Given that the sample mean is 100, the sample mean is 39, and the sample standard deviation is 13.
To find the 95% confidence interval for the population mean, we use the formula as follows:
Confidence Interval formula: CI = X ± Z* σ/√nWhere CI = Confidence IntervalX = Sample Mean
Z* = Z-Scoreσ = Standard Deviationn = Sample SizeHere, the sample size(n) is 100, the sample mean(X) is 39, and the sample standard deviation (σ) is 13.The formula for finding the Z-Score is:Z = 1 - α/2,
where α is the level of significance. α is the probability of the event not occurring, so we subtract it from one to get the probability of the event occurring.
Here, the level of significance is 0.05 since we need to find the 95% confidence interval.
Z = 1 - α/2 = 1 - 0.05/2 = 0.975Then we find the Z-Score from the Z-Score table, which is 1.96.
Therefore, the 95% confidence interval is:CI = X ± Z* σ/√n= 39 ± 1.96 (13/√100)= 39 ± 2.548Thus, the 95% confidence interval for the population mean is (36.452, 41.548).
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The 95% confidence interval for the population mean is
[tex]\[\large \left( 36.452,41.548 \right)\][/tex].
Sample size = 100
Sample mean = 39
Sample standard deviation = 13
Confidence level = 95%
To find the confidence interval, we use the formula given below:
Confidence interval formula is as follows:
[tex]\[\large \left( \overline{X}-z\frac{\sigma }{\sqrt{n}},\overline{X}+z\frac{\sigma }{\sqrt{n}} \right)\][/tex]
We are given, sample mean is 39
[tex]\(\overline{X}=39\)[/tex],
sample standard deviation is 13
[tex]\(\sigma=13\)[/tex],
sample size is 100
i.e. n=100, and confidence level is 95%
z=1.96 (From Z table)
By substituting all the given values in the formula, we get the confidence interval as,
[tex]\[\large \left( 39-1.96\frac{13}{\sqrt{100}},39+1.96\frac{13}{\sqrt{100}} \right)\][/tex]
Simplifying the above expression, we get,
[tex]\[\large \left( 39-2.548,39+2.548 \right)\][/tex]
Therefore, the 95% confidence interval for the population mean is
[tex]\[\large \left( 36.452,41.548 \right)\][/tex].
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i'll give brainiest to who answers this pls help
Answer:
The answer is 126 square inches.
Step-by-step expalation
A study looked at n=256 adolescents, where subjects wore a wrist actigraph, which allowed the researchers to estimate sleep patterns. Those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.6 millimeters of mercury (mm Hg) higher than that of other adolescents. The standard deviation of this difference is 1.8 mm Hg. Based on the results, test whether this difference is significant at the 0.01 level. 2. An SRS of 100 incoming freshman was taken to look at their college anxiety level. The mean score of the sample was 87.3 (on a 0 to 100 scale with a higher score indicating mores stress). Assuming population o = 8.1, construct a 95% confidence interval for the population mean. What sample size is required to get a margin of error less than or equal to .15?
There is a significance at the level 0.01.
We can use a two-sample t-test for this purpose.
A two-sample t-test is used to examine whether two data samples have a mean difference that is statistically significant.The null hypothesis for this test is that there is no significant difference between the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and that of other adolescents.
Hence, H0: μ1 = μ2
where μ1 is the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and μ2 is the mean systolic blood pressure of other adolescents.
The alternative hypothesis is that there is a significant difference between the two means:
H1: μ1 ≠ μ2
The level of significance (α) is 0.01, so the critical value of t can be found using a t-distribution table with 254 degrees of freedom (n1+n2-2=254).
The critical value at a 0.01 level of significance is ±2.576.
From the question, we know that the mean difference between the two groups is 5.6 mm Hg and the standard deviation of this difference is 1.8 mm Hg.
Therefore, the t-statistic can be calculated as:
t = (5.6 - 0) / (1.8 / sqrt(256))
= 56 / 1.8 = 31.11
Since the calculated t-statistic (31.11) is greater than the critical value (±2.576), we reject the null hypothesis.
Thus, we can conclude that there is a significant difference in systolic blood pressure between the two groups at the 0.01 level of significance.
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surface area does anyonr know it im confused on the formula
Answer:
131.92ft²
Step-by-step explanation:
okay, so we have to find the area of both circles, and the circumference then multiply that with the height, it's confusing, so:
3² x 3.14 = 28.26 x 2 = 56.52 so that the area of the bases
3 x 2 x 3.14 = 18.85 x 4 = 75.4
75.4 + 56.52 = 131.92
So the surface area of the cylinder is 131.92ft²
A projectile was launched from the ground with a certain initial velocity. The militaries used a radar to determine the vertical coordinate you of the projectile for two moments of time measured in seconds from the moment when the projectile was launched. The radar measurements showed that y(3) = 419 meters, 6) = 679 meters. Calculate the maximum of y() if it is known as follows 1. The projectile was moving along a vertical line 2. The acceleration due to gravity gis 9.81 meter second 3. There is an air resistance proportional to the velocity of the projectile. 4. The value of the empirical coefficient p is a constant 5. Time is measured in seconds, and distances are measured in meters A student solved the problem, rounded-off the numerical value of the maximum of y(t) to THREE significant figures and presented it below (15 points) meters your numerical answer must be written here Also, it is required to answer several additional questions as follows: 1. If p is the value of a positive empirical constant (its value is to be found), is the unknown initial velocity of the projectle, then the formula for the altitude y of the projectile at the moment of timetis given by the formula (1 point): = ロロロロロ 2. If p is the value of a positive empirical constant (its value is to be found) is the unknown initial velocity of the projectile, then the value of the velocity of the projectile at the moment of time is given by the formula (1 point): ( *Y-811.pl 3. The maximum of the altitude was achieved by the projectile when time expressed in seconds and rounded-odfo FOUR significant figures) was qual to (3 points) 9.354 DD0000 10:49 10.89 11 35 11.89 12.48.
The maximum altitude attained by the projectile is 720 meters. The maximum altitude was achieved by the projectile when time expressed in seconds and rounded off to four significant figures was equal to 10.89 seconds.
The formula for the altitude y of the projectile at the moment of time t is given by the formula: y(t) = [(v_0 / p)g][1 - exp(-pt / m)] + (m / p)g(t / p) where v_0 is the initial velocity of the projectile, p is the empirical constant, g is the acceleration due to gravity, m is the mass of the projectile, and t is the time.
The formula for the velocity of the projectile at the moment of time t is given by the formula: v(t) = (v_0 / p)exp(-pt / m) + (m / p)g.
Any object launched into space with only gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile. This doesn't imply that other forces don't affect it; it merely means that their impact is far smaller than that of gravity. A projectile's trajectory is its route after being fired. A projectile is something that is launched or batted, as a baseball.
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Scott has a rope 8 metres long. He says, “I need 9 pieces each 0.89 metres long.’’ Will Scott have enough ribbon?
A. Yes B. No
Answer:
B
Step-by-step explanation:
How did it go from "rope" to "ribbon", therefore, the statement is incorrect. This is a man-made equation that clearly has a mistake. If it was to say, "Will Scott have enough rope?" then the answer will be "YES"
Answer:
the answer is NO
Step-by-step explanation:
0.89 x 889 = 8.01
Therefore, he is 1cm short
Find the probability of the indicated event if P(E)=0.20 and P(F)=0.45. Find P(E or F) i PE and F)=0.10. P(E or F)-
The probability of event E is 0.20, the probability of event F is 0.45, and the probability of both E and F occurring is 0.10. Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.
Given that P(E) = 0.20 and P(F) = 0.45, we also know that P(E and F) = 0.10. Using the formula P(E or F) = P(E) + P(F) - P(E and F), we can substitute the values and calculate the probability of either event E or event F occurring.
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = 0.20 + 0.45 - 0.10
P(E or F) = 0.65
Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.
The concept behind this formula is that when we add the individual probabilities of E and F, we count their intersection (P(E and F)) twice. Since we want to avoid double-counting the intersection, we subtract P(E and F) from the sum of P(E) and P(F). This gives us the probability of either event E or event F occurring.
In this case, the probability of either event E or event F occurring is 0.65, indicating a relatively high likelihood of one of the events happening.
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4x^2+2x-1=0 in quaratic equations
Answer:
Step-by-step explanation:
"quaratic" should be "quadratic."
The coefficients of this quadratic are 4, 2 and -1. Thus, the discriminant is
b^2 - 4ac, or here, 4 - 4(4)(-1) = 20
Since the discriminant is positive, our quadratic has two real, different roots.
-2 ± (√4)(√5)
The roots are: x = ---------------------
2(4)
-1 ± √5
This reduces to x = ---------------
8
What must the values of x and y be so that the two houses are similar?
Answer:
x=12 and y=6
Step-by-step explanation:
because the angle are same and equal
The value of x is 12 and y is 6.
what is similarity?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical. For example, the sun and moon might appear the same size but they are actually different in size. However, we are similar figures since both the figures are circular in nature.
Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio or proportion(corresponding sides). Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides or scale factor must be the same. If two triangles are similar that means,
All corresponding angle pairs of triangles are equal.All corresponding sides of triangles are proportional.As per the situation we have given that
The similarity in figures show that the angles are equal.
Also, the corresponding sides are also equal.
Hence, the value of x is 12 and y is 6.
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How much can this water
tank hold?
20 ft
40 ft
cubic feet
ETOOTC
Volume of Cylinder = 7r2 x h
Use 3.14 for .
Do NOT round your answer.
Answer:
15 i don't think it is right
In a study of cell phone usage and bruin hemispheric dominanon, an Internet survey was e-mailed to 6960 subjects randomly selected from an online group involved with cars. There were 1305 surveys murad. U 0.01 significance level to test the claim that the return rate is less than 20%. Use the Pusle method and use the romal distribution as an approximation to the binomial atribution Setely the nel ypothesis wd attive hypothesis ОА 02 Hp02 OCH D03 Hp02 OLM OB 02 Hp02 OD. Hp.02 Hp02 OF HH02 The treat statinio iz- Round to two decimal places as needed.) The Punto e Round to the decimal places is needed.) fiecause the value is the significance level the hypothesis. There is evidence to support the claim that the retumisess than 20%
Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.
According to the given problem, an internet survey was e-mailed to 6960 subjects randomly selected from an online group involved with cars. The return rate of the survey was 1305.Use the Pusle method and use the romal distribution as an approximation to the binomial distribution to test the claim that the return rate is less than 20% at 0.01 significance level. We are to set the null and alternative hypotheses. The null hypothesis is the claim that we are testing against. The alternative hypothesis is what we conclude when we reject the null hypothesis.We can state the null hypothesis as;H0: p >= 0.20The alternative hypothesis is;Ha: p < 0.20Where p is the population proportion.Now, we calculate the test statistic using the Pusle method, which is given by;P = (1305/6960) = 0.18804q = 1 - p = 0.81196n = 6960The standard deviation can be calculated using the formula;σ = sqrt (n * p * q)σ = sqrt (6960 * 0.18804 * 0.81196)σ = 23.43Now, we calculate the z-score using the formula;z = (x - μ) / σz = (0.20 - 0.18804) / 0.00349z = 3.43Finally, we can calculate the p-value using the z-score table or calculator.The critical value of z at the 0.01 significance level is 2.33. Since our calculated z-score (3.43) is greater than the critical value (2.33), we reject the null hypothesis.Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.
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Tamara can mow an acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? Write an equation to model and solve the problem. Explain the answer in terms of the problem. Show all work.
Answer:
2 hours
Step-by-step explanation:
Please help me anyone any other answers would be reported
Answer:
Wait So...
Step-by-step explanation:
What Kind of Math is this?
An application layer IDS security device uses a Bayes based machine learning algorithm that is: - 99% sensitive, 99% of the time identifies true positive packets with malware payload - 95% specific, 95% of the time identifies true negative packets without malware payload. The IDS performs real time deep Malware Traffic Analysis in a high attack application environment where approximately 60% of the traffic is legitimate and 40% of the traffic contains malware, in which case the device drops the packets with malware. Calculate the probability of false negative packets, which is the worst case scenario and is equivalent to the probability for a successful attack. Note: Conditional Probability (A | B) = Probability (A and B) / Probability (B)
The probability of false negative packets, which represents the worst-case scenario of a successful attack, can be calculated using the sensitivity and prevalence of malware traffic.
The sensitivity of the IDS, which is the probability of correctly identifying packets with malware, is given as 99%. This means that out of all the packets containing malware, the IDS will correctly identify 99% of them as positive.
The prevalence of malware traffic in the high attack application environment is stated as 40%, meaning that 40% of the traffic contains malware.
To calculate the probability of false negative packets (P(false negative)), we need to determine the probability of the IDS incorrectly identifying packets without malware as negative. Since the specificity of the IDS is not provided, we can assume it to be 100% - 95% = 5%, as specificity and false positive are complements.
P(false negative) = 1 - sensitivity = 1 - 0.99 = 0.01
Therefore, the probability of false negative packets, which represents the worst-case scenario and is equivalent to the probability for a successful attack, is 0.01 or 1%.
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Solve the system of equations shown below?
um just testing 157x124
Answer:
Step-by-step explanation:
I need to know what is the given in this problem
well, the triangle is an isosceles with twin sides, and so twin sides stemming from a common vertex will make twin angles on the other sides, the heck all that means?
well, it means that the twin sides of BC and BD make twin angles at C and D, so
[tex]6x-9~~ = ~~3x+24\implies 3x-9=24\implies 3x=33 \\\\\\ x=\cfrac{33}{3} \implies x=11 \\\\[-0.35em] ~\dotfill\\\\ \underset{ C }{\stackrel{ 6(11)-9 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ D }{\stackrel{ 3(11)+24 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ B }{\text{\LARGE 66}^o}[/tex]
What kind of function is f(x)?
A. Exponential
B. Logarithmic
C. Rational
D. Polynomial
Thank you :)
The question is above!
;)
Answer:
umm 9/2
Step-by-step explanation:
Which expressions are equivalent to 6 + 12x
A 3(2+4x)
B. 3(2+6x)+2x
C. 5(1+2x)+1+2x
D7(1+2x)-2x-1
E 7 (1+2x)+2x-1
Answer:
A,C and D
Step-by-step explanation:
A: 3x2=6
3x4X=12X
6+12X
C: 5x1=5
5x2X=10X
5+10X+1+2X
6+12X
D: 7x1=7
7x2X=14X
7+14X-2X-1
6+14X-2X
6+12X
8m - 5.5 =10.1
Help Please
Answer:
= 1.95
Step-by-step explanation:
8 − 5.5 + 5.5 = 10.1 + 5.5
8 = 15.6
8 = 15.6
8 8
first 5.5 means 55/10 and 10.1 means101/10 when we change them to fraction.
8m=101/10+55/10=156/10
divide 8 by 8 and we get m
and again divide 156/10 for 8
m=1.95
population grows according to an exponential growth model: The initial population is Po 10, and the growth rate is r 0.2_ Then: Pi 10.2 Pz 10.4 Find an explicit formula for Pn: Your formula should involve n. Pn 10 ( 1.02) n Use your formula to find P9 Pg 11.95 Give all answers accurate to at least one decimal place
The population at time n=9 is approximately 11.95. The term "population" refers to the entire set of individuals, objects, or events that are of interest to a researcher or analyst.
Based on the given information, we have:
Initial population (P0) = 10
Growth rate (r) = 0.2
To find an explicit formula for Pn, we can use the formula for exponential growth:
Pn = P0 * (1 + r)^n
Substituting the given values:
Pn = 10 * (1 + 0.2)^n
Simplifying the formula, we have:
Pn = 10 * 1.2^n
Using this formula, we can find P9:
P9 = 10 * 1.2^9 ≈ 11.95
Therefore, the population at time n=9 is approximately 11.95.
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Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale), count the number of different ways of choosing 4 people for a committee. Assume no one can hold more than one office and that each person is to hold a different position on the committee.
There are 35 unique approaches to choosing 4 individuals for a board.
Given a gathering of understudies: G = {Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale}, the undertaking is to count the quantity of various approaches to picking 4 individuals for a panel with the suspicion that nobody can hold more than one office and that every individual is to stand firm on an alternate foothold on the council. There are two primary sorts of mix: With and without repetition, the case here is without repetition, as shown by the formulae "C(n, r)."
The following formula calculates the number of Probability selection options for r items from a set of n items: C(n, r) = n!/(n - r)!r!Where n is the quantity of things in the set, and r is the quantity of things to be chosen from the set. Applying the recipe to the above issue: The group consists of seven students, and we want to select four for the committee. C(7, 4) = 7!/(7 - 4)!4! = (7 × 6 × 5 × 4)/(3 × 2 × 1 × 4) = 35. Answer: 35. Subsequently, there are 35 unique approaches to choosing 4 individuals for a board.
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use Laplace transforms to solve the following differential equation
y' + 3y = f(t), y(0) = α, α is a constant.
The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).
We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:
sY(s) - y(0) + 3Y(s) = F(s)
Substituting y(0) = α, we get,
sY(s) - α + 3Y(s) = F(s)
Rearranging the equation and solving for Y(s), we have,
Y(s) = (F(s) + α)/(s + 3)
Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,
y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}
The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.
Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).
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which statement is true?
Answer:
B is the answer
because if you observe very well the angles look similar in a way when you turn it the other way round ...
NO LINKS I will give brainliest, it’s a graph pls answer if you know how. Where are the smart people
Answer:
The answer for (a) is at the picture
(b) The vertex is (-2,7)
(c) Yes the parabola open downward
(d) -(x+2)^2+7 the turning point is at (-2,7) since it is where the group curves
Step-by-step explanation:
What is the sample space for a spinner with four equal sections, numbered 1 to 4?
1, 2, 3, 4
4-1. 4-2. 4-3. 4-4
1-1,1-2, 1-3, 1-4
1, 2, 3, 4, 5
Answer:
the answer is 1-1, 1-2, 1-3, 1-4
Step-by-step explanation:
please help, is it x = 6, y = 6, y = x, or y = 2?
01:08:55
B
O
B
А
A'
2
D
C
ci
D'
Х
6
8
10
2
O x = 6
O y = 6
O y = x
O y=2
The equation for the line of reflection is x = 6
What is reflection?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, a graph, we need to find the equation of the reflection of the polygon graphed,
We can see, all the vertices on the polygon are being mirrored across the line x = 6.
So, we can say the line of reflection is x = 6.
Hence, the equation for the line of reflection is x = 6
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What number equals 8 when its cubed?
Step-by-step explanation:
2 would be the answer .
hope it helps u .
2 cubed = 8
equasion; 2 Cubed = [tex]2^{3}[/tex] = 2 × 2 x 2 = 8
i hope this helps <3
to Find the analyticity region of the function and find it's derivate of the following functions (a) √Z²-2 (b) Sen (log z²) 20 Find the Taylor serie around zero for fuz) = 4+2² and compute the Convergence radius
(a) To find the analyticity region of the function f(z) = √(z² - 2), we need to determine where the function is well-defined. The square root function is defined for non-negative real numbers. In this case, the expression inside the square root, z² - 2, should be greater than or equal to zero.
z² - 2 ≥ 0
Solving the inequality:
z² ≥ 2
Taking the square root of both sides, while considering both the positive and negative roots:
z ≥ √2 or z ≤ -√2
Therefore, the analyticity region of the function f(z) = √(z² - 2) is all values of z greater than or equal to √2 or less than or equal to -√2.
(b) To find the derivative of the function f(z) = Sen(log z²), we can use the chain rule.
Let's break it down:
f(z) = Sen(log z²)
First, find the derivative of the inner function log z²:
d/dz (log z²) = 1 / (z²) * 2z = 2 / z
Now, find the derivative of Sen(u), where u = log z²:
d/dz (Sen(u)) = cos(u) * du/dz
Substituting the value of u:
d/dz (Sen(log z²)) = cos(log z²) * (2 / z)
Therefore, the derivative of the function f(z) = Sen(log z²) is cos(log z²) * (2 / z).
(c) To find the Taylor series around zero for the function f(z) = 4 + 2z², we need to find the derivatives of the function at zero and use them to construct the series.
Let's find the derivatives:
f(z) = 4 + 2z²
f'(z) = 0 + 4z = 4z
f''(z) = 0 + 4 = 4
f'''(z) = 0
All higher-order derivatives will also be zero.
Now, let's construct the Taylor series around zero using these derivatives:
f(z) = f(0) + f'(0)z + (f''(0)/2!)z² + (f'''(0)/3!)z³ + ...
Since the higher-order derivatives are zero, the series simplifies to:
f(z) = 4 + 0z + (4/2!)z² + 0z³ + ...
Simplifying further:
f(z) = 4 + 2z²
The Taylor series around zero for the function f(z) = 4 + 2z² is simply the original function itself.
To compute the convergence radius of the series, we can observe that the function f(z) = 4 + 2z² is a polynomial, and all polynomials have an infinite convergence radius. Therefore, the convergence radius for this series is infinite.
In conclusion, to Find the analyticity region of the function and find it's derivate of the following functions the Taylor series around zero for the function f(z) = 4 + 2z² is 4 + 2z², and its convergence radius is infinite.
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Someone help me with this its in the picture!!!
Answer:
JK < KI < IJ
Step-by-step explanation:
The length of the side of a rectangle corresponds with the size of the angle opposite it.
m<K = 180 - (50 + 44) (sum of triangle)
m<K = 86°
IJ is opposite m<K = 86°
JK is opposite to m<1 = 44°
KI is opposite to m<J = 50°
The bigger the measure of an angle, the larger the side opposite it.
Therefore, form least to greatest, the side lengths of the triangle cam be ordered as follows:
JK < KI < IJ