Answer:
0.506
0.516
0.609
0.615
Step-by-step explanation:
There are 132
chairs in a room.
99 of the chairs are red.
What percentage of the chairs are red?
Answer:
75%
Step-by-step explanation:
99/132=0.75
Answer:
75% of the chairs are red
Step-by-step explanation:
99/132 chairs are red. When divided, that equals 0.75. 0.75 is equivalent to 75%.
Question Content Area A $9,000, 60-day, 8% note, dated April 15, is received from a customer on account. The face value of the note is
The face value of the note is $9,000.
What is the face value of a note?The face value of a note is the principal value mentioned or stated on the note.
The face value is different from the maturity value or the discounted value.
The maturity value refers to the face value plus accumulated interest.
The discounted value is a value less than the maturity value received for discounting the note before its maturity date.
The face value of the note = $9,000
Note period or maturity period = 60 days
Note interest = 8%
Note issuance date = April 15
Note maturity date = June 14
Maturity value = $9,120 ($9,000 + $9,000 x 8% x 60/360)
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5
A line passes through the point (-4, -7) and has a slope of.
4
Write an equation in slope-intercept form for this line.
ロ=ロ
X
8
5
The equation of the line in slope-intercept form is:
y = 4x + 9
Write an equation in slope-intercept formThe slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
In this case, we know that the line passes through the point (-4, -7) and has a slope of 4. So, we can plug in the values of x, y, and m into the slope-intercept form and solve for b:
-7 = 4(-4) + b
Simplifying the right side:
-7 = -16 + b
Adding 16 to both sides:
9 = b
So the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is:
y = 4x + 9
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A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
The correct statements describing the area and perimeter of the patio are:
The area of the patio is (1 + 2x)(2 - 3x) square yards.The perimeter of the patio is 2(3 - x) yards.The area and perimeter of the patio?The area of a rectangle is given by the product of its length and width. So, the area of the patio is:
Area = length x width
Area = (1 + 2x)(2 - 3x)
Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.
The perimeter of a rectangle is given by the sum of the lengths of all four sides.
So, the perimeter of the patio is:
Perimeter = 2(length + width)
Perimeter = 2(1 + 2x + 2 - 3x)
Perimeter = 2(3 - x)
Therefore, the perimeter of the patio is 2(3 - x) yards.
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Use the circle shown below to determine the following:
What is the measure of the central angle?
central angle = ______ degrees
Solve an equation for x.
x = ________
What is the measure of the angle that bisects the minor arc?
bisecting angle = ________ degrees
Determine the measure of the major arc.
Major arc = _______ degrees
(45 points will give brainiest for efort)
1.The measure of the central angle is 90°.
2.Equation of x=12.
3.The measure of the angle that bisects the minor arc is 45°.
4.The measure of the major arc is 270°.
How to deal with arcs?The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.
The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.
Radians to degrees conversion
5π * (180/π) = 90° degrees
Therefore, the measure of the central angle AOB is 90° degrees.
To find Equation of x,
8x=96°
x=96°/8
x=12
Hence, Equation of x will be 12.
The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:
(1/2) * 90° = 45°
The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:
2πr - 5π = 15π
for major arc,
We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:
15π * (180/π) = 270°
Therefore, the measure of the major arc ACB is 270°.
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equation of line perpendicular to y = -4x + 3 with point 8, 1
The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;
Slope, m = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 1/4(x - 8)
y = 1/4(x) - 1
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A triangular building is bounded by three streets. The building measures approximately 94 feet on the first street, 188 feet on the second street, and 168 feet on the third street. Approximate the ground area K covered by the building.
Answer: To find the area of a triangle, we can use the formula:
Area = (base x height) / 2
However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.
To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:
Area = √(s(s-a)(s-b)(s-c))
where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:
s = (a + b + c) / 2
Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.
So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:
s = (94 + 188 + 168) / 2 = 250
Next, we can use Heron's formula to find the area of the triangle:
Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet
Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:
Cost = 7329.53 x $3 = $21,988.59
Therefore, the approximate cost of the triangular lot is $21,988.59.
Step-by-step explanation:
If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of how many students' heights?
A.
Neither 99 nor 352
B.
352
C.
Both 99 and 352
D.
99
Answer:
If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the entire population, which includes all 352 students. Therefore, the answer is (B) 352.
It's worth noting that the sample of 99 students could be used to estimate the population variance if certain assumptions are met and appropriate statistical methods are used. However, the question specifically asks for the population variance, which refers to the variance of the entire population, not just the sample.
Answer:
If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the heights of all 352 students in the population.
Therefore, the answer is B. 352.
How do you Fractions and simplest
The procedure to simplify fractions is presented in this answer.
How to simplify fractions?The steps to simplify a fraction are given as follows:
Find the GCF of the numerator and denominator.Divide both the numerator and denominator by the GCF.Write the simplified fraction.For example, let's say we want to simplify the fraction 12/24:
Find the GCF of 12 and 24, which is 12.Divide both the numerator and denominator by 12: 12/12 = 1 and 24/12 = 2.The simplified fraction is 1/2.Another example, let's say we want to simplify the fraction 16/20:
Find the GCF of 16 and 20, which is 4.Divide both the numerator and denominator by 4: 16/4 = 4 and 20/4 = 5.The simplified fraction is 4/5.Note that a fraction is in its simplest form when its numerator and denominator have no common factors other than 1.
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Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
Question Content Area
a. What was the book value of the equipment at December 31 the end of the fifth year?
The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.
Define straight line methodThe straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:
Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life
The annual depreciation expense for the equipment is:
Depreciation expense = (cost - residual value) / useful life
Depreciation expense = ($212,000 - $14,000) / 15
Depreciation expense = $12,533.33 per year
The total depreciation expense for the first five years is:
Total depreciation expense = Depreciation expense x number of years
Total depreciation expense = $12,533.33 x 5
Total depreciation expense = $62,666.65
To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:
Book value = Cost - Total depreciation expense
Book value = $212,000 - $62,666.65
Book value = $149,333.35
Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.
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An airplane departs an airport under the following conditions: Airport elevation 1,000 ft Cruise altitude 9,500 ft Rate of climb 500 ft/min Average true airspeed 135 kts True course 215° Average wind velocity 290° at 20 kts Variation 3° W Deviation -2° Average fuel consumption 13 gal/hr Determine the approximate time, compass heading, distance, and fuel consumed during the climb.
The approximate time, compass heading, distance, and fuel consumed during the climb of the airplane are 18 minutes, 214°, 2,430 nautical miles, and 3.9 gallons, respectively.
To determine the approximate time, compass heading, distance, and fuel consumed during the climb of the airplane, we need to use some basic principles of navigation and aviation.
First, we need to calculate the climb time. Since the airplane is climbing at a rate of 500 ft/min and the cruise altitude is 9,500 ft, the time it takes to climb to the cruise altitude can be calculated as (9,500-1,000)/500 = 18 minutes.
To calculate the compass heading, we need to account for the variation and deviation. The true course is given as 215°, and the variation is 3° W, which means we need to subtract 3° from the true course to get the magnetic course.
Therefore, the magnetic course is 215° - 3° = 212°. Next, we need to account for the deviation, which is given as -2°, meaning we need to add 2° to the magnetic course to get the compass heading. Therefore, the compass heading is 212° + 2° = 214°.
The distance traveled during the climb can be calculated using the average true airspeed and the climb time. The distance is given by the formula: distance = airspeed x time. Therefore, the distance traveled during the climb is approximately 135 kts x 18 min = 2,430 nautical miles.
Finally, we can calculate the fuel consumed during the climb using the average fuel consumption rate. The fuel consumed is given by the formula: fuel consumed = fuel consumption rate x time. Therefore, the fuel consumed during the climb is approximately 13 gal/hr x 18 min/60 min = 3.9 gallons.
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Ah Tee sold an average of 147 copies of newspapers per day on weekdays and an average of 217 copies per day on Saturday and Sunday. Find the average number of copies he sold per day for the whole week.
Ah Tee sold an average of 167 copies per day for the whole week.
To solve this problemThe quantity of weekdays and weekends must be considered.
Assume that a week consists of 5 weekdays and 2 weekends (Saturday and Sunday).
Total copies sold during the workweek: 147 x 5 = 735217 x 2 = 434 copies were sold in total during the course of the weekend.Total copies sold for the entire week were 735 + 434 = 1169We divide the total number of copies sold for the week by the number of days in the week to determine the average number of copies sold per day for the whole week:
Average number of copies sold per day for the whole week = 1169 / 7 = 167
Therefore, Ah Tee sold an average of 167 copies per day for the whole week.
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A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results.
Annual income vs. age group
Less than
$
50
,
000
$50,000dollar sign, 50, comma, 000 At least
$
50
,
000
$50,000dollar sign, 50, comma, 000 Total
Ages
44
4444 and under
148
148148
68
6868
216
216216
Ages
45
4545 and above
38
3838
94
9494
132
132132
Total
186
186186
162
162162
348
348348
Which of the following statements is true of those polled?
According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.
How to find the correct sentence?To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.
According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).
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Find the area ___m^2
Answer: 28.27m^2
Step-by-step explanation:
Area of a circle: [tex]A = \pi r^{2} \\[/tex]
Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.
6/2 = 3m
[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]
3. What is the perimeter of a yard with length = 4x+6/2x+1 feet and width = x-3/2x+1 feet?
10x+6/2x+1 Feet
5x+3/4x+2 Feet
10x+6/4x+2 Feet
5x+3/2x+1 Feet
What is the equation of the following line (0,0) (4,2)
Please simplify the attachment
The evaluation of the expression consisting of surds indicates that we get;
(9·x + 42 - 69·√x)/(x - 49)
What are surds?A surd is a value under a square root sign, which can not be further simplified into fractions or whole numbers.
The expression (9·√x - 6)/(√x + 7), can be simplified by using the rationalization of surds technique as follows;
(9·√x - 6)/(√x + 7) = ((9·√x - 6)/(√x + 7)) × ((√x - 7)/(√x - 7))
(√x + 7) × (√x - 7) = ((√x)² - 7²) = (x - 49)
(9·√x - 6) × (√x + 7) = 9·x + 42 - 69·√x
Therefore; (9·√x - 6)/(√x + 7) = (9·x + 42 - 69·√x)/(x - 49)
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The rectangular prism is filled with 1
-centimeter cubes.
Count the cubes to find the volume of the How many centimeter cubes fit in the rectangular prism?
centimeter cubes
What is the volume of the rectangular prism?
cubic centimeters
Each cube has a volume of 1 cm³, and the rectangular prism contains 320 cubes, so the volume of the rectangular prism is 320 cm³.
What is volume?Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³).
Here,
Length side = 4 cubes
= 5 cm
Width side = 2 cubes
= 2 cm
Height side = 2 cubes
= 2 cm
The length of the rectangular prism is 4 cubes which are equal to 5 cm each, so the length is 4 x 5 cm = 20 cm. The width of the rectangular prism is 2 cubes which are equal to 2 cm each, so the width is 2 x 2 cm = 4 cm. The height of the rectangular prism is 2 cubes which are equal to 2 cm each, so the height is 2 x 2 cm = 4 cm.
To find the volume of the rectangular prism, we multiply the length by the width by the height:
Volume = length x width x height
Volume = 20 cm x 4 cm x 4 cm
Volume = 320 cubic cm
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Complete question:
Each cube in this rectangular prism is 1 cm³. What is the volume of the rectangular prism?
HELP PLEASE I NEED HELP
An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. She wants a 95% confidence interval with a margin of error at most =0.025
. She has no idea what the true proportion could be.
How large a sample should she take?
The instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.
What is confidence interval?A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. It is typically used in inferential statistics, where we use a sample to make inferences about a larger population.
According to question:To determine the sample size required to construct a 95% confidence interval with a margin of error of 0.025 or less, we need to use the formula:
n = (Z² * p * (1 - p)) / E²
where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (in this case, 95%, which corresponds to a Z-score of 1.96)
p = estimated proportion of students repeating the class (since we have no prior information, we will use 0.5 as a conservative estimate)
E = maximum allowable margin of error (in this case, 0.025)
Plugging in the values, we get:
n = (1.96² * 0.5 * (1 - 0.5)) / 0.025²
n = 384.16
Rounding up to the nearest whole number, the instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.
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A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, O) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.
Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is
- ----------that of the chart for platinum.
The --------of the graph tells you the unit rate in
Gold costs less than platinum per ounce because the slope of the graph for gold is less steeper than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars.
What is a steeper slope?In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
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If the graph of f(x) = 3^x is reflected over the x-axis, what is the equation of the new graph?
The equation of the reflected graph is y = -3ˣ.
To reflect a graph over the x-axis, we need to negate the y-coordinates of all the points on the original graph. In other words, if a point (x, y) is on the original graph, its reflection over the x-axis would be (x, -y).
Let's apply this concept to the exponential function f(x) = 3ˣ. The graph of this function is an upward sloping curve that passes through the point (0,1) on the y-axis. If we reflect this graph over the x-axis, the point (0,1) will be mapped to (0,-1), as the x-coordinate remains the same, but the y-coordinate changes sign.
To find the equation of the reflected graph, we need to replace y with -y in the equation of the original function f(x) = 3ˣ. This gives us:
-y = 3ˣ
To isolate y, we can multiply both sides by -1:
y = -3ˣ
This function is a downward sloping curve that passes through the point (0,-1) on the x-axis.
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Find the area of this
irregular shape.
2
a = [?] m²
9
7m
2m
5m
5m
5m
5m
2m
7m
Enter
4
The area of the irregular shape is 34m²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles
The shape above can be divided into three rectangles and the sum of the area of this rectangles is the area of the shape.
Area of rectangle 1
= l× w
= 7×2 = 14 m²
Area of rectangle 2
= l× w
= 5×2 = 10 m²
Area of rectangle 3
= l×w
= 5×2 = 10m²
Therefore , the area of the irregular shape is
14+10+10 = 34m²
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Jamie and Polly share £24 in the ratio 2:3. Work out how much money Jamie gets.
Answer:
Jamie gets £9.60
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5 parts
divide the amount by 5 to find the value of one part of the ratio.
£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then
2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2548 feet and Plane B is just taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 70.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitude be when they're at the same altitude?
When they are at the same altitude, the distance between the planes will be 3962 feet.
Why do aircraft go at 30000 feet?Because the air is less dense at high altitudes, planes can fly quicker and consume less fuel. Additionally, at altitudes of 30,000 feet or more, airplanes may steer clear of weather systems, improving the comfort level inside.
What's the maximum altitude an aircraft can travel?The majority of commercial airplanes are permitted to soar as high as 42,000 feet. This upper limit is frequently referred to as a "service ceiling."
The planes will be at the same altitude when t seconds have passed, in which case 25.25t + 2548 = 70.75t,
45.5t = 2548 t = 56 seconds,
and 70.75 * 56 = 3962 feet.
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Two students began a proof of the law of sines.
C
b
A
h
Student I
sin(A)
sin(B)
T
bsin(A) = h
asin(B) = h
a
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A) =
sin(B) =
-1/2
asin(A)= h
bsin(B) = h
asin(A)=bsin(B)
sin(A)=sin(B)
B
Which student correctly started the proof, and what should that student do next to complete the proof?
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Student 1 correctly started the proof.
To complete the proof using the law of sines, student 1 should use the fact that the sum of angles in a triangle is 180 degrees to obtain an expression for angle C, and then use the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side to obtain an expression for side c in terms of sin(A) and sin(B).
Here's the complete proof:
Starting with Student 1's work:
bsin(A) = h
asin(B) = h
Using the fact that the sum of angles in a triangle is 180 degrees:
C = 180 - A - B
Using the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side:
a/sin(A) = b/sin(B) = c/sin(C)
Substituting in the expressions for c and sin(C) in terms of sin(A) and sin(B):
a/sin(A) = b/sin(B) = 2h/(sin(A)+sin(B))
Simplifying:
a = 2hsin(A)/(sin(A)+sin(B))
b = 2hsin(B)/(sin(A)+sin(B))
c = 2hsin(C)/(sin(A)+sin(B)) = 2hsin(180-A-B)/(sin(A)+sin(B)) = 2h*sin(A+B)/(sin(A)+sin(B))
Therefore, the law of sines is:
a/sin(A) = b/sin(B) = c/sin(C) = 2h/(sin(A)+sin(B))
The diameter of a circle is 34 kilometers. What is the circle's circumference?
Fill in the missing number in each problem using the order of operations.
40+ _ / 9 - 3 = 40
Answer:
40 plus 19/ 9-3=40
2 TO THE POWER OF 17 WHAT DA ANSWER
Answer:
131072
Step-by-step explanation:
Answer: The answer is 131072.
Step-by-step explanation:
Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]
Rewrite 5/6 with a least common denominator equal to
5/6 can be rewritten with a least common denominator of 6 as 10/12.
What does Fraction means ?Fracture is part of the whole. A fraction consists of two parts, the numerator and the denominator. Numerator: The numerator represents the number above the fraction bar. For example, for 6/7, 6 is the numerator. Denominator: The denominator shows the number placed under the fraction bar.
We can write 5/6 in the lowest common denominator, we need to find the common multiple of 6. The smallest multiple is 2. So we can write 5/6 with the lowest denominator 6 as follows:
5/6 = (5/6) x (2/2) = 10/12
Therefore, 5/6 can be rewritten as 10/12 with a lowest common denominator of 6.
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