Answer:
Arc length = (147/360) x (2π x 7)
Arc length = (0.40833) x (2 x 3.14159 x 7)
Arc length = 0.40833 x 43.9823
Arc length = 17.9955
Please solve part A&B with the steps, don't solve one part only!!
Therefore the set S = {v1, v2, v3, v4} is linearly independent.
How to solveThe set S = {v1, v2, v3, v4} of vectors in R4 is linearly independent if the only solution of
c1v1 + c2v2 + c3v3 + c4v4 = 0
is c1, c2, c3, c4 = 0
Otherwise (i.e., if a solution with at least some nonzero values exists), S is linearly dependent.
With our vectors v1, v2, v3, v4, (*) becomes:
c1
3
0
-3
6 + c2
0
2
3
1 + c3
0
-2
-2
0 + c4
-2
1
2
1 =
0
0
0
0
Rearranging the left hand side yields
3 c1 +0 c2 +0 c3-2 c4
0 c1 +2 c2-2 c3 +1 c4
-3 c1 +3 c2-2 c3 +2 c4
6 c1 +1 c2 +0 c3 +1 c4 =
0
0
0
0
The matrix equation above is equivalent to the following homogeneous system of equations
3 c1
+0 c2 +0 c3 -2 c4 = 00 c1 +2 c2 -2 c3 +1 c4 = 0-3 c1 +3 c2 -2 c3 +2 c4 = 06 c1 +1 c2 +0 c3 +1 c4 = . 0We now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine whether the system has
the trivial solution only (meaning that S is linearly independent), or
the trivial solution as well as nontrivial ones (S is linearly dependent).
Row
Operation
1:
3 0 0 -2
0 2 -2 1
-3 3 -2 2
6 1 0 1 multiply the 1st row by 1/3
1 0 0 -2/3
0 2 -2 1
-3 3 -2 2
6 1 0 1
Row
Operation
2:
1 0 0 -2/3
0 2 -2 1
-3 3 -2 2
6 1 0 1 add 3 times the 1st row to the 3rd row
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
6 1 0 1
Row
Operation
3:
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
6 1 0 1 add -6 times the 1st row to the 4th row
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
0 1 0 5
Row
Operation
4:
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
0 1 0 5 multiply the 2nd row by 1/2
1 0 0 -2/3
0 1 -1 1/ 2
0 3 -2 0
0 1 0 5
Row
Operation
5:
1 0 0 -2/3
0 1 -1 1/2
0 3 -2 0
0 1 0 5 add -3 times the 2nd row to the 3rd row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 1 0 5
Row
Operation
6:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 1 0 5 add -1 times the 2nd row to the 4th row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 1 9/2
Row
Operation
7:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 1 9/2 add -1 times the 3rd row to the 4th row
1 0 0 -2 /3
0 1 -1 1/2
0 0 1 -3/2
0 0 0 6
Row
Operation
8:
1 0 0 -2/3
0 1 -1 1 2
0 0 1 -3 2
0 0 0 6 multiply the 4th row by 1/6
1 0 0 -2/3
0 1 -1 1 /2
0 0 1 -3/ 2
0 0 0 1
Row
Operation
9:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 0 1 add 3/2 times the 4th row to the 3rd row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 0
0 0 0 1
Row
Operation
10:
1 0 0 -2/3
0 1 -1 1/ 2
0 0 1 0
0 0 0 1 add -1/2 times the 4th row to the 2nd row
1 0 0 -2/3
0 1 -1 0
0 0 1 0
0 0 0 1
Row
Operation
11:
1 0 0 -2/3
0 1 -1 0
0 0 1 0
0 0 0 1 add 2/3 times the 4th row to the 1st row
1 0 0 0
0 1 -1 0
0 0 1 0
0 0 0 1
Row
Operation
12:
1 0 0 0
0 1 -1 0
0 0 1 0
0 0 0 1 add 1 times the 3rd row to the 2nd row
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
The reduced row echelon form of the coefficient matrix of the homogeneous system (**) is
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Since each column contains a leading entry (highlighted in yellow), then the system has only the trivial solution, so that the only solution of is c1, c2, c3, c4 = 0.
Therefore the set S = {v1, v2, v3, v4} is linearly independent.
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The question is below.
The formula for the volume of a rectangular prism is:
V = l x w x h
where V is the volume, l is the length, w is the width, and h is the height.
We know that the volume of Caleigh's jewelry box is 14 cubic inches, and the area of the base is 7 square inches. Since the base of the box is a rectangle, we can use the formula for the area of a rectangle to find the length and width of the base:
A = l x w
7 = l x w
We don't know the exact values of l and w, but we do know that their product is 7.
Now we can use the formula for the volume of a rectangular prism to find the height:
14 = l x w x h
We know that l x w = 7, so we can substitute 7 for l x w:
14 = 7 x h
Dividing both sides by 7 gives:
h = 2
Therefore, the height of Caleigh's jewelry box is 2 inches.
HELP PLS
1st: Find the volume of the pyramid shown and round your answer to the nearest tenth.
2nd: Find the slant height x of the regular pyramid shown and round your answer to the nearest tenth.
3rd: Find the Surface Area of this Pyramid.
1. The volume of the pyramid = 12 mm³.
2. Slant height (x) x ≈ 4.3 mm
3. Surface area of square pyramid = 86.4 mm²
How to Find the Volume of a Square Pyramid?1. The volume of the pyramid (V) = 1/3*a²h, where:
a is the base edge = 3 mm
h is the height = 4 mm
Plug in the values:
The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.
2. Slant height (x) = √(1.5² + 4²)
x ≈ 4.3 mm
3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²
= 86.4 mm²
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NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometric ratios for angle a are given as follows:
[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, the hypotenuse is of [tex]3\sqrt{13}[/tex], while the side lengths relative to angle A are given as follows:
Opposite: 9.Adjacent: 6.Hence the trigonometric ratios are given as follows:
[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.More can be learned about trigonometric ratios at brainly.com/question/24349828
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Find the mean and variance of 2, 2, 3, 3, 3, 4, 4, 4, and 4.
The mean of the data set is 3.33.
The variance of the data set is 0.47.
We have,
To find the mean of the data set,
We need to add up all the numbers and divide by the total number of values:
Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9
= 3.33 (rounded to two decimal places)
To find the variance,
We need to first find the squared difference between each value and the mean:
(2 - 3.33)^2 = 1.11
(2 - 3.33)^2 = 1.11
(3 - 3.33)^2 = 0.11
(3 - 3.33)^2 = 0.11
(3 - 3.33)^2 = 0.11
(4 - 3.33)^2 = 0.44
(4 - 3.33)^2 = 0.44
(4 - 3.33)^2 = 0.44
(4 - 3.33)^2 = 0.44
Next, we need to find the average of these squared differences:
Average of squared differences
= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9
= 0.47 (rounded to two decimal places)
Thus,
The mean of the data set is 3.33.
The variance of the data set is 0.47.
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What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.
A. 5/2 and 25/4
B. 5/2 and 7/4
C. 7/2 and 25/4
D. 7/2 and 7/4
SOMEONE PLEAS HELP!
Answer:
The answer to your problem is, A. 5/2 and 25/4
Step-by-step explanation:
In the problem the two similar figures, with side lengths 30 yds and 12 yds.
In order to solve the problem we need to find the ratio of the perimeters and the ratio of the areas of the larger figure to the smaller figure.
Using this information we know the the ratio of the perimeter of similar figure is equal to the scale factor and the ratio of the areas equal to the square of the scale factor.
the scale factor = 30/12 = 5/2
the ratio of the perimeter = 5/2
the ratio of the areas = (5/2)² = 25/4
Thus the answer to your problem is, A. 5/2 and 25/4
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
1. A limit imposed by the government on the quantity of a good or product that can be brought into the
country is called a
a. tariff
b. quota
c. foreign bill of exchange
d. value added tax
2. Which of the following would not be an effective argument for the U.S. to enact trade restrictions?
a. they shield U. S. workers from competition by cheap foreign labor
b. they may benefit the security and defense of the nation
c. they help the U.S. maintain diverse industries
d. they make foreign products cheaper to U.S. shoppers
OO
3. What does it mean if a country is on the gold standard?
DO
a. it sets the value of its currency in relation to a specific amount of gold
b. it creates specific standards by which gold is made into jewelry
O c.
O d. none of these
4. Economists tend to classify a country as less developed if the country's average level of Income is less
than
it uses gold instead of paper currency
a. $9,500 per person
b. the average per-person-income of neighboring countries
c. $3.040 per person
gen
d. a U.S. welfare recipient's income
5. Which of the following would not be considered a barrier to economic development?
O
a. high levels of political corruption
b. low population growth
c. low human capital
d. shortage of investment capital
37-09-71.AK
1. A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota. The Option B.
2. An option that is not be an effective argument for the U.S. to enact trade restrictions is hey make foreign products cheaper to U.S. shoppers. The Option D is correct.
3. If a country is on the gold standard, this means that it sets the value of its currency in relation to a specific amount of gold. The Option A is correct.
4. An economists tend to classify a country as less developed if the country's average level of Income is less than $3.040 per person. The Option C is correct.
5. The option that would not be considered a barrier to economic development is low population growth. The Option B is correct.
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Use the equation d=rt if r=26 and t=3
Step-by-step explanation:
r=26
t=3
d=rt
d=26×3
d=78
In casino games the player roll a pair of dice . If the first throw is a 7or 11 the player wins automatically what is the probability that theplayer will win on the first throw
The probability of winning on the first roll is 0.22
Solution-
As in the game of casino, two dice are rolled simultaneously.
So the sample space would be,
|S| = 36
Let E be the event such that the sum of two numbers are 7, so
E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
|E| = 6
P(E) = 6/36
Let F be the event such that the sum of two numbers are 11, so
F = {(6,5), (5,6)}
|F| = 2
P(F) = 2/36
Now,
P(E∪F)= 0.22
The probability of winning on the first roll is 0.22
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Question 3-(3 marks available) у, Question 4 10 (3 marks available) X y -X Quadratic Graphs a) Complete the table of values for y=x²+1 -2 -1 0 1 2 3 52 1 2 5 10 b) The graph of y = x² + 1 is drawn or the axes on the left. Use the graph to estimate the values of x when y = 4. Give your answers to 1 decimal place. Quadratic Graphs
The y-values are 5, 2, 1, 2, 5, 10 and 17.
Given that an equation of a curve, y = x²+1, we need to find the values of the y-intercept corresponding to the given x-intercept,
So,
y = x²+1
Putting the values of x,
x = -2,
y = (-2)²+1
y = 5
(-2, 5)
x = -1
y = (-1)²+1
y = 2
x = 0,
y = (0)²+1
y = 1
x = 1
y = 2
x = 2,
y = 2²+1
y = 5
x = 3,
y = 3²+1
y = 10
when x = 4,
y = 4²+1
y = 17
Hence, the y-values are 5, 2, 1, 2, 5, 10 and 17.
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Originally, a Petri dish contained 200,000 bacteria. After a scientist applied an antibiotic, the number of bacteria decreased by 75% per hour.
Which function could model this situation?
well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t[/tex]
From the 12 albums released by a musician the recording company wishes to release 10 in a boxed set. How many different boxes sets are possible?
Ask a dif site if this one dont have it
.- Para hallar el volumen de una esfera, el valor de su radio se debe
elevar a la potencia 3 y este resultado debe ser multiplicado por-
Un balón esférico tiene como volumen 1000 x 7 centímetros
cúbicos, ¿cuánto mide su radio?
3
A) 10 centímetros.
B) 300 centímetros.
C) 1,000 centímetros.
R) 3,000 centímetros.
3
TU.
7 times a number is 30 greater than the sum of twice the number and 5. what is the number
HELP ASAP! The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
all
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars.
Select the equation that matches this situation.
Choose 1 answer:
Choose 1 answer:
(Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w
A
5 = 15 \times w5=15×w5, equals, 15, times, w
(Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5
B
w = 15 +5w=15+5w, equals, 15, plus, 5
(Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15
C
w = 5 \times 15w=5×15
what is the fraction equivalent of the ratio of boys to girls in a class if there are 12 boys and 18 girls ?
The length of a rectangle is seven more than double the width. If the perimeter is 122 inches, find the
dimensions.
The width is:
The length is
The length of the rectangle is 43 inches.
The width of the rectangle is 18 inches.
Given that,
The length of a rectangle is seven more than double the width.
Let width = x
Length = 7 + 2x
Perimeter of the rectangle = 122 inches
The formula to find the perimeter of a rectangle is,
Perimeter = 2 (length + width)
Substituting,
122 = 2 (7 + 2x + x)
61 = 7 + 3x
3x = 54
x = 18
Width = 18 inches
Length = 7 + 2x = 7 + 36 = 43 inches
Hence the length and width are 43 inches and 18 inches respectively.
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Find the value of x for the following
The length x in the similar triangle is 7.06 units.
How to find the side of similar triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Therefore, let's use the similarity of the triangle to find the value of x in the triangle.
Hence, using the proportion,
y / 8 = 8 / 17
cross multiply
17y = 64
y = 64 / 17
y = 3.76470588235
y = 3.76
Therefore,
17 - 3.76 = 13.24
Hence,
13.24 / x = x / 3.76
cross multiply
x² = 49.7824
x = √49.7824
x = 7.05566439111
Hence,
x = 7.06 units
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Not drawn to scale
: Find the value of x in the figure at the right. Round your answer to the nearest tenth.
MUST SHOW WORK.
The value of x from the given isosceles triangle is 5.6 units.
Given that, the measure of equal sides of an isosceles triangle is 6 units and the base measures 5.9 units.
Draw perpendicular bisector to base, so we get halves as 5.9/2 =2.95
Let the length of perpendicular bisector be x.
By using Pythagoras theorem, we get
6²=2.95²+x²
36=8.7025+x²
x²=36-8.7025
x²=27.2975
x=5.2 units
We know that, sinθ=Opposite/Hypotenuse
sin68°=5.2/x
x=5.6 units
Therefore, the value of x from the given isosceles triangle is 5.6 units.
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Please answer the question
The correct statement about the product of 5/12 and 7 is given as follows:
C. The product is greater than 5/12 but less than 7.
How to calculate the product?The multiplication operation for this problem is given as follows:
5/12 x 7.
The factors of the operation are given as follows:
5/12 and 7.
When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:
5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.
35/12 is a number close to 3, which is:
Greater than 5/12.Less than 7.Hence option C is the correct statement.
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I need help ASAP!!
The length of a rectangle is 4 meters longer than its width.
The area of the rectangle is
117m^2.
What is the width of the rectangle?
HINT: you can use DESMOS for this kind of problem.
Answer:
w(w + 4) = 117
w^2 + 4w = 117
w^2 + 4w - 117 = 0
(w - 9)(w + 13) = 0
w = 9 meters
The width of the rectangle is 9 meters, and the length of the rectangle is 13 meters.
explain why the graph would look like the line y=x if you graph it
The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
How to explain the informationBoth the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.
A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.
Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.
In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
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5/3 divided by 7 (answer as a fraction)
Answer: 5/21
Step-by-step explanation: it just is
the answer is 5/21 (0.23)
What is 7/12x - y/6x^2 expressed in simplest form
The expression 7/12x - y/6x² in its simplest form is (7x - 2y)/(12x²).
We have,
To simplify the expression 7/12x - y/6x², we need to find a common denominator for the two terms.
The common denominator is 12x^2.
Multiplying the first term by x/x and the second term by 2/2, we get:
(7x)/(12x²) - (2y)/(12x²)
Combining the two terms, we get:
(7x - 2y)/(12x²)
Therefore,
7/12x - y/6x² in its simplest form is (7x - 2y)/(12x^2).
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please help im begging
The correct statements regarding the solutions of the quadratic function is given as follows:
Two complex solutions.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the general equation presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given by the equation as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.The function for this problem is given as follows:
y = 2x² - 8x + 10.
The coefficients are given as follows:
a = 2, b = -8 and c = 10.
Hence the discriminant is given as follows:
Δ = (-8)² - 4 x 2 x 10
Δ = 64 - 80
Δ = -16.
Negative discriminant, hence the equation has two complex solutions.
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Can someone help me with this problem?
7. Radius of circle P = 2 Radius of circle Q = 1
Coordinates of the point of tangency (4,2)
The equation of the tangency line is x = 4
8. AB is not a tangent. BC² ≠ AB² + AC²
9. The three radii of the circle are; CB, CF and CD
A diameter of the circle is BD
A tangent of the circle is GE
A chord of the circle is BD
A secant of the circle is AD
A point of tangency is F
How do we find the radius of a circle?
7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.
The radius then is 4/2 = 2.
The radius of circle q is 2/2 = 1
You could also use the formula
Distance = sqrt((x2 - x1)² + (y2 - y1)²)
8. √4² + √12² = √160
√13 = 169
Therefore AB is not tangent. It is less than BC
9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's
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how to convert 90% to a decimal point
Answer:
0.90
Step-by-step explanation:
Just like a decimal to a percentage number, you must multiply by 100. By converting a percentage number to a decimal point, you must divide it by 100. Which means, the decimal must move 2 times.
For example,
0.90 x 100 = 90%
This is decimal to percentage number, but in this case it is percentage to decimal.
90%.
Since the number ended at 0, put the decimal there and move it 2 times to get to your decimal point.
.90 = 0.90
There you'll get your answer! ^^
90% = 0.90
x and y are both differentiable functions of t x^2 + 3xy − y^2=9
Find dy/dt when x = 2 given dx/dt
= −1
The value of dy/dt is 4/3.
We have,
x² + 3xy - y² = 9
Now differentiating above equation w r t to 't' we get
d/dt x² + d/dt (3xy) - d/dt (-y²) = 0
d/dx (x²) . dx/dt + 3 dx/dt. dy/dt - 2y dy dt = 0
2x (-1) + 3(-1) dy/dt - 2y dy/dt = 0
dy/dt(-3 -2y)= -4
dy/dt = -4/(-3)
dy/dt = 4/3
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On Friday, three friends shared how much they read during the week
Barbara read the first 100 pages from a 320-page in the last 4 days
Judy read the first 54 pages from a 260-page book in the last 3 days.
Nancy read the first 160 pages from a 480-page book in the last 5 days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
Answer:
Step-by-step explanation:
Barbara read the first 100 pages from a 320-page in the last four days
Judy read the first 54 pages of a 260-page book in the previous three days.
Nancy read the first 160 pages from a 480-page book in the previous five days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
