Answer: 17.5 miles
Step-by-step explanation:
P=price, L=length
Firm A:
P=2L+10
Firm B:
P=2.40L+3
2.40L+3=2L+10
L=17.5
The fare would be the same for 17.5 miles for both firms.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have, 20=5x+k. . . (1)
30=10x+k. . . .(2)
solving these two equations we get x=2 and k = 10
Now let the length of the journey that both firm charge the same is equal to L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get
2L+10=2.40L+3
0.40L=7
L=17.5
Hence, The fare would be the same for 17.5 miles for both firms.
Learn more about linear equations here:
https://brainly.com/question/29739212
#SPJ2
Which of the following statements is not true concerning the equation x^2 - c = 0 for c > 0
A. A quadratic system in this form can always be solved by factoring.
B. This equation is not considered to be a quadratic equation because it is not in the form ax^2 + bx + c = 0
C. The left-hand side of this equation is called a difference of two squares
D. A quadratic equation in this form can always be solved using the square root property.
Which of the following steps would not be necessary when using the square root property to solve a quadratic equation?
A. After applying the square root property, solve the resulting equations.
B. Isolate the quantity being squared
C. The square root property may be applied only if the constant is positive
D. When taking the square root of both sides, use plus-minus on the square root of the constant.
Which of the following steps can be performed can be performed so that the square root property may easily be applied to 2x^2 = 16?
A. The square root property requires a quantity squared by itself on one side of the equation. The only quantity is squared by 16, so divide both sides by 2 before applying the square root property
B. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is X, so divide both sides by 16 before applying the square root property
C. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is X, so divide both sides by 2 before applying the square root property
Answer:
The correct option are;
1) D. A quadratic equation of this form can always be solved using the square root property
2) B. Isolate the quantity being squared
3) C. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is X so divide both sides by 2 before applying the square root property
Step-by-step explanation:
Where the quadratic equation is of the form x² = b, the square root property method can be used to solve the equation. Due to the nature of square roots, putting a plus-minus before the square root of the constant on the right hand side of the equation after taking the square roots of both sides of the equation, two answers are produced.
It is however to first isolate the term with the squared variable, after which the square root of both sides of the equation is taken.
If g(x) = (-2x²) - 3. Find g(0).
Answer:
-3
Step-by-step explanation:
When g(0), it means that x=0.
So, if we use 0 instead of x, the answer becomes:
-3
Answer:
-3
Step-by-step explanation:
g(0) = (-2(0)^2) -3
as anything multiplied with 0 is 0,
g(0) = 0 - 3
= - 3
X(X + 8) = 9
Algebra 2
Answer:
x = -9, 1
Step-by-step explanation:
x (x + 8 )= 9
x^2 + 8x = 9
x^2 + 8x - 9 = 0
(x + 9)(x - 1) = 0
x = -9, 1
Hope this helps!
Answer:
x = 3 and x = 0
Step-by-step explanation:
A way to solve is simplifying the given equation:
X^2 + 8x = 9
So
x = 3 and x = 0
3^2 + 8(0) = 9
9 + 0 = 9
9 = 9
A ship travels a distance of 700 km. On the return trip it averages 10km/hr faster and 8 hours less, tp travel the 700km back. Determine how long the original part of the trip took in hours
Answer:
The total duration of the trip is 48 hours.
Step-by-step explanation:
Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:
[tex]v =\frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
[tex]v[/tex] - Speed, measured in kilometers per hour.
Now, each stage is represented by the following expressions:
Outbound trip
[tex]v = \frac{700\,km}{\Delta t}[/tex]
Return trip
[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]
By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:
[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]
[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]
[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]
[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]
This equation can be solved by means of the Quadratic Formula, whose roots are presented below:
[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]
Only the first roots offers a physically resonable solution. Then, total duration of the trip is:
[tex]t_{T} = 28\,h +20\,h[/tex]
[tex]t_{T} = 48\,h[/tex]
The total duration of the trip is 48 hours.
BELL RINGER #2
A consultant charges $45 for each hour she works on a consultation, plus a flat $30
consulting fee. How many hours of work are included in a $210 bill for a consultation?
A. 2 4/5
B. 4
c. 4 2/3
D. 5 1 / 2
E. 7
Answer:
A. 2 4/5
Step-by-step explanation:
To find how many hours she worked for $210, you must get the amount of money she gets in 1 hour.
Because she charges $43 dollars every hour, and fines a fee of $30 flat, we must add both of the amount to get how many she earns in 1 hour.
So:
$45 + $30= $75
She earn $75 in 1 hour.
Next, divide $210 dollars that she earned for working for hour(s) to the amount of money she earned in 1 hour to find how many hours she worked.
So:
$210 ÷ $75= 2.8 hours
The answer is 2.8 hours
Because the given answers is in fraction, we must change the decimal into a fraction.
To change a decimal into a fraction, you must place the decimal over its place value.
Because 8 in the decimal 2.8 is in the tenths place, you must place it over 10
So:
2.8 into a decimal is 2 8/10
Simplify (only simplify if possible):
Divide 8 and 10 to their GCF which is 2.
So:
8 ÷ 2= 4
10 ÷ 2= 5
So the fraction and the answer is now:
2 4/5
I hope this helps! I'm sorry if it's wrong and too complicated.
68) Volume of a Bucket: Determine the volume of a cylindrical bucket in cubic inches if the bucket's radius is 5 in.
and the height is 12 in. The formula for the volume of a cylinder is V = yrah. Use the Te key on your calculator.
Answer:
V = 300[tex]\pi[/tex] in³ or 942.48 in³
Step-by-step explanation:
Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.
Plug in the values and solve:
V = [tex]\pi[/tex](5²)(12)
V = 300[tex]\pi[/tex] in³ or 942.48 in³
In the expression 3x^2+y+-5 which of the following choices is the exponent in the term 3x^2?
A. 3
B. 2
C. X
D. None of these choices
Answer:
2
Step-by-step explanation:
3x^2
The coefficient is 3
The variable is x
The exponent is 2
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
-7.5 and 5.4
Answer:
Step-by-step explanation:
m
What is the distance, in units, between the points [tex](2, -6)[/tex]and (-4, 3)? Express your answer in simplest radical form.
Answer: [tex]3\sqrt{13}[/tex]
Step-by-step explanation:
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(-4-2\right)^2+\left(3-\left(-6\right)\right)^2}[/tex]
[tex]=3\sqrt{13}[/tex]
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Answer:
octagonal: 8 faces, 16 edges, 9 verticestriangular pyramid: 3 faces, 6 edges, 4 verticestriangular prism: 3 faces, 9 edges, 6 verticesStep-by-step explanation:
A pyramid has twice as many edges as faces, and 1 more vertex than faces.
Octa- means 8.
Tri- means 3.
a) An octagonal pyramid has 8 faces, 16 edges, and 9 vertices.
b) A triangular pyramid has 3 faces, 6 edges, and 4 vertices.
__
A triangular prism will have 3 additional edges for the second "base", and 2 additional vertices.
c) A triangular prism has 3 faces, 9 edges, and 6 vertices.
__
Additional comments
We have not counted the base as a "face." We have only counted those that meet at the point of the pyramid.
There are as many vertices on the base as there are faces, and there is one more vertex where all the faces meet.
There is one edge at the base for each face, and there is one edge from the base vertex to the point of the pyramid for each face--a total of two edges per face.
__
A triangular pyramid is shown in the attachment.
sam ran 63,756 feet in 70 minutes what is sams rate in miles per hour? (there are 5,280 feet in one mile)
Divide total feet by feet in a mile:
63,756/5280 = 12.075 miles
Divide 70 minutes by 60 minutes per hour:
70/60 = 1.166666 hours( round to 1.17)
Miles per hour = total miles/ total hours:
12.075/1.17 = 10.32 miles per hour
Need Help Trigonometry
Answer:
tan(<G) = [tex] \frac{HI}{GI} [/tex]
Step-by-step explanation:
Given:
Right triangle ∆GHI,
Required:
Equivalent of tan(<G)
SOLUTION:
Recall the acronym for trigonometric ratios of angles in a right triangle: SOHCAHTOA.
Thus, the TOA in the acronym above stands for:
Tan(θ) = side opposite to θ ÷ side adjacent to θ
Where,
θ is the angle of interest = <G
Opposite side = HI
Adjacent side = GI
The equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]
Find the vertex of the parabola.
f (x) = x squared minus 6 x + 13
a.
( 4, 0)
c.
( 3, 4)
b.
(0, 3)
d.
( 4, 3)
Answer:
The vertex is (3,4)
Step-by-step explanation:
f (x) = x^2 - 6 x + 13
Completing the square
-6/2 = -3 and squaring it = 9
= x^2 -6x +9 +4
= ( x-3) ^2 +4
The equation is now in vertex form
a( x-h) ^2 +k
where the vertex is ( h,k)
The vertex is (3,4)
Answer:
C on edge
Step-by-step explanation:
What is the rate of change of the function? On a coordinate plane, a line with negative slope goes through points (0, 1) and (1, negative 1). –2 Negative one-half One-half 2 Mark this and return
Answer:
-2
Step-by-step explanation:
slope: (y² - y¹) / (x² - x¹)
(-1 - 1) / (1 - 0) = -2 / 1 = -2
y = -2x + b
plug in an (x, y) value to find b
1 = -2(0) + b
1 = -2 + b
b = 3
y = -2x + 3
rate of change is -2
Answer:
-2
Step-by-step explanation:
What is the solution to this system of equations? x+3y−z=6 4x−2y+2z=−10 6x+z=−12 (−4, 0, 12) (0, −2, −12) (2, 1, −3) (−3, 5, 6)
Answer:
Solution : (− 3, 5, 6)
Step-by-step explanation:
We have the following system of equations that we have to solve for,
[tex]\begin{bmatrix}x+3y-z=6\\ 4x-2y+2z=-10\\ 6x+z=-12\end{bmatrix}[/tex]
To solve this problem we can start by writing the matrix with their respective coefficients --- (1)
[tex]\begin{bmatrix}1&3&-1&|&6\\ 4&-2&2&|&-10\\ 6&0&1&|&-12\end{bmatrix}[/tex]
Now we can reduce this to row echelon form, receiving our solution --- (2)
[tex]\begin{pmatrix}1&3&-1&6\\ 4&-2&2&-10\\ 6&0&1&-12\end{pmatrix}[/tex] Swap row 1 and 3,
[tex]\begin{pmatrix}6&0&1&-12\\ 4&-2&2&-10\\ 1&3&-1&6\end{pmatrix}[/tex] Cancel leading coefficient in row 3,
[tex]\begin{pmatrix}6&0&1&-12\\ 0&-2&\frac{4}{3}&-2\\ 0&3&-\frac{7}{6}&8\end{pmatrix}[/tex] Swap row 2 and 3
[tex]\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&-2&\frac{4}{3}&-2\end{pmatrix}[/tex] Cancel leading coefficient in row 3
[tex]\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&0&\frac{5}{9}&\frac{10}{3}\end{pmatrix}[/tex]
At this point you can see that we have to cancel the leading coefficient in each row, to row echelon form. Continuing this pattern we have the following matrix,
[tex]\begin{bmatrix}1&0&0&|&-3\\ 0&1&0&|&5\\ 0&0&1&|&6\end{bmatrix}[/tex]
As you can see, x = - 3, y = 5, and z = 6, giving us a solution of (− 3, 5, 6). This is the fourth option.
Which of the following best represents the average rate at which the human hair grows (1 point)
a
0.25 inches per second
b
0.25 meters per hour
с
0.25 meter per month
d
0.25 inches per month
Answer:
D.0.25 inches per months
Step-by-step explanation:
The average rate or speed of human hair growth is about 0.25inches per month.
(a²b²-c²)(a²b²+c²)
simplify
Answer:
a⁴b⁴ - c⁴
Step-by-step explanation:
The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.
Answer:
a^4b^4 - c^4.
Step-by-step explanation:
(a²b²-c²)(a²b²+c²)
Difference of 2 squares:
= (a²b²)^2 - (c²)^2
= a^4b^4 - c^4.
The Stem-and-Leaf Graph shows the amount of money each student spends on food per day in dollars. What is the median for the data in this Stem-and-Leaf Plot? A. $55 B. $73 C. $81 D. $84
Answer:
B) $73
Step-by-step explanation:
add all of your values and divide by the amount of values
52+55+55+55+59+64+66+68+72+73+73+73+73+75+81+81+83+84+84+86+87=
1,499
1,499 divided by 21 = 71.3809523...
which rounds to 73
HOPE THIS HELPS!!! :)
The median is of $48 in the stem leaf plot and option B is correct.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The median of a data-set is the value that separates the bottom 50% from the upper 50% of values.
The graph has 16 values, already ordered.
It is an even number, hence the median is the mean of the 8th and the 9th values, which considering the key are both 48,
Hence, the median is of $48 and option B is correct.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ3
Stem-and-Leaf Plot shows the amount of money each student spends
on travel per day in dollars. What is the median for the data in this graph?
Stem Leaf
A) $35
B) $48
C) $53
D) $54
a line is perpendicular to y=4x-2 and intersects the point (4,-11). what is the equation of this perpendicular line?
Answer:
y = -1/4x - 10
Step-by-step explanation:
Hey there!
Well to the slopes of 2 perpendicular lines are reciprocals of each other meaning if the line has a slope of 4 then it’s perpendicular line has a slope of -1/4.
Now to find the y intercept we need to graph,
y = -1/4x and point (4, -11)
Look at the image below.
By looking at the image below we can tell that in order for the perpendicular line to go through point (4,-11) it would be -10.
The equation is y = -1/4x - 10
Hope this helps :)
Please answer this question now
Hi there! :)
Answer:
[tex]\huge\boxed{V = 359.01 mm^{3} }[/tex]
Use the formula V = 1/3(bh) to solve for the volume of the cone where b = πr² where π ≈ 3.14:
Find the area of the base:
b = π(7)²
b = 49π
b = 153.86 mm²
Find the volume:
V = 1/3(153.86 · 7)
V = 1/3(1077.02)
V = 359.006 ≈ 359.01 mm³.
Let f(x) = x2 − 8x + 5. Find f(−1)
Answer:
14
Step-by-step explanation:
[tex]f(x)=x^2-8x+5[/tex]
now substitute x for -1
[tex]f(-1)=(-1)^2-8(-1)+5[/tex]
now solve
[tex]f(-1)=1+8+5[/tex]
[tex]f(-1)=14[/tex]
there is your answer! hope this helps! :)
Type the correct answer in the box. Use numerals instead of words. The height of a baseball, in feet, is represented by this expression, where t is time in seconds. -16t squared+64t+3 The height of the baseball after 3.5 seconds is BLANK feet.
Answer:
31 Feets
Step-by-step explanation:
Given the expression for the height of a baseball:
Height(t) = -16t^2 +64t +3
Height in Feets ; time (t) in seconds
Height of baseball after 3.5 seconds :
Height(3.5) = -16(3.5)^2 + 64(3.5) + 3
Height = - 16(12.25) + 64(3.5) + 3
Height = - 196 + 224 + 3
Height = 31 Feets
Height after 3.5 seconds = 31 feets
3
4
x
+
6
=
1
+
1
3
x
Answer:
[tex]\boxed{x = -5/21}[/tex]
Step-by-step explanation:
Hey there!
To simplify we need to combine like terms and use the communicative property,
34x + 6 = 1 + 13x
-13x to both sides
21x + 6 = 1
-6 to both sides
21x = -5
Divide both sides by 21
x = -5/21
Hope this helps :)
Answer: I'm guessing you need me to solve this for you.
I interpreted the equation this way: 34x + 6 = 1 + 13x
The solution is -5/21.
Step-by-step explanation:
34x + 6 = 1 + 13x
Step 1: Simplify both sides of the equation.
34x + 6 = 13x + 1
Step 2: Subtract 13x from both sides.
34x + 6 − 13x = 13x + 1 − 13x
21x + 6 = 1
Step 3: Subtract 6 from both sides.
21x + 6 − 6 = 1 − 6
21x = − 5
Step 4: Divide both sides by 21.
21x/21 = -5/21
x = -5/21
Hope this helped you!
4x-8+9-6x=3x+6 cual es el valor de la x?
Answer:
El valor de x en esta ecuación es -1.
Step-by-step explanation:
4x - 8 + 9 - 6x = 3x + 6
En primer lugar, combinar términos similares en cada lado de la ecuación.
-2x + 1 = 3x + 6
A continuación, resta 3 veces en ambos lados de la ecuación.
-5x + 1 = 6
Ahora, resta 1 de ambos lados de la ecuación.
-5x = 5
Por último, divida por -5 en ambos lados de la ecuación.
x = -1
I will rate you a brainlest☆
Answer:
A 0.6 0.9 1.2 1.5 1.8
B 3/8 5/8 7/8 9/8 11/8
C -7 -5 -3 -2 -1
D 1, 1 1/3, 1 2/3, 2, 2 1/3
E 0.61 0.72 0.83 0.94 1.05
Step-by-step explanation:
Answer:
A. x x 1.2 1.5 1.8
B. 3/8 x x x 1 2/8
C. x x -3 -2 -1
D. 0 x x x 5 1/3
E. x x 0.83 0.94 1.05
Step-by-step explanation:
hope it helped
London answered 20 questions correctly on her multiple choice history final that had a total of 80 problems. What percentage of questions did London answer correctly on the final exam?
Answer:
25%
Step-by-step explanation:
correct/total
20/80
1/4
Changing to a decimal
.25
.25*100%
25%
Answer:
1/4 or 25%
Step-by-step explanation:
1). 20 / 80 = 1 / 4 = 25 %
Hope this helps
solve 2<2x+4<10 for x
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your inequality step-by-step.
[tex]2<2x+4<10[/tex]
[tex]2 + -4 < 2x + 4 + -4 < 10 + -4[/tex] (Add -4 to all parts)
[tex]-2 < 2x < 6[/tex]
[tex]\frac{-2}{2} < \frac{2x}{2} < \frac{6}{2}[/tex] (Divide all parts by 2)
[tex]-1 < x < 3[/tex]
So the answer is : [tex]-1 < x < 3[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Solve each system of equations 4x+6y=3 and -10x-15y=-4
Answer:
There is no solution
Step-by-step explanation:
they all subtract eachother out
Create a box plot for either the girls or boys data. Give 2 valid conclusions based on the data collected? (4 points)
Answer:
1) Please find attached the box and whiskers chart created with Excel
2) The conclusions are;
a) The measure of central tendency (the mean and the median) are approximately equal,
b) The standard deviation for the first five data points is 14.17 while the standard deviation for the whole ten data points is 23.99 as such the data values appeared more clustered at the center and show wider spread towards right ends of the chart
Due to the lack of correlation between the standard deviation and the five data values, the data is not uniformly distributed
Step-by-step explanation:
The given data is as follows;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
15, 18, 22, 32, 50, 50, 55, 56, 81, 81
The first quartile Q₁ = 22
The second quartile, Q₂ (Median) = 50
The third quartile, Q₃ = 56
The interquartile range IQR = 56 - 22 = 34
The minimum value = 15
The maximum value = 81
The mean = 46
The standard deviation = 23.99
Therefore, the measure of central tendency (the mean and the median) are approximately equal,
The data values appeared more clustered at the center and show wider spread towards the left and right ends of the chart
The standard deviation for the first five data points is 14.17 while the standard deviation for the last five data points is
Due to the lack of correlation between the standard deviation and the five data values, the data is not uniformly distributed.
In an examination ,80%examines passed in english,70%In mathematics and 60% in both subjects.if 45 examines failed in both subject.
1.draw a venn-diagram to represent the above information .
2.find the number of examines who passed only one subject.
3.find the number of student who failed in mathematics.
Answer:
1. Please refer to attached diagram.
2. 135
3. 135
Step-by-step explanation:
Given that
80%examines passed in English, n(E) = 80%
70%In mathematics, n(M) = 70%
and 60% in both subjects, n(E [tex]\cap[/tex] M) = 60%
45 examines failed in both subject.
1. Venn Diagram is attached in the answer area.
One circle represents the pass examines in Maths and
Other circle represents the pass examines in English.
Rectangle represents the total number of examines that appeared for the exam.
Rectangle minus the area of union of circles represent the number of students who failed in both subjects.
2. To find the number of examines who passed in only one subject.
i.e. n(E) - n(E [tex]\cap[/tex] M) + n(M) - n(E [tex]\cap[/tex] M) = (80 - 60 + 70 - 60)% = 30%
Let us find the number of students who passed in atleast one subject:
[tex]n(E\cup M) = n(E) +n(M)-n(E \cap M)\\\Rightarrow n(E\cup M) = (80 +70-60)\% = \bold{90\%}[/tex]
So, number of students who failed in both subjects = 100 - 90% = 10% of total students = 45
So, total number of students appeared = 450
So, number of examines who passed in only one subject = 450 [tex]\times[/tex] 30% = 135
3. Number of students who failed in mathematics.
100% - Passed in Mathematics = 100% - 70% = 30% of 450 = 135
