Answer: 7
Step-by-step explanation:
As our first step, we can divide 72 by 9 to discover the width of the first AND second painting. 72÷9=8
Now that we have discovered the width of the second painting, we will now solve the mathematical expression 56÷8.
Because 56 divided by 8 equals 7, the length of the second painting is 7 inches.
I need to make 500$ per week after tax in order to pay all my bills. The income tax is 20% What is the smallest pre-tax weekly salary I can earn and still be able to pay my bills after I pay my income tax?
I must earn at least $625 (or more) per week before tax to pay my bills.
Given,
To make $500 per week after tax in order to pay all my bills.
and, The income tax is 20%
To find the smallest pre-tax weekly .
Now, According to the question:
Let x be the amount to earn pre - tax.
The income tax is 20% = 20/100 = 0.2
Set up an inequality:
x - 0.2x > = 500
0.8 > = 500
x >= 500/0.8
x >= 625
Hence, I must earn at least $625 (or more) per week before tax to pay my bills.
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I need help with the problem!
a)The vertex of the function is (3, -1)
b)The line of symmetry is x= 3
c) The maximum is no maximum and minimum is (3, -1)
a) What is the vertex of the function of the parabola ?
[tex]f(x) = x^{2} -6x+8[/tex]
Transforming the function in the vertex form,
[tex]f(x) = a(x-h)^{2} +k[/tex]
[tex]f(x)=(x-3)^{2} -1[/tex]
The vertex of the function is given by,
(h, k) = (3, -1)
So ,the vertex of the function of the parabola is (3, -1)
b) What is the line of symmetry in the function?
In a parabola , the axis of symmetry is x = h.
Here, x = 3
So, the line of symmetry of the function of the parabola is x= 3
c) What is the maximum and minimum?
There is no maximum for the function because, the parabola opens upward. (Refer image for graph)The minimum for the function is the vertex (h, k) = (3, -1)What is a function of a parabola?
A parabola is the shape of a quadratic function's graph. Although the width or steepness of a parabola can vary as well as its direction of opening, they share the same fundamental U form. Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.To learn more about function of a parabola , refer:
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The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 62.
we are given
mean=42
Std=10
if the mean=42 + std =10 42+10=52
if the mean=42 - std=10 42-10=32
Rule -- 68-95-99.7
68% of the measures are within 1 standard deviation of the mean.
42+10=52
95% are within 2.
42+20=62
99.7% are within 3.
42+30=72
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
we are ask for the porcentage of request between 42-62 (between the mean and 2+std)
62 is two standard deviations above the mean.
Of the 50% of the measures below the mean, 95% are between 42 and 62, so
0.95(50)=47.5
The approximate percentage of light bulb replacement requests numbering between 42 and 62 is of 47.5%
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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Given the following function, find f(-3), f(0), and f (2) f(x)=5x-2
The output values of f(-3), f(0) and f(2) of the function f( x ) = 5x - 2 are -17, -2 and 8 respectively.
What are the output values of f(-3), f(0) and f(2) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = 5x - 2f( -3 ) = ?f( 0 ) = ?f( 2 ) = ?For f( - 3 );
To find the output value of f( -3 ), replace all the occurrence of x with -3 in the function and simplify.
f( x ) = 5x - 2
f( -3 ) = 5(-3) - 2
f( -3 ) = -15 - 2
f( -3 ) = -17
For f( 0 );
To find the output value of f( 0 ), replace all the occurrence of x with 0 in the function and simplify.
f( x ) = 5x - 2
f( 0 ) = 5(0) - 2
f( 0 ) = 0 - 2
f( 0 ) = -2
For f( 2 );
To find the output value of f( 2 ), replace all the occurrence of x with 2 in the function and simplify.
f( x ) = 5x - 2
f( 2 ) = 5(2) - 2
f( 2 ) = 10 - 2
f( 2 ) = 8
Therefore, the output value of f( 2 ) is 8, this forms an ordered pair of ( 2, 8 ).
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Kaitlin races her bicycle for 98 m. A wheel of her bicycle turns 49 times as the bicycle travels this distance. What is the diameter of the wheel? Use the value 3.14 for n. Round your answer to the nearest tenth
Answer:
0.6m
Explanation:
Given the following
Total distance covered = 98m
pi = 3.14
Circumference of the wheel is the distance travelled in one rotation. Hence;
distance travelled in one rotation = \pi d
d is the diamter of the wheel
distance travelled in 49 rotation = 49*\pi d
Since distance travelled in 49 rotation = 98m, then;
98 = 49*\pi d
Divide both sides by 49
98/49 = \pi d
2 = 3.14d
d = 2/3.14
d = 0.6m
Hence the diameter of the wheel is 0.6m
Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%. (2.4)
Justify which statistics methodology needs to be used in the above context and
a) Determine the probability of losing money.
b) Find the probability of losing money when the standard deviation is equal to 10%.
a) The probability of losing money when standard deviation is 5% is 2.27%
b) The probability of losing money when standard deviation is 10% is 15.87%
Given,
There is an investment whose return is normally distributed.
The mean of the distribution = 10%
The standard deviation of the distribution = 5%
a) We have to determine the probability of losing money:
Lets take,
x = -0.005%
Now,
P(z ≤ (-10.005 / 5) ) = P(z ≤ - 2.001) = 0.02275
Now,
0.02275 × 100 = 2.27
That is,
The probability of losing money is 2.27%
b) We have to find the probability of losing money when the standard deviation is 10%
Let x be 0.01%
Now,
P(z ≤ (-10.01/10)) = P(z ≤ -1.001) = 0.15866
Now,
0.15866 × 100 = 15.87
That is,
The probability of losing money is 15.87%
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Triangle HJK has vertices at H(2, 2) J(2, 4) and K(0, 2). What is the midpoint of the longest side of the triangle?
The coordinates of the vertices of triangle are given as H(2,2), (J(2, 4), K(0,2)
We would determine the longest side by applying the formula for finding the distance between two points which is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{x2-x1)^2+(y2-y1)^2} \\ \text{For HJ, x1 = 2, y1 = 2, x2 = 2, y2 = 4} \\ \text{Distance = }\sqrt[]{(2-2)^2+(4-2)^2}\text{ = }\sqrt[]{2^2}\text{ = 2} \\ \text{For JK, x1 = 2, y1 = 4, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{(0-2)^2+(2-4)^2}=\sqrt[]{(4+4)}=\text{ }2.83 \\ \text{For HK, x1 = 2, y1 = 2, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{0-2)^2+(2-2)^2}=\text{ }\sqrt[]{4}\text{ = 2} \end{gathered}[/tex]Thus, the longest side is JK. The formula for finding midpoint is
Midpoint = (x1 + x2)/2, (y1 + y2)/2
Midpoint = (2 + 0)/2, (4 + 2)/2
Midpoint = 2/2, 6/2
Midpoint = 1, 3
If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.7013. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
Apply the product rule to rewrite the product below using a single base and exponent then simplify: 3^2 *3^3 our base is Answerour exponent is Answerthis simplifies to Answer
Explanation:
[tex]3^2\text{ }\times3^3[/tex][tex]\begin{gathered} \text{The expression has same base.} \\ \text{Base = 3} \\ We\text{ take one base and bring the exponents together} \\ \text{The sign betw}en\text{ them changes from multiplication to addition} \end{gathered}[/tex][tex]\begin{gathered} 3^2\text{ }\times3^3\text{ = }3^{2\text{ + 3}} \\ \text{Exponent = 2 + 3} \\ \text{Exponent = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying:} \\ 3^{2+3}=3^5 \\ 3^5\text{ = 243} \end{gathered}[/tex]The start of a quadratic
sequence is
8, 18, 30, 44, 60, …
What is the nth term rule for this sequence?
Answer:
The correct option is D
98
The general term of the sequence is n(n+7)
what number need to be changed to make a linear function? And what does it have to turn into?
In order to have a linear function, the rate of change needs to be the same in each point
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For
(-18,2)=(x1,y1)
(-14,4)=(x2,y2)
[tex]m=\frac{4-2}{-14+18}=\frac{1}{2}[/tex]for
(-14,4)=(x1,y1)
(-12,5)=(x2,y2)
[tex]m=\frac{5-4}{-12+14}=\frac{1}{2}[/tex]for
(-12,5)=(x1,y1)
(0,12)=(x2,y2)
[tex]m=\frac{12-5}{0+12}=\frac{7}{12}[/tex]as we can see here are the two numbers so we will obtain the equation in order to know the number that needs to be change
[tex]y=\frac{1}{2}x+11[/tex]therefore if x=0
[tex]y=\frac{1}{2}(0)+11=11[/tex]the number we need to change is 12 and need to be changed for 11
(0,11)
a. The number that needs to be changed in order to create a linear function is 12
b. That number needs to be changed to 11 in order for the function to be linear
h(x) = x2 + 1 k(x) = x-2 (h - k)(3) = DONE
We are given two functions:
h(x) = x^2 + 1
and k(x) = x - 2
We are asked to find the value of:
(h - k) (3) (the value of the difference of the two functions at the point x = 3
So we performe the difference of the two functions:
(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3
So, this expression evaluated at 3 gives:
(h-k)(3) = 3^2 - 3 + 3 = 9
One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:
h(3) = 3^2 + 1 = 10
k(3) = 3 - 2 = 1
Then, the difference is : h(3) - k(3) = 10 - 1 = 9
So use whatever method feels more comfortable for you.
14 pointsWhich are the coefficients of the terms in the algebraic expression, x2 - 3x?O and -31 and -3O and 351 and 36
Answer:
The coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]Explanation:
The coefficients are the number that multiplies an algebraic term in an algebraic expression.
for example; the coefficient of 3x is 3.
[tex]3x=3\times x[/tex]For the question;
given the expression;
[tex]x^2-3x[/tex]The coefficient of x^2 is 1
[tex]x^2=1\times x^2[/tex]while the coefficient of x is -3
[tex]-3x=-3\times x[/tex]Therefore, the coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]Use area under the curve to complete probability for continuous probability dentist functionsuse the uniform distribution to compute probabilityfind the mean and standard deviation Love the uniform distribution1.One type of card stock which may be used for the cover of a booklet is uncoated paper with waymark as 65 pounds the standard thickness of 65# of card stuck is 9.5 points (0.0095”). A manufacturer determines that the thickness of 65# of card stuck produced followed a uniform distribution varying between 9.25 points and 9.75 points.A)Sketch the description for this situation.B)compute the mean and standard division of the thickness of the 65# cards stuck producedC)compute the probability that a randomly selected piece of 65# card stark has a thickness of a list 9.4 points.D)Compute the probability that a randomly selected piece of 65# card stock has thickness between 9.75 points.
If x is uniformly distributed over the interval [ a , b ] then,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{b-a}\text{ , a }\leq\text{ x }\leq\text{ b} \\ f(x)\text{ = 0 , otherwise} \end{gathered}[/tex]Also ,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Std deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \end{gathered}[/tex]It is given that ,
[tex]\begin{gathered} a\text{ = 9.25} \\ b\text{ = 9.75} \\ b\text{ - a = 9.75 - 9.25 = 0.5} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{0.5}\text{ 9.25 }\leq\text{ x }\leq\text{ 9.75} \\ f(x)\text{ = 0 otherwise} \end{gathered}[/tex](a)The distribution is as follows :
(b)The mean is calculated as,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Mean = }\frac{9.25\text{ + 9.75}}{2} \\ \text{Mean = 9.5} \end{gathered}[/tex]Standard deviation is calculated as,
[tex]\begin{gathered} \text{Standard deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \\ \text{Standard deviation = }\sqrt[]{\frac{(0.5)^2}{12}} \\ \text{Standard deviation }\approx\text{ 0.1443} \end{gathered}[/tex](c) The probability is calculated as,
[tex]\begin{gathered} P(\text{ atleast 9.4 points ) = P( x }\ge\text{ 9.4)} \\ P(\text{ atleast 9.4 points ) = }\int ^{9.75}_{9.4}(\frac{1}{0.5})dx \\ P(\text{ atleast 9.4 points ) = }\frac{9.75\text{ - 9.4}}{0.5} \\ P(\text{ atleast 9.4 points ) = 0.7} \end{gathered}[/tex](d) The probability is calculated as,
[tex]\begin{gathered} P(\text{between 9.45 and }9.75\text{ ) = P( 9.45 }\leq\text{ x }\leq\text{ 9.75 )} \\ P(\text{between 9.45 and }9.75\text{ ) = }\int ^{9.75}_{9.45}(\frac{1}{0.5})dx \\ P(\text{between 9.45 and }9.75\text{ ) =}\frac{9.75\text{ - 9.45}}{0.5} \\ P(\text{between 9.45 and }9.75\text{ ) = 0.6} \end{gathered}[/tex]The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
divide fraction2*1/3 / 7*3/8 =
Step-by-step explanation:
3.999 is the correct answer
Find the AreaA. 314.2 IN2B. 1256.6 IN2C. 31.4 IN2D. 62.8 IN2
Given:
Diameter = 20 in
Find-:
Area of circle
Explanation-:
The area of circle is:
[tex]A=\pi r^2[/tex]The radius of circle is:
[tex]r=\frac{D}{2}[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ D=\text{ Diameter} \end{gathered}[/tex]So the radius of given circle is:
[tex]\begin{gathered} D=20\text{ in} \\ \\ r=\frac{D}{2}\text{ in} \\ \\ r=\frac{20}{2}\text{ in} \\ \\ r=10\text{ in} \end{gathered}[/tex]The area of circle is:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(10)^2 \\ \\ A=100\pi \\ \\ A=314.159 \\ \\ A=314.2\text{ in}^2 \end{gathered}[/tex]So, the area of a circle is 314.2
You use substitution to solve a system of equations and after simplifying end with a statement that says 7=7 discrible what this statement means about the number of solutions and about the graph of the system
need help asap look at attachment
Answer: Width =14, Length = 18
Step-by-step explanation:
L = W + 4
2W + 2L = 64
W+ L = 32
2W+ 4 = 32
2W = 28
W = 14
determine if each expression is equivalent to [tex] \frac{ {7}^{6} }{ {7}^{3} } [/tex]
The question says we are to check the options that are equal
[tex]\frac{7^6}{7^3}[/tex]Using the law of indices
[tex]\frac{7^6}{7^3}=7^{6-3\text{ }}=7^3[/tex]So we will check all the options(applying the laws of indices)
The first option is
[tex]7^9(7^{-6})=7^{9-6}=7^3[/tex]yes, the first option is equivalent
We will move on and check the second option
[tex]\frac{7^{-8}}{7^{-11}}\text{ = }7^{-8+11}=7^3[/tex]Yes the second option is equivalent
We will move on to check the third option
[tex](7^5)(7^3)divideby7^{4\text{ }}=7^{5+3-4\text{ }}=7^4[/tex]No the third option is not eqquivalent to the question
We will move to tthe next option, fourth option
[tex]7^{-3\text{ }}\times7^{6\text{ }}=7^{-3+6}=7^3[/tex]yes this option is equivalent to the fraction
Moving on to the fifth option
[tex](7^3)^{0\text{ }}=7^{3\times0}=7^0=\text{ 1}[/tex]No the fifth option is not equivalent to the question
Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Step-by-step explanation:
1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.
[tex]y=ax^2+bx+c[/tex]2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.
[tex]y=(ax+c)(bx+d)[/tex]3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.
[tex]y=a(x+b)^2+c[/tex]The vertex of the parabola is written as (h, k) where b is the x - coordinate and c - is the y - coordinate
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Value of x and y are -51 and 8 respectively
What is Algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Let,
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Be, equation 1, 2 and 3 respectively
X+27+32 = 8 -----(1)
X+ 3y +32 = 10 -----(2)
X + 2y +42 = 9 -----(3)
From equation we can find the value of x
X+27+32 = 8
X + 59 = 8
X = 8 - 59
X = - 51
Substituting the value of x in equation 3
X + 2y +42 = 9
(-51) + 2y + 42 = 9
-51 + 42 + 2y = 9
-9 + 2y = 9
2y = 9 + 9
2y = 18
y = 18/2
y = 9
Hence, the value of x = -51 and y = 9
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For what value of x does 32x93x-4?oo 2o 3o 4
Solution
[tex]3^{2x}=9^{3x-4}[/tex]We can do the following:
[tex]3^{2x}=3^{2(3x-4)}[/tex]And we have this:
[tex]2x=6x-8[/tex][tex]4x=8[/tex][tex]x=\frac{8}{4}=2[/tex]This is Calculus 1 Linear Optimization Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Given:
Required:
We need to find the value of AB
Explanation:
Here ABC is the right anglr triangle
so
[tex]\begin{gathered} AB^2=BC^2+AC^2=36+36=72 \\ AB=6\sqrt{2} \end{gathered}[/tex]Final answer:
The minimum length of crease is
[tex]6\sqrt{2}[/tex]use your theorem from 2-37 about the angles in a triangle to find in the diagram below. show all work.
We have that, for any triangle, the sum of all its angles equals 180. In this case, we have the following:
[tex]96+2x+(x+12)=180[/tex]Now we solve for x to get the following:
[tex]\begin{gathered} 96+2x+x+12=180 \\ \Rightarrow2x+x=180-96-12 \\ \Rightarrow3x=72 \\ \Rightarrow x=\frac{72}{3}=24 \\ x=24 \end{gathered}[/tex]We have that x = 24, now to find the angles, we substitute this value on each expression:
[tex]\begin{gathered} 2x \\ x=24 \\ \Rightarrow2(24)=48 \\ x+12 \\ \Rightarrow24+12=36 \end{gathered}[/tex]therefore, the remaining angles are 48° and 36°
4. Identify the properties that are always true for the given quadrilateral by placing an X in the appropriate box. Property Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite a. Opposite sides are parallel. b. Only one pair of opposite sides is parallel C. Opposite sides are congruent Side Relationships d. Only one pair of opposite sides is congruent e. All sides are congruent. f. 2 pairs of consecutive sides are congruent.
There is quadrilateral, means it has 4 lines
Is a rhombus
10. A $152,000 home has an assessment rate of 52% and a tax rateof $48 per $1,000. Use the effective tax method to calculate theproperty tax .Hint: When you determine the effective tax rate, round the rateto three places.
Given
$152,000
52% assessment rate
$48 per $1,000
Procedure
First, let's calculate the assessment rate.
[tex]152000\cdot0.52=79040.0[/tex]Now let's calculate the taxes
[tex]79040.0\cdot\frac{48}{1000}=3793.92[/tex]Property taxes are equal to $3,793.92.
Put these five fractions in order, left to right, from least to greatest. 1 /3 2 /7 3/10 4/13 5/17
The five fractions can be arranged in order, from the left to right, from least to greatest as : 5/17 , 3/10 , 4/13 , 1 /3.
How can the fraction can be arranged from the from least to greatest?The fraction can be arranged from the from least to greatest by firstly convert the fraction to the decimal numbers so that one c b able to identify the highest and the lowest values.
The given fractions 1 /3 2 /7 3/10 4/13 5/17 can be converted to decimal numbers as 0.33 , 0.67 , 0.30 , 0.31 , 0.29 respectively and this can be arranged as 5/17 , 3/10 , 4/13 , 1 /3.
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