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.
Answers
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
Related Questions
Ken said that he is going to reduce the number of calories that he eats during the day. Ken's trainer asked him to start off small and reduce the number of calories by no more than 7%.
Answers
Answer:
Ok, this question seems incomplete, so i will answer it in a general way.
Suppose that regularly, Ken eats A calories during the day. (A is a positive number)
Now, Ken wants to reduce this number, but his nutritionist tells him to reduce no more than 7% (So the max reduction possible is a reduction of the 7%).
So after the reduction, Ken eats C calories per day.
First, the maximum reduction that Ken can do is when he reduces exactly 7% of the calories.
So if he regularly consumes A calories, the reduction will be of
(7%/100%)*A = 0.07*A
So after the reduction, the amount of calories that he consumes per day is:
C = A - 0.07*A = A*(1 - 0.07) = A*0.93
But this is the minimum amount of calories that he can consume, the actual range of possible options will be:
A < C ≤ A*0.97.
C is strictly smaller than A because we must have a reduction in the number of calories.
Those values of C is all the posible amounts of calories that Ken eats per day after the initial reduction in the number of calories per day.
plz help me asap!!!!!
What is the equation of the linear function represented by the table?
x
y
–5
14
–2
11
1
8
4
5
y = negative x + 9
y = negative x + 13
y = x + 13
y = x + 9
Answers
Answer:
It would be y = -x + 9
Step-by-step explanation:
Answer:
Y=-x+9
Step-by-step explanation:
Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
Answers
Answer:Answer:
[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]
Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]
The sum of the nth term of the sequence will be;
[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]
The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.
which ordered pair isa solution of the equation y=8x+3 A.Only (1,11) B.Only (-1,-5) C.Only (1,11) and (-1,-5) D Neither
Answers
Answer:
C (1,11) and (-1,-5)
Step-by-step explanation:
Prove: The square of the sum of
two consecutive integers is odd.
Answers
[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.
[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.
The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.
To prove that, The square of the sum of two consecutive integers is odd.
The expression to prove is,
Let us assume that two consecutive integers are n and (n + 1).
Hence, the expression is written as,
[n + (n + 1)]² = (2n + 1)²
= (2n)² + 2 × 2n × 1 + 1²
= 4n² + 4n + 1
= 2 (2n² + 2n) + 1
= odd
Therefore, the number in the blanks are 2 and 2.
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System of linear inequalities
Answers
Answer:
1.) ( -4, -2 ), ( -6, - 3 )
2.) ( 0, 2 ) , ( 0 , 4 )
Step-by-step explanation:
The inequality sign of >=, the greater than or equal to sign, the upper region will be shaded while for less than sign <, the lower region will be shaded.
Please find the attached file for the solution and the answer.
Simplify the expression so there is only one positive power for each base. (5^-2 x 4^-4)^-2
Answers
Answer:
Step-by-step explanation:
[tex](5^{-2}[/tex] × [tex]4^{-4}[/tex] [tex])^{-2}[/tex]
=[tex](5^{-2}[/tex][tex])^{-2}[/tex] x [tex](4^{-4})^{-2}[/tex] ∴[tex](a.b)^{n} =a^{n} .b^{n}[/tex]
=[tex]5^{-2.-2}[/tex] x [tex]4^{-4 . -2}[/tex] ∴[tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex] // here m is an exponent of [tex]a^{n}[/tex].
=[tex]5^{4}[/tex] x [tex]4^{8}[/tex]
What is the area of a triangle whose vertices are (4,0), (2,
3), (8,-6)?(using distance formula)
a) 2 sq. units b) 0 sq. units c) 1 sq. units d) 4 sq. units
Answers
Answer:
The correct option is;
b) 0 sq, units
Step-by-step explanation:
The vertices of the triangle are;
(4, 0), (2, 3), (8, -6)
The distance formula fr finding the length of a segment is given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where, (x₁, y₁) and (x₂, y₂) are the coordinates of the end points of the line
For the points (4, 0) and (2, 3) , we have;
√((3 - 0)² + (2 -4)²) = √13
Distance from (4, 0) to (2, 3) = √13
For the points (4, 0) and (8, -6) , we have;
√((-6 - 0)² + (8 -4)²) = √13 =
Distance from (4, 0) to (8, -6) = 2·√13
For the points (2, 3) and (8, -6) , we have;
√((-6 - 3)² + (8 -2)²) = 3·√13 =
Distance from (2, 3) to (8, -6) = 3·√13
Therefore, the perimeter of the triangle = 6·√13
The semi perimeter s = 3·√13
The area of the triangle, [tex]A = \sqrt{s\cdot \left (s-a \right )\cdot \left (s-b \right ) \cdot \left ( s-c \right )}[/tex]
Where;
a, b, and c are the length of the sides of the triangle;
[tex]A = \sqrt{3\cdot \sqrt{3} \cdot \left (3\cdot \sqrt{3} -\sqrt{3} \right )\cdot \left (3\cdot \sqrt{3} -2 \cdot \sqrt{3} \right ) \cdot \left ( 3\cdot \sqrt{3} -3\cdot \sqrt{3} \right )} = 0[/tex]
Therefore, the area = 0 sq, units.
what is the answer to x2 = 121.
Answers
Answer:
11 if you mean x^2
Step-by-step explanation:
Since we are solving for x, we need to just get x by its self. The only thing we have to do is get rid of the exponent of (^2). to do this, we have to take teh square root of both sides:
The square root of x^2 is x
The square root of 121 is 11
So the asnwer is x = 11
Step-by-step explanation: A common mistake in this problem would be to say that if x² = 121, x must equal 11.
However, you must set the equation equal to 0 first.
So our first step is to subtract 121 from both sides to get x² - 121 = 0.
Next, factor the left side to get (x + 11)(x - 11) = 0
So either x + 11 = 0 or x - 11 = 0.
Solving each equation from here, we find that x = -11 or x = 11.
So our answer is not just 11, it's {11, -11}.
I NEED THIS ANSWER IN THE NEXT 10 MIN PLS. WILL GIVE BRAINLEST!!! Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1.
Answers
Answer:
center=0,0 vertices=(0,5)(0,-5) foci=(0,4)(0,-4)
Step-by-step explanation:
used calculator
a police car drives a constant speed of 64 mph.how far can it travel in 2 hours
Answers
ABCDEFGHIJKLMNOPQRSTUVWXYZ
ANSWER QUICKLY PLZZZZZZ
ANSWER QUESTION C
Answers
Answer:
[tex] \boxed{12}[/tex]Step-by-step explanation:
E is 5 more than d
f is 7 less than d
a) e = d + 5
b) f = d - 7
c) plug the values of e and f
[tex] = d + 5 - (d - 7)[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = d + 5 - d + 7[/tex]
Since, two opposites add up to zero , remove them from the expression
[tex] = 5 + 7[/tex]
Add the numbers
[tex] = 12[/tex]
Hope I helped!
Best regards!
Negative solution for Multi-step equations
Answers
Answer:
[tex]\frac{1}{2}(4x+6)+3x=7x+9[/tex]
[tex]\frac{1}{2}(4x+8)+3x=7x+9[/tex]
Step-by-step explanation:
By putting the numbers in the given equation,
[tex]\frac{1}{2}(4x+6)+3x=7x+9[/tex]
2x + 3 + 3x = 7x + 9
5x + 3 = 7x + 9
(5x + 3) - 7x = (7x + 9) - 7x
(5x - 7x) + 3 = 9
-2x + 3 = 9
(-2x + 3) - 3 = 9 - 3
-2x = 6
[tex]-\frac{2x}{2}=\frac{6}{2}[/tex]
-x = 3
x = -3
Therefore, our equation is correct which has a negative result.
In place of 6 if we use 8, value of x will be negative again.
PLEASE HELP!! URGENT!! i will mark brainliest if its right!! In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and DF ≅ BD. Point C is the point of intersection between AG and BD while point E is the point of intersection between AG and DF. Prove ΔABC ≅ ΔGFE.
Answers
Answer:
See below.
Step-by-step explanation:
This is how you prove it.
<B and <F are given as congruent.
This is 1 pair of congruent angles for triangles ABC and GFE.
<DEC and <DCE are given as congruent.
Using vertical angles and substitution of transitivity of congruence of angles, show that angles ACB and GEF are congruent.
This is 1 pair of congruent angles for triangles ABC and GFE.
Now you need another side to do either AAS or ASA.
Look at triangle DCE. Using the fact that angles DEC and DCE are congruent, opposite sides are congruent, so segments DC and DE are congruent. You are told segments DF and BD are congruent. Using segment addition postulate and substitution, show that segments CB and EF are congruent.
Now you have 1 pair of included sides congruent ABC and GFE.
Now using ASA, you prove triangles ABC and GFE congruent.
URGENT PLEASE ANSWER !!
Answers
Answer:
(C) [tex]y = 2x+5[/tex]
Step-by-step explanation:
Looking at this graph, we can see that the slope of it is 2. We know this because for every time x increases by 1, y increases by 2.
We also know that the y-intercept of this graph is 5, since it intercepts the y-axis at the value 5.
We can easily create an equation with this info.
[tex]y = 2x + 5[/tex].
Hope this helped!
Answer:
C. y= 2x+5
Step-by-step explanation:
y=mx+b
(+b) is y- intercept
(mx) is the slope.
plot the y- intercept first which the line starts at (0,5)
since the slope isn't a fraction you turn it into one which would be
[tex] \frac{2}{1} [/tex]
explain the difference between legs and the hypotenuse of a right triangle
Answers
Answer:
The difference between the legs and the hypotenuse of a right triangle is that the hypotenuse will always be the longest side. Also, it will always be less than the two legs added together.
Step-by-step explanation:
Please help will give 5 stars with 1 thanks and 15 points
Answers
Answer:
mean is adding up all the numbers.
range means the difference between the Lowest and highest value.
Step-by-step explanation:
when we add the answer is 240.6.
divide it to 12..do the final answer is 20.05
range is 25.4_16.3
9.1
Answer:
Mean: 20.05
Range: 9.1
Step-by-step explanation:
To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.
20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3
= 240.6
Now, divide by the quantity which is 12 since there's 12 numbers.
240.6 divided by 12 = 20.05.
The mean is 20.05.
To find the range in the problem, you must subtract the smallest value from the largest value.
In this case, 16.3 is the smallest value and 25.4 is the largest.
25.4 - 16.3 = 9.1
9.1 is the range.
Hope this helps you!
Determine the value of x. 30° 45° 20° 60°
Answers
Answer:
x=30
Step-by-step explanation:
x+2x+3x=180
6x=180
x=180/6=30
yoyoyo pls help with math
Answers
Answer:
C
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AB}[/tex] = [tex]\frac{14}{35}[/tex] = [tex]\frac{2}{5}[/tex] → C
25. Solve for x.
[tex] \frac{x}{20} = \frac{1}{5} [/tex]
HELP as fast as you can if possible plz. thank you.
Answers
Answer:
x = 4
Step-by-step explanation:
x * 5 = 20 * 1
x = 4
Answer:
[tex]\boxed{x=4}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for x we need to cross multiply,
x/20 = 1/5
5x = 20
Divide both sides by 5
x = 4
Hope this helps :)
Select the equation written in slope-intercept form that corresponds to the given slope and y-intercept. m=6 b=-2
Answers
Answer:
y = 6x - 2
Step-by-step explanation:
slope-intercept form: y = mx + b
Note that:
m = slope = 6
b = y-intercept = -2
x = (x , y)
y = (x , y)
Plug in the corresponding numbers to the corresponding variables:
y = 6x + (-2)
y = 6x - 2
y = 6x - 2 is your answer.
~
Answer:
y = 6x-2
Step-by-step explanation:
The slope intercept equation form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 6x-2
3|2(2)-9|-2
need to evaluate the expression
Answers
Answer:
13
Step-by-step explanation:
3|2(2)-9|-2
First evaluate inside the absolute value
3|4-9|-2
3|-5|-2
Taking the absolute value of -5
3*5-2
Multiply
15 -2
13
Steps to solve:
3|2(2) - 9| - 2
3|4 - 9| - 2
3|-5| - 2
3(5) - 2
15 - 2
13
Best of Luck!
photo of freedom fighter quotes on white sheet.
pls send me fast
Answers
Answer:
Freedom is any case,
is only possible
by constantly
struggling for it.
Albert Einstein
The length of a rectangle is represented by the function L(x) = 4x. The width of that same rectangle is represented by the function W(x) = 7x2 − 4x + 2. Which of the following shows the area of the rectangle in terms of x? (L + W)(x) = 7x2 + 2 (L + W)(x) = 7x2 − 8x + 2 (L • W)(x) = 28x3 − 16x2 + 8x (L • W)(x) = 28x3 − 4x + 2
Answers
Answer:
(L ⋅ W)(x) = 28x3 − 16x2 + 8x
Step-by-step explanation:
I took the test hope it helps :3
The area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the length of the rectangle is L(x)=4x, and the width is W(x)=7x²-4x+2. Therefore, the area of the rectangle in terms of x is,
L(x)×W(x) = 4x × (7x²-4x+2)
(L · W) (x) = 28x³ - 16x² + 8x
Hence, the area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.
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Which set of integers represents the lengths of the sides of an isosceles triangle? A. {6,6,5} B. {3,4,5} C. {15,5,10} D. {1,1,3}
Answers
Answer:
A 6,6,5
Step-by-step explanation:
because an isosceles triangle has two it side equal
The set of integers represents the lengths of the sides of an isosceles triangle is A (6,6,5).
What Is an Isosceles Triangle?A triangle with two sides of equal length is an isosceles triangle.Properties of an Isosceles Triangle
Here is a list of some properties of isosceles triangles:
In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.In the isosceles triangle given above, the two angles ∠B and ∠C, opposite to the equal sides AB and AC are equal to each other.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. Types of Isosceles TrianglesGenerally, isosceles triangles are classified into three different types:
Isosceles acute triangle: An isosceles acute triangle is a triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement. Isosceles right triangle: The following is an example of a right triangle with two legs (and their corresponding angles) of equal measure. Isosceles obtuse triangle: An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90° and 180°), and the other two acute angles are equal in measurement.Therefore, set of integers represents the lengths of the sides of an isosceles triangle {6,6,5}.
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Marcus played 3 different activities this week after school. The time he spent playing is described below. Swam forof an hour Played soccer for 9/10 2/3 2/4 of an hour Jogged forof an hour Which statement correctly compares the times of 2 of his activities?
Answers
Answer:
A
Step-by-step explanation:
We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.
BRAINLIEST, THANKS AND 5 STARS IF ANSWERED BOTH CORRECTLY
Which set of points represents a function?
A. (-5, -4), (-4, -3), (-3, -2), (-2, -1)
B. (-6, 2), (6, -2) (-5, 3), (-5, -3)
C. (8, -1), (8, 2), (8, -3), (8, 4)
D. (1, 3), (-4, 4), (3, -2), (1, 0)
Which set of points represents a function?
A. (2, -5), (4, 0), (7, 0), (2, 5)
B. (-1, 4), (2, -4), (-1, -4), (-2, 4)
C. (-5, -1), (-2, -1), (1, -1), (4, -1)
D. (3, -5), (3, -1), (3, 2), (3, 4)
Answers
Answer:
Numer 1
A) (-5, -4), (-4, -3), (-3, -2), (-2, -1) Is a function
Number 2
C) (-5, -1), (-2, -1), (1, -1), (4, -1) is a function
in a function, all elements in domain "x" should have a pre-image "y" and they should be unique (one x can have only one value of y, but more than one x can have same same value of y) for all ordered pair (x,y)
it's not clearly possible to tell without knowing the actual set but with given information,
1. A
2. C
BC = 6, EF = 12 Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similar, then choose NOT. AA SAS SSS NOT
Answers
Answer:
SSS
Step-by-step explanation:
Answer:
SSS
Step-by-step explanation:
Option c or "SSS"
f(x) = x2. What is g(x)?
Answers
Answer:
g(x)=3x(superscript)2
Answer:
g(x) = 3x².
Step-by-step explanation:
In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).
Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.
So, g(x) = 3x².
Hope this helps!
X+2/x-2 - x+3/x-1 solve
Answers
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[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]
[tex]= \frac{-3x + 5}{x}[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
