Answers
The speed of the plane is equal to 120 mph.
What is speed?In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).
Mathematically, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Time = distance/speed
Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;
240/s = 80/s - 80
80s = 240s - 19200
19200 = 160s
s = 19200/160
s = 120 mph.
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Related Questions
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS?
Answers
We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.
In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:
1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.
2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.
3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.
Alternatively:
4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.
5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.
6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.
By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.
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Pamela had $17. She bought 7 burgers for $5.50 and 2 kilograms of orange for $5.30. Find the remaining amount she has now.
$4.20
$5
$6
$6.20
Answers
Answer:
$ 6.20 Cents
Step-by-step explanation:
17 - 5.50= 11.5
11.50 - 5.30= 6.2
Add A Zero at the end
You Get 6.20
advanced functions
solve 4(8-2x)=256
Answers
Answer:x=-28
Step-by-step explanation:
Distribute the 4 on the left side of the equation:
32 - 8x = 256
Move the constant term to the right side of the equation:
-8x = 256 - 32
-8x = 224
Divide both sides of the equation by -8 to isolate x:
x = 224 / -8
x = -28
Find Tan A 6-11, please?
Answers
Answer:
5) tan A = 0.42
6) Acute angle is less than 90°
7) Right angle is exactly 90°
8) Obtuse angle is greater than 90° but less than 180°
9) Straight angle is exactly 180°
10) Complementary angles add up to 90°
11) Supplementary angles add up to 180°
Step-by-step explanation:
tan A = opposite / adjacent
= 5/12
= 0.42
please help- (in need of answer please don't put gibberish this is serious work)
Answers
Answer:
W = V/(LH)
Step-by-step explanation:
All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation
at the movie theatre, child admission is $5.20 and adult admission is $9.60 on sunday, 131 tickets were sold for a total sales of $1020.00 how many adult tickets were sold that day
Answers
Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.
Definition of System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.
Amount of adult tickets soldIn this case, a system of linear equations must be proposed taking into account that:
"a" is the amount of adult tickets sold."c" is the amount of children tickets sold.You know:
At the movie theatre, child admission is $5.20 and adult admission is $9.60 On sunday, 131 tickets were sold for a total sales of $1020.00So, the system of equations to be solved is
a + c= 131
9.60a + 5.20c= 1020
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable c from the first equation:
c= 131 -a
Substituting the expression in the second equation:
9.60a + 5.20×(131 -a)= 1020
Solving:
9.60a + 5.20×131 -5.20a= 1020
9.60a + 681.2 -5.20a= 1020
9.60a -5.20a= 1020 - 681.2
4.4a= 338.8
a= 338.8÷ 4.4
a= 77
In summary, 77 adult tickets were sold that day.
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Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger � ( � ) H(t)H, left parenthesis, t, right parenthesis (in kg kgstart text, k, g, end text of pigs) as a function of time � tt (in hours) can be modeled by a sinusoidal expression of the form � ⋅ cos ( � ⋅ � ) + � a⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. When Harry wakes up at � = 0 t=0t, equals, 0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs. Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs. Find � ( � ) H(t)H, left parenthesis, t, right parenthesis.
Answers
The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.
Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.
Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)
Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.
When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.
According to the given formula,
H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.
As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.
Therefore, the angular frequency,b = 2π/2= π
Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Answer: H(t) = 7.5.cos(π.t) + 22.5.
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wo lines, A and B, are represented by the equations given below:
Line A: x + y = 6
Line B: x + y = 4
Which statement is true about the solution to the set of equations?
step by step how it was solved
There are infinitely many solutions.
There is no solution.
It is (6, 4).
It is (4, 6).
Answers
Answer:
there is no solution
Step-by-step explanation:
x + y = 6 → (1)
x + y = 4 → (2)
subtract (2) from (1) term by term
(x - x) + (y - y) = 6 - 4
0 + 0 = 2
0 = 2 ← false statement
this false statement indicates the equations have no solution
Question 23 of 41
What is the name of the Platonic solid shown below?
A. Octahedron
B. Dodecahedron
C. Hexahedron
D. Icosahedron
Answers
Answer:
That Platonic solid is a dodecahedron.
B is the correct answer.
In this case the linear equations are given:
A company offers two data plans for cell phones. The plan A the linear function for the
charge is given by
y=10x
where x represents the total number of megabytes. The Plan B charge is calculated using
the linear function
y = 4x + 75.
How many megabytes would a customer need to use for Plan be to be a better deal?
1) more than 12.5 megabytes
2) less than 18.75 megabytes
3)
Plan b is always a better deal because the charge per megabyte is less than in
plan A
4) More than 10 megabytes.
5) More than 20 megabytes
Answers
The customer would need to use more than 12.5 megabytes for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).
To determine when Plan B would be a better deal than Plan A, we need to compare the charges for both plans based on the number of megabytes used.
Plan A is represented by the linear function y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.
Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.
To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.
In other words, we need to find the x-value that satisfies the inequality:
4x + 75 < 10x
To solve this inequality, we subtract 4x from both sides:
75 < 6x
Then, we divide both sides by 6:
12.5 < x
Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.
This means that option 1) "more than 12.5 megabytes" is the correct answer.
For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.
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The meaningful domain of the linear model are all the possible values the x variable can take
on that make sense. The range is all the possible values for the linear model (the y values).
The top of the mountain is at 8920 feet and the base of the mountain is at 3300 feet
Identify
Domain
Range
Answers
Domain: The domain is the range of valid heights for the mountain, which is from 3300 feet to 8920 feet.
Range: The range is the set of all possible heights of the linear model, which in this case is also from 3300 feet to 8920 feet.
Domain: The domain of the linear model in this context would represent the possible values for the x variable, which is associated with the height of the mountain.
In this case, the meaningful domain would be the range of valid heights that the mountain can have.
Since the top of the mountain is at 8920 feet and the base is at 3300 feet, the meaningful domain would be the range of heights between 3300 feet and 8920 feet.
Therefore, the domain in this scenario would be [3300, 8920].
Range: The range of the linear model in this context would represent the possible values for the y variable, which is associated with the height of the mountain.
The range would be the set of all possible heights that the linear model can produce.
In this case, since the top of the mountain is at 8920 feet and the base is at 3300 feet, the range would encompass all the valid heights within this range.
Therefore, the range in this scenario would be [3300, 8920].
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Lashonda is on a game show. She will choose a box to see if she wins a prize. The odds in favor of Lashonda winning a prize are 9/2
. Find the probability of Lashonda winning a prize.
Answers
The probability of Lashonda winning a prize is 9/11.
To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.
Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.
In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.
The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.
To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.
In this case, the total number of outcomes is 9 + 2 = 11.
The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 9 / 11.
Therefore, the probability of Lashonda winning a prize is 9/11.
In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.
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Find the equations of the asymptotes of the hyperbola defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
Answers
The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
To find the equations of the asymptotes of the hyperbola defined by the equation:
[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]
We can rewrite the equation in the standard form by isolating the x and y terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]
Rearranging the terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]
Next, let's complete the square for both the x and y terms:
[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]
Expanding and simplify
[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]
Dividing both sides by -4913:
[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]
Comparing this equation to the standard form of a hyperbola:
[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]
We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).
The equations of the asymptotes can be found using the formula:
y - k = ±(b/a)(x - h)
Substituting the values we found:
y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)
Simplifying:
y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)
y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)
Rationalizing the denominators and simplifying:
y + 7 = ±(5/9) ×(x - 2)
Finally, rearranging the equation to isolate y:
y = ±(5/9)x - 10/9 - 7
Simplifying further:
y = ±(5/9)x - 79/9
In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
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Answer:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
Step-by-step explanation:
First, rewrite the given equation in the standard form of a hyperbola by completing the square.
Given equation:
[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:
[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]
Factor out the coefficient of the x² term and the coefficient of the y² term:
[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]
Factor the two perfect trinomials on the left side and simplify the right side:
[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]
Divide both sides by the number of the right side so the right side equals 1:
[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]
[tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]
[tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]
As the y²-term is positive, the hyperbola is vertical (opening up and down).
The standard equation of a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
Therefore, comparing this with the rewritten equation:
h = 2k = -7a² = 25 ⇒ a = 5b² = 81 ⇒ b = 9The formula for the equations of the asymptotes of a vertical hyperbola is:
[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]
Substitute the values of h, k, a and b into the formula:
[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]
Therefore, the equations for the asymptotes are:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
Whats the answer to this?
Answers
Answer: [tex]x=200[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]
[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]
[tex]\frac{1}{5}x-10=30[/tex]
[tex]\frac{1}{5}x=40[/tex]
[tex]x=\frac{40}{\frac{1}{5}}[/tex]
[tex]x=40*\frac{5}{1}[/tex]
[tex]x=200[/tex]
which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy
Answers
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
NEED NOW PLEASE HELP OUT
Answers
Answer:
x=50
Step-by-step explanation:
Make this equal to 180.
x+3x-35+x-35 = 180
5x = 180 + 70
5x=250
x=50
IfmWF = 143° and m/WBF = 117°. find mVL
Answers
Answer:
arc VL = 91°
Step-by-step explanation:
the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is
[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF
[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction
143° + VL = 234° ( subtract 143° from both sides )
VL = 91°
Need help with this question. PLS helpppppp
Answers
Answer:
x = 0.39 or
x = -1.72
Step-by-step explanation:
The quadrateic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]
eq: 3x² + 4x - 2
which is of the form ax² + bx + c = 0
where a = 3, b = 4 and c = -2
sub in quadratic formuls,
[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]
Please explain how to do this and what the answer is. The answer with best explaination gets Brainliest
Answers
Answer:
102
Step-by-step explanation:
we substitute x by 7
7^2+9(7)-10
49+63-10
=102
Find the value of x.
*
20%
x=
104
degrees
Answers
Answer:
x=4 explanation: I got it right
Carson is buying items at a store. His total comes to $41.09. He uses a gift
card and cash to pay the total. After using the gift card, he pays the
remaining $27.74 with cash. Which percentage best describes the part of
the total that Carson paid for with the gift card?
A. 28%
B. 30%
C. 33%
D. 36%
Answers
First you have to find the amount spent with the gift card.
41.09 - 27.74 = 13.35
$13.35 was spent with the gift card.
Now you have to find the percentage that 13.35 is of 41.09
13.35/41.09 = 0.324896568508153
0.324896568508153 x 100 = 32.48965685081528
32.48965685081528 would round up to 33
Therefore, the percentage that best describes the part of the total that Carson paid for with the gift card is 33%
4/5 x 5/7 x 7/9 x 9/11 x 11/13 x 13/15 x 15/17 x 17/19 x 19/21 x 21/23 x 23/25 x 25/27 27/28 x 29/37 x 31/35 x 33/33 x 35/31 x 37/29
Answers
The product of the given fractions is 224/61.
To calculate the product of the given fractions, let's simplify and cancel out any common factors.
We have:
(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)
Starting from the numerator and denominator of the first fraction, we observe the following cancellations:
5 in the numerator and denominator cancel out.
7 in the numerator and denominator cancel out.
9 in the numerator and denominator cancel out.
11 in the numerator and denominator cancel out.
13 in the numerator and denominator cancel out.
15 in the numerator and denominator cancel out.
17 in the numerator and denominator cancel out.
19 in the numerator and denominator cancel out.
21 in the numerator and denominator cancel out.
23 in the numerator and denominator cancel out.
25 in the numerator and denominator cancel out.
27 in the numerator and denominator cancel out.
Now, let's multiply the remaining fractions:
(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)
This simplifies to:
(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)
Simplifying further:
(4 x 29 x 31) / (28 x 35)
We can calculate this to get the final result:
(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.
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Properties of a determinant
Answers
Answer:
Reflection Property.
All-zero Property.
Proportionality.
Switching property.
Factor property.
Scalar multiple properties.
Sum property.
Triangle property.
After long study, tree scientists conclude that a eucalyptus tree will
3
grow at the rate of +
ft. per years, where t is time in years. Find the
5 (t+1)³
number of feet the tree will grow in the first year. Be sure to use the proper
units of measure.
Answers
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 3ft per year, where t is time in years. So, the tree will grow 5 feet in the first year.
We have to find the number of feet the tree will grow in the first year, given that 5(t + 1)³. The rate of growth of a tree is given as 3ft/year. Therefore, in the first year, the tree will grow 3 feet.
To find the number of feet the tree will grow in the first year, we substitute t = 0 in the given expression.
5(t + 1)³ = 5(0 + 1)³= 5(1)³= 5(1)= 5. Therefore, the tree will grow 5 feet in the first year.
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Problem
Express
0.0939
0.09390, point, 0939 as a fraction.
Answers
Answer:
m
Step-by-step explanation:
Net Present Value Method, Internal Rate of Return Method, and Analysis
The management of Advanced Alternative Power Inc. is considering two capital investment projects. The estimated net cash flows from each project are as follows:
Year Wind Turbines Biofuel Equipment
1 $420,000 $880,000
2 420,000 880,000
3 420,000 880,000
4 420,000 880,000
Present Value of an Annuity of $1 at Compound Interest
Year 6% 10% 12% 15% 20%
1 0.943 0.909 0.893 0.870 0.833
2 1.833 1.736 1.690 1.626 1.528
3 2.673 2.487 2.402 2.283 2.106
4 3.465 3.170 3.037 2.855 2.589
5 4.212 3.791 3.605 3.352 2.991
6 4.917 4.355 4.111 3.784 3.326
7 5.582 4.868 4.564 4.160 3.605
8 6.210 5.335 4.968 4.487 3.837
9 6.802 5.759 5.328 4.772 4.031
10 7.360 6.145 5.650 5.019 4.192
The wind turbines require an investment of $1,199,100, while the biofuel equipment requires an investment of $2,278,320. No residual value is expected from either project.
Required:
1a. Compute the net present value for each project. Use a rate of 10% and the present value of an annuity of $1 in the table above. If required, use the minus sign to indicate a negative net present value. If required, round to the nearest whole dollar.
Wind Turbines Biofuel Equipment
Present value of annual net cash flows $fill in the blank 1 $fill in the blank 2
Less amount to be invested $fill in the blank 3 $fill in the blank 4
Net present value $fill in the blank 5 $fill in the blank 6
1b. Compute a present value index for each project. If required, round your answers to two decimal places.
Present Value Index
Wind Turbines fill in the blank 7
Biofuel Equipment fill in the blank 8
2. Determine the internal rate of return for each project by (a) computing a present value factor for an annuity of $1 and (b) using the present value of an annuity of $1 in the table above. If required, round your present value factor answers to three decimal places and internal rate of return to the nearest whole percent.
Wind Turbines Biofuel Equipment
Present value factor for an annuity of $1 fill in the blank 9 fill in the blank 10
Internal rate of return fill in the blank 11 % fill in the blank 12 %
3. The net present value, present value index, and internal rate of return all indicate that the
is a better financial opportunity compared to the
, although both investments meet the minimum return criterion of 10%.
Answers
1a. Compute NPV by calculating the present value of net cash flows and subtracting the investment amount.
1b. Compute PVI by dividing NPV by the investment amount.
2. Determine IRR by finding the discount rate corresponding to an NPV of zero.
3. Compare NPV, PVI, and IRR to identify the better financial opportunity.
1a. To compute the net present value (NPV) for each project, we need to calculate the present value of the annual net cash flows and subtract the amount to be invested. Using the present value of an annuity of $1 from the table, we can fill in the following values:
Wind Turbines:
Present value of annual net cash flows: $420,000 * 1.736 + $420,000 * 2.487 + $420,000 * 3.170 + $420,000 * 3.791
Less amount to be invested: $1,199,100
Net present value: NPV_Wind_Turbines = Present value of annual net cash flows - Amount to be invested
Biofuel Equipment:
Present value of annual net cash flows: $880,000 * 1.736 + $880,000 * 2.487 + $880,000 * 3.170 + $880,000 * 3.791
Less amount to be invested: $2,278,320
Net present value: NPV_Biofuel_Equipment = Present value of annual net cash flows - Amount to be invested
1b. The present value index (PVI) can be calculated by dividing the NPV by the amount to be invested:
Present Value Index = NPV / Amount to be invested
2. To determine the internal rate of return (IRR) for each project, we need to find the discount rate at which the NPV becomes zero. We can use the present value of an annuity of $1 from the table to calculate the present value factor for an annuity of $1. Then, we can find the discount rate that corresponds to an NPV of zero.
Wind Turbines:
Present value factor for an annuity of $1: Fill in the values from the table
Internal rate of return: IRR_Wind_Turbines = Discount rate corresponding to NPV = 0
Biofuel Equipment:
Present value factor for an annuity of $1: Fill in the values from the table
Internal rate of return: IRR_Biofuel_Equipment = Discount rate corresponding to NPV = 0
3. Based on the calculations of NPV, PVI, and IRR, we can compare the two projects. The project with the higher NPV, PVI, and IRR is considered the better financial opportunity. Both investments meet the minimum return criterion of 10%, but the project with the higher financial indicators is preferred.
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Mason plans to study for 1 and 1-half hours. Once he has studied for 1-third of the planned time, he will take a break. Mason has been studying for 12 minutes.
Question
How many ,begin emphasis,more,end emphasis, minutes does Mason need to study before he takes a break? Enter the answer in the box.
Response area with 1 text input box
Answers
Answer:
He needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.
Step-by-step explanation:
To determine how many more minutes Mason needs to study before taking a break, we can calculate the remaining study time.
Mason plans to study for 1 and 1-half hours, which is equivalent to 90 minutes.
He will take a break once he has studied for 1-third of the planned time, which is 1/3 * 90 minutes = 30 minutes.
Mason has already studied for 12 minutes.
Therefore, he needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.
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Select the correct answer.
The number of hours that 20 people spent watching television per day, in relation to age, is graphed. This quadratic equation represents the model
for the set of data.
y = 0.004z²0.314z + 7.5
Based on the model, approximately how much time does an 18-year-old spend watching television each day?
O A.
OB.
O C.
O D.
3 hours
2 hours
7.5 hours
0.5 hour
Answers
Based on the quadratic function, an 18 year old would spend 3 hours watching television.
Using the quadratic function given :
y = 0.004z²-0.314z + 7.5The age is represented as the variable , 'z'
substitute z = 18 into the equation
y = (0.004*18²) - 0.314(18) + 7.5
y = 3.144
y = 3 hours approximately
Hence, an 18 year old spend approximately 18 hours watching television.
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In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Answers
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
GEOMETRY 80POINTS
ty
Answers
Answer:
37.98
Step-by-step explanation: