew millions of followers and helped spark a decade-long underground movement against the communist government.
In June 1979, the Pope travelled to Poland for the second time.
The foundation of the Solidarity trade union, which was a crucial force in the overthrow of Communism in eastern Europe, was reportedly set in motion as a result of this journey, which some historians claim was the most important of all his travels.
John Paul paid visits to Warsaw, Gniezno, Kraków, Nowy Targ, Auschwitz, and Jasna Gora while in Poland. Millions of fans attended the nine-day tour.
His visit to his homeland drew millions of followers and helped spark a decade-long underground movement against the communist government.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
Using percentage to calculate the actual amount, we found out that the real percentage were off.
PercentagePercentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
In this case, we have to find 70% of the original price and see if it's true.
70% of $49.99 will be;
70 / 100 = x / 49.99
0.7 = x / 49.99
x = 49.99 * 0.7
x = 34.993
The new price is supposed to be $34.99 and not $30
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A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?
c. Approximately normal
Answer: c approximately normal
Step-by-step explanation:
because the graph states that there is 100 random sample people with the rash using the cream and this ask what best describes the shape .
What is F − 3 for the function f a )= − 2a2 − 5a 4?.
The required value of the given function f(a) = -2a^2 - 5a + 4 at a = -3 is 1
What is function?Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.
According to given data:Function, f(a) = -2a^2 - 5a + 4
To find value of f(-3),
f(a) = -2a^2 - 5a + 4
Put a = -3 in th function
F(-3) = -2(-3)^2-5×-3+4
F(-3) = -18+15+4=1
F(-3) = 1
Thus, required value of f(-3) is 1
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Coorect Question:
What is f(-3) for the function f(a) = -2a2 - 5a + 4?
The perimeter of a rectangle is 96 yards and the length is 14 yards more than the width what are the dimensions of the rectangle
Answer:
17 yards and 31 yards.
Step-by-step explanation:
Since length is 14 more than width, lets call width: w and length: w+14
So perimeter is 96 so: 2w+2(w+14)=96
2w+2w+28=96 so 4w+28=96
4w=68 and finally w=17
So 17 yards and 31 yards.
I really need help to get this done, please.
The circle is partitioned into 9 parts and arc GH is only one of the parts, therefore, the length of arc GH is a ninth of the circumference of the circle which has the radius as a factor.
The ratio of the measure of arc length GH to the radius, r, where r = n is [tex]\frac{2\cdot \pi}{9}[/tex]What is the circumference of a circle?The circumference of a circle is the perimeter of the circle which is equal to the product of twice the radius and π.
The circumference of the circle is C = 2·π·r
The circle is divided into 9 parts
The arc GH is the arc to one part of the circle
The length of the arc GH = 2·π·r/9
The ratio of the arc GH to the radius, r = n is therefore;
When r = n,
Measure of arc length [tex]\widehat{GH}[/tex] = 2·π·n/9
Ratio of [tex]\widehat{GH}[/tex] to r = n is obtained using the formula;
[tex]Ratio = \dfrac{Measure \ of \ arc\ length \ GH }{n}[/tex]
[tex]\dfrac{\dfrac{2\cdot \pi\cdot n}{9} }{n} = \dfrac{2\cdot \pi }{9}[/tex]
The ratio of the measure of arclength GH to the radius (r = n) is [tex]\dfrac{2\cdot \pi }{9}[/tex]Learn more about the measure of an arc of a circle in geometry here:
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for each group in the following list, find the order of the group and the order of each element in the group. what relation do you see between the orders of the elements of a group and the order of the group?
The relation which we see between the orders of the elements of a group and the order of the group is smallest positive power.
G = U(20), order of each element of G = ?
The smallest positive power of an element that gives you your identity is the order of the element in a group. Three instances are covered: complex numbers, a 2x2 rotation matrix, and real number elements of finite order.
G = U(20) = {1,3,7,9,11,13,17,19}
⇒ 3° ≡ 1, 3¹ ≡ 3, 3² ≡ 9, 3³ ≡ 7, 3¹ ≡ 1(20)
∴ order of 3 = 4
7⁴ ≡ 1 (mod 20) → order (7) = 4
9² ≡ 1 (mod 20) → order (9) = 2
11² ≡ 1 (mod 20) → order (11) = 2
13² ≡ 9(mod 20) → 13⁴ ≡ 81(mod 20) → 13⁴ ≡ 1 (mod 20)
⇒ order (13) = 4
order 07 = 4
17 ≡-3(mod 20) ⇒ 17² ≡ yy (mod 20)
⇒ 17⁴ ≡ 81 (mod 20) ≡ 1 (mod 20) ⇒
19 = -1 (mod 20)
19² ≡ 1 (mod 20) ⇒ order (19) = 2
Hence we get the requires answer.
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A boy is mowing a rectangular lawn 40 ft. Long and 30 ft. Wide. He has cut all of it except for a rectangle that is 20 ft. Long and 15 ft. Wide. What fractional part of the lawn remains uncut?.
The fractional part of the lawn remains uncut = 1/4.
In this question, we have been given a boy is mowing a rectangular lawn 40ft long and 30ft wide.
He has cut all of it except for a rectangle that is 20ft long and 15ft wide.
The area of the rectangular lawn:
40 x 30 = 1200 sq. ft.
And the area of the uncut part of lawn would be:
20 x 15 = 300 sq. ft.
The fractional part of the lawn that remains uncut would be,
300 / 1200 = 1/4
Therefore, 1/4 part of the lawn remains uncut.
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in order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. assume the population standard deviation is 1.2 hours.
The standard error of the mean is?
a. 7.5
b. 0.014
c. 0.160
d. 0.133
With a 0.95 probability, the margin of error is approximately?
a. 0.26
b. 1.96
c. 0.21
d. 1.64
If the sample mean is 9 hours, then the 95% confidence interval is approximately?
a. 7.04 to 110.96 hours
b. 7.36 to 10.64 hours
c. 7.80 to 10.20 hours
d. 8.74 to 9.26 hours
A sample of 81 business students over a one-week period with the population standard deviation is 1.2 hours. We calculate the following using the standard formulae:
a) Standard error of the mean is 0.13.
b) Margin of error is 0.975.
c) If the sample mean is 9 hours, then 95% confidence interval is (8.608 , 9.392).
Confidence Interval
The error introduced during the random sampling process is the sampling error described in the estimation procedure in the form of margin of error (MOE). MOE is expressed by the following formula:
MOE = CV ×SE
where,
CV = critical value of distribution
SE = standard error Solution
Note that, Population standard deviation(σ) is known. So we use z distribution.
we have given that
Sample size, n = 81
Standard deviations, σ = 1.2 h
a)
Standard error = σ /√n
=> S.E = 1.2/√81 = 1.2/9
=> S.E = 0.13
b) We have to construct 95% confidence interval.
therefore, c = 0.95
=> α= 1 - c = 1- 0.95 = 0.05
then, α/2 = 0.05/2 = 0.025 and 1- α/2 = 0.975
the probability or P-vale is 0.975 then from Z-table the corresponding z value is 1.96
The margin of error formula:
MOE = Zα/2 (σ/√n)
= 1.96 (0.13 )
= 0.2548
Margin of error = 0.2548
c) Now , confidence interval for mean(u) formula
(X-bar - E ) < μ < (X-bar + E)
=> ( 9 - 0.392) < μ < (9 + 0.392)
=> 8.608 < μ < 9.392
=>(8.608 , 9.392)
Hence, standard error is 0.13
Margin of error is 0.2548 and confidence interval is (8.608 , 9.392).
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find the dimensions of the closed rectangular box with square base and volume 8000 cubic centimeters that can be constructed with the least amount of material.
The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.
Let the length and width of the rectangular box with a square base be x.
and the height is y.
The volume, V = 8000 = [tex]x^{2} y[/tex] --------(1)
The surface area, S = 2[tex]x^{2}[/tex] + 4xy . -------(2)
S = 2[tex]x^{2}[/tex] + 4xy and 8000/ [tex]x^{2}[/tex] =y -------( from 1 and 2)
so, S= 2[tex]x^{2}[/tex] + 4x(8000/ [tex]x^{2}[/tex])
S= 2[tex]x^{2}[/tex] + 32000/x
to find the least amount of material to be used, we will differentiate the surface area w.r.t x.
ds/dx= 0 = 4x - 32000/[tex]x^{2}[/tex]
therefore, we have, 4x = 32000/[tex]x^{2}[/tex]
4[tex]x^{3}[/tex] =32000
[tex]x^{3}[/tex] =8000
x=20
Hence, The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.
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What is the numerator of the simplified sum X X 2 3x 2?.
The simplified numerator of the sum is 4x + 6
Given,
We have the following expression for this situation:
x / (x² + 3x + 2) + 3/(x + 1)
And here's where we can start:
x(x + 1) + 3(x² + 3x + 2) / (x² + 3x + 2) (x + 1)
We may now factor the terms x² + 3x + 2 = (x + 1) (x + 2) on the denominator and distribute the terms on the numerator to get:
x² + x + 3x² + 9x + 6 / (x + 2) (x + 1)²
4x² + 10x + 6 / (x + 2) (x + 1)²
Now, the numerator can be factored as follows:
4x² + 10x + 6 = (2x + 2) (2x + 3)
And if we substituted that, we got:
(2x + 2) (2x + 3) / (x + 2) (x + 1)²
We can now apply common factor 2 to the numerator as follows:
2(x + 1) (2x + 3) / (x + 2) (x + 1)²
Additionally, the x+1 can be cancelled on the numerator and denominator as follows:
2(2x + 3) / (x + 2) (x + 1) = 4x + 6/ (x + 2) (x + 1)
Therefore,
The simplified numerator of the sum is 4x + 6
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there are 200 sixth-graders in a school. 170 of them want to take geometry, 175 of them want to take algebra, what is the least number of 6th graders who want to take part in both classes?
The least number of 6th graders who want to take part in both classes is 145.
The intersection of sets A and B is the set of all the elements which are common to both A and B. The intersection of sets is denoted by the symbol '∩'. Hence, we can write the intersection of A and B as A ∩ B.
The number of graders that want to take geometry is 170.
The number of graders that want to take algebra is 175.
A ∩ G= n(A) + n(G) -( AUB)
=175+170-200
= 345-200
= 145
Therefore, the least number of 6th graders who want to take part in both classes is 145.
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consider the random experiment to tossing two fair coins. what is the total number of outcomes of the random experiment?
Using Random Experiment of tossing two coin ,
the total number of outcomes of the random experiment is 4 .
Random Experiments:
Specifically, random experiments are the process of observing uncertainties. After the experiment, you will know the result of the random experiment. The results are the results of random experiments.
Sample Space: The set of all possible outcomes is called the sample space. Therefore, in the context of random experiments, the sample space is our universal set.
Random Experiment: Flip a Coin
Sample space , S={Head, Tail} or usually written as {H,T}.
When you repeat a random experiment several times, each is called a trial.
In the coin toss example, each trial is either heads or tails.
we have given a random experiment of tossing two fair coins then,
sample space, S = {HH, HT, TH, TT} = 4
So, the total number of randomized experiment outcomes is 4.
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What defines the symbols used in architectural plans?.
The legend defines architectural symbols and notations used in the plans.
Floor plan symbols make up their own language, just as construction workers have their own vocabulary that they use to communicate when working on projects as it’s essential for architects, designers and builders to understand this language, a floor plan includes an important element called a legend, which acts as a key that helps viewers interpret the drawing.
Therefore, the The legend defines architectural symbols and notations on the plan. Many standard symbols usually appear there for specific projects. However, there can be variations in how symbols look and what they represent, which makes consulting the legend for each project is essential.
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Someone help me please
The required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
a]
1 cm = 200 km,
Distance between A and B = 2.4 cm = 2.4 [200 km]
= 480 km
b]
Jafar drove for (A to B) = 480 km
Kenzi drove for B to C = 2.7 [200] = 540 km
Difference = 540 - 480 = 60km
Thus, the required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.
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