The given chain which has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of k0=50 mm.
If the 4-kg block A is released from rest in the position s=2 m. Using energy methods, determine the angular velocity of the sprocket at the instant s=4 m.First of all, draw a FBD of the system at s=2 m and at s=4 m.At s=2 m Let the velocity of the block A be v2m/s.At s=4 m Let the velocity of the block A be v4m/s.Let the angular velocity of the sprocket be ω rad/s. Draw FBD at both states and clearly label datum.For the block A at s=2 m Velocity of the block A, v=0 (Initial velocity)
Kinetic energy of the block A,KE1=12mv²=12×4×(0)²=0Potential energy of the block A,PE1=mgh=4×9.81×2=78.48JFor the block A at s=4 mLet h be the height by which the [tex],KE1=12mv²=12×4×(0)²=0[/tex]block A falls. Velocity of the block A, [tex]v=√2gh=√2×9.81×h[/tex]Kinetic energy of the block A,KE2=[tex]12mv²=12×4×[√2gh]²=8gh[/tex] Joule (J)Total potential energy of the system at s=2 m,PE1=2×g×k0 Joule (J)When the block falls from s=2 m to s=4 m, the change in the potential energy of the system is,ΔPE=PE2-PE1Where,PE2=2×g×(2k0) Joule (J)Let the change in the potential energy of the system be ΔPE1 Joule (J).
So,ΔPE1=PE2-PE1=2gk0 Joule (J)The total energy of the system is conserved.
So,ΔPE1=KE2ω²+Iω²Where,ΔPE1 is the change in the potential energy of the systemKE2 is the kinetic energy of the block A when it is at s=4 mI is the moment of inertia of the sprocket about its axisω is the angular velocity of the sprocket at s=4 mSo,ω²=ΔPE1KE2+Iω²Substitute the values of ΔPE1, KE2 and I in the above equation.
[tex]ω²=(2gk0)8gh+mr²ω²=(2×9.81×50×10⁻³)8×h×h+2×1×(50×10⁻³)²ω²=0.7848h²+2.5×10⁻³[/tex]
Therefore,ω=√(0.7848h²+2.5×10⁻³) rad/s.
Substitute the value of h=2 m in the above equation.ω=2.808 rad/s.So, the angular velocity of the sprocket at the instant s=4 m is 2.808 rad/s.
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Using laws of logarithms, write the given expressions usingsums and/or differences of logarithmic expressions which donot contain the logarithms of products, quotients, or powers.a. log(45x) = log(45)+log(x). Previewb. log (x⁵⁵) = 55log(x). Previewc. 10 log(⁵√x) = 1/5log(x)^10. Preview2/5 log(x)¹⁰ syntax ok
Additionally, you should focus on answering the specific question being asked and ignore any typos or irrelevant parts of the question.
Using laws of logarithms, the given expressions can be written using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers as follows:
a.[tex] log(45x) = log(45) + log(x)b. log(x⁵⁵) = 55log(x)c. 10 log(⁵√x) = log(x)^(10/5) = log(x)^2 = 2log(x)2/5 log(x¹⁰) = (2/5)log(x) + (2/5)log(x) + ... + (2/5)log(x) (10 times)= 2log(x^10)[/tex]
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a charger has a power rating of 12 w. if you charge 6 cents per kilowatt hour, how much do you make in 1 day
The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.
P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.
Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.
Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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Liam has 11/4 packets of red clay.If he crafts a sculpture using 5/3 packets, how much clay does he have left?
Answer:
Step-by-step explanation:
Liam has 11/4 packets of red clay, which is equal to 33/12 packets of clay.
If he uses 5/3 packets of clay for crafting, he would have used 20/12 packets of clay.
To find how much clay he has left, we need to subtract the used amount from the original amount:
33/12 - 20/12 = 13/12
Therefore, Liam has 13/12 packets of clay left.
Answer this for points
help me plsss
Which function is graphed here?
Of(x)=√x-2
Of(x)=√x+2
Of(x)=-3√x-2
Of(x) = -√√x+2
Answer:
I'm pretty sure it's C. isnnxixiab
Three identical small circles are drawn inside one large circle, as shown in the diagram.
The centres of the small circles lie on the diameter of the large circle.
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
what is circle ?A circle is a geometric form made up of all points that are spaced apart by a predetermined amount, known as the radius, from a specific point known as the center. The circumference of a circle is determined by the formula C = 2r, where r denotes the radius and (pi) denotes a mathematical constant roughly equivalent to 3.14159. Numerous areas of mathematics, science, and daily living frequently involve circles. They have a number of crucial characteristics that make them helpful in a variety of applications.
given
The line section PQ is the following length:
PQ is equal to [tex]sqrt(3r2/4) = sqrt(3)/r.[/tex]
In a similar manner, we can determine how long the line section QR is:
OQ2 - OR2 = QR2 = r2/4 - r2 = QR2 = -3r2/4
Therefore, QR is a line that goes beyond the spot R rather than a line segment.
The length of the large circle's diameter AB is determined by adding the lengths of PQ, QR, and RP, each of which is equivalent to (sqrt(3)/2)r. As a result, we have:
[tex]AB = 3 * (sqrt(3)/2) (3sqrt(3)/2)r = r[/tex]
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
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Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
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PLS HELP WILL GIVE BRAINLIEST
Triangle FUN has vertices located at F (-1, -4), U (3, -5), and N (2, 6).
Part A: Find the length of UN. Show your work.
The length of the segment UN is 11.05 units.
How to find the length of the segment UN?For any pair of points (x₁, y₁) and (x₂, y₂), the distance between the two points is given by the formula:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we know that the points are:
U = (3, -5)
N = (2,6)
The distance between these two points is then:
distance = √( (3 - 2)² + (-5 - 6)²)
distance = √122 = 11.05
The length of the segment is 11.05 units.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer: 35 Millimeters
Step-by-step explanation: Add all the numbers around your shape and you got the perimeter :)
Answer: 35 mm
Step-by-step explanation:
Add all sides together: 4+13+13+5 = 35
Can you help me with this
Answer:c
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Halla m∆1 y m∆2.
ayuda porfaa
Hi! I understand that you want help finding the values of m∆1 and m∆2. To provide a step-by-step explanation, I need more information about the problem, such as the type of triangles, angles, or side lengths involved. Please provide more context or details, and I will be happy to help you.
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A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
A person has $785.35 after 7 years in the account.
What is continuous compound interest?Interest that is compounded continuously to the principal amount. This interest rate provides exponential growth for a period of time.
The formula of continuous compound interest rate;
[tex]V = Pe^{rt}[/tex],
Where P is the principal amount, r is the interest rate and t is the time period.
A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously.
Using the formula:
[tex]V = Pe^{rt}[/tex], where P = $398, r = 0.097 (9.7% as a decimal), and t = 7 years, we can calculate the value of the account after 7 years as:
V = 398[tex]e^(0.0977)[/tex]
V = 398[tex]e^{0.679}[/tex]
V = 784.818126761
V = $785.35 (rounded to the nearest cent)
Therefore, the amount of money in the account after 7 years is $785.35.
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if you have minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency?
Yes, if you have minimums and maximums that are several standard deviations away from the rest of the data observations, medians would be the best measure of central tendency.
Having minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency. This is because, when there are outliers or extreme values in a dataset, the mean can be influenced and it may not be an accurate representation of the central tendency.
However, the median is not affected by extreme values or outliers since it only depends on the middle value of the dataset. Therefore, if the dataset has outliers, it is better to use the median as a measure of central tendency to provide a more accurate representation of the data.
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assume that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. using the propensity scoring method, their responses would be
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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Determine weather the series is arithmetic or geometric,then find the indicated sum
The series, based on the general terms, can be found to be arithmetic. The indicated sum is - 544.
How to determine if a series is arithmetic or geometric ?To determine if the series is arithmetic or geometric, we must first find the common difference (arithmetic) or common ratio (geometric).
Term 1 (p=1): 19 - 2(1) = 17
Term 2 (p=2): 19 - 2(2) = 15
Term 3 (p=3): 19 - 2(3) = 13
There is a common difference of -2 so this is arithmetic.
The formula for the sum of an arithmetic series is:
Sum = (n x (a1 + an)) / 2
The series is: ∑ (p = 1 to 34) (19 - 2p)
To find the last term, we plug in p = 34:
an = 19 - 2(34)
= 19 - 68
= -49
The sum is therefore:
Sum = (34 x (17 + (-49))) / 2
Sum = -544
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Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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2.40 in a certain binary communication channel, it is equally likely to send a 1 or a 0 (both probabilities are equal to 1/2). the probability of an error given that a 1 is sent is 2/9, while the probability of an error given a 0 is sent is 1/9. (a) what is the probability that a 1 is received? (b) what is the (unconditional) probability that an error occurs? (c) what is the probability that a 1 was sent, given a 1 was received?
(a) The probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, is 7/8.
To solve this problem, we can use Bayes' theorem and conditional probability.
(a) The probability that a 1 is received can be found using the law of total probability. We can calculate it by considering the probabilities of two mutually exclusive events: receiving a 1 when a 1 is sent and receiving a 1 when a 0 is sent.
Let P(1) be the probability that a 1 is sent and P(0) be the probability that a 0 is sent. Both probabilities are equal to 1/2 since they are equally likely.
The probability of receiving a 1 when a 1 is sent is 1 minus the probability of an error when a 1 is sent, which is 1 - (2/9) = 7/9.
The probability of receiving a 1 when a 0 is sent is the probability of an error when a 0 is sent, which is 1/9.
Using the law of total probability:
P(1 received) = P(1 sent) x P(1 received | 1 sent) + P(0 sent) x P(1 received | 0 sent)
P(1 received) = (1/2) x (7/9) + (1/2) x (1/9)
P(1 received) = 7/18 + 1/18
P(1 received) = 8/18
P(1 received) = 4/9
Therefore, the probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs can be calculated by considering the probabilities of two mutually exclusive events: an error occurs when a 1 is sent and an error occurs when a 0 is sent.
Using the law of total probability:
P(Error) = P(1 sent) x P(Error | 1 sent) + P(0 sent) x P(Error | 0 sent)
P(Error) = (1/2) x (2/9) + (1/2) x (1/9)
P(Error) = 2/18 + 1/18
P(Error) = 3/18
P(Error) = 1/6
Therefore, the (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, can be calculated using Bayes' theorem:
P(1 sent | 1 received) = (P(1 sent) x P(1 received | 1 sent)) / P(1 received)
P(1 sent | 1 received )= (1/2) x (7/9) / (4/9)
P(1 sent | 1 received) = (1/2) x (7/9) * (9/4)
P(1 sent | 1 received) = 7/8
Therefore, the probability that a 1 was sent, given that a 1 was received, is 7/8.
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Algebraic Inequalities
Help due today
Answer: i am certain that the answer is -6
what central idea about mathematical instruction does the author express in passage 1?
An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.
Most students pseudo-work and end up wasting valuable time.
The correct option is (C)
This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.
The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.
The correct option is (C).
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The given question is incomplete, complete question is:
What central idea about studying does the author express in Passage 1?
A Straight-A students know how to work harder than other students.
B The only way to become a straight-A student is efficient study habits.
C Most students pseudo-work and end up wasting valuable time.
D An all-night study session can help you catch up on school assignments.
suppose that a conveyor used to sort packages by size does not work properly. we test the conveyor on several packages (with h0:incorrect sort) and our data results in a p-value of 0.016. what probably happens as a result of our testing?
If the p-value of a hypothesis test is 0.016, it means that the probability of observing the data or more extreme data assuming the null hypothesis (i.e., the conveyor works properly) is 0.016. So, we reject the null hypothesis.
This p-value is relatively small and falls below the conventional significance level of 0.05. Therefore, we can reject the null hypothesis that the conveyor works properly and conclude that the conveyor is not sorting packages correctly.
However, we cannot determine the cause of the problem with the conveyor from this hypothesis test alone. Further investigation is necessary to identify the root cause of the issue and determine the appropriate corrective actions.
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In the figure, m∠1= (5x)°, m∠2= (4x + 10)° and, m∠3= (10x − 5)°. What is m∠3,
in degrees?
Answer: I think this is a triangle because there are 3 angles.
All triangles have the entire sum 180*
(5x) + (4x + 10) + (10x-5) = 180
x = 175/19
Answer - 1750/19 (Decimal: 92.105263)
Step-by-step explanation:
10 (175/19)
10/1 * 175/19
10 175
1 19
= 1750
19
in cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. one such method is called
In cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. One such method is called standardization.
Cluster analysis is a data mining approach that is widely utilized in data processing, image analysis, and other data-based analytics applications. It groups items that have comparable characteristics into clusters by separating them from other objects that do not share the same features.
Standardization is the process of converting variables with various scales to a common scale so that they can be compared fairly.
Standardization involves transforming all of the variables into comparable units of measurement by converting them into z-scores. This allows for the comparison of values without being affected by the different units of measurement.
The method that can be used to reduce bias due to the difference in units of measurement in cluster analysis is standardization, which converts variables with various scales to a common scale so that they can be compared fairly. This ensures that each variable contributes equally to the distance between the clusters.
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what is 9 divided by 2.5
Answer: 3.6
Step-by-step explanation:
It's 3.6, hope it helped! :D
Activity 2 Synthesis
1. Precious says you can estimate the area of a circle by calculating 32. What do you think
each part of her expression means?
2. Do you agree with Precious? Use your earlier work to help support your thinking.
the yoko fund earns 11.2% during the year while the risk-free rate is 3.1%. the yoko fund has a beta of 1.20 and a standard deviation of 17.5%. the treynor ratio is closest to: a. 0.463 b. 0.640 c. 6.750 d. 9.333
For the Yoko Fund, the Treynor ratio is 6.0%, although none of the answer choices provided is a close approximation, we can choose option c. 6.750
The Treynor ratio measures the excess return earned by an investment per unit of systematic risk (i.e., beta). It is calculated as the difference between the return of the investment and the risk-free rate, divided by the investment's beta.
The formula for the Treynor ratio is:
Treynor Ratio = (Return of the Investment - Risk-Free Rate) / Beta
In this case, the return of the Yoko Fund is 11.2%, the risk-free rate is 3.1%, the beta is 1.20, and we are given the standard deviation of the Yoko Fund's returns, which is 17.5%.
Using the formula, we get:
Treynor Ratio = (11.2% - 3.1%) / 1.20
= 6.0%
Therefore, the Treynor ratio for the Yoko Fund is 6.0%.
None of the answer choices is exactly equal to 6.0%, but the closest one is (c) 6.750.
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HELP ASAP!!!!!!!!!!!!
Which cannot be the angle measurements of triangle ABC?
Measure of angle A = 55 degrees, measure of angle B = 65 degrees, measure of angle C = 60 degrees
Measure of angle A = 60 degrees, measure of angle B = 60 degrees, measure of angle C = 60 degrees
Measure of angle A = 57 degrees, measure of angle B = 58 degrees, measure of angle C = 65 degrees
Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees
Answer:
A=61
B=57
C=61
Step-by-step explanation:
The sun of the three angles must give us 180 degrees. so the sum of these three angles is giving us 179 wrong degrees.
Which three side length best describes the triangle in the diagram
Answer:
i think that it is d or c just guessing
−6(3/8+3/4)= ??????????????????????????????????
AS A FRACTION
Answer:
-27/4
3/8+3/4=3/8+(3×2)(3×2)
3/8+4/8=7/8
-6×7/8
=-27/4
Help ASAP due today!!
The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all of them. In other words, it is the smallest number that is divisible by each of the given numbers without leaving a remainder. [tex]3(5/8) + 2(3/8) = 6.[/tex]
What is the integer?To add the mixed numbers 5 3/8 and 3 2/8, we need to convert them to fractions with a common denominator. Since both have a denominator of 8, we can add the whole numbers to the fractions to get:
[tex]5 3/8 = 5 + 3/8 = 40/8 + 3/8 = 43/8[/tex]
[tex]3 2/8 = 3 + 2/8 = 24/8 + 2/8 = 26/8[/tex]
Now we can add these fractions:
[tex]5 3/8 + 3 2/8 = 43/8 + 26/8 = 69/8[/tex]
So the sum of [tex]5 3/8[/tex] and [tex]3 2/8[/tex] as a fraction is [tex]69/8[/tex] .
The LCM is often used when adding or subtracting fractions with different denominators, since we need to find a common denominator to perform the operation. To do this, we can find the LCM of the denominators and use it as the common denominator.
To write equivalent fractions with a common denominator, we need to find the least common multiple of the denominators, which in this case is 8.
For [tex]3(5/8)[/tex] :
[tex]3(8/8) + 5/8 = 24/8 + 5/8 = 29/8[/tex]
For [tex]2(3/8):[/tex]
[tex]2(8/8) + 3/8 = 16/8 + 3/8 = 19/8[/tex]
To add these fractions, we simply add their numerators:
[tex]3(5/8) + 2(3/8) = 29/8 + 19/8 = 48/8 = 6[/tex]
Therefore, [tex]3(5/8) + 2(3/8) = 6.[/tex]
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