The squares cut from the corners should be large in width and length 6 to hold the box as much as possible. The dimensions of the box with the largest volume are 6 x 6.
If the squares cut from the corners are h × h inches
The open-top box will have
A height of h
A width of 12 - 2h
and a length of 12 - 2h
So its volume will be
V(h) = h × (12 - 2h) × (12 - 2h)
= 4h³ - 48h² + 144h (square inches)
dV/dh= 12h² - 96h + 144
Critical points occur when the derivative (dV/dh) is zero.
12h² - 96h + 144 = 0
h² - 8h + 12 = 0
(h − 2)(h − 6) = 0
It is clear that h = 6 is not the crucial point for the maximum as it would produce widths and lengths of zero (and so a volume of zero).
In order to cut out squares measuring 6 × 6 inches from the corners of the bigger sheet, the most volume may be obtained.
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a robotic machine fills containers with an acid solution at the rate of 140 3 t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 . how many ml are put into a container in 60 seconds? round to the nearest whole number.
The container put 320 ml amount of the acid in 60 seconds.
Given, a robotic machine fills containers with an acid solution at the rate of 140 + 3t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 .
we have to find the amount of acid solution put into the container in 60 sec
As, Amount of acid be A(t)
A(t) = 140 + 3t
A(60) = 140 + 3(60)
A(60) = 140 + 180
A(60) = 320
So, the container put 320 ml amount of the acid in 60 seconds.
Hence, the container put 320 ml amount of the acid in 60 seconds.
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which term below is a number that describes how the data is dispersed across the entire range of data? a.) shape b.) outlier c.) spread d.) center
the spread data is dispersed across the entire range of data.
What is range of data?
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
When we plot data, we are considering the shape of the data. We plot the data based on the histogram, for example. The data's shape is Shape.
Outliers are different observations from the majority of the observations and are clustered in the center. Spread is the dispersion of the data throughout the entire range.
Hence, the spread data is dispersed across the entire range of data.
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an online gardening magazine wants to understand why its subscriber numbers have been increasing. what kind of reports can a data analyst provide to help answer that questio
Reports that describe how many customers shared positive comments about the gardening magazine on social media in the past year. Reports that compare past weather patterns to the number of people asking gardening questions to their social media. Reports that examine how a recent 50%-off sale affected the number of subscription purchases. Reports that predict the success of sales leads to secure future subscribers.
What is data analyst?In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data. A data analyst examines data to find significant consumer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information. Although it is recommended that data analysts have a basic understanding of statistics and mathematics, many of their tasks may be completed without it. However, data analysts often need to be familiar with statistics, linear algebra, and calculus.
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Find the distance between (2, 3) and (−4, −9). Round your answer to the nearest hundredth, if necessary.
Answer:
I think it would be 13.42 because round 13.41640786… would be 13.42
I hope this helps
The credit remaining on a phone card (in dollar) i a linear function of the total calling time made with the card (in minute). The remaining credit after 29 minute of call i $26. 23, and the remaining credit after 55 minute of call i $22. 85. What i the remaining credit after 59 minute of call?
Following 60 minutes of calls, the credit balance is $22.33 on a phone card.
Explain the term linear function?The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). 1 independent variable but one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.For the stated equation-
It's necessary to use the credit that remains after 60 minutes of calls.
Credit balance is $26. 23 - 29 minutes later.
Credit balance is $22. 85 - 59 minutes later.
Take the minutes as 'x' they are and the remaining credit as 'y' it is;
(29, 26. 23)
(59, 22. 85)
The equation will be because it is a linear function:
Y - y1 = m(x - x1)
Slope m = (y2 - y1)/(x2 - x1)
m = (22.85 - 26.23)/(55 - 29)
m = -3.38/30
m = - 0.13
Put the values in equation of the line.
y - 26. 23 = -0.13 (x - 29)
y = -0.13x + 30
For x = 59 minutes, remaining credit;;
y = -0.13(59) + 30
y = 22.33
Thus, following 60 minutes of calls, the credit balance is $22.33 on a phone card.
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A survey of all beings on planet Dubble found that 60% preferred joogh juice to all other juices. If 9 beings preferred joogh juice, how many beings were surveyed altogether?
Answer: 15
9 60
------- = -------
? 100
Multiply 9 and 100, then divide by 60
You will get 15
Since 9 beings preferred joogh juice and that was 60% of the beings who were surveyed, that must mean 15 beings were surveyed in total.
if n people of different heights are lined up in a queue, what is the probability that at least one person is just behind a taller person?
Probability of at least one people behind taller person = n-1/n.
From the question, we have
n people of different heights are lined up in a queue
Probability of at least one people behind taller person = 1 - 1/n =n-1/n
Probability:
The term probability refers to possibility. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. To determine the possibility of certain events, probability has been employed in mathematics. The likelihood of anything happening is often referred to as probability. You can better understand the outcomes of a random experiment by applying this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur.
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the sum of three nonnegative numbers is 36, and one of the numbers is twice one of the other numbers. what is the maximum value of the product of these three num- bers?
324 is the maximum value of the product of these three numbers
What is maxima and minima?
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.
The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.
Let the three nonnegative numbers are x,y,z
According to the question
x+y+z=36
and y=2x
therefore, 3x+z=36--------------------------------------------------(1)
z=36-3x
Let 3xz= u--------------------------------------------------------------(2)
differentiating equation 2
du/dx=3z + 3xdz/dx
or
du/dx= z + xdz/dx
differentiating equation 1
3 + dz/dx = 0
dz/dx = -3
du/dz = 36-3x + x(-3)
du/dx = 12 - 2x--------------------------------------------------------------(3)
for maxima put du/dx = 0
x=6-------------------------------------------------------------------------------(4)
again differentiating du/dx = 12 - 2x
d2u/dx2=-2
which means 3xz= u is maximum at x=6
from equation 1 and 4
we get 18+z=36
z=18
Therefore 3xz= 3(6)(18)=324
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1.through:(5,-1), perp. to y=5/4x-2
2. through:(2,3). perp. to y=-2/5x+2
Answer:
[tex]y=-\frac{4}{5} x+3[/tex][tex]y=\frac{5}{2} x-2[/tex]
A certain type of car has room for 4 passengers.
How many passengers could fit in 78 cars?
How many cars would be needed to fit 78 passengers?
Answer:
1) 312
2) 20
Step-by-step explanation:
4x78=312
78 divided by 4=19.5 rounded up =20
If 5x + 2 = 7x - 7, then x =
Answer:
if 5x + 2 = 7x - 7 then the answer is x = 9/2.
on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?
The statement which is true about the two equilateral triangles is b)The two triangles are the same shape but not the same size. So, correct option is b.
In calculation, a symmetrical triangle is a triangle where every one of the three sides have a similar length. In the natural Euclidean calculation, a symmetrical triangle is likewise equiangular; that is, every one of the three inward points are additionally compatible to one another and are each 60°. It is likewise an ordinary polygon, so it is additionally alluded to as a normal triangle.
Some of hypotheses which are made sense of utilizing symmetrical triangle:
Morley's trisector hypothesis expresses that, in any triangle, the three marks of convergence of the contiguous point trisectors structure a symmetrical triangle.Napoleon's hypothesis expresses that, in the event that symmetrical triangles are built on the sides of any triangle, either all outward, or all internal, the focuses of those symmetrical triangles themselves structure a symmetrical triangle.The side length of the primary symmetrical triangle is 3 inches.The side-length of the second symmetrical triangle is 4 inches.Since both the triangles are symmetrical triangles, in this way they have same shape.
Be that as it may, the two triangles have different side lengths in this way they have different size.
Hence, option b is correct.
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(Complete question) is:
on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?
a. The two triangles are the same size but not the same shape.
b. The two triangles are the same shape but not the same size.
c. The two triangles are the same size and same shape.
d. It is impossible to construct equilateral triangles with these side lengths.
if the roots of the characteristic equation of a second order differential equation that models a unforced circuit are 2 and -3
A polynomial equation is used to analyze the behavior of the problem's solutions and is known as the characteristic equation of a second-order differential equation.
It is frequently used to simulate real-world events, such as the operation of electrical circuits. The behavior of the differential equation's solutions may be predicted when the characteristic equation's roots are 2 and -3. The roots of the characteristic equation can be used to identify the properties of an unforced circuit when a second-order differential equation is used to represent it.
The circuit will behave oscillatory when the roots are 2 and -3. As a result, the output of the circuit will oscillate frequently, with the frequency of the oscillations being defined by the variation between the roots. The oscillations in this instance will occur at a frequency of 5 Hz.
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The correct question is-
What behavior of the differential equation's solutions can be determined when the roots of the characteristic equation are 2 and -3?
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HELP
If
m = 1 68
and
m = 6 35 ,
then find the measures for each of the remaining numbered angles. Justify your
answers with definitions and/or theorems
Using the triangle sum theorem and other definitions, the measures of the other numbered angles are:
m∠5 = 68°
m∠3 = 35°
m∠4 = 112°
m∠7 = 145°
m∠2 = 77°
What is the Triangle Sum Theorem?In a triangle, all the three interior angles will add up to give a sum of 180 degrees according to the triangle sum theorem.
What is the Alternate Interior Angles Theorem?The alternate interior angles theorem states that any two angles that lie alternate to each other, they will have the same angle measure
Given the angle measures:
m∠1 = 68°
m∠6 = 35°
Therefore:
m∠5 = m∠1 [alternate interior angles theorem]
m∠5 = 68°
m∠3 = m∠6 [alternate interior angles theorem]
m∠3 = 35°
m∠4 = 180 - m∠5 [definition of linear pair]
m∠4 = 180 - 68
m∠4 = 112°
m∠7 = 180 - m∠6 [definition of linear pair]
m∠7 = 180 - 35
m∠7 = 145°
m∠2 = 180 - m∠5 - m∠6 [triangle sum theorem]
m∠2 = 180 - 68 - 35
m∠2 = 77°
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2x
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A tax of 5% is applied to the bill.
Zoe decides to leave a tip of 15% on the entire bill (including the tax).
let the bill cost $x.
So, the price after tax and tip
= x+ 5% of x+ 15% of x
= x + 0.05x + 0.15x
= x + 0.20x
= 1.2x
Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x
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Explain how you use the table to find f(-2) and f(3).
Answer:
f(-2)=-12
f(3)= -2
Step-by-step explanation:
f(x) is original form
So for f(-2) we find where x is -2 and in this case f(x) is -12
And for f(3) we do similar but since x=3 isn’t on the table we see a pattern that whne x goes up one f(x) adds 2 so 3 is -2
Hopes this helps
equivelent ratio of 4/5
Answer: One of those 2 it should be?
Step-by-step explanation:
Decimal form:
0.8
Exact form :
4/5
Which is true about the quotient below? -11/10
The truth about the quotient -11/10 is that it is written as an improper fraction, which can also be written as a mixed number.
What is the quotient?The quotient is the result of a division operation.
To determine the quotient, the dividend is divided by the divisor.
The dividend is the number being divided while the divisor is the number dividing.
Division operation is one of the basic mathematical operations. Other mathematical operations are subtraction, addition, and multiplications.
These basic mathematical operations determine mathematical results undertaken by manipulating numbers, constants, and variables using mathematical operands.
What is an improper fraction?An improper fraction is one that whose numerator is greater than the denominator.
Improper fractions can be converted to mixed numbers (whole numbers and proper fractions).
Thus, we can conclude that the quotient -11/10 is written as an improper fraction.
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Every week maria puts $25 into her savings account. She has $680 in her account now. Which equation shows how to calculate how much money she will have in her account next week?.
The equation that demonstrates how to determine how much money Maria will have in her savings account the following week is (B) the amount in savings the following week = $680 + $25.
What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, the correct equation will be:
We know that Maria puts $25 every week into her savings account.
We also know that she has $680 in her account.
Now, to get the amount that will be in her savings account next week will be:
$680 + $25
Therefore, the equation that demonstrates how to determine how much money Maria will have in her savings account the following week is (B) the amount in savings the following week = $680 + $25.
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Complete question:
Every week Maria puts $25 into her savings account. She has $680 in her account now. Which equation shows how to calculate how much money she will have in her account next week?
A. Amount in savings next week +$25=$680
B . Amount in savings next week =$680+$25
C. Amount in savings next week =$680×$25
D. $680− the amount in savings next week =$25
How much would you pay monthly on a $6,000 loan if you pay 12. 5 percent for 10 years?.
If we pay 12.5 percent for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A % is a number that has neither dimensions nor a defined unit of measurement.
To calculate the percentage, we must divide the value by the entire amount and then multiply the result by 100.
So, if the interest rate is 12.5%, our total loan payment would be:
112.5/100 × 6,000 = $6,750.
The monthly payment would be if there was no buildup and other agreement in payment:
6750/12*10
6750/120
$56.25
Therefore, if we pay 12.5% for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.
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Complete question:
How much would you pay monthly on a $6,000 loan if you pay 12.5 percent for 10 years?
a. $87.90
b. $70.32
c. $55.58
d. $125.00?
Identify the expression or expressions equivalent to -5 + 4(-3x+6) -4x
The equivalent expression of -5 + 4(-3x+6) -4x is -29 - 16x
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
-5 + 4(-3x+6) -4x
Open the bracket in the above expression
This gives
-5 + 4(-3x+6) -4x = -5 - 12x - 24 -4x
Collect the like terms in the above expression
This gives
-5 + 4(-3x+6) -4x = -5 - 24 - 12x -4x
Evaluate the like terms in the above expression
This gives
-5 + 4(-3x+6) -4x = -29 - 16x
Hence, the equivalent expression is -29 - 16x
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B. The President uses technology to produce the following random numbers.
26 17 58 68 2 17 1 29 33 51
Determine the numbers for 9 faculty members who will be included in the sample.
The numbers for 9 faculty members who will be included in the sample are 26, 17, 58, 68, 2, 1, 29, 33, 51
What is a simple random sample?
A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen. A straightforward random sample is intended to offer an unbiased representation of a group.
Given, the President uses technology to produce the following numbers:
26 17 58 68 2 17 1 29 33 51
Now, 9 faculty members will be included in the sample is:
26, 17, 58, 68, 2, 17, 1, 29, 33, 51
In the above data, 17 occurs with repeated frequency then we will make 17 once.
Hence, the required answer is 26, 17, 58, 68, 2, 1, 29, 33, 51
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The product of two consecutive odd
integers is 21 more than twice the larger
integer. Find the two integers.
A: Translate the problem into an equation.
B: Solve.
C: Show all of your work for bonus credit.
A: Translate the problem into an equation.
The integers when product of two consecutive odd integers is 21 more than twice the larger
integer are 5 and 7.
How to calculate the integer?Let the integers be x and x + 2. Since the product of two consecutive odd integers is 21 more than twice the larger integer. This will be:
x(x + 2) = 2(x + 2) + 21
x² + 2x = 2x + 4 + 21
x² + 2x = 2x + 25
Collect like terms.
x² + 2x - 2x - 25
x² - 25
x² - 5²
= (x - 5)(x + 5)
x - 5 = 0
x = 0 + 5
x = 5
The higher number will be:
= x + 2
= 5 + 2
= 7
The numbers are 5 and 7
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what can you change in 3 (x + 4) - 2(x+4) + 0.5(x + 4) to get 1.5
Please Help!
To make the expression 3(x + 4) - 2(x + 4) + 0.5(x + 4) equals 1.5, we make x in the linear equation equals -3
Linear EquationA linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
There are linear equations in one variable and linear equations in two variables.
In this problem given we have to simplify and equation the expression to 1.5 to make it an equation.
3(x + 4) - 2(x + 4) + 0.5(x + 4) = 1.5
3x + 12 -2x -8 + 0.5x + 2 = 1.5
3x - 2x + 0.5x + 12 - 8 + 2 = 1.5
1.5x + 6 = 1.5
Collect like terms
1.5x = 1.5 - 6
x = -3
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A rectangle has a perimeter 112 ft. Its length is 4 feet greater than its width. Find the dimensions of the rectangle.
Answer:
Step-by-step explanation:
Petimeter=2L+2w
width=x unknown
length=x+4
P=2L+2W
112= 2(x+4)+2x
112=2x+8+2x
112=4x+8
subtract 8 on both sides
104=4x
divide by 4
x=26
width is 26
length is 30
check 26+36+30+30=112
a jury pool consists of 30 people, 16 men and 14 women. compute the probability that a randomly selected jury of 12 people is all male.
The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
What is the probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
An order does not matter so it is a Combination.
There are 16 men and we are going to choose 12 --> ₁₆C₁₂
There are 30 people and we are going to choose 12 --> ₃₀C₁₂
₁₆C₁₂ / ₃₀C₁₂
[tex]= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}[/tex]
= 0.00002104211
= 2.1 × 10⁻⁵
Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
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0.
E
e
t
15. Luke needs a new fence around his garden,
but the gate across the narrow end of the
garden will not be replaced. Write and
evaluate a numerical expression to find
how many feet of fencing Luke needs.
14 ft
3 ft
12 ft
14 ft
After evaluating , we get that the number of feet of fencing that Luke needs is 40 ft .
In the question ,
it is given that ,
Luke if fencing his garden ,
and the gate across the narrow end is not replaced .
From the figure given below ,
we see that , the lengths of the garden are , 3 ft , 14 ft , 14 ft and 12 ft .
So , the perimeter of the figure is = 3 + 14 + 14 + 12
Since , the gate is not fenced , length of the gate (3 ft) will be subtracted .
So , we get ,
= 14 + 14 + 12
= 40 ft .
Therefore , the Luke need to fence 40 ft of the garden.
The given question is incomplete , the complete question is
Luke needs a new fence around his garden, but the gate across the narrow end of the garden will not be replaced. Write and evaluate a numerical expression to find how many feet of fencing Luke needs .
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. in a city, a house can only belong to one of three counties, with 20% of the houses in the first county, 30% in the second and 50% in the third. a garage is attached to 70% of the houses in the first county, 80% of those in the second county and 90% of those in the third one. what is the probability that a house belongs to the second county, knowing that it has a garage attached to it? assume event a: a house belongs to the first county; event b: a house belongs to the second; event c: a house belongs to the third; event g: a house has an attached garage.
For given situation, the probability that a house belongs to the second county, knowing that it has a garage attached to it = 0.8
Assume event a: a house belongs to the first county;
event b: a house belongs to the second;
event c: a house belongs to the third;
event g: a house has an attached garage.
20% of the houses in the first county,
⇒ P(a) = 20%
30% of the houses in the second county
⇒ P(b) = 30%
50% of the houses in the first county.
⇒ P(c) = 50%
a garage is attached to 70% of the houses in the first county,
⇒ P(a ∩ g) = 70%
a garage is attached to 80% of the houses in the second county
⇒ P(b ∩ g) = 80%
and a garage is attached to 90% of the houses in the third county.
⇒ P(c ∩ g) = 90%
We need to find the probability that a house belongs to the second county, knowing that it has a garage attached to it.
i.e., P(b ∩ g) which is 80% = 0.8
Therefore, the probability that a house belongs to the second county, knowing that it has a garage attached to it is 0.8
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Can you show this answer to me
Selena got 5 out of 6 answers correct on her science quiz her friends Ana got 4 answers out of 6 correct on her quiz her which friend answered a greater fraction of the questions correctly
Selena got the greater fraction of the questions correctly as 5/6 > 4/6.
Explain the term fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as denominator of a complex fraction. The numerator of a proper fraction is smaller than the denominator.For the stated data in the question.
Correctly answered by Selena in science quiz = 5/6
In decimal form.
5/6 = 0.833
Correctly answered by Ana in science quiz = 4/6 .
In decimal form;
4/6 = 0.666
Now,
0.666 > 0.8333
Thus,
5/6 > 4/6
Therefore, Selena got the greater fraction of the questions correctly as 5/6 > 4/6.
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solve: XC ÷X Show your answer in standard form
Answer:
Step-by-step explanation:
Given that
XC÷X
= XC/X
here X in the nominator as well as denominator will cancel each other. Then Remaining result is
= C