The equations of the circles that have centers on the x-axis are;
A. (x - 2)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
What is the general form of the equation of a circle?The equation of a circle is; (x - h)² + (y - k)² = r², where;
(h, k) = The coordinates of the center of the circle
r = The radial length of the circle
The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²
The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .
The correct option is therefore;
A. (x - 4)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
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Write 0.75 as a fraction in its simplest form
Answer:
0.75 can be written as :-
[tex] \frac{75}{100} [/tex]
and in simplest form it is:-
[tex] \frac{3}{4} [/tex]
so the answer is 3/4
I NEED HELP WITH STATISCTICS
Answer:
20cm
Step-by-step explanation:
Help I need the answer to this
The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).
What is graph of a logarithmic function?The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).
To plot the graph of the given function, we simply need to use a graphing calculator.
The given function is;
f(x) = -3log₃(x + 8) - 4
To find the asymptotes of the graph;
x + 8 > 0
x > -8
The vertical asymptotes is at x = -8
The two points with integer coordinates are (2, -7) and (1, -10)
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c) Mrs. Chamling earns Rs 6,000 in a week. She spends Rs 250 for food Rs 75 for transportation everyday. (i) Write a mathematical expression to show this information. (ii) How much money does she save in a week? Cl LC and she divided the In this way, whole prime and compos of numbers, set of are the subset of 3.2 Prime and Prime numbe
(i) The mathematical expression to show Mrs. Chamling's earnings and expenses can be written as:
Weekly earnings = Rs 6,000
Daily food expenses = Rs 250
Daily transportation expenses = Rs 75
Total weekly expenses = (Rs 250 + Rs 75) x 7 = Rs 2,275
Total weekly savings = Weekly earnings - Total weekly expenses
= Rs 6,000 - Rs 2,275
= Rs 3,725
(ii) Mrs. Chamling saves Rs 3,725 in a week.
As for the second part of the question, I am not sure what is being asked. The sentence is incomplete and unclear. Please provide more information or context so I can assist you better.
please help. i’m struggling on part C
a) The area formula for the rectangle is equal to A = r² · sin 2θ.
b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.
c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm
How to find the maximum possible area of a rectangle inscribed in a semicircle
In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:
A = w · h
A = (2 · r · cos θ) · (r · sin θ)
A = 2 · r² · sin θ · cos θ
A = r² · sin 2θ
Where:
w - Width, in centimeters.h - Height, in centimeters.A - Area, in square centimeters.r - Radius, in centiemters. θ - Angle, in degrees.Second, perform first derivative test: (r - Constant)
A = 2 · r² · cos 2θ
2 · r² · cos 2θ = 0
cos 2θ = 0
θ = 45°
Third, perform second derivative test: (θ = 45°)
A'' = - 4 · r² · sin 2θ
A'' = - 4 · r² (MAXIMUM)
Fourth, determine the maximum possible area of the rectangle:
A = 4² · sin 90°
A = 16 cm²
Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)
w = 2 · r · cos θ
w = 2 · 4 · cos 45°
w = 8 · √2 / 2
w = 4√2 cm
w = 5.66 cm
h = r · sin θ
h = 4 · sin 45°
h = 4 · √2 / 2
h = 2√2 cm
h = 2.83 cm
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Intro
Nautilus Clothing's stock has a 50% chance of producing a 15% return, a 20%
chance of producing a 21% return, and a 30% chance of producing a -13% return.
Part 1
What is the stock's expected return?
Select the correct answer. Consider this quadratic equation. x2 + 1 = 2x – 3 Which expression correctly sets up the quadratic formula? A. B. C. D.
The expression x = (2 ± √(-12)) / 2 is negative, this quadratic equation does not have real solutions.
The quadratic formula, we need the quadratic equation in the form ax^2 + bx + c = 0. The given equation is x^2 + 1 = 2x - 3. To set it up correctly, we need to move all terms to one side of the equation to have a zero on the other side.
Rearranging the equation, we get x^2 - 2x + 4 = 0. Now we can identify the coefficients a, b, and c.
The correct expression to set up the quadratic formula is:
B) x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 - 2x + 4 = 0, we have:
a = 1
b = -2
c = 4
Plugging these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4 * 1 * 4)) / (2 * 1)
Simplifying further, we get:
x = (2 ± √(4 - 16)) / 2
x = (2 ± √(-12)) / 2
Since the expression inside the square root is negative, this quadratic equation does not have real solutions.
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Note the full question may be :
Consider the quadratic equation 2x^2 + 5x - 3 = 0. Which expression correctly sets up the quadratic formula?
A) x = (-b ± √(b^2 - 4ac)) / (2a)
B) x = (-b ± √(b^2 + 4ac)) / (2a)
C) x = (-b ± √(4ac - b^2)) / (2a)
D) x = (b ± √(b^2 - 4ac)) / (2a)
NO LINKS!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Cosines
1. B= 36°, c = 19, a = 11
2. a = 21, b = 26, c = 17
Answer:
1) A = 32.6°, C = 111.4°, b = 12.0
2) A = 53.6°, B = 85.7°, C = 40.7°
Step-by-step explanation:
Question 1
Given values of triangle ABC:
B= 36°c = 19a = 11First, find the measure of side b using the Law of Cosines for finding sides.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
As the given angle is B, change C for B in the formula and swap b and c:
[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]
Substitute the given values and solve for b:
[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]
[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]
[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]
[tex]\implies b=11.9929519...[/tex]
Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
To find the measure of angle A, swap a and c in the formula, and change C for A:
[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]
[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]
[tex]\implies \cos(A)=0.842229094...[/tex]
[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]
[tex]\implies A=32.6237394...^{\circ}[/tex]
To find the measure of angle C, substitute the values of a, b and c into the formula:
[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]
[tex]\implies \cos(C)=-0.364490987...[/tex]
[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]
[tex]\implies C=111.376260...^{\circ}[/tex]
Therefore, the remaining side and angles for triangle ABC are:
b = 12.0A = 32.6°C = 111.4°[tex]\hrulefill[/tex]
Question 2To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
Given sides of triangle ABC:
a = 21b = 26c = 17Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:
[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]
[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]
[tex]\implies C=40.690560...^{\circ}[/tex]
To find the measure of angle B, swap b and c in the formula, and change C for B:
[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]
[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]
[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]
[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]
[tex]\implies B=85.6625640...^{\circ}[/tex]
To find the measure of angle A, swap a and c in the formula, and change C for A:
[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]
[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]
[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]
[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]
[tex]\implies A=53.6468753...^{\circ}[/tex]
Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:
A = 53.6°B = 85.7°C = 40.7°Harper recorded the heights of plants, in inches, as shown in the table.
nd the mean of the data.
11 12 13 14 15 16 17 18 19 20 21
Heights of Plants (in.)
The mean height of the plants whose heights are shown by the data set is 16 in.
Calculation of meanTo find the mean:
Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176
Total number of values = 11 (since there are 11 values in the data set)
Mean = Sum of the values / Total number of values
= 176 / 11
= 16
In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.
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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?
Answer:
$12270.46----------------------
Use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.Plugging in the values, we get:
A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46Find the solution set for the equation. |9x-5|+3=8
Answer: 10/9, 0
Step-by-step explanation:
Which point is located at 2,1
Answer: Point P
Step-by-step explanation: over 2 up 1 (2,1)
Answer: M
Step-by-step explanation:
helpppppppppp meeeeee please
The missing sides of the triangle are given as follows:
[tex]SX = 4\sqrt{3}[/tex]RS = 12.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.For the angle of 30º, we have that:
6 is the opposite side.RS is the hypotenuse.Hence the hypotenuse RS is obtained as follows:
sin(30º) = 6/RS
1/2 = 6/RS
RS = 6 x 2
RS = 12.
Applying the cosine, we have that:
cos(30º) = 6/SX
[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]
[tex]SX = \frac{12}{\sqrt{3}}[/tex]
[tex]SX = 4\sqrt{3}[/tex]
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The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8?
0-20
X
-3
-1
-
1
4
8
10
Mark this and return
y
14
10
6
0
?
-12
Save and Exit
Next
Submit
Answer:
The Value of Y is -8
Step-by-step explanation:
I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.
So therefore, the value of y is -8. Hopes this helps :p
Answer and why!!!!!!
The expression (yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp) is simplified to obtain
2/y
How to simplify the expressionThe given expression is
(yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp)
The expression is simplified individually, using different each equation in the expression
yx + y + px + p
= y(x + 1) + p(x + 1)
= (y + p)(x + 1)
5x² + 10x +5
= 5(x² + 2x + 1)
= 5(x² + 1)
(10x + 10)
= 10(x + 1)
(y² + yp)
= y(y + p)
bringing the equations together and simplifying further
(y + p)(x + 1) / 5(x² + 1) * 10(x + 1) / y(y + p)
= 10(x + 1)(x + 1) / 5y(x² + 1)
= 10(x² + 1) / 5y(x² + 1)
= 2/y
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The volume of a tree stump can be modeled by considering it as a right cylinder. Xavier measures its height as 2.1 ft and its circumference as 61 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.
The volume of the stump is 7451.9 cubic inches.
How to find the volume of the stump in cubic inches?The volume of a cylinder can be calculated using formula below:
V = πr²h
where r is the radius and h is the height of the cylinder
We have circumference (C) = 61 in.
Let's find the radius (r) using the formula:
C = 2πr
61 = 2 * 22/7 * r
r = 9.70 in
h = 2.1 ft = 2.1 * 12 = 25.2 in
Substituting into V = πr²h:
V = 22/7 * 9.70² * 25.2
V = 7451.9 cubic inches
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What is 692837 divided by 28736
Answer:24.1104189866
Step-by-step explanation:
the answer to What is 692837 divided by 28736 is 24.1104189866
14. The graph below represents the number of books checked out at a library. What
is the constant of proportionality (unit rate per hour)?
The required constant of proportionality is 5.
A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.
So, the slope is given as,
m = rise/run
From the graph put the value for any point, we choose (2, 10)
So,
m = 10/2
m = 5
Thus, the required constant of proportionality is 5.
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Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories. Make sure you include work.
Answer:
To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.
From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:
Number of stories: 5
Number of cards used: 40
To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).
Ratio = Number of stories / Number of cards used
Ratio = 5 / 40
Now, we can use this ratio to calculate the number of cards needed for 100 stories:
Number of cards for 100 stories = Ratio * Number of stories
Number of cards for 100 stories = (5 / 40) * 100
Calculating the result:
Number of cards for 100 stories = (0.125) * 100
Number of cards for 100 stories = 12.5
Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.
Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.
p, q and r are prime numbers such that pqr3=270.
Work out the values of p, q and r.
b. Work out the highest common factor of 270 and 105.
The highest common factor of 270 and 105 is 15.
How to find the highest common factorfinding the prime factorization of 270.
The prime factorization of 270 can be written as:
270 = 2 * 3^3 * 5
From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.
So the values of p, q, and r are:
p = 2
q = 3
r = 5
Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.
The prime factorization of 270 is:
270 = 2 * 3^3 * 5
The prime factorization of 105 is:
105 = 3 * 5 * 7
To find the HCF, we need to find the common factors and choose the highest one.
The common factors of 270 and 105 are 3 and 5.
The highest common factor of 270 and 105 is 3 * 5 = 15.
Therefore, the highest common factor of 270 and 105 is 15.
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what is 27% in a equivalent form using the two other forms of notian: fraction,decimal,or percent
You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).
Or as a decimal 0.27.
Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?
A.
40
B.
62
C.
84
D.
100
The sum of Jerry's and Carrie's ages is 52. Jerry is 4 years older than Carrie. What is Jerry's age?
Answer:
28
Step-by-step explanation:
let's assumed that
x = Jerry's age
y = Carrie's age
if Jerry 4 years older that Carrie
x = y + 4
x + y = 52
(y + 4) + y = 52
2y + 4 = 52
2y = 48
y = 24
x = y + 4
x = 24 + 4
x = 28
#CMIIWPLS HELP ME, WILL GIVE BRAINLIEST!!!!!!!!!!!!!
sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2
Find the volume of the pyramid above
Find the surface are of the pyramid above pls help
The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²
What is a pyramid?A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
Surface area of a pyramid is expressed as;
area of 4 lateral face + area of base
area of base = 440²
= 193600 units²
area of a lateral = 1/2 bh
= 1/2 × 440 × 356
= 78320
For four surfaces = 4 × 78320 = 313280
Total surface area = 313280+78320
= 391600 units ²
Volume of a pyramid is expressed as;
V = 1/3base area × height
V = 1/3 × 440² × 280
V = 18069333.33 units³
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HELP PLS DUE IN 5 MINUTES!!!!!!!!!!
Answer:
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Step-by-step explanation:
Find the percentage and round to the nearest hundredth
7.2% of $ 8,650,00
The percentage is given by the expression A = ( 7.2 % ) ( 8650.00 ) and the value of A = $ 622.80
Given data ,
Let the initial amount be represented as P
Now , the value of P is
P = $ 8,650.00
On simplifying the equation , we get
Let the percentage value be d = 7.2 %
On simplifying the percentage , we get d = 0.072
So , A = 0.072 ( 8,650.00 )
Multiplying the expression , we get
A = $ 622.80
Therefore , the value of A is A = $ 622.80
Hence , the expression is A = $ 622.80
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Please help me, first time I got it wrong
The conditional value probability is solved and P ( F | E ) = 6/17
Given data ,
P ( E ) = 0.85
P ( F ) = 0.4
P ( E ∩ F ) = 0.3
Now , the formula for conditional probability to calculate P(F|E):
P(F|E) = P(E ∩ F) / P(E)
We are given that P(E) = 0.85 and P(E ∩ F) = 0.3, so we can substitute those values in:
P(F|E) = 0.3 / 0.85
Simplifying this fraction, we get:
P(F|E) = 6/17
Hence , the probability of F given that E has occurred is 6/17 or approximately 0.35.
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Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles.
3.4 cm, 3.1 cm, 6.6 cm
We can see here that the given side lengths cannot be used to form a unique triangle because the shorter sides do not add up to the longer side.
What is a triangle?The fundamental geometric shape of a triangle has three sides and three angles. It is a triangular polygon with three edges.
We can see here that in order to determine if the given side lengths:
3.4 cm, 3.1 cm, 6.6 cm
can form a unique triangle, many different triangles, or no triangle, we need to check if they satisfy the triangle inequality theorem.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's check the conditions:
3.4 cm + 3.1 cm = 6.5 cm
6.5 cm > 6.6 cm (Not satisfied)
3.4 cm + 6.6 cm = 10 cm
10 cm > 3.1 cm (Satisfied)
3.1 cm + 6.6 cm = 9.7 cm
9.7 cm > 3.4 cm (Satisfied)
he specified side lengths cannot be used to create a triangle because the total of the two shorter sides' lengths (3.4 cm and 3.1 cm) is not larger than the length of the longest side (6.6 cm).
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What is 1/3 of 343???????????
The number that is one-third of 343 is 49.
1/3 of 343 can be found by multiplying 343 by 1/3:
1/3 x 343 = (1/3) x (343) = 343/3
To simplify the result, we can divide both the numerator and denominator by the greatest common factor (GCF) of 343 and 3, which is 7:
343/3 = (343 ÷ 7) / (3 ÷ 7) = 49/1
Therefore, 1/3 of 343 is 49.
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