Let V be an inner product space, S and S0 be subsets of V, and W be a finite-dimensional subspace of V. To prove the other side,
1 ) Suppose (e1,…,en) is basis for W. Suppose x∈(W⊥)⊥. Consider the projection w of x onto W, specifically:
w=⟨x,e1⟩e1+…+⟨x,en⟩en∈W.
Then, x−w is perpendicular to each ei, since
⟨x−w,ei⟩=⟨x,ei⟩−∑j=1n⟨⟨x,ej⟩ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩⟨ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩δij=⟨x,ei⟩−⟨x,ei⟩=0.
Since the linear map ⟨⋅,x−w⟩ is constantly 0 on the basis of W, it is constantly zero on all of W, hence x−w∈W⊥.
But then, since x∈(W⊥)⊥, we have ⟨x−w,x⟩=0, and since ⟨x−w,w⟩=0,
∥x−w∥2=⟨x,x−w⟩−⟨w,x−w⟩=0,
i.e. x=w∈W, completing the proof.
2 ) Suppose that w∈(W⊥)⊥
then ⟨w,x⟩=0
for all x∈W⊥
If w∉W, then w=v+v′ where v∈W and v′∈W⊥∖{0}.
Then.
0=⟨w,x⟩=⟨v,x⟩+⟨v′,x⟩=⟨v′,x⟩
for all x∈W⊥.
However, v′∈W⊥ and ⟨v′,v′⟩≠0 so it is a contradiction.
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please help me with this question
Answer:
see explanation
Step-by-step explanation:
the equation for direct variation is
y = kx ← k is the constant of variation
divide both sides by x , then
k = [tex]\frac{y}{x}[/tex]
calculate k for each ordered pair from the table
k = [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]
k = [tex]\frac{1}{-2}[/tex] = - [tex]\frac{1}{2}[/tex]
k = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]
since k is constant for all ordered pairs
then the table shows a direct variation with equation
y = - [tex]\frac{1}{2}[/tex] x
---------------------------------------------------------------------------------
similarly for the second table
k = [tex]\frac{5}{2}[/tex]
k = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]
k = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex]
since k is not constant for all ordered pairs then NOT direct variation
Fill in the table using this function rule y = 4 + 5x
The missing values of y are 19, 29, 34, and 49.
What are the values of y in the table?
The values of y missing in the table is determined by substituting the value of x into the given linear equation.
y = 4 + 5x
when x = 3, the value of y is calculated as;
y = 4 + 5 (3) = 19
when x = 5, the value of y is calculated as;
y = 4 + 5 (5) = 29
when x = 6, the value of y is calculated as;
y = 4 + 5 (6) = 34
when x = 9, the value of y is calculated as;
y = 4 + 5 (9) = 49
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2.
Ghana Railways Co-operation has 20 trains for its operation. It is observed that x trains can
accommodate 2 passengers, y trains 3 passengers and trains 5 passengers. However, the total
number of passengers always present at Ghana Railways is 64. During market day, 3 of x trains, 2
of y trains and 4 of z trains for a total of 10 trains were used. Determine the values of x, y and z.
The value of x, y, and z for the train and number of passengers are 0, -32, and 32 respectively.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The total number of trains are 20. This is represented as:
x + y + z = 0
The accommodation of passengers is represented as:
2x + 3y + 5z = 64......(2)
During market day the train used is:
3x + 2y + 4z = 64.......(3)
Multiply the equation 2 with 3 and equation 3 with 2:
6x + 9y + 15z = 192
6x + 4y + 8z = 128
Subtract the two equations:
5y + 7z = 64..........(4)
Multiply the first equation by 2:
2x + 2y + 2z = 0
2x + 3y + 5z = 64.
Subtract the two equations:
-y - 3z = -64
y + 3z = 64..........(5)
Multiply the equation 5 by 5.
5y + 15z = 320
5y + 7z = 64
Subtract the two equations:
8z = 256
z = 32
Substitute the value of z in equation 5:
y + 3z = 64.
y + 3(32) = 64
y + 96 = 64
y = - 32
Using equation 1:
x + y + z = 0
x - 32 + 32 = 0
x = 0
Hence, the value of x, y, and z are 0, -32, and 32 respectively.
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Which of the following statements are equivalent to the statement "price increased by 1/2 of what it was before"?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2/3% of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Answer:
(B) The price is 150% of the price before
(E) The price is now 1.5 of what it was before
Step-by-step explanation:
You want to identify statements equivalent to "price increased by 1/2 of what it was before".
New priceFor some initial price of p, the new price is ...
p + 1/2p . . . . price increased by 1/2 of what it was before
This can be simplified to ...
p(1 +1/2) = p(1.50) . . . . price is now 1.5 of what it was
Expressed as a percentage, the multiplier is ...
p(1.50 × 100%) = p(150%) . . . . price is 150% of the price before
The correct choices are ...
(B) The price is 150% of the price before
(E) The price is now 1.5 of what it was before
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what is the scale factor from XPZ to TPR.
A. 3/4
b. 4/3
c. 24
d. 15
As the ratio of the lengths of the altitudes in related triangles, the altitude PS is 15 in length and represents the scale factor from XPZ to TPR.
what is scale factor ?The ratio of just an object's main sample to that of its new, smaller representation is described as the exponent (bigger or smaller). For example, to make a rectangle with sides proportional 2 cm and 4 cm longer, scale each side by a specific integer, therefore in case 2. If the original and new dimensions are determined, it is possible to calculate the scaling factor. The following straightforward formula can be used to find a figure's scale factor: Scale factor is equal to the new shape's size divided by the previous structure's diameter. Think about two quantities that are the same except for their size.
given
Find the scaling factor going from XPZ to TPR first.
TR/XZ = (6 + 6)/(8 + 8) =12/16 =3/4
You can write the following percentage because the scale factor is equal to the ratio of the lengths of the altitudes in related triangles.
PS/PY =3/4
Write the ratio.
PS/20 =3/4
For PY, substitute 20.
PS = 15/ 20 times per side, then simplify.
As the ratio of the lengths of the altitudes in related triangles, the altitude PS is 15 in length and represents the scale factor from XPZ to TPR.
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Constant Rate of Change: 2/3
Initial Value:10
The linear relation of the given Rate of Change and Initial Value is y = 2/3x + 10
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Note that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
We are given the parameters as;
Constant Rate of Change: 2/3
Initial Value:10
Since we know that linear relation between x and y is y = m x + b, where
m is the rate of change
b is the initial value
Therefore,
y = 2/3x + 10
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In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. (2x - y) + (2y - x)y' = 0, y(1) = 3
The initial value problem (2x - y) + (2y - x)y' = 0, y(1) = 3 has the particular solution y = -x²/2 + 2x + 1/2, and is valid for all x except for x = 2y.
An initial value problem is a differential equation that is given with an initial condition, which is a specific value for the solution of the equation at a particular point.
Problem 9 and 10 involve solving the same initial value problem: (2x - y) + (2y - x)y' = 0, y(1) = 3. To solve this initial value problem, we must find the general solution to the differential equation and then use the initial condition to determine the particular solution.
First, we must find the general solution to the differential equation (2x - y) + (2y - x)y' = 0. We can rearrange the equation to get (2y - x)y' + (2x - y) = 0. This is a separable differential equation, so we can separate the variables and integrate both sides to get:
y' = -(2x - y)/(2y - x)
∫(y')dy = -∫(2x - y)/(2y - x)dx
y = -x²/2 + 2x + C
Where C is an arbitrary constant of integration. To find the particular solution, we can use the initial condition y(1) = 3. We can substitute this into the general solution to find the value of C:
3 = -1/2 + 2 + C
C = 3 + 1/2 - 2 = 1/2
So the particular solution is y = -x²/2 + 2x + 1/2. This solution is valid for all values of x such that 2y - x ≠ 0, which means that the solution cannot be evaluated for x = 2y. This is because the denominator in the differential equation would be zero, which would make the equation undefined.
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During Valentine's week, more people buy boxes of chocolates than in a normal week and chocolatiers offer their chocolates in special red boxes which cost more to produce than the everyday box.
The graph shows the market for chocolates during a normal week.
Draw a curve to show the effect when people buy more boxes of chocolates during Valentine's week. Label it 1.
Draw a curve to show the effect of chocolatiers offering their chocolates in special red boxes. Label it 2.
Draw a point to show the new equilibrium price and new equilibrium quantity.
The only price at which consumer and producer plans are in agreement is the equilibrium price, which is reached when the quantities of a good that consumers want to buy and a good that producers want to sell are equal.
What is the difference between equilibrium price and new equilibrium quantity?The equilibrium price, which is obtained when the quantity of a good that consumers want to buy (quantity requested) and the quantity of a good that producers want to sell (quantity provided) are equal, is the only price at which consumer and producer plans are in sync. This common quantity is referred to as the "equilibrium quantity".
If supply and demand are balanced in an economy, the equilibrium price will be reached. Thus, the manufacturer can create the same quantity of a good (supply) that consumers can purchase at this price (demand). As a result, supply and demand are met. Additionally, at this time, both buyers and sellers win. In addition, the equilibrium price contrasts with the idea of disequilibrium, in which supply and demand are not equal.
Supply and demand for a good are in equilibrium when the quantity is the same. In order to create economic equilibrium and equilibrium quantity, the supply and demand curves finally cross. This is hypothetically the most effective state the market can achieve and the state to which it naturally tends.
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A survey asks customers in a clothing store catering to teenagers the following question: Should the mall prohibit loud and annoying rock music in the food court?
The mall should not prohibit loud and annoying rock music in the food court.
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.
Given that surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock
The survryed was on 850 teenagers
Therefore, Number of teenage that evade light hard rock = 32% of 850
=32/100 x850
=272
Hence, we can conclude that the mall should not prohibit loud and annoying rock music in the food court.
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find the slope of the tangent line to the curve y at x. then write the equation of this tangent line. question content area bottom part 1 the slope of the line tangent to the curve y at x is 36. part 2 the equation of the line tangent to the curve y at x is y minus y equals 36 (x minus 3 ).
the equation of the line tangent to the curve y at x = 3 is y = 36x - 102. The slope of the tangent line to the curve y at x = 3 is 36.
The equation of the line tangent to the curve y at x = 3 can be written using the point-slope form of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and m and (x1, y1) are known. In this case, m = 36 and (x1, y1) = (3, y). Substituting these values into the equation above, we get:
y - y = 36(x - 3)
y = 36x - 102
So the equation of the line tangent to the curve y at x = 3 is
y = 36x - 102.
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A phone company charges each customer a monthly fee of $11.25. In addition, it charges $0.05 per minute for in-state calls and $0.13 per minute for out-of-
state calls. What is the total monthly charge for a customer who made 300 minutes of in-state calls and 50 minutes of out-of-state calls?
Please help me with both I’ll mark your answer brainly
1. line parallel to given line is: y = 5/3 x + 2
2.
parallel line becomes: y = 1/2x - 6
perpendicular line becomes: y = - 2x + 14
What is slope intercept form?Slope intercept form is a method of formulating an equation for a line in the form y = mx + b in mathematics. The b stands in for the line's y-intercept, while the m denotes the line's slope. In order to identify a point on a line or to solve for y given an input of x, the slope intercept form is utilised. A straight line's slope and the location of its y-axis intersection are utilized to get the general equation of the line using the slope intercept equation. y = mx + b is the formula for the slope intercept.
1.
3y - 5x = 15
or, 3y = 5x + 15
or, y = 5/3 x + 5
This is slope intercept form of line.
Thus, slope (m) = 5/3
Parallel lines have same slope. Thus, all lines having slope m = 5/3 will be parallel to each other.
Thus, example of line parallel to given line is: y = 5/3 x + 2
2.
for parallel line:
Given that,
y = 1/2x - 4
The slope intercept form of line is: y = mx + b
goes through the point (8, -2)
now comparing these two equations we get:
y = 1/2x + b
or, -2 = 1/2 (8) + b
or, b = - 6
thus, parallel line becomes: y = 1/2x - 6
for perpendicular line:
y = 1/2x - 4
as we know, m₁ = - 1/m₂
so, slope becomes: - 2
Thus, y = mx + b
after putting the point (8, -2) we get the value of b:
-2 = -2 (8) + b
or, b = 14
Thus, perpendicular line becomes: y = - 2x + 14
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The art club is designing a rectangular mural for the school hallway. Three
corners are located at (21,21),(21, 1), and (4.1) on a coordinate plane. Find the
fourth vertex and graph the rectangle on the coordinate plane below.
Fourth vertex:
The 4th vertex of the rectangle is given by D ( 4 , -1 ) and the graph is plotted
What is the area of a rectangle?The product of the rectangle's length and its breadth determines the area of the rectangle.
Rectangle area equals length times width
Given data ,
Let the area of the rectangle be represented as S
Let the rectangle be represented as ABCD
The coordinates of A = A ( -1 , -1 )
The coordinates of B + B ( -1 , 1 )
The coordinates of C = C ( 4 , 1 )
So , the length of the rectangle = 4 units
The width of the rectangle = 2 units
So , the area of the rectangle S = 4 x 2 = 8 units
And , the 4th vertex of rectangle D = D ( 4 , -1 )
Hence , the coordinate D of rectangle is D ( 4, -1 )
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davey read 58 pages on saturday and p pages on
The value of p is 15
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Davey reads 58 pages on Saturday and on rest of the days p pages per day
Therefore everyday he reads 58+p pages per day
If he reads for 10 days and he reads a total 1408 pages then we have
In a week there is one Saturday
thus
9p+58=1408
9p=1350
p=15
Thus on the other days p is equal to 15 pages per day.
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The complete question is Davey reads 58 pages on Saturday and p pages on other days and on a span of 10 days he reads 1408 pages. Find the value of p.
Graph 7/3≥z on a number line
Answer:
See below
Step-by-step explanation:
Each pair of numbers determines by what percentage the second is greater than the first and by what percentage the first number is less than the second.
100 and 110
The percentage of the second is greater than the first and the first number is less than the second will be 10% and 9.09%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolised by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Each pair of numbers determines by what percentage the second is greater than the first. Then we have
P = [(110 - 100) / 100] x 100
P = (10/100) x 100
P = 0.10 x 100
P = 10%
The percentage of the first number is less than the second is given as,
P = [(110 - 100) / 110] x 100
P = (10 / 110) x 100
P = 0.0909 x 100
P = 9.09%
The percentage of the second is greater than the first and the first number is less than the second will be 10% and 9.09%.
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what is 1 over 3 of 3 eights?
Answer:
Step-by-step explanation:
To solve the problem, we start by labeling 1/3 of 3/8 like this:
N1/D1 of N2/D2
Then we use this fraction of a fraction formula to solve the problem:
(N1 x N2) / (D1 x D2)
When we enter 1/3 of 3/8 into the formula, we get:
(1 x 3) / (3 x 8) = 3/24
Therefore, the answer to 1/3 of 3/8 in its lowest form is:
1/3 of 3/8 = 1/8
So, use ___ as a factor _____ times to find the value of (−3)^4
Answer:
Use -3 as a factor 4 times to find the value of (-3)^4. The answer is 81
Step-by-step explanation:
To solve (−3)^4, use -3 as a factor four times. This can be done by multiplying -3 by itself four times: (-3)(-3)(-3)(-3) = 81. Alternatively, you can use the square root property to find the value of (−3)^4. The square root property states that if a number is multiplied by itself two times, then the square root of that number is equal to one of the numbers used in the multiplication. In this case, the square root of 81 is -3, which is equal to one of the numbers used in the multiplication. Therefore, (−3)^4 = 81.
Gordon borrowed $600 from the bank. Gordon’s interest is $14.25 for 90 days. What rate of interest did Gordon pay using the ordinary interest method?
The rate of interest that Gordon paid using the ordinary interest method is 9.63%.
What is the ordinary interest method?The ordinary interest method is based on 360 days instead of 365 days.
The rate of interest based on the ordinary interest method uses the same formula as the rate of interest based on the 365 days calendar method.
Principal amount of loan = $600
Interest for 90 days = $14.25
Rate of interest = R
R = (Interest x 100)/(Principal x Time)
= $14.25 x 100 x 360/($600 x 90
= $513,000/$54,000
= 9.5%
Thus, the rate of interest paid by Gordon for borrowing $600 from the bank and paying $14.25 for 90 days is 9.5%.
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let's say we are selecting a piece of fruit from a bowl.
Let's say there are 8 peaches and 6 other pieces of fruit.
What is the probability of selecting a peach?
What is the probability of not selecting a peach?
What is the total of these two probabilities, and why?
What is the probability of selecting a plum?
What is the total of these two probabilities, and why?
Answer:
The probability of selecting a peach is 8/14, or approximately 0.57.
The probability of not selecting a peach is 6/14, or approximately 0.43.
The total of these two probabilities is 1, because any given selection must either be a peach or not a peach.
The probability of selecting a plum cannot be determined because the number of plums in the bowl is not specified.
The sum of the probabilities of selecting a peach and a plum cannot be determined for the same reason as in 4.
Step-by-step explanation:
Work out the percentage change when a price of £40 is increased to £70.
give simple working out :)
Answer:
To calculate the percentage change when a price of £40 is increased to £70, we can use the following formula:
Percentage Change = (New Value - Old Value) / Old Value * 100
Plugging in the numbers:
Percentage Change = (£70 - £40) / £40 * 100 = £30 / £40 * 100 = 75%
So the price has increased by 75%.
Erica is making plans to build a fence on her property line. She uses the map shown. Find the m<1
Check the picture below.
now, we're assuming the street is a straight line and the line above the 100° is also another straight line, so hmmm the shaded polygon is really a 6-sided polygon, a hexagon.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\\\ 142+72+148+130+80+\measuredangle 1=720\implies 572+\measuredangle 1=720\implies \boxed{\measuredangle 1=148}[/tex]
Suppose That The Fifty States Are The Observational Units (Subjects) Of Interest. Identify Which Of The Following Are Legitimate Variables (V) And Which Are Not (N). a. The Number Of States That
b. the percentage of the state's residents over 65 years of age
c. the highest speed limit in the state
d. whether or not the state's name consists of the one word
The different scenarios given in the question are categorized as legitimate variables or not as given below.
What is a variable?
A variable is a symbol used to denote a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable. A variable is a letter that stands in for an unknown; it always represents a number but can take on several meanings when used in an expression.
a) Numer of states that have a female governor has only one value and it cannot be varied. So it is not a legitimate variable(N).
b) The percentage of state's residents over 65 years of age is a legitimate variable (L) because the number will vary for different states.
c) The highest speed limit in the state is a legitimate variable(L) as the limits are different for different states.
d) Whether or not the state's name consists of one word is a legitimate variable(L) as it varies for different states.
Therefore the different scenarios are categorized as legitimate variables or not.
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Also when you answer it can you show work please and Thank you
Answer: 21.98
Step-by-step explanation:
The formula for circumference is r times 2 times pi
so, the circumference is
7x3.14=21.98
Between which two whole numbers does the product of 6 and 4 1/12
lies?
By multiplication, we know that the product of the numbers 6 and 4 1/12 comes between the whole numbers 24 and 25 respectively.
What do we mean by multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication.
Multiply in mathematics refers to the continual addition of sets of identical sizes.
One of the fundamental mathematical processes is multiplication.
The result of multiplying two or more numbers together is known as the product.
So, we have:
6 * 4 1/12
6 * 48+1/12
6 * 49/12
49/2
24.5
Which is: 24 < 24.5 < 25
Therefore, by multiplication, we know that the product of the numbers 6 and 4 1/12 comes between the whole numbers 124 and 25 respectively.
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W - 0.2 = 0.8
What helps solve the equation
what does W mean
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{w - 0.2 = 0.8}\\\\\large\text{ADD 0.2 to both sides:}\\\\\mathsf{w - 0.2 + 0.2 = 0.8 + 0.2}\\\\\large\text{SIMPLIFY it:}\\\\\mathsf{w = 0.8 + 0.2}\\\\\mathsf{w = 1}\\\\\\\\\huge\text{Therefore, your answer should be:}\\\\\huge\boxed{\mathsf{w = 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Answer:
[tex] \sf \: W = 1 [/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of W.
The equation is,
→ W - 0.2 = 0.8
Then the value of W will be,
→ W - 0.2 = 0.8
→ W = 0.8 + 0.2
→ [ W = 1 ]
Hence, the value of W is 1.
What would the acceleration need to for a 5kg hammer to create a force of 10N?
How do I solve this problem?
The acceleration needs to for a 5kg hammer to create a force of 10N is 2 m / s².
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
Given that the weight is 5 kg and the force applied is 10N. The acceleration will be calculated as below,
Force = Mass x Acceleration
Acceleration = Force / Mass
Acceleration = 10 / 5
Acceleration = 2 m/ s²
Therefore, the acceleration will be 2 m/ s².
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Fernando lives in a house that is 8 meters below sea level. Fernando goes to school every day, which is 2 meters above sea level. How many meters does Fernando travel, in altitude, when going from home to school?
When going from home to school, Fernando travel 10 meters.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
Fernando lives in a house that is 8 meters below sea level.
Fernando goes to school every day, which is 2 meters above sea level.
The total distance from home to school,
= 8 + 2
= 10 meters.
Therefore, the distance is 10 meters.
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suppose a math class contains 25 students, 14 females (7 of whom speak french) and 11 males (4 of whom speak french). compute the probability that a randomly selected student is male, given that the student speaks french. round your answer three decimal places (if necessary)
The probability that a randomly selected student is male, given that the student speaks french is 0.3636.
Total number of student in a maths class is 25.
Out of those 25 students 14 are females.
And the remaining student 11 are male
The number of students who can speak French are from female side 7 and from male side is 4
So total number of students who can speak french is 11
Using the probability formula,
P = favorable outcome/Total
Probability that a randomly selected student is male, given that the student speaks french is,
P = 4 / 11
P = 0.3636
Therefore, The probability that a randomly selected student is male, given that the student speaks french is 0.3636.
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Triangles ABC and DEF are similar triangles. Use this fact to solve the exercise. Round to the nearest tenth. Find side DE. Let J = 3, K = 4, and L = 12
The value of side DE is 9 units
How to determine the value of side DEFrom the question, we have the following parameters that can be used in our computation:
ABC~ ADEF.
So, we have the following equoialent ratio
J : K = DE : L
Substitute the known values in the above equation, so, we have the following representation
3 : 4 = DE :12
Express as fraction
So, we have
DE/12 = 3/4
Make DE the subject
DE = 12 * 3/4
Evaluate the expression
DE = 9
Hence, the value is 9
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