(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)
(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)
(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:
(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),
(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),
(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)
(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:
(1,1,1), (2,2,2), (3,3,3)
In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.
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Express 4 + ln 2 - ln 4 as a single natural logarithm. a. ln 2 b. ln 4 c. ln 64
The single natural logarithm expression is ln(2). Therefore, correct answer is (a)
Logarithmic Equations:The expression in the form [tex]e^a=b[/tex] can also be written as In b = a which is called as logarithmic expression.
Properties of Logarithms:
1. In (mn) = In m + In n
2. In [tex]a^m =[/tex] m In a
3. In [tex]e^a[/tex] = a.
How to express as a single natural logarithm?The natural logarithm expression is:
4 + ln 2 - ln 4
Apply the product and quotient rule of natural logarithm:
4 + ln 2 - ln 4 = In (4 × 2/4)
Evaluate the quotient:
4 + ln 2 - ln 4 = In (2)
Hence, the single natural logarithm expression is ln(2).
The correct option is (a)
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Answer:
B: ln 4.
Step-by-step explanation:
-0.75, -3, -12, -48... Find the 9th term
Answer:
-49,152
Step-by-step explanation:
if you multiply -0.75, times 4 it equals -3 so do that until you get the ninth term. (Multiply each term by 4).
Determine the unknown angle measures of △DEF. Round to the nearest degree.
m∠D =
°
m∠F =
°
m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.
Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:
m∠D + m∠F + m∠E = 180°
We can rearrange the equation to solve for m∠E:
m∠E = 180° - m∠D - m∠F
Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.
For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:
m∠E = 180° - 40° - 65° = 75°
Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
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Answer: the answer is
m∠D = ✔ 46°
m∠F = ✔ 44°
Step-by-step explanation: I got it correct. it will be show below.
you can compare two marginal distributions to see if the corresponding two variables are related. true/false
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two variables.
Comparing two marginal distributions can help you identify if there is a relationship between two variables. You can plot the distributions and look for evidence of a relationship such as a linear trend or a pattern of higher or lower values compared to one another. Additionally, you can use statistical tests such as the Pearson correlation coefficient or Spearman's rank correlation coefficient to measure the strength of the relationship between the two variables.
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two .
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Mrs. Mack is looking at the blueprints for a new factory. On the blueprint, the factory floor is a rectangle with a length of 0.3 meter and a width of
0.25 meter. The factory will be built by using a scale factor of 140.
Mrs. Mack wants to know the area of the factory floor. She decides to do this by first determining the dimensions of the factory floor.
What will be the length of the factory floor?
Enter your answer in the box
Answer:
42 meters
Step-by-step explanation:
The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.
Answer:
42 meters
Step-by-step explanation:
its correct :)
A lightbulb consumes 600 watts per day. How long does it take to consume 3450 watt hours
5.75 hours long to consume 33450 watt hours
The time it takes for a lightbulb to consume 3450 watt hours can be calculated using the formula: time = energy/power. In this case, the energy is 3450 watt hours and the power is 600 watts.
To find the time, we can plug the values into the formula:
time = 3450 watt hours / 600 watts
time = 5.75 hours
Therefore, it takes 5.75 hours for the lightbulb to consume 3450 watt hours.
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A dish has an area of 400 square inches. What is the length of the radius rounded to the nearest tenth of an inch?
Answer:
11.3 inches
4th option
Step-by-step explanation:
Area of a circular object = πr² where r = radius
Given area = 400 square inches,
πr² = 400 square inches
r² = 400/π
r = √(400/π)
r = 20/√π
= 11.3 inches rounded to one decimal place(tenth)
Find an equation of the plane that contains the curve with the given vector equation. r(t) = (t, t3, t)
The equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
The equation of the plane that contains the curve with the vector equation r(t) = (t, t3, t) can be found by taking the cross product of two vectors that are on the plane. Let the two vectors be v1 = (1, 0, 1) and v2 = (1, 3t2, 1). Taking the cross product of these two vectors yields v1 x v2 = (3t2, -1, -3t2). This vector is perpendicular to the plane. Therefore, the equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.
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Please check my answers and give explanation of why it is wrong if it is wrong 20 points!
The solution is, the correct option is, A.) tan 37 = x/12.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
now, from the given figure we get,
tan 37 = x/12
Hence, The solution is, the correct option is, A.) tan 37 = x/12.
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Which of the following shows the simplified form of sine of x over the quantity 1 plus cosine of x (end quantity)?
A. sin x − tan x
B. sin x − cot x
C. csc x − cot x
D. 1
The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1. Option D
How to find the simplified form of the expressionThe question can be interpreted as sin(x) / (1 + cos(x))
sin(x) / (1 + cos(x)) = (sin(x) / cos(x)) / (1/cos(x) + cos(x)/cos(x))
= tan(x) / (1 + sec(x))
= (sin(x)/cos(x)) / (cos(x)/(cos(x)+1))
= (sin(x)/cos(x)) / ((cos(x)+1)/cos(x))
= sin(x) / (cos(x) + 1)
Therefore, the simplified form of sin(x) / (1 + cos(x)) is:
sin(x) / (1 + cos(x)) = sin(x) / (cos(x) + 1) = 1
Hence, The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1
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show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation. what are the equivalence classes of f and of t?
we have seen that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection.
What's more, the equivalence classes of F,T are :
[tex][F]_{R}[/tex] = Set, all things considered,
[tex][T]_{R}[/tex] = Set of all redundancies .
We have been given :
A= Set of every single compound suggestion
R= Logical equivalence of compound propositions .
We need to show that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection i.e.R is an equivalence connection .
Then, at that point, we have find the equivalence classes of F and T .
To show that R is an equivalence connection, we need to demonstrate that the connection R is reflexive, transitive and symmetric .
Reflexive
We will let a ∈ A.
As, a compound suggestion is in every case logically comparable to itself .
In this manner, a ≡ a, which suggests that (a,a) ∈ R.
Thus,R is reflexive .
Symmetric
We will let(a,b) ∈ R.
This implies that a ≡ b.
On the off chance that an and b have a similar truth table, b and a have a similar truth table .
Thus, by the evenness of logical equivalences, we get : b ≡ a
which suggests (b, a) ∈ R.
In this way, R is symmetric.
Transitive
We will let (a,b) ∈ R and (b,c) ∈ R.
This infers that :
a ≡ b
b ≡ c .
If an and b have a similar truth table and in the event that b and c have a similar truth table then,a and c
have a similar truth table.
Thus, by transitivity of logical equivalences, we get: a ≡ c
which suggests that (a,c) ∈ R.
Along these lines, R is transitive.
Presently, we can infer that R is an equivalence connection.
Presently, we need to find the equivalence classes of Fand T.
The equivalence class of F has every one of the logical equivalences that are misleading. Also, such logical equivalences are contradictions.
Accordingly,
[tex][F]_{R}[/tex] = Set, everything being equal.
The equivalence class of T have every one of the logical equivalences that are valid. Furthermore, such logical equivalences are redundancies .
Hence,
[tex][T]_{R}[/tex] = Set, all things considered.
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how much is 120 euros to dollars
By using the current currency exchange rate , the value of 120 Euros is equivalent to $128.4 .
The "Euro" is the official currency of the European Union, which includes 19 of its member states. and The "US dollar", is official currency of the United States.
The Currency Exchange Rate between euros and dollars can vary depending on market conditions, but
The current exchange rate is approximately 1 euro = 1.07 US dollars.
By using this exchange rate, we can calculate that 120 euros is equal to ;
⇒ 120 euros × 1.07 US dollars/euro = 128.4 US dollars .
Therefore, 120 euros is equivalent to 128.4 US dollars at the current exchange rate.
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how to convert 50 mph to kmh?
The speed of 50 mph is equivalent to 80.47 km/h.
Mph is an abbreviation for miles per hour, and it is a unit of measurement commonly used in the United States. On the other hand, km/h stands for kilometers per hour, and it is a unit of measurement commonly used in most other countries.
To convert 50 mph to km/h, we need to use a conversion factor that relates the two units.
The conversion factor we need to use in this case is 1 mile = 1.60934 kilometers. This means that for every mile covered, there are 1.60934 kilometers covered. To convert 50 mph to km/h, we simply need to multiply 50 by the conversion factor, as shown below:
50 mph x 1.60934 km/mi = 80.47 km/h
Therefore, 50 mph is equivalent to 80.47 km/h. This means that if you were driving at 50 mph in the United States, you would be traveling at a speed of 80.47 km/h if you were to convert to km/h in another country.
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Sections taken through the narrow width of an entire building are known as ______________________________ sections.
Sections taken through the narrow width of an entire building are known as transverse sections.
What is building?A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.
Given is a structural analysis blank statement as -
"Sections taken through the narrow width of an entire building are known as __________ sections.
Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.
Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.
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50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
Answer:
20
Step-by-step explanation:
If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines
I need help ASAP
what is the domain of y=-16x^2+1700
The domain of the equation y = -16x^2 + 1700 is the set of all real numbers.
Explanation:
To find the domain of the equation y = -16x^2 + 1700, we need to determine the set of all real numbers for which the equation is defined.
Since the equation is a quadratic equation, it is defined for all real values of x. There are no restrictions on the values of x that can be plugged into the equation.
Therefore, the domain of the equation y = -16x^2 + 1700 is the set of all the real numbers.
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solving systems of equations by substitution examples 3x + y = 13. 5x -2y = 7.
Answer:
x = 3, y = 4
Step-by-step explanation:
3x + y = 13
5x - 2y = 7
To solve by substitution, you solve one of the equations for a variable, and then plug it into the other equation.
I'm going to choose to solve the first equation for y, as that will be the easiest.
y = -3x + 13 (subtract 3x from both sides)
Now we plug this equation into the y in the second equation and solve for x.
5x - 2(-3x + 13) = 7 (distribute)
5x + 6x - 26 = 7 (combine like terms)
11x - 26 = 7 (add 26 to both sides)
11x = 33
x = 3
Now that we know x is 3, we can plug it in a solve either equation for y.
y = -3(3) + 13
y = -9 + 13
y = 4
Find the length of side in simplest radical form with a rational denominator.
Answer:
x=2sqrt2
Step-by-step explanation:
The legs are equal, thus the sides are x, x, and hypotenuse is 4. This means that x^2+x^2=4^2. Thus, 2x^2=16 => x^2=8 => x= sqrt8 => x=2sqrt2
Suav deposits $450 every quarter into an account earning a quarterly interest rate of 2.225%. How much would he have in the account after 10 years, to the nearest dollar?
The amount in the account after 10 years is $4,978.365.
What is Interest?Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principle refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.
Given:
P= $450
R= 2.225%
n= 10
So, Amount = d [[tex](1+i)^n[/tex] - 1 ] / i
A = 450 x [[tex](1+0.02225)^{10[/tex] - 1 ] / 0.02225
A = 450 x (1.24615249763-1) / 0.02225
A = 450 x 0.24615249763/ 0.02225
A = 4,978.365
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I ride four times faster than I jog. If a trip took me 45 minutes and I spent 15 of these minutes jogging 3km, how far did I ride ?
Answer:
24km
Step-by-step explanation:
15 min (jogging)
30 min (cycling)
3km/15 min (jogging)
1km/5min (jogging)
4km/5min (cycling)
30÷5= 6
4×6= 24km
Distance covered during riding is 24 km.
What is meant by speed ?Speed of an object is defined as the rate of change of the distance travelled.
Here,
Speed is the distance travelled in a given time.
Total time given, t = 45 minutes
Time taken for jogging, t₁ = 15 minutes
So, time taken for riding, t₂ = t - t₁
t₂ = 45 - 15
t₂ = 30 minutes
Distance covered during jogging, d₁ = 3 km
Therefore speed of jogging, v₁ = d₁/t₁ = 3/15
v₁ = 0.2 km/min
So, speed of riding, v₂ = 4v₁ = 4 x 0.2
v₂ = 0.8 km/min
Therefore distance covered during riding, d₂ = v₂ x t₂
d₂ = 0.8 x 30
d₂ = 24 km
Hence,
Distance covered during riding is 24 km.
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What is the measure of arc e b c? 40° 90° 140° 220°
The measure of the arc is option (c) 140°
In geometry, an arc is a curved line that is a part of a circle's circumference. The measure of an arc can be calculated using the angle of the arc, which is measured in degrees.
In the case of EBC, the measure of the arc is 140°. This is because we can use the Angle-Side-Angle (ASA) congruence theorem, which states that two triangles are congruent if and only if two angles and the included side are equal.
In the case of EBC, we know that angle A equals 40° and angle C equals 90° so the only variable left is the measure of the arc, which is equal to 140°.
Therefore, the measure of EBC is 140°. This can be verified by drawing the triangle and measuring the arc with a protractor.
Therefore, option (c) is the right one.
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Complete Question:
What is the measure of arc EBC when the values of Angle a nd c are 90 and 40 degree respectively.
a) 40°
b) 90°
c) 140°
d) 220°
Yoni drove a total of 9/24 of a mile on Tuesday and Wednesday. She drove 1/6 of a mile on Tuesday.
How far did Yoni drive on Wednesday?
9/24mile
1/6 mile
5/24mile
24 miles
As per the total distance, the distance that Yoni drive on Wednesday is option (c) 5/24 miles.
To find out how far Yoni drove on Wednesday, we must first determine the total distance she drove over the two days.
Tuesday, Yoni drove 1/6 of a mile, which can be expressed as 6/24 of a mile. Wednesday, she drove an additional 9/24 of a mile.
This means that, in total, she drove 15/24 of a mile.
Since we already know that Yoni drove 6/24 of a mile on Tuesday, we can subtract this amount from the total distance she drove over the two days to find out how far she drove on Wednesday.
Subtracting 6/24 of a mile from 15/24 of a mile, we get 9/24 of a mile, which is the distance Yoni drove on Wednesday.
Therefore, Yoni drove 5/24 of a mile on Wednesday
Then the correct option is (c).
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how to calculate inverse sin?
The inverse of the sine can be calculated by using the formula sin^-1(x) = arcsin(x)
To calculate the inverse sine (sin^-1) of a value, you can use a scientific calculator or look up the value in a trigonometric table. However, if you want to understand how to do it manually, follow these steps:
Make sure the value you are calculating the inverse sine of is between -1 and 1, inclusive. If it is not, the inverse sine is undefined.
Write down the value you want to find the inverse sine of.
Use the formula: sin^-1(x) = arcsin(x), where x is the value you wrote down.
Substitute the value of x into the formula and calculate the inverse sine using a calculator or by using a series expansion or Taylor series approximation.
The inverse sine function returns a value in radians, so you may need to convert it to degrees if that's the unit you're working with.
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Use <,>, or =
1.9 ? 1.90
0.05 ? 0.2
3.88 ? 6.38
The comparision between decimal number are 1.9 = 1.90, 0.05 < 0.2, 3.88 < 6.38
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system.
Therefore, one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Here we can see that
1.9 = 1.90
0.05 < 0.2
3.88 < 6.38
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What is the equivalent fraction for the following fraction using 5 as the multiplier?
Will give brainlest!!!
3/8
Answer:
Step-by-step explanation:
The answer is 15/40
Because 3 times 5 is 15 and 8 times 5 is 40
Answer:
15/40
Step-by-step explanation:
the equivalent fraction for 3/8 using 5 as a multiplier is :
3 x 5 / 8 x 5
= 15 / 40
The system of equations below represents the amount in dollars that Brianna paid for 5 paint brushes and 3 art canvases and Ahmed paid for 10 paint brushes and 6 art canvases. {5x+3y=4710x+6y=94 Did Brianna and Ahmed pay the same price for the items?
There is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
What is the system of equations?
A system of equations is a set of one or more equations that are to be solved simultaneously. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.
In this case, the system of equations represents the amount that Brianna and Ahmed paid for 5 paintbrushes and 3 art canvases, and 10 paintbrushes and 6 art canvases, respectively. The system of equations is:
5x + 3y = 47 (Brianna's purchase)
10x + 6y = 94 (Ahmed's purchase)
To determine whether Brianna and Ahmed paid the same price for the items, we can compare the value of x and y that satisfy both equations. To do this, we can solve the system of equations using any method we prefer, such as elimination or substitution. Here, we'll use the method of substitution:
From the first equation, we can solve for y in terms of x:
5x + 3y = 47
3y = 47 - 5x
y = (47 - 5x)/3
Substituting this expression for y into the second equation, we get:
10x + 6y = 94
10x + 6((47 - 5x)/3) = 94
Simplifying, we get:
10x + 94 - 10x = 94
94 = 94
This equation is always true, regardless of the value of x.
Therefore, there is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
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Turn the (a) Are they taking the test? (b) Write a letter. a lette (c) Don't make a noise. (d) Please bring some noodles. (e) Let him complete his work. (f) Does she compose poems? (g) Has she composed a song? (h) Did he To following sentences into passive voice. Opleted Linder
Hello Everyone, please help me with this blanks
Note that the prompt is geared at testing the ability of the to understand certain vocabulary terms. The terms are given as follows:
aggrandizebombastdeignelicitendemicflauntmendaciousobviateorthographypaleontologypanacheparoxysmrecoilsaturnineshibbolethThe completed paragraphs are given below.
The first paragraph is completed as follows:
When Dr. Carter is not fulfilling his duties as the professor of paleontology at Ganton College, he is in the jungles of South America supervising excavations of ancient creatures. During the last dig, Dr. Carter recoiled when a poisonous snake tried to bite him. Now he wears tall boots and gloves to obviate the risk of dangerous animals endemic to the region.
He will definitely elicit the need for such safety measures. Some of the incoming scientists will accuse him of self-aggrandizement despite the fact that the sociable doctor always avoids using too much panache when speaking about safety; he'll flaunt his amazing findings when he returns to the campus at the end of the summer. He can put his bombast to better use in the classroom.
The second paragraph is completed as follows:
Baker deigned to give a semi-friendly nod to his Nazi captors, and he immediately suffered the consequences. Baker then endured the loud paroxysm of his cellmates: "What was that? What, are you working for them, too?"
He understood their paranoia. Just weeks before, a(n) mendacious rebel captive had revealed the escape plan to the guard. The prisoners, including Baker, had to abandon months of secrecy and labor that went into the construction of the tunnel. They had not yet regrouped; most of the saturnine prisoners simply lay in their cells, defeated.
Baker sat against the wall and thought about his capture. He had misused the shibboleth that the Nazis used to identify foreign spies. and the lack of orthography on his forged travel documents instantly signaled that he was not the German officer he claimed to have been. They must need information, he reasoned, or they would have executed him by now.
The definition of terms are given as follows:
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Which of these fractions are terminating decimals
9/20
1/35
14/35
1/16
Out of the given fractions, 9/20, 14/35, and 1/16 are terminating decimals, while 1/35 is a non-terminating decimal.A terminating decimal is a decimal number that ends or terminates after a finite number of digits.
In other words, the decimal representation of the fraction does not go on forever.
To determine if a fraction is a terminating decimal, we need to convert it into a decimal by dividing the numerator by the denominator. If the result is a finite decimal, then the fraction is a terminating decimal; otherwise, it is a non-terminating decimal.
Now, let's apply this method to the fractions given in the question:
9/20: To convert 9/20 into a decimal, we divide 9 by 20, which gives 0.45. Since the decimal terminates after two digits, 9/20 is a terminating decimal.
1/35: To convert 1/35 into a decimal, we divide 1 by 35, which gives 0.02857142857... The decimal goes on forever, so 1/35 is a non-terminating decimal.
14/35: To convert 14/35 into a decimal, we divide 14 by 35, which gives 0.4. Since the decimal terminates after one digit, 14/35 is a terminating decimal.
1/16: To convert 1/16 into a decimal, we divide 1 by 16, which gives 0.0625. Since the decimal terminates after four digits, 1/16 is a terminating decimal.
In summary, out of the given fractions, 9/20, 14/35, and 1/16 are terminating decimals, while 1/35 is a non-terminating decimal.
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mike wrote 4 checks for $30 each, withdrew another $40 and deposited $80. What was the overall change in the amount of money he had?
((30$ x4)+40$)-80$=80$
