Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.
How do we calculate the original amount using PV formula?To solve this question, the following present value (PV) formula will be used:
PVn = Pn / (1 + r)^n ........................... (1)
Where:
PVn = Present value of an amount paid in year n
P = Amount paid in year n
r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179
n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4
Using equation (1), we can therefore proceed as follows:
PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18
PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45
PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04
Therefore, we have:
Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67
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Which of the following is the square of a binomial?
A. 4m^2 - 6mn + 9n^2, B. 16x^2 + 24xy + 9y^2, C. c^2 - 2cd - d^2, D. a^2 + b^2.
All options except Option D , a² + b² , is the square of the binomial.
What is a Binomial ?A polynomial that contains only two term is called a Binomial.
The sum of square of a binomial is the sum of square of the first term , square of second term and twice of the product of the first and second term.
(a+b)² = a² +b² +2ab
(a-b)² = a² +b²-2ab
The options have to be broken down into this form to check whether they are square of a binomial
Option A : 4m² - 6mn + 9n² = (2m -3n)²
Option B: 16x² + 24xy + 9y²=(4x+3y)²
Option C : c²- 2cd - d²=(c-d)²
Option D : a² + b² cannot be written as the square of binomial.
All options except Option D is the square of the binomial.
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Write this percentage as a fraction in its simplest form. 96 %
(pls)
Answer:
24/25
Step-by-step explanation:
96%=0.96. 96/100=48/50=24/25
find the equation of a line that is parallel to y=3x+6 and passes through A
) (0,-2) B. (2,5) C.(4,1)
Answer:
Step-by-step explanation:
We'll look for an equation with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0.
A line parallel to y=3x+6 will have the same slope, 3.
We can write y=3x+b. Any value of b can be used to generate a parallel line.
If we want that line to go through a specific point, such as (0,-2), we need to find a value of b that shifts the line so that it includes (0,-2). This can be done by using that point in the equation y=3x+b:
y=3x+b
-2=3*(0)+b for point (0,-2)
b = -2
The equation becomes y=3x-2
See the attached plot.
===========================
Do that same thing for the remaining two points.
For B: (2,5) The equation is y=3x-1
For C: (4,1) The equation is y=3x-11
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
A. Write down the facts.
B. Organize into a table.
C. Guess at the solution and see if you are close.
D. List potential formulas.
E. Form an equation.
F.Draw a diagram.
Answer:
a, b, d, e
maybe c
Step-by-step explanation:
What is the exact value of x
x = 6(√2)
Step 1:
Say, 6 is perpendicular and x is the hypotenuse.
Step 2:
As we know sine is the ratio of perpendicular and hypotenuse.
∴ [tex]sin 45 = \frac{perpendicular}{hypotenuse}=\frac{6}{x}[/tex] ......................................(1)
Step 3:
As we know, sin45 = 1/√2
∴ put the value in equation 1
⇒ [tex]\frac{1}{\sqrt{2}} = \frac{6}{x}[/tex]
By solving the above equation, we get,
x = 6(√2)
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what is the term to term rule of 3,6,17,48,87
Answer:
term to term rule. • a rule that defines the value of each term in a sequence. if the previous terms are known, e.g. the Fibonacci sequence. xn = xn-1 + xn-1.
Step-by-step explanation:
To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is 'start at 17 and subtract 3'. The next two terms of the sequence are 5 and 2, giving the sequence as: Question.
EASY QUESTION Miguel plots points A, B, and C in the coordinate plane.
A. Distance between A and B is: 5 units.
B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.
What is an Equilateral Triangle?An equilateral triangle has three sides that have the same length.
Given the vertices with their coordinate points as:
A (-3, 2)
B (-6, -2)
C (0, -2)
Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:
AB = √[(−6−(−3))² + (−2−2)²]
AB = √25
AB = 5 units
BC = √[(−6−0)² + (−2−(−2))²]
BC = √36
BC = 6 units
AC = √[(−3−0)² + (2−(−2))²]
AC = 25
AC = 5 units
Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.
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Based on the graph how many distinct real numbers solutions does the equation X^3 + 6x^2 + 12x + 8 = 0 have?
Answer:
no real roots
Step-by-step explanation:
Find discriminant of quadratic equation:
A
= 62 - 4aC
2 Identify a,b,c
Identify a,b,c through coefficient:
a
b
C
6
= 12
8
Substitute and calculate
Substitute the value of a,b,c and calculate
discriminant (b2 - 4ac) :
-48
Determine number of solution Determine number of solution with
discriminant:
no real roots
A pendulum is raised to a certain height and released from point A, as shown in the image below. At its release, the pendulum is also given an initial velocity of 14 m/s. Assuming that the effects of friction and air resistance can be ignored, what will be the maximum height that the pendulum can reach - that is , what is the height at point B? (Recall that g = 9.8 m/s2.)
Answer:
D. 20 m
Step-by-step explanation:
The potential energy at Point B will be the sum of the potential and kinetic energies at point A.
__
energy formulasFor mass M, the potential energy at h meters above a rest height is ...
PE = Mgh
The kinetic energy of mass M with velocity v is ...
KE = 1/2Mv²
point A energyA pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...
PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg
point B energyWhen the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...
PE = Mgh
196M J/kg = M(9.8 m/s²)h
h = (196M)/(9.8M) m = 20 m
The height of the mass at point B will be 20 meters.
The length of each side of a square is 8.5 cm rounded to 1 decimal place.
Write the error interval for the perimeter, p, in the form a _< p
Answer:
make it more clear its not clear enough to understand the question
Choose the best answer
-3a>0 and 8-9a<-19
Answer:
The first option
Step-by-step explanation:
the sign only flips when there is a negative number.
i hope this is correct
pls help me dis is due at 3:00 pm 2day ASAP attachment above ^
|
Answer:
s=0.20p
Step-by-step explanation:
20% off an product means to subtract 20% of the original price from the original price.
Two points are:
A. always collinear and always coplanar.
B. always collinear and sometimes coplanar.
C. sometimes collinear and sometimes coplanar.
D. sometimes collinear and never coplanar.
Does the table represent a function? Why or why not?
X
y
4
5
OA. Yes, because there is the same number of x-values as y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
C. No, because two of the y-values are the same.
O
D. No, because one x-value corresponds to two different y-values.
579
03232
The correct answer is option D which is No because one x-value corresponds to two different y-values.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
We can see from the table that the value of x at 5 is giving two different values of y that is 2 and 3. For a function, it is not possible to have two different outputs for the same input.
Therefore the correct answer is option D which is No because one x-value corresponds to two different y-values.
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hannah and andrea were selling tickets to the homecoming dance. they were set up in different
locations, and while andrea sold h number of homecoming tickets, hannah sold 3h. what
information can we gather about the relationship between how many tickets andrea sold and how
many hannah sold?
The relationship between the number of tickets is that Hannah sold three times as many tickets as Andrea.
How to determine the relationship?From the question, we have:
Andrea = h
Hannah = 3h
This means that:
Hannah = 3 * Andrea
So, the relationship is that Hannah sold three times as many tickets as Andrea.
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A bag contains 8 red m&m's, 3 brown m&m’s, and 7 green m&m’s. Draw one m&m what’s the probability of drawing a brown m&m?
Answer:
8+3+7=18
probability of brown m&m is
[tex] \frac{3 }{18 } [/tex]
As the sample size increases, the margin of error _____.
As the sample size increases, the margin of error decreases.
What is margin of error?A margin of error is known to be a statistical measurement that states the difference between apparent and projected results in a random sample survey.
From the formula:
MOE = z × √σ²/n
Where
σ = standard deviation
z = quantile
n = sample size
MOE = margin of error
From the formula, sample size is inversely proportional to the margin of error.
Hence, as the sample size increases, the margin of error decreases.
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What is the length of the line?
Answer:
5 units
Step-by-step explanation:
Use Pythagorean Theorem
x = 4 units y = 3 units
4^2 + 3^2 = L^2
16 + 9 = L^2
L = 5
Answer:
5 units
Step-by-step explanation:
By the Pythagorean theorem:
c² = a² + b²
c = length of the line
a = 4
b = 3
Then:
c² = 4² + 3²
c² = 16 + 9
c² = 25
√c² = √25
c = 5
What are the correct trigonometric ratios that could be used to determine the length of ln? check all that apply. sin(20°) = startfraction l n over 8 endfraction cos(70°) = startfraction 8 over l n endfraction tan(70°) = startfraction l n over m n endfraction sin(20°) = startfraction 8 over l n endfraction cos(70°) = startfraction l n over 8 endfraction
The correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].
The complete question is attached with the answer below:-
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-
Cos 70 = Base / Hypotenuse
So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.
Cos 70 = LN = 8
Therefore the correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].
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Answer:
A & E
Step-by-step explanation:
Jus took it on edge
last and final one for the school year lol
Answer:
X=-46
Step-by-step explanation:
-(-46-10)
-(-56)
56 degrees
Help to solve give brainliest
Answer:
(B) 32Step-by-step explanation:
equation of The line L : y = -(1/2)x + 6
A(8 , b) ∈ L then b = -(1/2)(8) +6 then b = -4 + 6 = 2
Therefore ,
A(8 , 2)
AB = 2
CD = 6
BC = 8
…………………………………………
Area of the trapezoid ABCD
= (CB÷2)×(AB + CD)
= (8÷2)×(6+2)
= 32
Which of the following is a trinomial?
OA. √11x-7
OB.
B. X-1
8
OC. 2x+4
OD. 5x2+3x+6
5x² + 3x + 6 is the only trinomial from the given expressions
What is Expression?An expression is combination of variables, numbers and operators.
A trinomial is a polynomial with three terms. In the given options, we need to identify the expression that has exactly three terms.
√11x - 7, has two terms: √11x and -7.
It is not a trinomial because it doesn't have three terms.
x - 1, has two terms: x and -1.
It is not a trinomial for the same reason as option OA.
2x + 4, has two terms: 2x and 4.
It is not a trinomial because it doesn't have three terms.
5x² + 3x + 6, has three terms: 5x², 3x, and 6.
It fits the definition of a trinomial because it has three terms.
Therefore, 5x² + 3x + 6, as it is the only expression among the options that is a trinomial.
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In a scale drawing, 3 inches
represents 10 miles. How many
inches represent 45 miles?
Answer:
13.5 inches
Step-by-step explanation:
3inches:10 miles
x inches: 45 miles
do cross multiply:
3*45=135
10*x=10x
so 135=10x
x=13.5 inches
Anne wants to create a data display to summarize prices of the 264 homes for sale in her area.
The data display that is best for Anne's purpose is: D. a histogram, because the bars show the frequency of data points within different ranges.
What is histogram?Histogram is a graph that help to the following into different rages
Distribute dataGroup and organize dataDisplay frequency distributionSummarize data etc.Based on the data given Anne should make us of histogram based on the fact that the graph shows the frequency of the data points that are within different ranges.
Therefore the correct option is D.
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In the figure below, find the exact value of y. (Do not approximate your answer.)
Image is attached, this is for a mastery grade, please help!
Will give brainliest to first right answer! Thank you!
The exact value of the y in the similar right triangle is 2.2360679775 units
How to find the side of a triangle?The triangles are similar.
Similar triangles have corresponding sides of equal ratio.
The corresponding angles of similar triangle are equal.
Therefore, using similar ratio,
y / 5 = 1 / y
cross multiply
y × y = 5 × 1
y² = 5
square root both sides
y = √5
Therefore,
y = 2.2360679775 units
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Answer:
Step-by-step explanation:
Givens
Observe the small triangle at the right. The smallest side is one.
The hypotenuse is y
In the largest tringle, the hypotenuse is 5
The smallest side is y
You can set up a ratio for this situation
Equation
smallest side - smallest triangle Largrest triangel -- largest side
============================ =========================
hypotenuse - smallest triangle hypotenuse -- largest triangle
1/y = y / 5 Cross Multiply
Solution
y^2 = 1*5 Take the square root of both sides.
√y^2 = √5
y = √5
or
y =
Enter the coordinates of the point
on the unit circle at the given angle.
330°
(-)
[?]
Answer: [tex](\frac{\sqrt{3} }{2} ,-\frac{1}{2} )[/tex]
Step-by-step explanation:
this forms a 30 degree reference angle
and this is in the 4th quadrant
When the angle is 30 degrees, the coordinates are:
[tex](\frac{\sqrt{3} }{2} ,-\frac{1}{2} )[/tex]
The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).
How to convert the polar coordinate to a cartesian coordinate?The polar coordinate system in geometry is a two-dimensional latitude and longitude that uses the distance from a reference point and the angle from an optical axis are used to identify each point's location on a plane. This polar axis is the ray emanating from the pole in the direction of the point of comparison, which is referred to as the pole.
The cartesian coordinate is (x, y) and polar coordinate is (r, θ). Then the relation is given as,
x = r cos θ
y = r sin θ
The angle is 330° and the radius is one. Then we have
x = 1 x cos 330°
x = (√3) / 2
y = 1 x sin 330°
y = - 1/2
The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).
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PLEASE ANSWER ASAP!!!!!!!!!!!! MUCH APPRECIATED!!
Based on the amount being deposited into the account each month, and the interest, the account will triple in value on 25 months..
When will the value of the account triple?First find the value of the account when tripled:
= 1,000 x 3
= $3,000
We can then use a spreadsheet to find the number of periods it will take to triple.
Convert the interest to a monthly figure as:
= 3.15% / 12
= 0.2625%
When you put the figures into the spreadsheet as shown, the number of months would be 25 months.
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Point Q is on line segment PR . Given PQ=16 and PR=19, determine the length of QR
Answer:
QR = 3
Step-by-step explanation:
given that Q is on the segment PR , then
PQ + QR = PR ( substitute values )
16 + QR = 19 ( subtract 16 from both sides )
QR = 3
The calculated length of the segment QR is 3 units
How to determine the length of the segment QRFrom the question, we have the following parameters that can be used in our computation:
Point Q is on line segment PR
PQ = 16 and PR = 19
using the above as a guide, we have the following:
PQ + QR = PR
substitute the known values in the above equation, so, we have the following representation
16 + QR = 19
So, we have
QR = 19 - 16
Evaluate
QR = 3
Hence. the length of the segment QR is 3
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cindy bought 7/8 yards of ribbon at the craft store . jacob bought 4/5 the length of ribbon as cindy. how many yards of ribbon did jacob buy.
Answer:
7/10
Step-by-step explanation:
what is the area of the base?