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In order to find the scale factor between the triangles, we can compare the sides PR and PT, which are corresponding sides between the triangles.
The side PR has a length of 27 units, and the side PT has a length of 9 units, so we can find the scale factor by dividing one length by the other:
[tex]\text{scale factor}=\frac{PR}{PT}=\frac{27}{9}=3[/tex]Now that we have the scale factor, we can find the length of PS by comparing it with the corresponding side PQ:
[tex]\begin{gathered} \text{scale factor}=\frac{PQ}{PS} \\ 3=\frac{24}{PS} \\ PS=\frac{24}{3}=8 \end{gathered}[/tex]If the length of PS is 8 units and S is above the x-axis to the right, its coordinates will be (8, 0).
Related Questions
Find the value of X and each arc measurex =mGK=mHJ = mHGJ =mGKJ=
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where:
[tex]\begin{gathered} m\angle GK=9x-22 \\ m\angle GH=61 \\ m\angle HJ=5x-7 \\ m\angle KJ=34 \\ so\colon \\ 9x-22+61+5x-7+34=360 \\ \end{gathered}[/tex]add like terms:
[tex]14x+66=360[/tex]Solve for x:
[tex]\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=\frac{294}{14} \\ x=21 \end{gathered}[/tex]Hence:
[tex]\begin{gathered} m\angle GK=9x-22=9(21)-22=167 \\ m\angle HJ=5x-7=5(21)-7=98 \end{gathered}[/tex]Solve the following system of equations graphically on the set of axes below.y = -1/3x - 4 y = 2/3x + 2
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Given:
[tex]\begin{gathered} y=-\frac{1}{3}x-4 \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]Therefore, the system of solution is (-6,-2)
Type the correct answer in each box. Use numerals instead of words.Sabrina is researching the growth of a population of horses on a ranch. She models the population of horses using the function below, where n is the number of years after she begins the research and b is an unknown base.
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The initial number of horses is given by n=0.
Replacing on the equation:
[tex]\begin{gathered} w(0)=15\ast b^0 \\ w(0)=15\ast1 \\ w(0)=15 \end{gathered}[/tex]The initial number of horses is 15.
Now, if b= 1.35
We need to convert it to percentage:
b = 1.35 = 135%
Therefore, the growth is:
135%-100% = 35%
Then,
If b = 1.35, the annual percentage growth rate of the number of horses would be 35%.
A geometric sequence has allpositive terms. The sum of thefirst two terms is 15 and the sumto infinity is 27.a Find the value of the commonratio.b Hence, find the first term.
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a) Common ratio = 2/7
b) First term = 135/7
Explanations:The formula for finding the sum of a geometric progression is expressed as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Since the sum of the first two terms is 15, then
S2 = 15
n = 2
Substitute into the formula:
[tex]\begin{gathered} S_2=\frac{a\mleft(r^2-1\mright)}{r^{}-1} \\ 15=\frac{a(r+1)\cancel{r-1}}{\cancel{r-1}} \\ 15=a(r+1) \end{gathered}[/tex]Also, the sum to infinity of a geometric sequence is expressed as:
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ _{} \end{gathered}[/tex]Substitute the given values into the formula:
[tex]27=\frac{a}{1-r}[/tex]Solve both expressions simultaneously
[tex]\begin{gathered} 15=a(r+1) \\ 27=\frac{a}{1-r} \end{gathered}[/tex]
Divide both expressions to have:
[tex]\frac{15}{27}=\frac{1-r}{r+1}[/tex]Cross multiply and solve for the common ratio "r"
[tex]\begin{gathered} 15(r+1)=27(1-r) \\ 15r+15=27-27r \\ 15r+27r=27-15 \\ 42r=12 \\ r=\frac{12}{42} \\ r=\frac{2}{7} \end{gathered}[/tex]Hence the value of the common ratio is 2/7
b) Get the first term of the sequence;
Using the formula:
[tex]\begin{gathered} 27=\frac{a}{1-r} \\ 27=\frac{a}{1-\frac{2}{7}} \\ 27=\frac{a}{(\frac{5}{7})} \\ a=27\times\frac{5}{7} \\ a=\frac{135}{7} \\ \end{gathered}[/tex]Hence the first term of the sequence is 135/7
I need help converting standard form to vertex form with quadratic equations. The equation is: y = -x^2 + 12x -4I think I am supposed to complete the square, but I am unsure how to do this. I am also unsure about what to do with the negative sign. I would love clear, step by step instructions on the process so I can know how to do it in the future.
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Okay, here we have this:
Considering the provided equation in standard form, we are going to convert it to vertex form step by step, so we obtain the following:
y = -x²+ 12x -4
Considering that the model of an equation in standard form is y=ax²+bx+c. First we are going to axtract "a" from the first two terms:
y=-1(x²-12x)-4
Now, we are going to complete the square for the expressions with x, so we have:
y=-1(x²-12x+36-36)-4
y=-1((x - 6)²-36) -4
And, finally we are going to simplify:
y=-1(x - 6)²+36-4
y=-(x - 6)²+32
We obtain that the equation in vertex form is y=-(x - 6)²+32.
Use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram p( 4p + 9)
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Given data:
The given expression is p( 4p + 9).
The given expression can be written as,
[tex]p(4p+9)=4p^2+9p[/tex]Thus, the simplification of the given expression is 4p^2 +9p.
Write a compound inequality for the graph shown below.Use x for your variable.-10 -9 -8 -7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10xor x < 2and□<口>OOSONOS?AorX
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Given:
Given that graph of the inequality.
Required:
To write a compound inequality for the given graph.
Explanation:
From the given graph,
[tex]x<-1[/tex]and x
[tex]x\ge2[/tex]Final Answer:
[tex]x<-1\text{ or }x\ge2[/tex]2.) for the line represented by the given equation, find both the X intercept and the y-intercept. (Don’t simply look on the graphing calculator ). Make sure you indicate which answer is the x-intercept and which is the y-intercept . Then graph the line
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Answer:
To find the y-intercept, we substitute x=0 in the given equation:
[tex]\begin{gathered} y=\frac{1}{2}\cdot0+3, \\ y=3. \end{gathered}[/tex]Therefore, the y-intercept has coordinates (0,3).
To find the x-intercept, we set y=0, and solve for x:
[tex]\begin{gathered} 0=\frac{1}{2}x+3, \\ 0-3=\frac{1}{2}x+3-3, \\ -3=\frac{1}{2}x, \\ 2\cdot(-3)=2\cdot(\frac{1}{2}x), \\ x=-6. \end{gathered}[/tex]Therefore, the x-intercept has coordinates (-6,0).
Finally, the graph of the given equation is:
To qualify for a certain need-based scholarship, a student must get a score of at least 75 on a qualification test. In addition, the student's family must make less than $40.000 a year. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.WRITE TWO INEQUALITIES AND ONE POSSIBILITY:
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In this problem we have to define the variables, so we can call the score of the student as x and the amount of money of the family let's call y so the inequalitys are:
[tex]\begin{gathered} x>75 \\ y<40000 \end{gathered}[/tex]Ned Robinson buys a microwave for $149.99, a microwave cart for $119.95, andmicrowave cookware for $19.95. The sales tax rate is 5.5 percent. What is thetotal purchase price?
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Ned Robinson buys a microwave for $149.99.
A microwave cart for $119.95.
A microwave cookware for $19.95.
tax rate is 5.5 %
total amount =
[tex]\begin{gathered} 149.99+119.95+19.95=28.89 \\ \end{gathered}[/tex]thus 5.5% of 28.89 is,
[tex]\begin{gathered} 28.89\times\frac{5.5}{100} \\ =15.94 \end{gathered}[/tex]thus total bill is,
[tex]28.89+15.94=44.83[/tex]Select the correct answer. Select the place of the digit 2 in this number. 296,743 ten thousands hundred thousands one thousands hundreds tens ones
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the place of the digit 2 in the number 296,743 is: hundred thousands
PART E.)In terms of the trigonometry ratios for triangle BCD, what is the length of line BD. Insert text on the triangle to show the length of line BD. When you’re done use the formula for the area of a triangle area equals 1/2 times base times height write an expression for the area of triangle ABC this when you do this base your answer on what u did in part E
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Sine formula
[tex]\sin (angle)=\frac{\text{opposite side}}{hypotenuse}[/tex]Considering angle C from triangle BCD, the opposite side is side BD and the hypotenuse is side BC which length is a units. Then:
[tex]\begin{gathered} \sin (\angle C)=\frac{BD}{a} \\ \text{ Isolating BD} \\ \sin (\angle C)\cdot a=BD \end{gathered}[/tex]The area of a triangle is calculated as follows:
[tex]A=\frac{1}{2}\cdot\text{base}\cdot\text{height}[/tex]In triangle ABC the base is b units long and its height is segment BD, then the area of triangle ABC is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot BD \\ \text{ Substituting with the previous result:} \\ A=\frac{1}{2}\cdot b\cdot a\cdot\sin (\angle C) \end{gathered}[/tex]
I did something wrong here according to my teacher. Can you help?
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Answer:
• Line of Symmetry: x=-0.5
,• Vertex: (-0.5, 5.5)
,• Maximum
,• y-intercept: (0, 3)
Explanation:
Given the quadratic function:
[tex]y=-10x^2-10x+3[/tex]Comparing with the form y=ax²+bx+c:
[tex]a=-10,b=-10,c=3[/tex](a)Line of Symmetry
The equation of symmetry is determined using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =\frac{-(-10)}{2(-10)} \\ =\frac{10}{-20} \\ x=-0.5 \end{gathered}[/tex](b)Next, we find the corresponding y-value.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(-0.5)^2-10(-0.5)+3 \\ y=5.5 \end{gathered}[/tex]The vertex of the parabola is (-0.5, 5.5).
(c)Since the value of a is negative, the vertex is a maximum.
(d)y-intercept
The y-intercept is the value of y when x=0.
[tex]\begin{gathered} y=-10x^{2}-10x+3 \\ y=-10(0)^2-10(0)+3 \\ y=3 \end{gathered}[/tex]The y-intercept is at (0, 3).
the width of a rectangular rug is 3 1/4 inches longer than twice its length. if the perimeter of the rug is 54 1/2 inches, which equation represents this situation?
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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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Simply the expression 11s(4)
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44s
Explanation:[tex]\begin{gathered} \text{Given:} \\ 11s(4) \end{gathered}[/tex]To simplify the expression, we will expand the parenthesis:
[tex]\begin{gathered} 11s(4)\text{ = 11s }\times\text{ 4} \\ 11\text{ and 4 are numbers so we will multiply them together} \\ 11\text{ }\times\text{ 4 = 44} \end{gathered}[/tex][tex]\begin{gathered} 11s(4)\text{ = 11 }\times\text{ s }\times\text{ 4} \\ =\text{ 44 }\times\text{ s} \\ =\text{ 44s} \end{gathered}[/tex]The angle of elevation from ground level to the top of a water tower that is 280 ft away measures 27 degrees. What is the height of the tower?
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We can draw
x represents the height of the water tower
we have a right triangle
we can use a trigonometric function
[tex]\tan (27)=\frac{x}{280}[/tex]we need to clear x
[tex]x=\tan (27)\cdot280=142.66\text{ ft}[/tex]A marketing research company desires to know the mean consumption of meat per week Among people over age 31 they believe that the meat consumption has mean of 3.1 pounds and want to construct a 85% confidence interval with the maximum error of 0.06 pounds assuming a standard deviation of 0.8 pounds what is the minimum number of people over age 31 they must include in their sample? Round your answer up to the next integer
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ANSWER:
369
STEP-BY-STEP EXPLANATION:
Given:
Mean (μ) = 3.1
Standard deviation (σ) = 0.8
Margin of error (E) = 0.06
At 85% confidence level the z is:
[tex]\begin{gathered} \alpha=1-\text{ confidence level} \\ \\ \alpha=1-85\%=1-0.85=0.15 \\ \\ \alpha\text{/2}=\frac{0.15}{2}=0.075 \\ \\ \text{ The corresponding value of z according to the table is:} \\ \\ Z_{\alpha\text{/2}}=1.44 \end{gathered}[/tex]We can determine the sample size using the following formula:
[tex]\begin{gathered} n=\:\left(\frac{Z_{\alpha\text{/2}}\cdot\sigma}{E}\right)^2 \\ \\ \text{ We replacing:} \\ \\ n=\left(\frac{1.44\cdot0.8}{0.06}\right)^2 \\ \\ n=368.64\cong369 \end{gathered}[/tex]The size of the sample is 369
What is the exact solution of cos 2x? Thank you!
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Answer:
119/169
Explanation:
We use the following trig identity
[tex]\cos2x=1-2\sin^2(x)[/tex]Now in our case, we know that
[tex]\sin x=-\frac{5}{13}[/tex]therefore, our formula gives
[tex]\cos2x=1-2*(\frac{5}{13})^2[/tex]which simplifies to give
[tex]\boxed{\cos2x=\frac{119}{169}.}[/tex]consider the function w(x) = 2x^3 + 15x^2 -36x - 6 on interval -6 ≤ x ≤ 2
On the given interval this function has absolute:
Minimum at the point -
Maximum at the point -
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The minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
What is absolute value?Absolute value describes the distance from zero that a number is on the number line, without considering direction.
Given a function, f(x) = 2x³+15x²-36-6
f'(x) = 6x²+30-36
Let f'(x) = 0
6x²+30-36 = 0
On solving, we get,
x = 1 or -6
Putting x = 1,-6, 2 for maximum and minimum values
f(1) = -25
f(-6) = 318
f(2) = -2
Hence, the minimum absolute value of the function is at x = 1 and the maximum absolute value is at x = -6.
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Divide by multiplying by the reciprocal of the divisor 1/4 / 2/7
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We want to divide 1/4 / 2/7
If we take the reciprocal of the 2/7, it means that the division sign will change to multiplication. Reciprocal of 2/7 = 7/2
Thus, the expression will be
1/4 x 7/2
= 7/8
The table below shows Addison's novel collection on her bookshelf.
Please help me with this I need it fast (view the image)
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The total number of books is 11 thus the ratio of fiction novels to all novels will be 5/11 thus, option (C) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Number of nonfiction books = 2
Number of mystery books = 4
Number of fiction books = 5
Total number of books = 2 + 4 +5 = 11
Thus, the ratio of fiction books to all books,
⇒ 5/11
Hence "The total number of books is 11 thus the ratio of fiction novels to all novels will be 5/11".
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The following data values represent a population. What is the variance of thepopulation? μ = 11. Use the information in the table to help you.X8101214(x-μ)²9119OA. 10B. 5O C. 11OD. 20
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The variance is calculated given the formula:
[tex]\begin{gathered} Variance=\frac{\sum(x-\mu)^2}{N} \\ \\ \sum(x-\mu)^2=9+1+1+9 \\ \\ \sum(x-\mu)^2=20 \end{gathered}[/tex]The sample
Blake is cutting drdles out of construction paper. Each circle has a radius of 6 inches. How
much paper will he use to cut 10 circles (round your answer to the nearest tenth of a square
inch)?Use 3.14 for #.
Anyone can help like now?☹️
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He is cutting circles. Each circle has 6 inches of radius. He needs 10 circles.
So, the area of one circle is A=pir²
A=3.14*6²
A=3.14*36
A=113.04
But there are 10 of them, so the total area will be 1130.4 in² of construction paper.
In the figure, BC||DE Angles_____1.CAF and EFA2.GAC and DFE3.CAF and EFH4.GAB and EFAare congruent______1.By the linear pair Theorem.2. because they are corresponding angles of parallel lines cut by transversal.3. by the vertical angles theorem.4. by the transitive property of congruence.GAC - CAFE because they are corresponding angles of parallel lines cut by a transversal.LAFE - HFD by the Vertical Angles Theorem.GAC - HFD by the_____1. Addition 2. Subtraction3. Substitution4. TransitiveProperty of Congruence.
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CAF and EFH are congruent because they are corresponding angles of parallel lines cut by transversal.
Explanation:
BC is parallel to DE
Checking the options for angles that are congruent(the same):
1) CAF and EFA
Both angles are not corrsponding angles. They are not equal
2) GAC and DFE are not equal. DFE is a straight line.
3) CAF and EFH are corresponding angles. Hence the angles are congruent.
4) GAB and EFA are not equal. Hence, they are not congruent.
Hence, CAF and EFH are congruent because they are corresponding angles of parallel lines cut by transversal.
Determine number of lines of symmetry for this figure
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There are 4 lines of symmetry in the figure. The angle of rotation that map the figure onto itself is angle 90°.
What is a line of symmetry?
This refers to the line that cuts a shape or an object into two equal and symmetrical parts. It also is called the axis of symmetry or mirror line this is because it divides the figure symmetrically, thus dividing the parts to look like mirror reflections of each other.
Types of Symmetry
.Rotational symmetry
.Reflection symmetry
.Translation symmetry
.Glide reflection symmetry.
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The profit P(x) obtained by manufacturing and selling x units of a certain product is given by P(x) = 60x - x2. Determine the number of units that must be produced and sold to maximize the profit. What is the maximum profit?
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Answer:
The number of units that must be produced and sold to maximize the profit is 30 units
[tex]30\text{ units}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]Explanation:
Given that the profit P(x) obtained by manufacturing and selling x units of a certain product is given by;
[tex]P(x)=60x-x^2[/tex]The maximum point is at;
[tex]P^{\prime}(x)=0[/tex]Differentiating P(x);
[tex]\begin{gathered} P^{\prime}(x)=60-2x=0 \\ 60-2x=0 \\ 2x=60 \\ x=\frac{60}{2} \\ x=30 \end{gathered}[/tex]The number of units that must be produced and sold to maximize the profit is 30 units
Substituting x into p(x);
[tex]\begin{gathered} P(30)=60(30)-30^2 \\ P(30)=900 \end{gathered}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]Find the quotient and remainder using long division.x4 − 5x3 + x − 4 / x2 − 7x + 1
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Given:
[tex]\frac{x^4-5x^3+x-4}{x^2-7x+1}[/tex]Required:
To find the quotient and remainder using long division.
Explanation:
Now
[tex]\begin{gathered} x^^2+2x+13 \\ ----------- \\ x^2-7x+1)x^4-5x^3+x-4 \\ \text{ }-x^4+7x^3-x^2 \\ --------------- \\ \text{ }+2x^3-x^2+x \\ \text{ }-2x^3+14x^2-2x \\ ---------------- \\ \text{ }+13x^2-x-4 \\ \text{ }-13x^2+91x-13 \\ ----------------- \\ \text{ }90x-17 \end{gathered}[/tex]Final Answer:
The quotient is
[tex]x^2+2x+13[/tex]The remainder is
[tex]90x-17[/tex]Solve the inequality and graph the solution set on a real number line. Express the solution set in interval notation|x2 + 3x - 29 > 25The solution set is(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
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Given:
[tex]|x^2+3x-29|>25[/tex]A swimmer dives into the pool from a 6 foot platform modeled by the following y=x- 12x + 6. What was the maximum depth that the swimmer reached?
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The expression that models the swimmer dive is given by:
[tex]y=x^2-12x+6[/tex]Which is a parabolla, the maximum depth of the swimmer will be the value of "y" that corresponds to the vertex of this shape. We can calculate the vertex of the parabola by using the following formula:
[tex]x=-\frac{b}{2a}[/tex]Whera a is the number multiplying x² and b is the number multiplying x. Applying the data from the problem we have:
[tex]x=-\frac{(-12)}{2}=6[/tex]We can now find the depth by applying this value of x to the expression, we have:
[tex]\begin{gathered} y=(6)^2-12\cdot6+6 \\ y=36-72+6 \\ y=30 \end{gathered}[/tex]The maximum depth was 30 feet.
complete the number sentence to solve enter this answer in simplest form 6 students share 8 granola bars equally how many granola bars does each student get?
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4/3 of each granola bar ( 1 1/3)
1) Given that 6 students share 8 granola bars we can write the following fraction with 8 on the numerator and 6 on the denominator since it is a division:
[tex]\frac{8}{6}=\frac{4}{3}\text{ or 1.333}[/tex]2) Each student will get 4/3 of each granola bar or 1 and 1/3