Evaluate the triple integral ∭ 8x^2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)
Answers
Answer:
2/15
Step-by-step explanation:
given that the triple integral = ∫∫∫ 8x^2 dv
and T is the solid tetrahedron with vertices : (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)
hence the equation of the plane: x + y + z = 1
T [ (X,Y,Z) : 0≤x≤1, 0≤y≤1-x, 0≤z≤1-x-y ]
attached below is the detailed solution ( we multiply our answer after evaluation with the coefficient of 8 as attached to the initial expresssion)
By evaluating the triple integral where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) the value calculated is 2/15.
Given :
The triple integral ∭ 8x^2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1).
The following calculation can be used to evaluate the triple integral:
[tex]\rm I = \int\int\int 8x^2dV[/tex]
T[(x,y,z) : [tex]0 \leq x \leq 1[/tex] ; [tex]0 \leq y \leq 1-x[/tex] ; [tex]0 \leq z \leq 1-x-y[/tex] ]
Now put the limits in the above integral.
[tex]\rm I = \int\limits^1_0\int\limits^{1-x}_0\int\limits^{1-x-y}_0 {8x^2} \, dz \, dy \, dx[/tex]
[tex]\rm I = \int\limits^1_0\int\limits^{1-x}_0 {8x^2} (1-x-y) \, dy \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0\int\limits^{1-x}_0 {x^2-x^3-x^2y} \, dy \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0 {x^2(1-x)-x^3(1-x)-x^2\dfrac{(1-x)^2}{2}} \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0 {x^2-x^3-x^3+x^4-x^2\dfrac{(1+x^2-2x)}{2}} \, dx[/tex]
[tex]\rm I = 4\left( \int\limits^1_0 {2x^2-4x^3+2x^4-x^2-x^4+2x^3} \, dx\right)[/tex]
[tex]\rm I = 4\left( \int\limits^1_0 {x^2+x^4-2x^3} \, dx\right)[/tex]
[tex]\rm I = 4\left( {\dfrac{x^3}{3}+\dfrac{x^5}{5}-\dfrac{x^4}{2}} \right)^1_0[/tex]
[tex]\rm I = 4\left( {\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{2}} \right)[/tex]
[tex]\rm I = \dfrac{2}{15}[/tex]
By evaluating the triple integral where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) the value calculated is 2/15.
For more information, refer to the link given below:
https://brainly.com/question/24308099
Related Questions
How do we find the perimeter?
Answers
Answer:
perimeter = 4z - 8
Step-by-step explanation:
perimeter of a square box = 4 times the side
P = 4 ( z - 2)
P = 4z - (4*2)
P = 4z - 8
The equation y = x + 3 represents a linear function. Which ordered pair does not lie on the graph of this function?
A. (–10, -7)
B. (13, 16)
C. (–14, –11)
D. (–20, 17)
plz hurry
Answers
The equation is y = x +3 .
We have to check which one of the option does not fulfill the given equation .
Taking 1st option :-
Where x = -10 and y = -7
→ -7 = - 10 +3
→ -7 = -7
Hence this lies on graph.
Taking 2nd option :-
Where x = 13 and y = 16
→ 16 = 13 + 3
→ 16 = 16
It also lies on graph .
Taking 3rd option :-
→ Where x = -14 and y = -11
→ -11 = -14 +3
→ -11 = -11
This will also lie on graph .
Taking 4th option :-
Where x = -20 and y = 17
→ 17 = -20 + 3
→ 17 = 17
This will also gonna lie on graph .
The linear function f is defined by f(x)= cx + d, where c and d are constants. If f(50) = 27,000 and f(100)= 38,000, what is the value of c?
Answers
Answer:
c = 220Step-by-step explanation:
f(x) = cx + d
For the first equation
f(50) = 27,000
Substitute the value of x that's 50 into the expression
That's
50c + d = 27,000
For the second equation
f(100) = 38,000
Substitute the value of x that's 100 into the expression
We have
100c + d = 38,000
Subtract the first equation from the second one to eliminate d
That's
100c - 50c + d - d = 38,000 - 27,000
50c = 11,000
Divide both sides by 50
We have the final answer as
c = 220Hope this helps you
In a small town, 68% of the people owned Television, 72 % owned Radio and
12 % owned neither Television nor Radio
Represent the information on a Vena diagram
What percentage of the population owned Television only?
Bondu and Ansah fomed a company and agreed that their annual profit will be
shared in the ratio 4 : 5 respectively. Ir at the end of the year, Ansah received
GHE 5,000.00 more than Boadu, how much was Boadu's share?
Answers
Answer:
1. 68% owned a TV
2. 20,000.00
Step-by-step explanation:
1. answer is in the question
2. if Ansah got 5,000.00 more that Bondu that means Ansah is 5, if Ansah is 5 and gets 5,000.00 more that means the difference of 1 is 5,000.00 or 1= 5,000.00
4*5,000.00 = 20,000.00
A regulation soccer field for international play is a rectangle with a length between 100 m and I 1 O m and a width between 64 111 and 75 m. What are the smallest and largest areas that the field could be
Answers
Answer:
The smallest area the field could be is 6,400 m²The largest area the field could be is 8,250 m²Step-by-step explanation:
Given;
smallest possible length of the international soccer field, L₀ = 100 m
smallest possible breadth of the international soccer field, B₀ = 64 m
Largest possible length of the international soccer field, L₁ = 110 m
Largest possible breadth of the international soccer field, B₁ = 75 m
Area of a rectangle is given by;
A = L x B
The smallest area the field could be is calculated as;
A₀ = L₀ x B₀
A₀ = 100 m x 64 m
A₀ = 6,400 m²
The largest area the field could be is calculated as;
A₁ = L₁ x B₁
A₁ = 110 m x 75 m
A₁ = 8,250 m²
Solve for x x-23=17 NEED TO KNOW FAST PLEASE!!!!
Answers
Answer:
x = 40
Step-by-step explanation:
Adding 23 to both sides gives us:
x - 23 + 23 = 17 + 23
x = 40
Answer:
[tex] \boxed{ \bold{ \bold{ \sf{x = 40}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 23 = 17}[/tex]
Move constant to right hand side and change it's sign
[tex] \sf{x = 17 + 23}[/tex]
Add the numbers
[tex] \sf{x = 40}[/tex]
Hope I helped!
Best regards!!
Solve for x: -1 < x + 3 < 5
O 2 < X < 8
0-4 < x < 2
O 2 > >8
04 >x>2
Answers
Answer:
B) -4<x<2
Step-by-step explanation:
-1 < x + 3 < 5
-3 -3 -3
-4 < x + < 2
We have some unknown number x and we're adding 3 to it getting x+3
To isolate x, we need to undo the operation happening to it. So we need to undo the addition of 3. We'll subtract 3 from all sides
-1 < x+3 < 5
-1-3 < x+3-3 < 5-3 ... subtract 3 from all sides
-4 < x+0 < 2
-4 < x < 2 ... answer is choice B6. For every 12 burpees Melinda did, she did 20 squats.
If Melinda did a total of 128 squats and burpees, how many did she do of each?
(20 Points)
48 burpees & 80 squats
48 burpees & 82 squats
46 burpees & 80 squats
46 burpees &. 82 squats
Answers
Answer:
48 burpees & 80 squats
Step-by-step explanation:
Let burpees= x
Let squat = y
For every 12 burpees Melinda did, she did 20 squats.
X/y =12/20
20x= 12y
X= 0.6y
Melinda did a total of 128 squats and burpees
X+y= 128
But x= 0.6y
0.6y +y= 128
1.6y= 128
Y= 128/1.6
Y= 80
X+y= 128
X+80= 128
X=128-80
X= 48
The area of a rectangular piece of land J is 220 square metres.Its width is 12.5.what is the perimeter of the land ?
Answers
Answer:
60.2m
Step-by-step explanation:
area =breadth × width
220m^2 = x × 12.5
x = 17.6
perimeter = 2(a+b)
perimeter = 2(12.5+17.6)
perimeter = 60.2m
Which of the following triangles can be proven similar through AA?
Answers
Answer:
C (Your chosen answer) is correct
Step-by-step explanation:
AA (Angle-Angle) Similarity postulate is exactly what it sounds like: Two triangles can be proven similar if they have two congruent angles.
We can tell what angles are congruent through the markings:
(A) and (B) can be immediately be eliminated, because one or more tringle in the pair does not have enough markings to prove congruency, so therefor cant be proven to be similar.
(D) is a little more difficult to decipher, but when you look closely, you can tell that the markings are not identical, so therefor the angles are not congruent.
(C) is correct because it has identical markings which makes the angles congruent.
Hope this helps :)
Option C is correct because it has identical markings which makes the angles congruent by AA.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Two triangles can be proven similar if they have two congruent angles.
Option A and B are not similar through AA because one or more tringle in the pair does not have enough markings to prove congruency, so therefore they are not similar.
Option C is correct because it has identical markings which makes the angles congruent by AA.
Hence, Option C is correct because it has identical markings which makes the angles congruent by AA.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ2
Consider the system of equations. y = −2x + 4 y = − 1/3x − 1
Answers
Hey there! I'm happy to help!
We have two values for y. Since y=y, this means that −2x + 4 and − 1/3x − 1 are equal as well, so we can put them in an equation and solve for x.
−2x + 4 = − 1/3x − 1
We subtract 4 from both sides.
-2x=-1/3x-5
We add 1/3 x to both sides.
-5/3x=-5
We divide both sides by -1 2/3.
x=3
Now, we plug this into one of the original equations to find y.
y=-2(3)+4
y=-6+4
y=-2
Therefore, the solution is (3,-2) or x=3 and y=-2.
I hope that this helps! Have a wonderful day! :D
What is (20-(-16))=20+16=36
Answers
Answer:
Step-by-step explanation:
i think its 5/144=0.03472
A rectangle has a width of 55 centimeters and a perimeter of 224 centimeters. What is the rectangle's length
The length is
cm.
Answers
Answer:
[tex]as \: we \: know \: perameter \: of \: rectngle = 2(length \ + beadth)[/tex]
[tex]and \: also \: perimeter \: = 224cm[/tex]
[tex]therefore \: we \: can \: write \: that 2(length + bredth) = 224cm [/tex]
let the length be l
and breadth is 55 cm
[tex]2(l + 55) = 224[/tex]
[tex]l + 55 = \frac{224}{2} [/tex]
[tex]l + 55 = 112[/tex]
[tex]l = 112 - 55[/tex]
[tex]l = 57[/tex]
so the length of rectangle is 57 cm
David uses drawing software to rotate the regular hexagon about its center. Through which angle measures can he rotate the hexagon to map it onto itself? Select each correct answer. 30° 45º 60° 120° 180°
Answers
Answer:
60, 120 and 180.
Step-by-step explanation:
It maps onto itself every 60 degrees.
So as they are multiples of 60 it will map onto itself at 120 and 189 degrees also.
The measure of the angle by which David can rotate the hexagon to map it onto itself is 60°, 120°, and 180°. The correct options are C, D, and E.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that David uses drawing software to rotate the regular hexagon about its center. Now, since the measure of the center angle of a hexagon made by any of its sides is 60°.
Further, if the hexagon is rotated by any angle that is divisible by 60° then it will result in the same hexagon.
Hence, the measure of the angle by which David can rotate the hexagon to map it onto itself is 60°, 120°, and 180°.
Learn more about Angle here:
https://brainly.com/question/7116550
#SPJ2
the question is below:
Answers
Answer:
x = 19.5, RQS=43
Step-by-step explanation:
It is important to note that RQS and TQS are supplementary, meaning their angles will add up to 180. Knowing this, we can create and solve the equation to find x..
(2x+4) + (6x+20) = 180
8x + 24 = 180
8x = 156
x = 19.5
Now that we know the value of x, we can substitute it into the equation for RQS, 2x+4.
2(19.5)+4
39+4
43
Hope this helped!
Answer:
[tex]x=19.5^o[/tex]
[tex]\angle RQS=43^o[/tex]
Step-by-step explanation:
Notice that the addition of these two angles give you and angle of [tex]180^o[/tex], therefore we can write the following equation to represent such addition:
[tex](2x+4)^o + (6x+20)^o=180^o\\2x+6x+4^o+20^o=180^o\\8\,x+24^o=180^o\\8\,x=180^o-24^o\\8\,x=156^o\\x=156^o/8\\x=19.5^o[/tex]
Therefore, the value of the angle RQS is:
[tex]\angle RQS=(2\,x+4)^o=(2\,*\,19.5^o)+4^o=43^o[/tex]
The price of an item was reduced 25% to $30 what was the original price of the item
Answers
Answer:
$40
Step-by-step explanation:
Let the original price of the item be x.
From the first statement, the price of the item was reduced 25% to $30. This means that new price of the item is now 75% (0.75) of the original price(x), and this new price is equal to $30. i.e
0.75x = 30
Now, let's solve for x.
0.75x = 30 [divide both sides by 0.75]
[tex]\frac{0.75x}{0.75}[/tex] = [tex]\frac{30}{0.75}[/tex]
x = 40.
Therefore, the original price of the item was $40
Step-by-step explanation:
40 is the answer for your question
6/x = 2x+4/5
Multiply each side by the common denominator to find the
quadratic equation equivalent to this equation.
Answers
Answer:
5x² + 2x - 15 = 0
Step-by-step explanation:
Given
[tex]\frac{6}{x}[/tex] = 2x + [tex]\frac{4}{5}[/tex]
Multiply through by 5x ( common denominator )
30 = 10x² + 4x ( subtract 30 from both sides )
0 = 10x² + 4x - 30 ( divide through by 2 )
0 = 5x² + 2x - 15 , that is
5x² + 2x - 15 = 0
seven less than the quotient of nineteen and a number
Answers
Step-by-step explanation:
Let the number is n. We need to write an expression for "seven less than the quotient of nineteen and a number"
The quotient of nineteen and a number is [tex]\dfrac{19}{n}[/tex] and 7 less than this is [tex]\dfrac{19}{n}-7[/tex]
Now if n = 2, put the value of n in above expression,
[tex]\dfrac{19}{n}-7=\dfrac{19}{2}-7\\\\=\dfrac{5}{2}\\\\=2.5[/tex]
So, the value of the above expression is 2.5 at n = 2.
Answer:
19/n-7
and 2.5
Step-by-step explanation:
If u actually read the other guy's work
Lets say you have a bunch of pennies that you are dividing into different groups. How many pennies could you have when you break the pennies into groups of 2 , you have 1 penny left over
Answers
Answer: We have an odd number of pennies.
Step-by-step explanation:
So we have N pennies.
When we wan to divide the N pennies into groups of 2, we have a penny left over.
This means that N is not divisible by 2.
The problem is that there are infinite natural numbers that are not divisible by two, this is the set of odd numbers.
And remember that an odd number can be written as:
N = 2*k + 1.
where k is an integer.
Then we want to divide this by 2 (divide N into groups of 2)
we have:
N/2 = (2*k + 1)/2 = 2*k/2 + 1/2 = k + 1/2.
So we have k groups of 2 pennies, and a penny leftover that we can not divide into two.
AB = 5 units and CD = 5 units, what is the length of your new segment, AD?
Answers
Answer:
New segment AD = 10 units
Step-by-step explanation:
Given:
AB = 5 units
CD = 5 units
Find:
New segment AD.
Computation:
⇒ New segment AD = AB + CD
⇒ New segment AD = 5 units + 5 units
⇒ New segment AD = 10 units
Any help? I don’t get this q can anyone help me do this
Answers
For number 5 - .3 ( 3.60 ÷ 12 = .3)
For number 6 - .32 ( 2.56 ÷ 8 = .32)
For number 7 - 2 ( 2.36 ÷ 2 = 1.18)
Can someone please help me
Answers
Answer:
D. -2/5
Step-by-step explanation:
Slope= [tex]\frac{delta Y}{Delta X} =\frac{-2}{5}[/tex]
Answer:
D
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (14, - 2)
m = [tex]\frac{-2-4}{14+1}[/tex] = [tex]\frac{-6}{15}[/tex] = - [tex]\frac{2}{5}[/tex] → D
1 way ANOVA analysis was used to test the effectiveness of 3 kinds of headache medicines (Advil, Tylenol, and Excedrin). The analysis involved 21 people (7 per group), and used an alpha level of 0.01. What is the Critical Value
Answers
Answer:
The critical region is F >F ₀.₀₁ (2,18) = 6.01
Step-by-step explanation:
For 1 way ANOVA the degrees of freedom Between Samples would 2 and within Samples would be 18 .
Alpha is given to be = 0.01
v1 = k-1 and v2 = n-k
Where k is the number of rows and n is the total number of values
v1= 3-1= 2 and v2 = 21-3= 18
So if we look up the table we find the values of the critical region to be 6.01
Hence the critical region is less and equal to 6.01
The critical region is F >F ₀.₀₁ (2,18) = 6.01
What is the equation of the line?A. y=3/4x−1 B.y=4/3x+1 C.y=3/4x+1 D.y=4/3x−1
Answers
Answer:
B. y = 4/3x + 1
Step-by-step explanation:
The offered choices are in slope-intercept form:
y = mx + b
where m represents the slope (rise/run) and b represents the y-intercept.
The graph crosses the y-axis at y=1, so the y-intercept is +1. That eliminates choices A and D.
The slope is greater than 1, so choice C is eliminated. You know the slope is greater than 1 because the line goes up more than 1 unit for a 1-unit change to the right. If you look where the line crosses grid points, you see that it rises 4 units for a run of 3 units to the right. That means ...
m = rise/run = 4/3
The equation is ...
y = 4/3x +1 . . . . matches choice B
Answer:
B. y = 4/3x + 1
Step-by-step explanation:
First, find the slope using rise/run (y2 - y1) / (x2 - x1)
Use the points (0, 1) and (3, 5)
Plug in the numbers:
(5 - 1) / (3 - 0)
= 4/3
Looking at the graph, we can see the y intercept is (0, 1) so we can plug in 1 into the equation y = mx + b as b:
y = mx + b
y = 4/3x + 1
if 5 lbs cost 9 dollars how much does 1 lbs cost
Answers
Answer: $1.80
Step-by-step explanation:
9=5x
9/5= 1.8
Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 8x+y+z= 4.
Answers
Answer:
[tex]\displaystyle \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 \int\limits^{4 - 8x - y}_0 {} \, dz \ dy \ dx = \frac{4}{3}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Integration
IntegralsFubini’s Theorem [Box]: [tex]\displaystyle \iiint_R{f(x, y, z)} \, dV = \int\limits^{b_1}_{a_1} \int\limits^{b_2}_{a_2} \int\limits^{b_3}_{a_3} {f(x, y, z)} \, dx \, dy \, dz[/tex]
Volume Formula: [tex]\displaystyle V = \iiint_D \, dV[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
Given: Tetrahedron Solid
Function: 8x + y + z = 4 and coordinate planes x, y, and z
Step 2: Find Volume Pt. 1
Find limits of integration for each variable.
[z] Solve for z: [tex]\displaystyle z = 4 - 8x - y[/tex][y] Set z = 0 [z coordinate plane]: [tex]\displaystyle 0 = 4 - 8x - y[/tex][y] Solve for y: [tex]\displaystyle y = 4 - 8x[/tex][x] Set y = 0 [y coordinate plane]: [tex]\displaystyle 0 = 4 - 8x[/tex][x] Solve for x: [tex]\displaystyle x = \frac{1}{2}[/tex]Define: [tex]\displaystyle \left[\begin{array}{ccc} 0 \leq z \leq 4 - 8x - y \\ 0 \leq y \leq 4 - 8x \\ 0 \leq x \leq \frac{1}{2} \end{array}[/tex]Step 3: Find Volume Pt. 2
Substitute in variables [Volume Formula]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 \int\limits^{4 - 8x - y}_0 {} \, dz \ dy \ dx[/tex][z Integral] Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 {z \bigg| \limits^{4 - 8x - y}_0} \ dy \ dx[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 \int\limits^{4 - 8x}_0 {4 - 8x - y} \ dy \ dx[/tex][y Integral] Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {\Big( 4y - 8xy - \frac{y^2}{2} \Big) \bigg| \limits^{4 - 8x}_0} \ dx[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {\Bigg[ 4(4 - 8x) - 8x(4 - 8x) - \frac{(4 - 8x)^2}{2} \Bigg]} \ dx[/tex][Integrand] Simplify: [tex]\displaystyle V = \int\limits^{\frac{1}{2}}_0 {8(2x - 1)^2} \ dx[/tex]Integrate [Integration Rules and Properties]: [tex]\displaystyle V = \frac{4(2x - 1)^3}{3} \bigg| \limits^{\frac{1}{2}}_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = \frac{4}{3}[/tex]∴ the volume of the given tetrahedron solid is equal to 4/3.
---
Learn more about double/triple integrals: https://brainly.com/question/17433118
Learn more about multivariable calculus: https://brainly.com/question/12269640
---
Topic: Multivariable Calculus
Unit: Triple Integrals
please help me with this
Answers
Answer: C
Step-by-step explanation:
The formula to find average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. Since the problem is asking for the average rate of change from the second to fifth year, we plug in a=2 and b=5.
[tex]\frac{f(5)-f(2)}{5-2}[/tex]
f(5)=420.4
f(2)=408.04
[tex]\frac{420.4-408.04}{5-2}=4.12[/tex]
Now, we get 4.12 dollars per year for the average rate of change.
What is the solution to this equation? 4x = 124 A. X= 120 (B. x = 41 C. X= 496 D. X = 31
Answers
Answer:
D. X = 31
Step-by-step explanation:
[tex]4x = 124 \\ x = \frac{124}{4} \\ x = 31[/tex]
Arthur, Yusuf, and Bill had some stamps in the ratio 3: 5: 6. When Yusuf gave some stamps to Arthur and Bill gave Arthur 42 stamps more than what Yusuf gave Arthur, they all had the same number of stamps each. How many stamps did Yusuf have at first?
Answers
Answer:
210 stamps
Step-by-step explanation:
Given:
Arthur ⇒ a = 3 kYusuf ⇒ y = 5kBill ⇒ b = 6kYusuf gave x stamps to Arthur, then:
y = 5k -xa = 3k + xBill gave Arthur 42 stamps more than Yusuf gave to Arthur, then:
b = 6k - (x+42)a = 3k + x + x + 42Now all 3 have same amount of stamps:
5k -x = 6k - x - 42 = 3k + 2x + 42From the first part of the equation we get:
6k - 5k = 42 + x - xk = 42How many stamps did Yusuf have at first?
y = 5k y =5*42 y = 210 stampsYusuf had 210 stamps at first
The given graph shows the cigarette consumption (in billions) in the United States for the years 1900 to
2007
Choose the best estimate for the number of cigarettes smoked in 1960.
550 billion
QI 450 billion
525 billion
480 billion
Answers
Answer:520 billion
Step-by-step explanation:
Answer: 2.00e5
Step-by-step explanation: