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Work Shown:
x = brother's age, which is some positive whole number
x-6 = sister's age, since she is 6 years younger than her brother
The product is the result of multiplication, so we multiply x and (x-6) to get 135
x*(x-6) = 135
x^2-6x = 135
x^2-6x-135 = 0
Use the quadratic formula to solve from here
We plug in a = 1, b = -6, c = -135
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-135)}}{2(1)}\\\\x = \frac{6\pm\sqrt{576}}{2}\\\\x = \frac{6\pm24}{2}\\\\x = \frac{6+24}{2}\ \text{ or } \ x = \frac{6-24}{2}\\\\x = \frac{30}{2}\ \text{ or } \ x = \frac{-18}{2}\\\\x = 15\ \text{ or } \ x = -9\\\\[/tex]
x represents the brother's age, in years. So x must be positive.
Since x must be positive, this means we rule out x = -9
The value x = 15 is the only practical solution.
If x = 15, then x-6 = 15-6 = 9
The brother is 15 years old and the sister is 9 years old.
The product of their ages is 15*9 = 135, which confirms the answers.
Which of the following are solutions to the quadratic equation? Check all that apply. x² + 10x + 25 = 7
A. 5
B. -5
C. √7-5
D. -√7-5
E. √7 +5
F. √7
Answer: C, D
Step-by-step explanation:
[tex]x^2 +10x+18=0\\\\x=\frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2}\\\\x=\frac{-10 \pm \sqrt{28}}{2}\\\\x=-5 \pm \sqrt{7}[/tex]
HELP ASAPPPP PLEASE!!!!
Answer:
(c) 45°
Step-by-step explanation:
A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.
ApplicationHere, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.
The measure of angle ABC is 45°.
C. 45°
Step-by-step explanation:When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.
Clockwise
This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.
Acute vs Obtuse
There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.
Your students have been working on algebra equations involving inequalities. The rule for learning the > sign is:
The rule for learning the > sign is demonstrating eating with the right hand.
InequalityThe inequality signs are;
Greater than >Let was than <Equal to =Greater than or equal to ≥Less than or equal to ≤The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.
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A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?
Answer:
0.4
Step-by-step explanation:
4+3+2+1 =10
5m÷10 =0.5
(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)
2 : 1.5 : 1 : 0.5
longest piece= 2 (2m)
4+1= 5
2÷5= 0.4
(0.4×4=1.6, 0.4×1=0.4)
1.6 : 0.4
so the shortest piece is 0.4!
I just need help on what the answer is and understanding this question, thank you.
The graph represents the potential area of a concrete rectangle, based on length and width.
Which inequality in vertex form represents the graphed region?
A)y less-than negative 2 (x + 16) squared minus 32
B)y less-than negative one-half (x minus 16) squared + 32
C)y less-than negative 2 (x minus 16) squared + 32
D)y less-than negative one-half (x + 16) squared minus 32
The inequality of the graph is y < -1/2(x - 16)^2 + 32
How to determine the inequality?A quadratic function is represented as:
y = a(x - h)^2 + k
The vertex of the graph is
(h, k) = (16, 32)
So, we have:
y = a(x - 16)^2 + 32
The graph pass through the point
(x, y) = (12, 24)
So, we have:
24 = a(12 - 16)^2 + 32
Evaluate the like terms
-8 = a(-4)^2
This gives
16a = -8
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x - 16)^2 + 32
y = -1/2(x - 16)^2 + 32
The graph is a less than graph.
So, we have
y < -1/2(x - 16)^2 + 32
Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32
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Which equation is the inverse of y = 9x² - 4?
0y= ± √x+4
9
O y = ±₁
+4
9
Oy= 2√x+4
3
INX
+√√√x 2
Oy= 3 3
[tex]y=9x^2-4\\9x^2=y+4\\x^2=\dfrac{y+4}{9}\\x=\pm\sqrt{\dfrac{y+4}{9}}=\pm\dfrac{\sqrt{y+4}}{3}\\\\\text{inverse: }y=\pm\dfrac{\sqrt{x+4}}{3}[/tex]
The inverse of the function y = 9x² - 4 is y = ±√((x + 4)/9). The correct option is A.
What is the inverse of the function?To find the inverse of a function, we need to swap the positions of the input variable (usually x) and the output variable (usually y), and then solve for y. The resulting equation will be the inverse function.
To find the inverse of the function y = 9x² - 4, we need to swap the positions of x and y and then solve for y.
So, starting with y = 9x² - 4:
y = 9x² - 4
x = 9y² - 4 (swapping x and y)
x + 4 = 9y² (adding 4 to both sides)
y² = (x + 4)/9 (dividing both sides by 9)
y = ±√((x + 4)/9) (taking the square root of both sides, plus or minus)
So the inverse of the function y = 9x² - 4 is:
y = ±√((x + 4)/9)
Note that since we have a plus or minus sign in the expression, this means that the inverse is actually two functions: one that gives the positive square root, and one that gives the negative square root.
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The sun
of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
The Third would be 72
Step-by-step explanation:
The sum of the two is 16+22=38. the third one is 72-38=34
Which of the following best represents the linear regression equation for the
×-values and log(y)-values of the data shown below?
By using Microsoft excel to plot the data on a scatter plot, the linear regression equation can best be represented by: A. y = 12.11.1.36^x
What is a regression line?A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that linear regression equation for the x-values and log(y)-values is given by:
y = 12.11.0.30^x
Thus, it can best be represented by: y = 12.11.1.36^x
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how can I solve for x? Answers ASAP
Using the inscribed angle theorem, the value of x is: 9.
What is the Inscribed Angle Theorem?Note that an intercepted arc is regarded as part of the circumference of a circle, which is between a chord and a tangent. Thus, based on the inscribed angle theorem, the inscribed angle measure = 1/2(the intercepted arc measure).
So, we would have:
m∠DEF = 1/2(arc DE)
m∠DEF = 4x + 19
arc DE = 360 - (28x - 2) = 360 - 28x + 2
arc DE = 362 - 28x
Plug in the values
4x + 19 = 1/2(362 - 28x)
Solve for x
2(4x + 19) = 362 - 28x
8x + 38 = 362 - 28x
8x + 28x = 362 - 38
36x = 324
x = 324/36
x = 9
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Which ordered pair is a solution to the inequality 3x-4y<12 ?
The ordered pair (2,-1) is a solution the inequality.
Given the inequality is 3x-4y<12.
An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.
By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.
1. (4,0)
Here x=4 and y=0
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(0)<12
12<12
This is not true
2. (0,-3)
Here x=3 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(0)-4(-3)<12
12<12
This is not true.
3. (2,-1)
Here x=2 and y=-1
Substitute this in the inequality 3x-4y<12, we get
3(2)-4(-1)<12
6+4<12
10<12
This is true.
4. (4,-3)
Here x=4 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(-3)<12
12+12<12
24<12
This is not true.
Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).
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For the inequality y−x>−x2−1, where is the graph shaded and is the curve solid or dotted?
The curve will be dotted and upper portion of the graph will be shaded.
Inequality expressionInequality are expressions not separated by an equal sign Given the following inequality
y−x>−x2−1
Equate to zero
y > x^2 + x -1
Since the inequality sign in the given expression is a less than sign, hence the curve will be dotted.
Also, since the inequality sign is a "greater than", hence upper portion of the graph will be shaded.
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Assume that the function f is a one
-to-one function.
(a) If f (7)
= 5, find f-1 (5)
Your answer is
(b) 18 f-1 (-3) = -2, find f(-2).I
Your answer is
For the given inverse functions we have:
a) f⁻¹(5) = 7
b) f(-2) = -3
How to work with inverse functions?
Remember that if f(x) and g(x) are inverse functions, then:
[tex]f(x) = y\\then\\g(y) = x[/tex]
a) Now we know that:
f(7) = 5
Then if f⁻¹(x) is the inverse, we have:
f⁻¹(5) = 7
b) Now we know that:
f⁻¹(-3) = -2
Again, using the rule for inverse functions, we will have:
f(-2) = -3
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An Annuity Immediate Has 32 Initial Quarterly Payments Of 20 Followed By A Perpetuity Of Quarterly Payments Of 25 Starting In The 9th Year. Find The Present Value At A Nominal Rate Of 16%
The present value of the nominal rate of the annuity will be $535.
How to calculate the annuity?Annuity amount = 20
Number of annuities = 32
APR = 16%
PV of annuities = 357
Number of years to perpetuity = 8
Quarterly perpetuity = 25
PV of perpetuity at 9th year = 625
PV of perpetuity today = 178
Total PV = 357 + 178 = 535
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Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes.Solve the inequality. How many pounds of tomatoes can Lisa buy
Answer:
At maximum, she can buy 5 tomatoes.
Step-by-step explanation:
If you solve the inequality, as so:
1.2x+1.8 <=7.8
1.2x <= 6
x <= 5
If the function is:
What is f(-4)?
Answer:
D. -11
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]
[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]
[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]
f(-4) means to substitute x = -4 into the function.
As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:
[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]
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Answer is D. -11
Answer:
Solution Given:
f(-4) depends on the condition x≤-4,
so
f(-4)=2*-4-3=-8-3=-11
Sheffield corporation shipped $20400 of merchandise on a consignment to Gooch company. Sheffield paid frieght cost of $2000. Gooch company paid $480 for local advertising wich is reimbursed from Sheffield . By year end 62% of the merchandise had been sold for $21500.Gooch notified Sheffield , retained a 10% commission , and remitted the cash due Sheffield . Prepare sheffield journal entry when the cash is received
The appropriate journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.
Journal entrySheffield corporation entries
Debit Cash $18,870
[$21500-($480+ ($21500×10%))]
Debit Advertising expense $480
Debit Commission expense $2,150
(21,500×10%)
Credit Revenue from consignment sales $21,500
Debit Cost of goods sold $13,888
[($20400+$2000)×62%]
Credit Inventory on consignment $13,888
Therefore journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.
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what does 21/10 divided by 2 4/5 represent in this situation
I need help with this slope
Answer:
B, C
Step-by-step explanation:
Look at the lower blue point.
Its coordinates are (4, 3).
The x-coordinate, 4, stands for minutes.
The y-coordinate, 3, stands for number of boxes.
This is a slope of 3/4, corresponding to 0.75 boxes per minute, or 3 boxes every 4 minutes.
Answer: B, C
Answer:
3 boxes are filled every 4 minutes.
Step-by-step explanation:
Look at the graph; at the bottom of the graph, it is shown that every __ minutes, __ boxes are filled. If you look at the first shown blue point on the left of the graph, it shows that on the fourth minute, three boxes are filled, as from the axis, you go right four and up three.
At the movie theater, child admission is $5.50 and adult admission is $9.00. on Thursday, 148 tickets were sold for a total sales of $992.50. how many adult tickets were sold that day
Answer:
51 Adult tickets were sold that day.
Step-by-step explanation:
Let c = child and a = adult
c + a = 148 5.50c + 9.00a = 992.50
Change the first equation so that it is either in the form c = or a =and then plug that number into the second equation.
I am going to change the first equation to c = by subtracting a from both sides
c = 148 - a
Now I am going to plug 148 -a for c in the second equation.
5.5(148 - a) + 9a = 992.5 Next distribute the 5.5
814 - 5.5a + 9 a = 992.5 Add the a terms together
814 + 3.5a = 992.5 Subtract 814 from both sides
3.5a = 178.5 Divide both sides by 3.5
a = 51
The margin of sampling error is obtained by multiplying the standard error with the _______.
The margin of sampling error is obtained by multiplying the standard error with the critical value.
What is the margin of sampling error?
The margin of sampling error is a statistic that tells a researcher by how many percentage points the result gotten from the sample value would differ from that of the population. This value is obtained by multiplying the standard error with the critical value.
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In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between ________and_________ miles.
The level of confidence for this estimate is ________%
Using the interpretation of the confidence interval, it is found that:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
Considering the mean and the standard error, the bounds of the interval are:
a = 9.72 - 0.22 = 9.50 miles.b = 9.72 + 0.22 = 9.94 miles.Hence:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.More can be learned about confidence intervals at https://brainly.com/question/25890103
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Which of the relations given by the following sets of ordered pairs is a function?
O {(2,-8), (1, — 4), (0, 0), (1, 4), (2, 8)}
O {(3, -3), (3, -1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(-2,5), (7,5), (-4, 0), (3, 0), (1, -6)}
Answer:
Option (4)
Step-by-step explanation:
Each value of x maps onto only one value of y, so it is a function.
2x+9=1x-5 what is x?
Answer:
2x+9=1x-5
2x-1x=-5-9
x=-14
If
xn = (n−1)cos(n2 +n+1) 2n−1
EXERCISES
then xn has a convergence subsequence.
The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
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The width of a rectangular house is 22 feet. What is the perimeter of this house if it has the same area as a house that is 33 ft wide and 50 ft long
1) 184 feet
2) 200 feet
3) 194 feet
4) 206 feet
Answer:
3) 194 feet
Step-by-step explanation:
The other house:
"a house that is 33 ft wide and 50 ft long"
area = LW = (33 ft)(50 ft) = 1650 ft²
This house:
LW = A
L × 22 ft = 1650 ft²
L = 75 ft
P = 2(L + W)
P = 2(75 ft + 22 ft)
P = 194 ft
Answer: 3) 194 feet
Answer:
3) P = 194 ft.
Step-by-step explanation:
[tex]A=wl[/tex]
[tex](30)(50)=22l[/tex]
[tex]1650=22l[/tex]
[tex]l=1650/22=75[/tex]
the dimensions of the house are: (22 × 75)
Perimeter:
[tex]p=2(22)+2(75)=44+150=194[/tex]
Hope this helps
find the volume of the solid generated by rotating the
region bounded by the curves y=0, y= (x^2)+x, x=2
and x=0 about the y-axis
The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.
How to find the volume of the solid generated?To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.
So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]
Now given that the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.
So, we integrate from x = 0 to x = 2.
[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]
[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]
So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.
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Now suppose b stays the same. Then, a must be its previous value to satisfy the new inequality.
When the coordinate satisfies the original inequality, if a stays the same, b must be greater than its previous value to satisfy the new inequality.
How to illustrate the information?It should be noted that inequality provides an interval to the solution.
This is illustrated graphically. Let's illustrate this with an example, suppose a =1, b = 3
a - b < 0.
1 - 3 < 0
-2 < 0
If a stays the same value, b will be greater than 1.
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A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road sign is about 38.2 inches tall The road sign is about 38.2 inches tall The road sign is about 23.5 inches tall The road sign is about 23.5 inches tall The road sign is about 41.6 inches tall The road sign is about 41.6 inches tall The road sign is about 43.7 inches tall
The height of the equilateral triangle is 41. 6 inches. Option C
How to determine the height
The formula for finding the height of an equilateral triangle is given as;
h = (a√3)/2
we have a = 48 inches
Let's substitute the value
Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]
Height = [tex]\frac{48 * 1. 732}{2}[/tex]
Height = [tex]\frac{83. 14}{2}[/tex]
Height = [tex]41. 6[/tex] Inches
Thus, the height of the equilateral triangle is 41. 6 inches. Option C
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Our peak time this week will be 8:00 AM to 12:00 PM, which requires 32% more agents than the afternoon requirements of 473 agents.” Representative: “So, you will need to have __________ in the morning shift.
The number of agents required in the morning shift 8:00 AM to 12:00 PM is 624.36 agents
PercentagePeak time = 8:00 AM to 12:00 PMAgent required in the afternoon = 473 agentsAgent required in the morning = (32% of 473) + 473
= (32/100 × 473) + 473
= (0.32 × 473) + 473
= 151.36 + 473
= 624.36 agents
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Blossom company , a machinery dealer leased manufacturer equipment to Mays corporation on January 1, 2017. The lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year . The first payment is received on January 1, 2017 . Blossom had purchased the machine during 2016 for $75000 collectibility of lease payments is reasonable predictable, and no important uncertainties surround the amount of cost yet to be incurred by blossom se the annual rentel to ensure a 8% rate of return . The machine has an economic life of 8 years with no resiidaul value and reverts to blossom at the termination of the lease.A. Compute the amount of the lease receivable
The amount of the lease receivable will be $146999.
What are lease receivable?It should be noted that lease receivables means all the payments under the operative documents in respect of:
(i) the Purchaser Basic Rent,
(ii) the Maximum recourse amount,
(iii) the Purchaser Balance and
(iv) any purchase by the Lessee of the Properly up to the amount of the Capital then outstanding.
In this case, the lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year and the first payment is received on January 1, 2017.
The lease receivable will be:
= PVAD8%,7 × Lease payment
= 5.62288 × 26143
= $146999
In conclusion, the lease receivable is $146999.
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