The equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
What is meant by the perimeter of the rectangle?For the given question;
Let the dimensions of the rectangle be;
Length lWidth wPerimeter PFor the condition, width of a rectangular rug is 3 1/4 inches longer than twice its length.
w = 2×l + 3 1/4
Solve the mixed fraction;
w = 2×l + 13/4
Now, the perimeter is;
P = 2(l + w)
P = l x w
Put the value of w.
P = 2 ( l + 2×l + 13/4) ....eq1
P = 54 1/2 inches = 109/4
Put in eq 1
109/4 = 3 l + 13/4
109/4 = 24 l + 13
Multiplying equation by 4.
109/4 = 24 l + 13
Thus, the equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
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Which value is equivalent to -7?A. -(-7)B. |-71C. 171D.-|-71
Check Option A.
[tex]-(-7)=+7[/tex]Not equivalent to -7.
Check Option B.to -7.
[tex]|-7|=7[/tex]Not equivalent to -7.
Check Option C.
[tex]|7|=7[/tex]Not equivalent to 7.
Check Option D.
[tex]-|-7|=-7[/tex]Therefore, Option D is right.
Helppppppppppp test helppppp for today plssss help 6 and 7
7)
The triangles ABC and JGH are similar figures.
For two figures to be simmilar, the coresponding angles must be congruent and the corresponding sides must be proportional.
For these triangles:
The corresponding sides of the simimilar figures are proportional, you can express this as:
[tex]\frac{JH}{AC}=\frac{JG}{AB}=\frac{GH}{BC}[/tex]This expression indicates that the proportion between the corresponding sides is the same for all three pairs of sides. Using this information, we can determine the value of side GH
The proportion between the corresponding sides of the triangles is:
[tex]\frac{JH}{AC}=\frac{5.8}{11.6}=\frac{1}{2}[/tex]Now calculate GH as:
[tex]\begin{gathered} \frac{GH}{BC}=\frac{1}{2} \\ \frac{x}{6}=\frac{1}{2} \\ x=(\frac{1}{2})\cdot6 \\ x=3 \end{gathered}[/tex]Now the corresponding angles of the similar figures must be congruent, i.e. have the same measure so that:
[tex]\begin{gathered} \angle A=\angle J=31º \\ \angle C=\angle H=59º \end{gathered}[/tex]So a and y are
x=3
y=59º
. Noah may choose between two accounts in which to invest $4000. Account A offers 2.2% annual interest
compounded monthly. Account B offers continuous compound interest. Noah plans to leave his investment
untouched (no further deposits and no withdrawals) for 15 years.
(a) Which account will yield the greater balance at the end of 15 years?
(b) How much more money does Noah earn by choosing this more profitable account?
Answer:
Using the compound amount formula, account B will yield the greater balance at the end of 15 years and Noah earn $4 more money by choosing this more profitable account.
In the given question,
Noah may choose between two accounts in which to invest $4000.
Principal Amount(P) = $4000
Account A offers 2.2% annual interest compounded monthly.
Rate(r) = 2.2% = 0.022
In a year have twelve month so n=12
Account B offers continuous compound interest.
Noah plans to leave his investment untouched for 15 years.
Time(t) = 15
Formula for amount after t years = P(1+ r/n)^nt
Amount after 15 years = 4000(1+ 0.022/12)^12*15
Simplifying
Amount after 15 years = 4000(1+0.00183)^180
Amount after 15 years = 4000(1.00183)^180
Amount after 15 years = 4000*1.39
Amount after 15 years = $5560
Account B offers compounded continuously.
So formula used = Pe^(rt)
Amount after 15 years = 4000*e^(0.022*15)
Amount after 15 years = 4000*e^(0.33)
Amount after 15 years = 4000*1.391
Amount after 15 years = $5564
(a) We have to find which account will yield the greater balance at the end of 15 years.
As we can see in Account A amount after 15 years is $5550 and in Account B amount after 15 years is $5564.
So account B will yield the greater balance at the end of 15 years.
(b) We have to find how much more money does Noah earn by choosing this more profitable account.
Noah earn money more by profitable account=Account B amount-Account A amount
Noah earn money more by profitable account=$5564-$5560
Noah earn money more by profitable account=$4
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Will give brainliest if someone answers this problem correctly
The equation of the line in fully simplified slope intercept form is y = -5x + 8.
From the graph:
Take any two points:
suppose (1,3) and (2,-2)
slope m = y2 - y1 / x2 - x1
= -2 - 3 / 2 - 1
= -5/1
= -5
substitute m and (1,3) in y = mx + c
3 = -5*1 + c
3 = -5 + c
c = 3+5
c = 8
y = mx+c
y = -5x + 8.
Therefore the equation of the line in fully simplified slope intercept form is y = -5x + 8.
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What is 73 divided by 6
Answer:
12,1666666667
Step-by-step explanation:
Out of 200 people eating at a diner, 70% ordered sandwiches. How many people ordered sandwiches? Select one: 130 people
if 70% of 200 people ordered sandwiches then the number of people who ordered sandwiches
= 70% * 200
= 70/100 * 200
= 140 People
The 3rd option
I need help finding the answer and to show work
6) 4r + 8 + 5 = -15 - 3r
4r + 3r = -15 -8 - 5
7r = -28
r = -28/7
r = -4
8) 3n - 15 = 7n + n
-15 = 7n + n - 3n
-15 = 5n
n = -15/5
n = -3
the radius of a circle is 1 what is the length of an arc that subtends an angle of 10pi/9 radians
To convert from radians to degrees, you have to know that 180 degrees is equal to one pi
[tex]\frac{10\text{ pi}}{9}\text{ = }\frac{10X180^{\circ}}{9}=200^{\circ}[/tex]Angle 360 -200 = 160
[tex]\begin{gathered} lengthofarc=\frac{\emptyset}{360}X\frac{2\pi\text{ r}}{1} \\ =\text{ }\frac{160}{360}X\frac{2\pi\text{ X 1 }}{1} \end{gathered}[/tex]length of arc =2.7925
The length of the arc is approximately 2.8
findvthe volume of the cylinder below to the nearest cubic foot.
Answer: The volume of the cylinder is 164.9 cubic foot
Given data
The diameter of the cylinder = 5ft
Height of the cylinder = 8.4 ft
Radius = diameter / 2
radius = 5/2
Radius = 2.5 ft
[tex]\begin{gathered} \text{Volume = }\pi\cdot r^2\cdot\text{ h} \\ \text{Volume = 3.14 }\cdot2.5^2\cdot\text{ 8.4} \\ \text{Volume = 3.14 x }6.25\text{ x 8.4 } \\ \text{Volume = }164.85ft^3 \\ Tothenearesttenth164.9ft^3 \end{gathered}[/tex]The answer is 164.9 cubic foot
At East Zone University (Ezu) thereare 564 students taking College Algebra or English Comp . 454 are taking college Algebra ,148 are taking English Comp and 38 are taking both College Algebra and English Comp . How many are taking Algebra but Not English Comp?
Step 1: Write the information given in a set notation.
[tex]\begin{gathered} n(U)=564,U\Rightarrow\mleft\lbrace The\text{ entire students}\mright\rbrace \\ E\Rightarrow\mleft\lbrace e\text{nglish comp.}\mright\rbrace \\ C\Rightarrow\mleft\lbrace\text{college algebra}\mright\rbrace \\ \end{gathered}[/tex]Step 2: State the number of students that partake in each subject.
[tex]\begin{gathered} n(C\cap E)=38 \\ n(C\cap E^{\prime})=454-38=416 \\ n(E\cap C^{\prime})=148-38=110 \\ n(C\cup E)^{\prime}=x \end{gathered}[/tex]Step 3: Draw a Venn diagram showing the information above
Step 4: To find the number of students that College Algebra but not English comp., we will check for the number of students that take only College Algebra. This is shown below
[tex]n(C\cap E^{\prime})=416[/tex]Hence, the number of students that are taking Algebra but Not English Comp is 416
Go5. Given functions f(x) = 9x – 2, g(x) = 5 – 3x/2, and h(x) = 4x – 7/4(a) Find g(-8).(b) Find the value of x that makes g(x) = -7.(c) Find the value of x that makes f(x) = g(x).(d) Find the value of x that makes f(x) = h(x)(e) Find the x-intercept of h(x).
Answer
a) g(-8) = 17
b) When g(x) = -7, x = 8
c) When f(x) = g(x), x = (2/3)
d) When f(x) = h(x), x = (1/20)
e) x-intercept of h(x) = (7/16)
Explanation
f(x) = 9x - 2
g(x) = 5 - 3x/2
h(x) = 4x - 7/4
(a) Find g(-8).
g(x) = 5 - 3x/2
g(-8) means the value of g(x) when x = -8
g(-8) = 5 - [3×-8/2]
= 5 - (-12)
= 5 + 12
= 17
(b) Find the value of x that makes g(x) = -7.
g(x) = 5 - 3x/2
When g(x) = -7,
5 - 3x/2 = -7
5 - (3x/2) - 5 = -7 - 5
-(3x/2) = -12
[tex]\begin{gathered} \frac{-3x}{2}=-12 \\ \text{Cross multiply} \\ -3x\text{ = 2}\times-12 \\ -3x\text{ = -24} \\ \text{divide both sides by -3} \\ \frac{-3x}{-3}=\frac{-24}{-3} \\ x\text{ = 8} \end{gathered}[/tex](c) Find the value of x that makes f(x) = g(x).
f(x) = 9x - 2
g(x) = 5 - 3x/2
When f(x) = g(x)
9x - 2 = 5 - (3x/2)
9x + (3x/2) = 5 + 2
(21x/2) = 7
[tex]\begin{gathered} \frac{21x}{2}=7 \\ \text{Cross multiply} \\ 21x\text{ = 2}\times7 \\ 21x=14 \\ \text{Divide both sides by 21} \\ \frac{21x}{21}=\frac{14}{21} \\ x=\frac{14}{21}=\frac{2}{3} \end{gathered}[/tex](d) Find the value of x that makes f(x) = h(x)
f(x) = 9x - 2
h(x) = 4x - 7/4
When f(x) = h(x)
9x - 2 = 4x - (7/4)
9x - 4x = 2 - (7/4)
5x = (1/4)
[tex]\begin{gathered} 5x=\frac{1}{4} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{1}{4\times5} \\ x\text{ =}\frac{1}{20} \end{gathered}[/tex](e) Find the x-intercept of h(x).
h(x) = 4x - 7/4
The x-intercept is the value of x when h(x) = 0
When h(x) = 0
4x - (7/4) = 0
4x = (7/4)
[tex]\begin{gathered} 4x=\frac{7}{4} \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{7}{4\times4} \\ x=\frac{7}{16} \end{gathered}[/tex]Hope this Helps!!!
Students and adults purchased tickets for a recent school play. All tickets were sold atthe ticket booth (discounts of any type) were not allowed.Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 wascollected. 200 tickets were sold.a. Write a system of equations that can model the number of student and adulttickets sold at the ticket booth for the play.
Given:
Cost of students tickets is, c (s) = $8.
Cost of adult tickets is, c (a) = $10.
Total cost collected for by selling the tickets is, c (t) = $1,760.
Number of tickets sold is, n = 200.
The objective is to find the system of equations that can model the number of students and adults tickets sold at the booth.
Consider the number of students as x and number of adults as y.
Then, the equation of total numner of students will be,
[tex]\begin{gathered} \text{Number of students+Number of adults=n} \\ x+y=200\ldots\ldots\ldots..(1) \end{gathered}[/tex]Now, the cost equation can be calculated as,
[tex]\begin{gathered} c(s)\cdot x+c(a)\cdot y=c(t) \\ 8x+10y=1760\ldots\ldots..\ldots..(2) \end{gathered}[/tex]Hence, the system of equations that can model the number of students and adults tickets are x + y = 200 and 8x + 10y = 1760,
Part of the proceeds from a garage sale was $305 worth of $5 bills if there were ) more bills than $20 bills find the number of each denomination
We are asked how many $20 bills and $5 bills can make up $305. To do that we will first divide 305 and 20, like this:
Now, we need to find a number that when multiplied by 20 is the closest to 305, that number is 15, since:
[tex](15)(20)=300[/tex]Therefore:
Now, subtract 300 from 305 and we get:
multiply or divide as indicated. be sure to reduce all answers to lowest terms. ( the numerator and denominator of the answer should not have any factors in common)
we have the expression
[tex]\frac{3a^2+3a}{a^2-36}\cdot\frac{a^2-6a}{12a}[/tex]Simplify
we have that
a^2-36=(a+6)(a-6)
3a^2+3a=3a(a+1)
a^2-6a=a(a-6)
substitute in the given expression
[tex]\frac{3a(a+1)}{(a+6)(a-6)}\cdot\frac{a(a-6)}{12a}[/tex]Simplify
[tex]\frac{(a+1)}{(a+6)}\cdot\frac{a}{4}[/tex]therefore
the answer is
[tex]\frac{(a^2+a)}{(4a+24)}[/tex]Which equation represents a line which is parallel to y=0?A. x=1B. y=x+3C. y=xD. y=6
ANSWER
D. y = 6
EXPLANATION
Parallel lines have the same slope.
In this problem, the given line is y = 0, which is a horizontal line at y = 0. Because it is a horizontal line, its slope is 0. From the options, we have to find which line has a slope of 0.
• Option A: x = 1 is a vertical line passing through x = 1. Its slope is undefined → ,not parallel,.
,• Option B: the slope of this line is 1 → ,not parallel.
,• Option C: the slope of this line is also 1 → ,not parallel.
,• Option D:, y = 6 is also a horizontal line, so its slope is 0 → ,this line is parallel ,to the given line.
James received 60 texts yesterday. Of those texts 3/5 were from his friend Chris. Of the texts from Chris 1/3 referenced football. How many texts did James receive about football?
Out of the 60 texts that James recieved,
[tex]60\cdot\frac{3}{5}\cdot\frac{1}{3}=12[/tex]12 were about football.
During World War I, mortars were fired from trenches 3 feet below ground level. The mortars had a velocity of150 ft/sec. Determine how long it will take for the mortar shell to strike its target.• What is the initial height of the rocket? -3 ft.• What is the maximum height of the rocket? 348.56 ft• How long does it take the rocket to reach the maximum height ? 4.68750 sec.• How long does it take the rocket to hit the ground (ground level)? 9.35 sec.• How long does it take the rocket to hit a one hundred feet tall building that is in it's downward path?[ Select]• What is the equation that represents the path of the rocket? Select]
E:Given f(x) = log x and g(x) = -x + 1,which is the graph of (fog)(x)?-2-2COMPLETEThe domain of (fog)(x) isDONEX>0x < 0X > 1x <1
Given data:
The first function is f(x) = log x .
The second function is g(x) = -x + 1.
The expression for (fog)(x) is,
[tex]\begin{gathered} \mleft(fog\mright)\mleft(x\mright)=f(g(x)) \\ =f(-x+1) \\ =\log (-x+1) \end{gathered}[/tex]The domain of the above function is x<1.
Two number cubes are rolled what is the probability that the sum of the numbers rolled is either a 1 and a 4 in either order
The first thing we have to know is that a cube with numbers is a dice that has 6 faces and that its numbers go from 1 to 6, so the probability that the sum of both dice gives 1 is zero, since the minimum that we are going to give is 2
[tex]P(sum=1)=0[/tex]Now for the sum of both dice of 4 we have the following combinations
• 1 and 3
,• 3 and 1
,• 2 and 2
We have 3 combinatorics that we have to get the probability of each of the combinations in order to find our final probability
[tex]\begin{gathered} P(1|3)=P(1)P(3)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(3|1)=P(3)P(1)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(2|2)=P(2)P(2)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \end{gathered}[/tex]The probability that the sum of 4 would be the sum of the probabilities of the combinatorcs
[tex]\begin{gathered} P(sum=4)=P(1|3)+P(3|1)+P(2|2) \\ P(sum=4)=\frac{1}{36}+\frac{1}{36}+\frac{1}{36} \\ P(sum=4)=\frac{3}{36} \\ P(sum=4)=\frac{1}{12} \end{gathered}[/tex]What is the probability of getting a 1 and a 4 in either order?The probability of getting any number on a die will be 1/6 if we can get a 1 or a 4 then our population will be 2/6
[tex]\begin{gathered} P(1|4)=\frac{2}{6} \\ P(4|1)=\frac{2}{6} \\ P(1\&4)=\frac{2}{6}\cdot\frac{2}{6} \\ P(1\&4)=\frac{4}{36} \\ P(1\&4)=\frac{1}{9} \end{gathered}[/tex]Parts of a CircleFor this assignment, you will draw and label the parts of a circle. Follow the directions below to construct your circle. When you are finished, you may scan your drawing and upload it. If you do not have a scanner, you may take a picture with a digital camera or cell phone and then embed the image into a Word document.Draw circle A.Draw radius AB.Draw diameter CD.Draw chord EF.Draw central angle GAH.
It's important to consider that a radius is a segment from the center of the circle to the circumference, diameter is a segment that crosses the center of the circle and divides the circle into two equal parts, a chord is a segment that goes from one point on the circumference to another without intersecting the center of the circle, at last, a central angle is an angle formed by two radii and it has the center as the vertex.
First, let's draw circle A.
Second, let's draw radius AB.
Third, let's draw diameter CD.
Fourth, let's draw chord EF.
At last, let's draw angle GAH.
Determine the slope of the line represented by the equation: y=3/10x+6
The slope intercept form is given by the equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given:
[tex]y=\frac{3}{10}x+6[/tex]Based on the given, it is already in the slope intercept form, and by inspection, we can determine the slope of the line is equal to 3/10.
is 53 prime or composite numberhow can I find the numbers for 58
Answer:
Factors of 58: 1,2,29 and 58
58 It is a composite number.
Step-by-step explanation:
The factors of 58 are the numbers that divide 58 leaving 0 as the remainder.
For example, 58/29=2, the remainder of 0.
Factors of 58: 1,2,29 and 58
58 It is a composite number.
Which expressions simplify to a rational answer?Select each correct answer. 3√⋅2√52⋅−√2√9√⋅16−−√11−−√⋅5√
Among the given options, [tex]5\sqrt{2}.\sqrt{2}[/tex] and [tex]\sqrt{9}.\sqrt{16}[/tex] gives us a rational number.
The given options are -
1. [tex]\sqrt{3}. \sqrt{2}[/tex]
2. [tex]5\sqrt{2}.\sqrt{2}[/tex]
3. [tex]\sqrt{9}.\sqrt{16}[/tex]
4. [tex]\sqrt{11} .\sqrt{5}[/tex]
Now, Considering the 1st option, that is, [tex]\sqrt{3}. \sqrt{2}[/tex]
3 and 2, both are nonperfect squares,
[tex]\sqrt{3}. \sqrt{2} =\sqrt{6}[/tex] which is an irrational number.
Now, Considering the 2nd option, that is, [tex]5\sqrt{2}.\sqrt{2}[/tex]
[tex]5\sqrt{2}.\sqrt{2} = 5*2 = 10[/tex] which is a rational number.
Now, Considering the 3rd option, that is, [tex]\sqrt{9}.\sqrt{16}[/tex]
9 and 16, both are perfect squares,
So, [tex]\sqrt{9}.\sqrt{16} = 3*4 = 12[/tex] which is a rational number.
Considering the 4th option, that is,
3 and 2, both are nonperfect squares, [tex]\sqrt{11} .\sqrt{5}[/tex]
[tex]\sqrt{11} .\sqrt{5} = \sqrt{55}[/tex] which is an irrational number.
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Find mZCEF if mZCEF= 2x + 30,mZDEC = x + 102, and mZDEF = 132°DEFA) 30°C) 410B) 29°D) 320
1) Gathering the data
m∠CEF=2x +30
m∠DEC=x+102
m∠DEF=132
2) From the picture we infer that
m∠DEF = m∠CEF+m∠DEC
132 = m∠CEF +x +102
132-x-102=m∠CEF
m∠CEF=30
Write and equation of a line that passes through the point (5, -9) and is perpendicular to the line 2x + 11y = 22
The general equation of the line in slope - intercept form is :
[tex]y=m\cdot x+b[/tex]Where m is the slope and b is y - intercept
Given the line : 2x + 11y = 22
We need to write it in slope - intercept form to find the slope of it
so,
[tex]\begin{gathered} 2x+11y=22 \\ 11y=-2x+22 \\ y=-\frac{2}{11}x+2 \end{gathered}[/tex]So, the slope of the given line = -2/11
The required line is perpendicular to the given line
So, the product of the slope of the two lines = -1
So, if the slope of the given line is m , the slope of the required line will be = -1/m
So, the slope of the required line = 11/2
The equation of the required line will be :
[tex]y=\frac{11}{2}x+b[/tex]Using the given point ( 5 , -9 ) to find the value of b
So, when x = 5 , y = -9
[tex]\begin{gathered} -9=\frac{11}{2}\cdot5+b \\ -9=\frac{55}{2}+b \\ b=-9-\frac{55}{2}=-\frac{73}{2} \end{gathered}[/tex]so, the equation of the line is :
[tex]y=\frac{11}{2}x-\frac{73}{2}[/tex]And the standard form will be :
[tex]\begin{gathered} 2y=11x-73 \\ \\ 11x-2y=73 \end{gathered}[/tex]
f(x) = 4x - 3g(x) = x^3 + 2xFind (f-g)(4)
Given:
Two functions are given as below
[tex]\begin{gathered} f(x)=4x-3 \\ g(x)=x^3+2x \end{gathered}[/tex]Find:
we have to find the value of (f - g)(4).
Explanation:
we will find the value of (f - g)(4) as following
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x)=4x-3-(x^3+2x)=2x-x^3-3 \\ (f-g)(4)=2(4)-(4)^3-3=8-64-3=-59 \\ (f-g)(4)=-59 \end{gathered}[/tex]Therefore, the value of (f - g)(4) = -59
Consider 4 consecutive odd integers. What is the sum of the 2nd and the 4th numbers if the first number is n?1. 2n+82.4n+123. n+64. 3n+6
4 consecutive odd integers
the next consecutive odd number is only 2 more than the first number so: n+2
n = first number
n + 2 = second number
n + 4 = third number
n + 6 = fourth number
the sum of the 2nd and the 4th numbers is:
n + 2 + n + 6 = n + n + 2 + 6 = 2n +8
2n + 8
Hence, option 1 is the correct answer
find the slopes of the line that goes thru the following points
Given:
Find-: Slope of the line.
Sol:
The slope of line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} (x_1,y_1)\text{ = First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}[/tex]Choose any point:
[tex]\begin{gathered} (x_1,y_1)=(-1,-4) \\ \\ (x_2,y_2)=(0,-1) \end{gathered}[/tex]So, the slope of the line is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-1-(-4)}{0-(-1)} \\ \\ m=\frac{-1+4}{0+1} \\ \\ m=\frac{3}{1} \\ \\ m=3 \end{gathered}[/tex]Slope of line is 3.
An animal shelter provides a bowl with 1.35 liters of water for 6 cats.About how much water will be left after the cats drink their average daily amount of water?Water ConsumptionAverage Amount(Liters per day)AnimalCanada Goose0.24Cat0.15Mink0.10Opossum0.30Bald Eagle0.16liter(s) of water will be left after the cats drink their average daily amount of water.
Data
1.35 litres of water
6 cats
0.15 litres per day
Procedure
Amount of water taken by the 6 cats
[tex]0.15\cdot6=0.9[/tex]Left
[tex]1.35-0.9[/tex]0.45 litres of water will be left
The mean mark of 10 boys is 58.If the mean mark of 7 of them is 61, what is the mean mark of the remaining 3 boys
As for the 10 boys altogether,
[tex]\begin{gathered} \operatorname{mean}=58 \\ \text{and} \\ \operatorname{mean}=\frac{1}{10}\sum ^{10}_{i=1}\text{mark}_i \end{gathered}[/tex]Thus,
[tex]\Rightarrow580=\sum ^{10}_{i=1}\text{mark}_i[/tex]On the other hand, as for seven of the boys
[tex]\begin{gathered} \operatorname{mean}=61=\frac{1}{7}\sum ^7_{j=1}\text{mark}_j \\ \Rightarrow427=\sum ^7_{j=1}\text{mark}_j \end{gathered}[/tex]Thus, regarding the remaining three boys,
[tex]\Rightarrow\sum ^3_{k=1}mark_k=580-427=153[/tex]Finally, the mean of those remaining three kids is
[tex]\begin{gathered} \text{MEAN}=\frac{1}{3}\sum ^3_{k=1}mark_k=\frac{1}{3}\cdot153=51 \\ \Rightarrow\text{MEAN}=51 \end{gathered}[/tex]Thus, the mean mark of the remaining 3 boys is 51