Answer: You are incorrect, the slope is correct, but the actual y-intercept is 205 ft.
Then the equation is:
y = (-15 ft/min)*x + 205 ft
Step-by-step explanation:
Ok, let's solve this.
We know that water is drained from a reservoir, let's assume that we can model this situation with a linear relation:
y = a*x + b
Where x is time, y is the height of the water in the reservoir, a is the slope (in this case represents how much changes the height of the water in the reservoir in one unit of time) and b is the initial height of the water in the reservoir.
We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For this particular case we know that after 2 minutes the height of the water is 175 ft, then we have the point (2 min, 175 ft)
and after 5 minutes (so 7 minutes in total), the height of the water is 100ft, then: (7 ft, 100ft)
Then the slope of this:
a = (100 ft - 175 ft)/(7 min - 2 min) = (-75ft/5min) = - 15 ft/min
Then our line is something like:
y = (-15ft/min)*x + b
To find the value of b, we can use the fact that when x = 2 min, y = 175 ft
So if we replace these two values in the equation we get:
175ft = (-15 ft/min)*2 min + b
175 ft = -30 ft + b
175 ft + 30 ft = b
(here is your problem, it seems like you subtracted instead of adding in this part)
205 ft = b
Then the equation is:
y = (-15 ft/min)*x + 205 ft
So you are incorrect (but only for a little bit), you computed wrong the y-intercept.
What’s the simplest form?
Answer:
slope = - 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 6, 6) and (x₂, y₂ ) = (- 3, - 3)
m = \(\frac{-3-6}{-3-(-6)}\) = \(\frac{-9}{-3+6}\) = \(\frac{-9}{3}\) = - 3
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 140.
Select the correct answer below and fill in the answer box to complete your choice.
PLZ HELP MEEE
Given:
Length of the rectangle = \(x+4\)
Width of the rectangle = \(x\)
The perimeter of the rectangle is less than 140.
To find:
The inequality for the given situation and solve it.
Solution:
We have,
\(l=x+4\)
\(w=x\)
We know that, the perimeter of a rectangle is
\(P=2(l+w)\)
\(P=2(x+4+x)\)
\(P=2(2x+4)\)
\(P=4x+8\)
It is given that the perimeter of the rectangle is less than 140.
\(P<140\)
\(4x+8<140\)
\(4x<140-8\)
\(4x<132\)
Divide both sides by 4.
\(x<\dfrac{132}{4}\)
\(x<33\)
Therefore, the correct option is A because the sign of inequality is < and the solution of inequality is \(x<33\).
The first glass contained 12 ounces of water. The second glass contained 11 ounces of water. The third glass contained 7 ounces of water. If water was poured from the first and second glasses into the third glass until each glass contained the same amount, then how many ounces of water would be in each glass
Step-by-step explanation:
Answer:
A: 19/40
Step-by-step explanation:
LCD = 40
7*5=35 ->35/40
3*8=24 ->24/40
combine like terms
for simplicity, I'll use a mixed number
1 19/40
subtract your "full glass"
1 19/40 - 1 = 19/40
-3/4 x + 1/2 = 3/4 solve for x please
Answer:
\(x = -\frac{1}{3}\)
Step-by-step explanation:
1/2 = 2/4Plug 2/4 in: -3/4x + 2/4 = 3/4Subtract 2/4 from each side, so it now looks like this: -3/4x = 1/4Divide each side by -3/4, so it cancels out the -3/4 next to x. It should now look like this: x = -1/3I hope this helps!
x² + 2x + 16 = 0, which number would have to be added to "complete the square"?
for x² + 2x + 16 = 0, we have to add (2/2)² number would have to be added to "complete the square"
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
x² + 2x + 16 = 0
Subtract 16 on both sides
x² + 2x = -16
(Add (2/2)² on both sides)
x² + 2x + 1 = -16 + 1
Factor using Perfect Square Trinomial and add -16 and 1
(x + 1)² = -15
Square root on both sides
x + 1 = ±√-15
Subtract 1 on both sides and use i = √-1
x = -1 ± i√15
Hence, for x² + 2x + 16 = 0, we have to add (2/2)² number would have to be added to "complete the square"
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During 2022, each of the assets was removed from service. The machinery was retired on January 1. The forklift was sold on June 30 for $13,000. The truck was discarded on December 31. Journalize all entries required on the above dates, including entries to update depreciation, where applicable, on disposed assets. The company uses straight-line depreciation. All depreciation was up to date as of December 31, 2021
Loss on disposal of plant assets = $46400 - $32550
Loss on disposal of plant assets = $13850
How to solveDate Account titles and Explanation Debit Credit
Jan. 01 Accumulated depreciation-Equipment $81000
Equipment $81000
June 30 Depreciation expense (1) $4000
Accumulated depreciation-Equipment $4000
(To record depreciation expense on forklift)
June 30 Cash $13000
Accumulated depreciation-Equipment (2) $28000
Equipment $40000
Gain on disposal of plant assets (3) $1000
(To record sale of forklift)
Dec. 31 Depreciation expense (4) $5425
Accumulated depreciation-Equipment $5425
(To record depreciation expense on truck)
Dec. 31 Accumulated depreciation-Equipment (5) $32550
Loss on disposal of plant assets (6) $13850
Equipment $46400
(To record sale of truck)
Calculations :
(1)
Depreciation expense = (Book value - Salvage value) / Useful life
Depreciation expense = ($40000 - $0) / 5 = $8000 per year
So, for half year = $8000 * 6/12 = $4000
(2)
From Jan. 1, 2019 to June 30, 2022 i.e 3.5 years.
Accumulated depreciation = $8000 * 3.5 years = $28000
(3)
Gain on disposal of plant assets = Sale value + Accumulated depreciation - Book value
Gain on disposal of plant assets = $13000 + $28000 - $40000
Gain on disposal of plant assets = $1000
(4)
Depreciation expense = (Book value - Salvage value) / Useful life
Depreciation expense = ($46400 - $3000) / 8
Depreciation expense = $5425 per year
(5)
From Jan. 1, 2017 to Dec. 31, 2022 i.e 6 years.
Accumulated depreciation = $5425 * 6 years = $32550
(6)
Loss on disposal of plant assets = Book value - Accumulated depreciation
Loss on disposal of plant assets = $46400 - $32550
Loss on disposal of plant assets = $13850
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equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)
The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).
Equation of a circle
A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.
We know that,
Equation of the circle passing through the origin is given by:-
\(x^2+y^2=r^2\)
Where,
r is the radius of the circle, and
(x,y) are the coordinates of each point of the circle.
Hence, we can write,
The radius of the circle will be :-
\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)
Hence, r = 4 units.
Hence, the equation of the circle is given by:-
\(x^2+y^2=16\)
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please help this is for my study guide thanks! (Find volume)
The formula to calculate the volume of a sphere is:
\(V=\frac{4}{3}\pi\cdot r^3\)Start by finding the radius using the diameter and dividing it by 2
\(\begin{gathered} r=\frac{D}{2} \\ r=\frac{2}{2} \\ r=1ft \end{gathered}\)then, replace the radius in the formula and find the volume
\(\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot r^3 \\ V=\frac{4}{3}\cdot\pi\cdot(1)^3 \\ V=\frac{4\pi}{3} \end{gathered}\)In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).
Sample size, n=400
Sample proportion, p = 40 / 400
= 0.1
We use normal approximation, for this, we check that both np and n(1-p) >5.
Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation = root( p * (1-p) /n )
= 0.015
For constructing Confidence interval,
Margin of Error (ME) = z x SD = 0.0294
95% confidence interval is given by Sample Mean +/- (Margin of Error)
0.1 +/- 0.0294 = (0.0706 , 0.1294)
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most mis's use sophisticated mathematical models or statistical techniques. group of answer choices true false
The statement "Most MIS's use sophisticated mathematical models or statistical techniques" is generally true.
Management Information Systems (MIS) play a crucial role in modern organizations by providing valuable insights into various aspects of the business.
These systems gather data from different sources and transform it into meaningful information for decision-making purposes.
To make sense of the collected data, MIS rely on sophisticated mathematical models and statistical techniques.
Mathematical models are used to represent real-world situations and relationships mathematically.
These models can range from simple equations to complex algorithms that simulate and predict business processes.
By using mathematical models, MIS can analyze data, identify patterns, and make predictions or projections.
Statistical techniques, on the other hand, provide methods for summarizing and analyzing data to extract meaningful information.
MIS employ statistical techniques such as regression analysis, hypothesis testing, data visualization, and forecasting to uncover insights and support decision-making.
By leveraging these sophisticated mathematical models and statistical techniques, MIS can handle large volumes of data, identify trends and patterns, perform predictive analysis, and provide valuable insights for effective decision-making in areas such as resource allocation, strategic planning, inventory management, and customer behavior analysis.
Therefore, it is safe to say that most MIS's utilize sophisticated mathematical models and statistical techniques to process and analyze data, enabling organizations to make informed decisions based on accurate and meaningful information.
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Solve the system using the substitution technique:(−6, −3.6)(0.6, 0.8)(6, 4.4)(−0.6, 0)
Given
The system of equations,
\(\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}\)To find the solution using substitution technique.
Explanation:
It is given that,
\(\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}\)That implies,
\(\begin{gathered} (1)\Rightarrow-2x+3y=1.2 \\ \Rightarrow3y=1.2+2x \end{gathered}\)And,
\(\begin{gathered} (2)\Rightarrow-3x-6y=1.8 \\ \Rightarrow-3x-2(3y)=1.8 \end{gathered}\)Substitute 3y=1.2+2x in the above equation.
That implies,
\(\begin{gathered} -3x-2(1.2+2x)=1.8 \\ -3x-2.4-4x=1.8 \\ -7x=1.8+2.4 \\ -7x=4.2 \\ x=\frac{4.2}{-7} \\ x=-0.6 \end{gathered}\)And, substitute x=-0.6 in (1).
That implies,
\(\begin{gathered} (1)\Rightarrow-2(-0.6)+3y=1.2 \\ \Rightarrow1.2+3y=1.2 \\ \Rightarrow3y=1.2-1.2 \\ \Rightarrow3y=0 \\ \Rightarrow y=0 \end{gathered}\)Hence, the solution is (-0.6,0).
Super Express Couriers charges a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30.
If Kevin's postage fee was 150 less than 5 times the weight of his parcel, how much did his parcel weigh?
Answer:
Step-by-step explanation:
я хз
The weight of Kevin's parcel is 60 g.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30. and Kevin's postage fee was 150 less than 5 times the weight of his parcel,
Let the weight of the parcel be x
Establishing the equations,
5x - 150 = 30 + 2x
5x - 2x = 30 + 150
3x = 180
x = 180/3
x = 60
Hence, the weight of Kevin's parcel was 60g
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given tan θ = -15/8 where pi/2<θ
The solution for θ in the equation tan(θ) = -15/8 is 2.1 + πn
How to determine the solution for θFrom the question, we have the following parameters that can be used in our computation:
tan(θ) = -15/8
Evaluate the quotient of -15 and 8
So, we have the following representation
tan(θ) = -1.875
Using a graphing calculator, we take the arctan of both sides
So, we have the following representation
θ = 2.1 + πn
Where n is any integer
Hence, the value of θ is 2.1 + πn
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5. Betty is thinking of two consecutive integers whose sum is 41. Let x represent
the smaller unknown integer.
a. How could you represent the larger unknown integer in terms of x?
Answer:
x+1
Step-by-step explanation:
Since it's a consecutive integer it's 1 added to the smaller integer, which is x.
simplify (2) to the power of -3
We are to simplify
\(2^{-3}\)From the the laws of indices,
\(\begin{gathered} x^{-m}\text{ =}\frac{1}{x^m} \\ \end{gathered}\)Aplying this law to the question, we have
\(\begin{gathered} 2^{-3}=\frac{1}{2^3} \\ =\frac{1}{8} \\ \text{ The answrer is }\frac{1}{8} \end{gathered}\)∠A and ∠B are vertical angles. If m∠A=(7x-20)° and m∠B=(6x-1)°,then find the measure of ∠A.
It's important to understand that vertical angles are always ≅.
So we can say that the m<A = m<B.
So we can setup the equation 7x - 20 = 6x - 1.
Start by subtracting 6x from both sides and we have x - 20 = -1.
Now add 20 to both sides to get x = 19.
If x = 19, then the m<A is 7(19) - 20 or 133 - 20 which is 113.
Answer: The measure of angle A is 113°
Step-by-step explanation:
7x - 20 = 6x -1
+20 +20
7x = 6x + 19
-6x -6x
1x = 19
x = 19
7(19) -20 = 113
6(19) - 1 = 113
f(x) = 2x² + 12x + 2001 1) Axis of Symmetry: 2) Vertex: 3) Max or Min: 4) Y-Intercept: 5) X-intercepts: 6) Increasing Interval: (7) Decreasing Interval: (8) End Behavior: 9) Positive Interval: (0) Negative Intervals:
Since the discriminant is negative, the equation has no real roots and therefore the function does not have any x-intercepts.
Why it is?
To analyze the function f(x) = 2x² + 12x + 2001:
Axis of Symmetry: The axis of symmetry of a parabola is given by the equation x = -b/2a. In this case, a = 2 and b = 12, so the axis of symmetry is x = -12/(2*2) = -3.
Vertex: The vertex of a parabola is located on the axis of symmetry. Using x = -3 as the axis of symmetry, we can find the y-coordinate of the vertex by plugging it into the function: f(-3) = 2(-3)² + 12(-3) + 2001 = 1983. Therefore, the vertex is (-3, 1983).
Max or Min: Since the coefficient of the x² term is positive, the parabola opens upwards, so the vertex is a minimum point. Therefore, the function has a minimum value at x = -3.
Y-Intercept: To find the y-intercept, we set x = 0: f(0) = 2(0)² + 12(0) + 2001 = 2001. Therefore, the y-intercept is (0, 2001).
X-intercepts: To find the x-intercepts, we set f(x) = 0 and solve for x: 2x² + 12x + 2001 = 0. This quadratic equation does not factor, so we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Plugging in the values, we get:
x = (-12 ± √(12² - 4(2)(2001))) / (2*2) = (-12 ± √(144 - 16008)) / 4
x = (-12 ± √(-15864)) / 4
Since the discriminant is negative, the equation has no real roots and therefore the function does not have any x-intercepts.
Increasing Interval: The function is increasing to the left of the vertex and decreasing to the right of the vertex. Therefore, the increasing interval is (-∞, -3).
Decreasing Interval: The decreasing interval is (-3, ∞).
End Behavior: As x approaches positive or negative infinity, the dominant term of the function becomes 2x², which grows without bound. Therefore, the end behavior of the function is that it approaches positive infinity as x approaches either positive or negative infinity.
Positive Interval: The function is positive everywhere since the coefficient of the x² term is positive.
Negative Intervals: The function does not have any negative intervals since it is positive everywhere.
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Solve: 5x² = -18x + 8
Answer: x=-4
Step-by-step explanation:
Compare the following fraction 8/14 and 4/7
Answer:
These fractions are equivalent, with 4/7 being the simplest form of both.
Step-by-step explanation:
8/14 can be simplified to 4/7 also by dividing both sides by two :)
Find the missing side. Round to the nearest tenth.
Step-by-step explanation:
sin x = 12/16 = 0.75
x = arc sin 0.75 = 48.6°
cos x = 36/40 = 0.90
x= arc cos 0.90 = 25.8°
cos x = 10/15 = 0.6667
x= arc cos 0.6667 = 48.2°
tan x = 30/18 = 1.6667
x = arc tan 1.6667 = 59.0°
2. for each of the following situations, state the predictor variable and the outcome variable. a. a study is done to test if the number of risky behaviors changes with increasing age. b. a study is done to test if the level of education of children changes based on the number of family members.
In situation a, the predictor variable is age, as it is being tested to see if it affects the outcome variable, which is the number of risky behaviors. So, age is the independent variable and the number of risky behaviors is the dependent variable.
In situation b, the predictor variable is the number of family members, as it is being tested to see if it affects the outcome variable, which is the level of education of children. So, the number of family members is the independent variable and the level of education of children is the dependent variable.
It is important to identify the predictor variable and the outcome variable in any study as this helps in understanding the relationship between the two variables and in interpreting the results accurately.
For situation A, the predictor variable is "age," and the outcome variable is "number of risky behaviors." As age increases, the study aims to see if the number of risky behaviors changes.
For situation B, the predictor variable is "number of family members," and the outcome variable is "level of education of children." The study examines whether the children's level of education changes based on the number of family members.
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If the mean of a symmetrical distribution is 245, which of the following values
could be the median of the distribution?
O A. 215
O B. 245
O C. 305
D. 275
Answer:
275
Sorry I do not have a explanation it just came to my head
Answer: B 245 is the answer I just took it and 275 is wrong
Step-by-step explanation:
PLSSSS HEP ITS URGENT!!
1+6=6x6/6
Answer:
7=6
Step-by-step explanation:
since it is times 1 plus 6 = 6 times 6 divided by 6
1+6=6x6/6
1+6 is 7
6 times 6 is 36 then 36 divided by 6 is 6
then you get 7=6
Please help me with this question it is in the picture
Answer:
complementary angles
Step-by-step explanation:
The sum of the angles is 67+23 = 90
When angles sum together to 90, the are called complementary
Answer:
Option A
Step-by-step explanation:
The measures of the two angles have a sum of 90°.
\(67+23=90\)
Therefore, they are complementary angles, since complementary angles have a total measure of 90°.
Option A is the best answer.
Brainilest Appreciated.
A) Tell which measure of central tendency best describes the data.
Time spent on the internet (min/day): 75,38,43,120,65,48,52.
B) Tell which measure of central tendency best describes the data.
Weight of books (oz): 12,10,9,15,16,10.
A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.
The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.
B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.
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Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2 What is the other solution to the equation? x=−6 x=−4 x=2 x=4
Answer:
Step-by-step explanation:
We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.
If \(3-2|.5x+1.5|=2\) then
\(-2|.5x+1.5|=-1\) What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:
\(|.5x+1.5|=.5\)
Now we can set up the 2 main equations for this which are
.5x + 1.5 = .5 and .5x + 1.5 = -.5
Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.
Solving the first one:
.5x = -1 so
x = -2
Solving the second one:
.5x = -2 so
x = -4
We want to find the other solution of the given absolute value equation.
The other solution is x = -4
We know that:
3 - 2*|0.5*x + 1.5| = 2
It has one solution given by:
- 2*|0.5*x + 1.5| = 2 - 3 = -1
|0.5*x + 1.5| = 0.5
0.5*x + 1.5 = 0.5
0.5*x = 0.5 - 1.5 = -1
0.5 = -1/x
Then we have x = -2
To get the other solution we need to remember that an absolute value equation can be written as:
|x - a| = b
or:
(x - a) = b
(x - a) = -b
Then the other solution to our equation comes from:
|0.5*x + 1.5| = 0.5
(0.5*x + 1.5) = -0.5
0.5*x = -0.5 - 1.5 = -2
x = -2/0.5 = -4
The other solution is x = -4
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a beam having a circular cross-section of diameter, D, is designed to resist a maximum bending moment of 80kNm. the maximum allowable bending stress is 500MPa what is the minimum required diameter, D, of the cross section of the beam?
To determine the minimum required diameter (D) of the cross-section of the beam, we need to consider the maximum bending moment and the maximum allowable bending stress.
The bending stress in a beam is given by the formula:
σ = (M * c) / I
Where σ is the bending stress, M is the maximum bending moment, c is the distance from the neutral axis to the outermost fiber (which is equal to half of the diameter for a circular cross-section), and I is the moment of inertia of the cross-section.
Rearranging the formula, we have:
D = (2 * M) / (σ * π)
Substituting the given values, with M = 80 kNm (converted to Nm) and σ = 500 MPa (converted to N/m²), we can calculate the minimum required diameter (D):
D = (2 * 80,000 Nm) / (500,000,000 N/m² * π)
D ≈ 0.255 meters or 255 mm
Therefore, the minimum required diameter of the cross-section of the beam is approximately 0.255 meters or 255 mm to resist the maximum bending moment of 80 kNm within the allowable bending stress of 500 MPa.
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what is 0.73 is decimal as either fraction
73/100
Is 0.73 as a simplified fraction
helpppppp
on a timer so need ASAP
what is 3600x0+1=2?
thanks i appreciate it
Answer:
actually it = 1 but there's your answrr
Step-by-step explanation:
3600x0 = 0
0+1=1