Answer:
Step-by-step explanation:
Given:
Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).
Triangle ABC reflected over the x-axis to get the triangle A'B'C'.
To find:
The coordinates of the image A'B'C'.
Solution:
If a figure reflected over the x-axis, then rule of transformation is
Now, using this rule, we get
Therefore, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).
Evaluate. 12⋅(1/4+1/3)to the power of2+2/3 Enter your answer as a mixed number in simplest form by filling in the boxes.
12×(1/4+1/3)to the power of2+2/3 using PEDMASand INDICIES rule gives 7^8/3
What is Indices? lndicies is expressed as Ax^n. Where A is the coefficient, x is the base and n is the power or index.
12×(1/4+1/3)to the power of2+2/3
Evaluating the expression
= (12×( 1/4+1/3))^2+2/3
using PEDMAS
= (12× 7/12)^8/3
opening the bracket, we therefore have
= 7^8/3
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Simplify the trigonometric expression. cos(theta+pi/2)
We have to simplify the expression:
[tex]\cos (\theta+\frac{\pi}{2})[/tex]We could see it graphically:
We see that for any angle theta, the cosine of theta + pi/2 is equal to negative sin of theta.
Then we can write:
[tex]\cos (\theta+\frac{\pi}{2})=-\sin (\theta)[/tex]The answer is -sin(theta).
Select True or False for each statement.
A right triangle always has obtuse exterior angles at two vertices.
Answer:
true
Step-by-step explanation:
it is true ........
Explanation:
A right triangle has exactly one angle that is 90 degrees. This is called a right angle.
The other two angles are acute, which means they are less than 90 degrees. An example would be 30 degrees and 60 degrees.
If 30 degrees is an interior acute angle, then 180-30 = 150 degrees is the exterior obtuse angle. Similarly, the adjacent angle to the 60 is 180-60 = 120 degrees.
This example shows we have two obtuse exterior angles. This applies to any right triangle, and not just this particular one.
Edgar drew a scale drawing of the town library. The scale of the drawing was 5
centimeters: 2 meters. The parking lot is 34 meters wide in real life. How wide
is the parking lot in the drawing?
Answer:
85 cmStep-by-step explanation:
The scale factor is:
5 cm ÷ 2 mFind the width of the parking lot in the drawing:
5 cm ÷ 2 mx cm ÷ 34 mCross multiply and find the value of x:
x = 5*34/2x = 85 cmWhich equation is true when A.n = 1.2 B.
1.2n=10 n+1=1.2 C. 5+n=6.2 D. 10n=1.2
The true equation is 5 + n = 6.2.
Here we have to find the equation for which n = 1.2.
So the first equation is
10n = 1.2
So for this, we get the value of n as:
n = 1.2/10
= 0.12
which is not equal to 1.2.
So it is not correct
The second equation is:
n + 1 = 1.2
n = 0.2
which is not equal to 1.2
So it is also not correct.
The third equation is:
5 + n = 6.2
n = 6.2 - 5
= 1.2
So it is correct.
The fourth equation is:
1.2n = 10
n = 10/1.2
= 8.33
Here n is not equal to 1.2
So it is also correct.
Therefore the correct equation is 5 + n = 6.2.
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need help due tommorow
Finding the ratio of
a)1:9
b)2 : 7
c) 2 : 5
What is Ratio?
A ratio indicates how often one number contains another number. For example, if a fruit bowl contains 8 oranges and 6 lemons, the ratio of oranges to lemons is 8 to 6. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to whole fruit is 8:14.
Given,
Total no. of students = 42
a) Students who prefer punk to students who prefer hip-hop
No. of students in punk = 2
No. of students in hip-hop = 18
The Ratio will be,
punk : hip-hop = 2:18
= 1:9
b) Students who prefer rock to total no. of students that are surveyed
No. of students in rock = 12
Total no. of students = 42
The Ratio will be,
rock : total students = 12 : 42
= 2 : 7
c) Students who prefer rock or classic rock to students who prefer all music
No. of students in rock = 12
Total no. of students who likes other music = 42 - 12
= 30
The Ratio will be,
rock : total students with different music = 12 : 30
= 2 : 5
Hence, The ratio comparison in three different way
a)1:9
b)2 : 7
c) 2 : 5
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What is the answer to 2(7x-3)+9
Answer:
14x+3 is the answer I think
The solution to the given equation would be [tex]14x+3[/tex].
Hope this helps!
Solve the problems.
Prove: BD = CD
The Angle-Side-Angle (ASA) criterion states that any two angles and the side included between them of one triangle are identical to the corresponding angles and the included side of the other triangle if two triangles are congruent. One of the requirements for two triangles to be congruent is angle side angle.
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal.
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Given,
M∠1 = M∠2
(On joining BD and CD)
M∠ADB = M∠ADC
In ΔABD and ΔADC
M∠ADB = M∠ADC (Given)
M∠BAD = M∠DAC (Given)
AD = AD (Common Sides)
⇒ ΔABD ≅ ΔADC (Angle Side Angle Property)
So, BD = CD (Corresponding sides are equal to a Congruent Triangle)
Hence, proved that BD = CD.
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How long is the control line? I couldn’t figure this out
Solution:
Given the circle with center A as shown below:
The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.
The length of the arc AC is expressed as
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}[/tex]Given that
[tex]\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}[/tex]we have
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}[/tex]Hence, the length of the control line is 85.94366927 feet.
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.042 for the estimation of a population
proportion? Assume that past data are not available for developing a planning value for p*. Round up to the next whole number.
The sample size should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power.
As given in the question,
Confidence level is 95% and the margin of error is 0.042
So,
1 - α = 0.95,
α = 0.05,
E = 0.042
planning value (p) = 0.5
To calculate Sample size the formula is:
[tex]n = \frac{p(1-p)(Z_{a/2})^2}{E^2}[/tex]
From the table we can find that:
[tex]Z_{a/2} = 1.96[/tex]
Putting the values given in the question in formula:
[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]
n = 545.6
Hence the sample size is 545.6
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Evaluate and simplify the expression
when a = 2 and b = 4.
4a - 2(a + b) + 1 = [?]
Answer:
-3
Step-by-step explanation:
4(a) - 2(a + b) + 1 = [?]
4(2) - 2(2+4) + 1
8 - 4 - 8 + 1
appilcation of bodmas
4 - 8 + 1
- 4 + 1
-
3
please di it quickly I just need to confirm answer
The Solution:
Given:
[tex]\begin{gathered} V=(-5,3) \\ \\ W=(\frac{3}{2},-\frac{1}{2}) \end{gathered}[/tex]Required:
To find the value of V - W
[tex]V-W=\lbrace(-5-\frac{3}{2}),(3--\frac{1}{2})\rbrace=(-6\frac{1}{2},3\frac{1}{2})=(-\frac{13}{2},\frac{7}{2})[/tex]
Therefore, the correct answer is [option 3]
1. The data set represents the number of cars in a town given a speeding ticketeach day for 10 days.2 4 5 5 7 7 8 8 8 121. What is the median? Interpret this value in the situation.*
ANSWER:
7
STEP-BY-STEP EXPLANATION:
We have the following data:
[tex]2,4,5,5,7,7,8,8,8,12[/tex]The median is the data value that separates the upper half of a data set from the lower half. Therefore:
In this case, being even, the two data are half, but since the value is the same, that is, 7, the median is equal to 7.
The interpretation of this value is in the middle of the 10 days (days 5 and 6), 7 would be the number of cars in a town given a a speeding ticket.
Consider the following equation of the circle. Graph the circle
Explanation
Given the equation;
[tex](x+6)^2+(y+7)^2=4[/tex]Using a graphing calculator, the graph of the circle becomes;
Answer:
16. The height, h, in feet of an object above the ground is given by h = -16t² +64t+190, t≥0, where t is the time in seconds. a) b) c) d) When will the object be 218 feet above the ground? When will it strike the ground? Will the object reach a height of 300 feet above the ground? Find the maximum height of the object and the time it will take.
the maximum height is 254 feet.
Answer:
a) 0.5 seconds and 3.5 seconds.
b) 5.98 seconds (2 d.p.)
c) No.
d) 254 feet at 2 seconds.
Step-by-step explanation:
Given equation:
[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]
where:
h is the height (in feet).t is the time (in seconds).Part aTo calculate when the object will be 218 feet above the ground, substitute h = 218 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]
Therefore, the object will be 218 feet about the ground at 0.5 seconds and 3.5 seconds.
Part bThe object strikes the ground when h is zero. Therefore, substitute h = 0 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]
As t ≥ 0,
[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]
[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]
Therefore, the object strikes the ground at 5.98 seconds (2 d.p.).
Part c
To find if the object will reach a height of 300 feet above the ground, substitute h = 300 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]
Therefore, as t is a complex number, the object will not reach a height of 300 feet.
Part dThe maximum height the object can reach is the y-coordinate of the vertex.
Find the x-coordinate of the vertex and substitute this into the equation to find the maximum height.
[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]
[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]
Substitute t = 2 into the equation:
[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]
Therefore, the maximum height of the object is 254 feet.
It takes 2 seconds for the object to reach its maximum height.
rThe number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs012.34P(x)0.640.250.060.03.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
N = Number of data
x1...xn = Samples
[tex]s=\sqrt[]{\frac{\sum ^n_{n\mathop=1}(y-\mu)^2}{n-1}}[/tex]Let's calculate first:
[tex]\sum ^n_{n\mathop=1}yn=0.64+0.25+0.06+0.03+0.02=1[/tex]Now:
[tex]\sum ^n_{n\mathop=1}yn^2=(0.64)^2+(0.25)^2+(0.06)^2+(0.03)^2+(0.02)^2=0.477[/tex]So:
[tex]s=\sqrt[]{\frac{0.477-\frac{(1)^2}{5}}{5-1}}=0.2631539473\approx0.3[/tex]A football team was able to run the ball for 8 yards on their first play. On the second play they lost 12 yards. The third play they lost another 11 yards. What was their total yards they gained?
The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Subtraction = Minus of any two or more numbers.
Summation = addition of two or more numbers or variable
Let's consider all gained yards by positive (+) and all lost yards by negative (-).
Given that,
In the first play = +8 yards (gain)
In second play = -12 yards (lost)
In the third play = 11 yards (Lost)
So total yards = +8 - 12 - 11 = -15 (Lost)
Therefore, the football team lost 15 yards.
Hence "The total yards gained or lost is the algebraic sum so the resultant yards is -15 yards thus they lose 15 yards".
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If XD = 2X – 6 and XV = 3x – 6 and WY and XV bisect at D, what is XV?
The diagonal WY bisects the diagonal XV at point D, which means that XV is divided into two equal line segments XD and XV.
[tex]XD=XV[/tex]Replace the equation above with the given expressions for both line segments:
XD= 2x-6
XV= 3x-6
[tex]2x-6=3x-6[/tex][tex]undefined[/tex]Out of 450 applicants for a job, 249 are female and 59 are female and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places.
The probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that 249 are female and 59 are female and have a graduate degree out of 450 applicants.
We are given following in the question;
M: Applicant is male.
G: Applicant have a graduate degree
F : Applicant is female.
The Total number of applicants = 450
Number of female applicants = 249
Number of female applicants have a graduate degree = 59
Therefore,
P(G/F) = P([tex]G^F[/tex])/P(F)
= 59/207 or 0.236
Hence, the probability that a randomly chosen applicant has a graduate degree, given that they are female is 0.236.
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What is x2 + 6x complete the square
You have the following expression:
x² + 6x
In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:
6 = 2ab
a=1 because is the coeffcient of the term with x², then for b you obtain:
b = 6/2(1) = 3
the third term of the trynomial is the squared of b.
The radius, R, of a sphere is 4.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.) --0- V = 3 em Х 5 ?
The formula to calculate the volume of a sphere is given to be:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius.
From the question, we have the following parameters:
[tex]\begin{gathered} \pi=3.14 \\ r=4.8 \end{gathered}[/tex]Therefore, the volume is calculated to be:
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times4.8^3 \\ V=463.0 \end{gathered}[/tex]The volume is 463.0 cm³.
please help! I do not understand and it is due tonight!!!!!!!
Consider that there are, generally, the following types of angles pairs,
1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.
2. Complementary Angles: Angles that are adjacent and together form a right angle.
3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.
a.
The adjacent angles to angle 4 are angles 1 and 3.
There are no complementary angles associated with angle 4.
The supplementary angles to angle 4, are angles 1 and 3.
Thus, the angle pairs that include angle 4 are,
[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.
The adjacent angles to angle 5 are angles 6 and 7.
There are no complementary angles associated with angle 5.
The supplementary angles to angle 5, are angles 6 and 7.
Thus, the angle pairs involving angle 5 are,
[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]Figure out how many offspring there would be for the fifth and sixth generations using the equation
Explanation
We are given the following:
The table above models the function:
[tex]\begin{gathered} f(x)=a(4)^x \\ where \\ a=initial\text{ }value\text{ }(when\text{ }the\text{ }generation)=0 \\ x=generation \end{gathered}[/tex]We are required to determine how many offspring there would be for the fifth and sixth generations using the equation.
This is achieved thus:
[tex]\begin{gathered} \text{ Offspring:} \\ Fifth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=5 \\ F\imaginaryI fth\text{ }generat\imaginaryI on\to6(4)^5=6144 \end{gathered}[/tex][tex]\begin{gathered} Sixth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=6 \\ S\imaginaryI xth\text{ }generat\imaginaryI on\to6(4)^6=24576 \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} 5th\text{ }generation=6144 \\ 6th\text{ }generation=24576 \end{gathered}[/tex]I'll give brainliest!
Answer:
24
Step-by-step explanation:
8y^0 + 2y^2 * x^-1
8(4)^0 + 2(4)^2 * 2^-1
8 + 2 * 16 * 2^-1
8 + 2 * 2^-1 * 16
8 + 2^1 - 1 * 16
8 + 16
24
Hope this helps! :)
The equation for a line that has a y-intercept of -8 and passes through (-4,2) is y=-5/2x-8 True False
1) Let's verify whether that's true or not, plugging in that point into the equa
(-4,2)
[tex]\begin{gathered} 2=\frac{-5}{2}(-4)\text{ -8} \\ 2=10-8 \\ 2=2 \end{gathered}[/tex]Since this is an identity, in other words, the left side is equal to the right side then we can say that's true.
So that's true y=-5/2x-8 is the equation of the line that has in one of its points the y-coordinate y=-8
I'll give brainliest!
Answer:
x equals to 11!!!
Answer:
11.
Step-by-step explanation:
1.02 x 10^11 = 102,000,000,000
Hope this helps!
Brainliest please, thanks!
There is a 5% chance that the mean reading speed of a random sample of 21
second grade students will exceed what value?
There is a 5% chance that second graders will be faster than 94.597 wpm.
Sample size = 21
standard deviation = 10 wpm
SE = 10/sqrt(21) = 2.18 as a consequence.
Let X be the average reading speed of 21 second-grade students. z = (X - 91)/2.18 Normal(91,2.18) (91,2.18).
If the 95th percentile of a standard normal variable z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.
So there's a 5% chance that the average reading speed of a random sample of 21 second-graders will be faster than 94.597 wpm.
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A composite figure is created using asquare and a semicircle. What is the area ofthe figure?12 in200.52202.52204.52206.52
The area of the composite figure will be the sum of the area of the square and the area of the semicircle. The formula for determining the area of a square is expressed as
Area = length^2
From the diagram,
length = 12
Area of square = 12^2 = 144
The formula for determining the area of a semicircle is expressed as
Area = 1/2 * pi * radius^2
Radius = diameter/2
The diameter of the semicircle is 12. Thus,
radius = 12/2 = 6
pi = 3.14
Area of semicircle = 1/2 * 3.14 * 6^2 = 56.52
Area of composite figure = 144 + 56.52 = 200.52 in^2
The first option is the correct answer
Function A gives the audience in millions
Using function concepts, it is found that:
a) The meaning of each expression is given as follows:
A(4) = audience after four hours.A(0.5) = 1.5 = the audience after 0.5 hours is of 1.5 million peopleb) The expression is: A(4) = 1.3.
c) The expression is: A(2) = A(2.5).
FunctionIn the context of this problem, the format of the function is:
A(t).
In which the meaning of each variable is given as follows:
t is the time in hours after the beginning of the show.A(t) is the audience, in millions of hours.Which gives the meaning of each expression in item a.
For item b, the expression is given as follows:
A(4) = 1.3.
As 4 hours after the episode premiered, the audience was of 1.3 million people.
For item c, the expression is given as follows:
A(2) = A(2.5).
As the audience after 2 hours = 120 minutes is the same as the audience half an hour = 30 minutes later.
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Garcia Co. owns equipment that cost $81,600, with accumulated depreciation of $43,200.
Record the sale of the equipment under the following three separate cases assuming Garcia sells the equipment for (1) $50,600 cash, (2) $38,400 cash, and (3) $33,300 cash.
(1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
(2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
Depreciation :-Depreciation is the gross reduction in the book value of an asset due to regular use or wear and tear.
A capital gain occurs when Garcia Co. receives an amount in excess of the book value of the equipment.
If Garcia Co. receives an amount equal to the book value of the equipment, no profit or loss will result from the disposal.
If Garcia Co. receives an amount below the book value of the equipment, it will experience a capital loss.
In the given question cost of equipment is $81,600 with accumulated depreciation of $43,200 so that the book value will be
$81,600 - $43,200 = $38,400.
Now (1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
For (2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
For(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
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