The original price of the sofa before the discount is $241.11.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Let the original price of the sofa be x.
Given that 72% of the original price is $173.60, this can be written mathematically as follows:
72/100 × x = 173.60
72x = 17360
x = 241.11
Hence, the original price of the sofa before the discount is $241.11.
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Find the length of GH.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
G(-9, -4)
OA. About 3 units
OB. 53 units
O C. 9 units
12345678910
D. About 7.3 units
-2
-3
-4
-5
H(-2,-6) 7
-6
-8
-9
The length of GH is about 7.3 units. The solution has been obtained by using the formula of distance between two points.
What is distance between two points?
The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation
[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex] is used to calculate the distance between two points. One can use this formula to get the separation between any two points on an x-y plane or coordinate plane.
We are given two points as G(-9,-4) and H(-2,-6)
Using the distance formula,
[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]
[tex]d=\sqrt{(-2 +9)^{2} + (-6 +4)^{2} }[/tex]
[tex]d=\sqrt{(7)^{2} + (-2)^{2} }[/tex]
[tex]d=\sqrt{49 + 4 }[/tex]
[tex]d=\sqrt{53 }[/tex]
d = 7.3 units
Hence, the length of GH is about 7.3 units.
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when finding the reflection of a fraction do you convert it to a decimal or just reflect the fraction
A fraction can be converted to a decimal number by dividing the numerator—the piece at the top of the fraction—by the denominator, which can be done with a calculator. A decimal number that represents the value of the fraction is the answer.
What exactly is reflection fraction?The geometry and location of the primary source of radiation directly affect the ratio of flux between direct and reflected radiation, known as the "reflection fraction."
What does "reflection" in math mean?Flip is the mathematical term for reflection. An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. When one figure "reflect[s]" another, that phrase is used.
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Show that the following recurring decimal are rational. (1) 0,4 (2) 0,21 (5) 0,124 (6) 0,124 (3) 0,14 (7) -1,124 (4) (8) 19,45 -2,35
The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.
(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.
(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.
(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.
(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.
(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.
(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.
In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
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The height of a vase is 45. 7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height of the vase?
The shortest possible height of the vase would be 45.650 centimeters.
Rounding to the nearest tenth of a centimeter, the height of a vase is 45.7 centimeters. The vase's height can be as short as possible. Include three digits in your response.
Rounding to the nearest tenth, the vase's height is 45.7.The vase's smallest possible height will be 45.65 due to the fact that the figure is rounded to a tenth digit of 7 after the tenth digit.Using the, we can determine that the tenth digit is 7 - 1 = 6 before rounding.In order for the hundredth digit to be rounded to 1, the smallest value that could be assigned to it is 5.The value placed at 1,000 could take the smallest digit value up to three decimal places.To know more about height of vase here
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A square-shaped painting has a length and a width of 1 foot. A line painted
diagonally on the painting has a length of V2 feet. About how long is the length of
the diagonal line, to the nearest tenth of a foot?
The diagonal V2 of the square will be √2 feet.
What are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
as side=1 foot
By applying Pythagorean theorem,
Diagonal²=side²+side²
therefore,
V2²=1²+1²
=2
V2= √2 feet
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Find X and Y.
TEACHING TEXTBOOKS GEOMETRY
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The equations are given below.
2y = 180° - 126°
2y = 54°
y = 27°
2x + 1 = 180° - 85°
2x + 1 = 95°
2x = 94°
x = 47°
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
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The complete question is attached below.
-10 + 17 < 2x - 10
solve the equality
Answer: x>17/2
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
2x/2 > 17/2
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Let's solve your inequality step-by-step.
−10+17<2x−10
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
[tex]\frac{2x}{2} > \frac{17}{2} \\\\ x > \frac{17}{2}[/tex]
Hope this helped :0
solve for x 4x+23=x+2
Answer: x = -7
Step-by-step explanation: Subtract 23 from both sides. 4x + 23 - 23 = x + 2 - 23, than simplify and subtract x from both sides
The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the face value of a 10-year term insurance policy on a 25-year-old female given that the annual premium for the insurance policy is $384. 59. If need be, round your answer to the nearest cent.
a. 80,290. 19
b. 86,038. 03
c. 85,274. 94
d. 79,296. 69
The correct option is Option C - 85.274.94.
The face value of the 10-year term insurance policy on a 25-year-old Female given that the annual premium for the insurance policy of $384.59 is 85,274. 94.
Given:
Annual premium for the insurance policy = $384. 59
According to the chart at the conclusion of the answer, the amount paid per $1,000 of coverage for a female 25 year old for a 10 year policy is 4.51.
Face value = (1,000 x Annual premium) / Amount paid for 25 year old female for 10 year policy)
Face value = (1000 x 384.59) /4.51
Face Value = 384590 / 4.51
Face Value = 85274.94
Therefore the face value is 85274.94.
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The table is given by the image shown at the end of the answer.
A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 47 type I ovens has a mean repair cost of $75. 51, with a standard deviation of $23. 53. A sample of 54 type II ovens has a mean repair cost of $71. 32, with a standard deviation of $18. 43. Conduct a hypothesis test of the technician's claim at the 0. 01 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens
The value of test statistics z=1.04
First, state the null and alternative hypotheses:
[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]
Use z-statistics:
[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]
where x₁ and x₂ are the means and:
[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]
Calculating the value of test statistics:
[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]
[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]
[tex]y=\sqrt{11.780+7.460}[/tex]
[tex]y=\sqrt{19.24}[/tex]
y = 4.386
Now substitute the y value in equation (1)
[tex]z=\frac{75.57-71.32}{4.386}[/tex]
z = 1.04
The test statistics is z = 1.04
The decision rule for rejecting the null hypothesis is: α≤ test statistics
Using the z-score table, it is possible to determine the p-value, which is:
value = 0.877
Comparing the p-value with the level of significance (α = 0.05):
0.877 > 0.05
Therefore, we fail to reject the null hypothesis.
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The circle graph below represents the number of students at a middle school who buy lunch. If 624 students go to the school, about how many students do not buy lunch? Students who do not buy lunch Students who buy lunch 255⁰
The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.
Approximately what percentage of pupils skip lunch at school?In comparison to only 4% of children aged 6 to 13 years old, nearly one in ten adolescents (aged 14 to 17) admitted to skipping lunch.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022. Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.To learn more about percentage refer to:
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The number of students who do not buy lunch is 624 students - 420 students = 204 students.
Approximately how many pupils skip lunch at school?The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.
Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:
(255° / 360°) x 624 students = 420 students
Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.
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Emily filled up her car with gas before embarking on a road trip across the country.
Let G represent the number of gallons of gas remaining in her gas tank after driving
for thours. The table below has select values showing the linear relationship between
t and G. Determine the number of hours driven until the tank is empty.
Answer:
7 hours
Step-by-step explanation:
So you know in the second to third row of boxes how a hour and a half later the car loses 3 gallons of gas let's says another hour and a half goes by and the car has 1 gallon of gas left so each 30 minutes the car lost gas so now that we have that 1 gallon of gas left 30 minutes went by and now we are out gas
What happens when X is replaced with (x-3)
In a scenario when X is replaced with (x-3) then it means that the value of x will be reduced by 3 units.
What is Substitution?This is referred to as the process which involves the replacement of a word , number or phrase with another when performing different types of operations.
During an arithmetic operation and X is replaced with (x-3), then it means that the value of X will be reduced by 3 units and an example is given below:
Let's assume X is 5 and we substitute it with (x-3) will therefore become (5-3) = 2. This depicts that there has been a reduction by 3 units thereby making it the correct choice.
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NGC 5866
is about 44 million light years, or 13.5 megaparsecs, from
the Milky Way. How fast is NGC 5866 receding?
It has a diameter of about 60,000 light-years (18,400 parsecs).
Size of NGC 5866?A distance of 44 million light-years separates NGC 5866 from Earth in the Northern constellation Draco (13.5 Megaparsecs). Even though it has a diameter only around two-thirds that of the Milky Way and a mass similar to our galaxy, it has a diameter of about 60,000 light-years (18,400 parsecs).NGC 5866, a lenticular galaxy, contains many intricate dust lanes that appear black and red, but its disk is largely composed of brilliant stars, giving it a more subtly blue undertone.Numerous globular clusters—gravitational groups of nearly a million stars—that are gravitationally bound are scattered throughout the outer halo. Through the halo, it is also possible to detect background galaxies that are millions to billions of light-years away from NGC 5866.To learn more about diameter refer to:
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Find the greatest common factor 12 of and 48.
Answer: I believe the answer is 12
Given cot A = 8 5 cotA= 5 8 and that angle A A is in Quadrant I, find the exact value of csc A cscA in simplest radical form using a rational denominator.
The exact value of csc A is (√89) /5
How to find the exact value of csc A?Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Since cot A = 8 /5 and that angle A is in Quadrant I.
tan A = 5/8 (Remember: tan = 1/cot and tan = opposite/adjacent)
opposite = 5 and adjacent = 8
hypotenuse = √(5² + 8²) = √89
sin A = 5/(√89) (sin = opposite/hypotenuse)
csc A = (√89) /5 (csc = 1/sin)
Thus, the exact value of csc A is (√89)/5
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A three-column table is given.
Part A C D
Part 14 28 63
Whole 50 40 B
What is the value of B in the table?
12
36
68
90
The value of B in the table will be D. 90
How to explain the proportional relationship!The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio changes.
In this case, the relationship between part and whole is 7:10.
Therefore, the value of B will be:
= 10 / 7 × 63
= 10 × 9
= 90
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two hot air balloons, one purple and one gold, took off at the same time. the purple balloon started from sea level and the gold balloon started from a hill 15 1515 meters above sea level. the gold balloon began climbing at a constant rate of 2 22 meters per second. the purple balloon began climbing at 2.5 2.52, point, 5 meters per second. after how many seconds were the balloons at the same altitude?
The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.
Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.
We know that:
Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)
Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)
We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:
0 + 2.5t = 1515 + 222t
2.5t = 1515 + 222t
2.5t - 222t = 1515
0.5t = 1515 - 1515
t = 0
So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.
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Please Help me On this Question thank you if you do!
Answer:
3rd one
Step-by-step explanation:
Answer:
3rd one
Step-by-step explanation:
C The triangles in this picture are similar. Find the height of the tree.
Answer:
30 ft
Step-by-step explanation:
h/(40 + 8) = 5/8
h = 30
a) A rhombus of side 5cm has acute angles of
840 Find the
the length
Of the diagonals of the rhombus
The length of the diagonals of the rhombus is 3.5cm.
A rhombus's diagonals are always perpendicular to one another and always the same length. It contains four right angles, hence an acute angle of 840 is an obtuse angle. We are aware that in a rhombus, the diagonal is the hypotenuse of a right triangle, and the other two sides make up each half of the side.
Consequently, we can use the Pythagorean theorem to determine the diagonal's length:
c = √(a² + b²)
where an is the rhombus's half-length side and b is the other half, and c is the length of the diagonal. So we have:
a = (5cm) / 2 = 2.5cm
b = (5cm) / 2 = 2.5cm
c = √(2.5² + 2.5²) = √(6.25 + 6.25) = √12.5 = 3.5cm
Therefore, the length of the diagonals of the rhombus is 3.5cm.
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Segment AB is tangent to ⊙T at B. What is the radius of ⊙T? Triangle ABT where T forms the centre of a circle. B is a point on the circumference of the circle. The side AT intersects the circumference at the point C. AC equals 25 and Ab equals 45.
Answer:
28
Step-by-step explanation:
AB and TB are perpendicular because the tangent and radius are perpendicular. So you have a right triangle. Triangle ABT is a right triangle.
Also, TB is a radius of the circle, but so is TC. They are the same length.
Use Pythagorean Theorem to solve this problem.
AB^2 + TB^2 = AT^2
see image.
proofs in geometry transversal angels please help me
Following are the different types of angles:
In the 1 figure, ∠1 and ∠2 are same - side interior anglesIn the 2 figure, ∠1 and ∠2 are Alternate interior anglesIn the 3 figure,∠1 and ∠2 are corresponding anglesWhat is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The unit circle's sixteen unique angles, each indicated at the terminal point and measured in radians. These angles are frequently used as a parameter in trigonometric functions like the sine or cosine.
In the 1 figure,
∠1 and ∠2 are same - side interior angles
In the 2 figure,
∠1 and ∠2 are Alternate interior angles
In the 3 figure,
∠1 and ∠2 are corresponding angles
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two people are picked at random from a group of 50 and given $10 each. after that, independently of what happened before, three people are picked from the same group - one or more people could have been picked both times - and given $10 each. what is the probability that at least one person received $20?
The probability that at least one person received $20 is 0.3
In math the term called probability is defined as a number that reflects the chance or likelihood that a particular event will occur.
Here we know that two people are picked at random from a group of 50 and given $10 each.
Here we have also know that three people are picked from the same group - one or more people could have been picked both times - and given $10 each.
Then the probability is calculated based on the binomial distribution is written as,
=> P = (50 3) 10³ (1 - 10) ⁵⁻³
When we simplify this one then we get the value of p as 0.3.
Then the following values are calculated through it,
μ = 15
σ = 3.24
σ² = 10.5
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of flour John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
An inequality which shows the constraint on the amount of flour John has to make pies and cobblers is: B. 3x + 3y ≤ 16
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
3x + 3y ≤ 16
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Ë Solve & Share
|) Rose bought a length of copper pipe. She used
1
1
2
yard to repair a water line in her house. How much
pipe does she have left? Solve this problem any way
you choose.
7/8 yard
She left the 1/6 yards pipes.
Now, According to the question:
Rose bought a length of 4/6 copper pipe.
She used 1/2 yard to repair a water line in her house.
To find how much pipe does she have left?
Pipes available = 4/6 yards
Pipes used = 1/2 yards
Pipes left = total pipes bought - she doesn't suit that way
Pipes left = Total pipes available - pipes used
= 4/6 yards - 1/2 Yards
= 4-3/6
= 1/6 yards
Pipes left = 1/6 yards
Hence, She left the 1/6 yards pipes.
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The given question is incomplete, complete question is:
Rose bought a length of 4/6 copper pipe. She used 1/2 yard to repair a water line in her house. How much pipe does she have left? Solve this problem any way.
question 6
Match each number that is in scientific notation to its calculator shorthand representation
The calculator short hand notations are;
a) -4E3
b) -3E4
c) 3E4
d) 4E3
What is the calculator short hand notation?We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.
It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.
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A train left Vicky's town and traveled for 4 hours and 50 minutes to Wildgrove. Then it traveled 2 hours and arrived in Westminster at 12:28 P.M. What time did the train leave Vicky's town?
Answer:
5:38 am
Step-by-step explanation:
Since the train arrived at it's final destination at 12:28 pm and it took two hours to get there. Subtract two hours from the final destination time and it's 10:28 am. Then it took 4 hours and 50 minutes to arrive to Wildgrove, so subtract four hours of the time when the train arrived. It is now 6:28 am. Subtract fifty minutes from that and you would get 5:38 am.
p.s. There are time calculators online if you need an answer if this is kinda hard to understand
Elizabeth rode her bike 6 1/2 miles from her house to the library And then another 2 2/5 miles to his friend Milo's house, how far would she travel from her house to Carsons house?
Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.
The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:
Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]
To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:
[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2
[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5
[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2
So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:
13/2 + 12/5 + 5/2 = 57/5
Then, convert 57/5 into a mixed number, and we get:
57/5 = [tex]11\frac{2}{5}[/tex]
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creating a historgram algebra
The way that algebra can help in the creation of a histogram is that it helps organize and analyze the data in the histogram.
How does algebra help with histograms ?Algebra can be used to determine the range of values in the data set, and to create bins or intervals for the histogram. Algebra can be used to calculate the frequency of data points in each bin. This is important for creating the histogram, as it will determine the height of each bar.
Algebra can also be used to calculate the mean, median, mode, and standard deviation of the data set, which can provide a summary of the distribution of the data.
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Full question is:
Creating a historgram algebra. How does algebra help in creating a histogram ?