Teresa borrowed $8,000 at a rate of 15.5% , compounded semiannually. Assuming she makes no payments, how much will she owe after 3 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.
What is compound interest?The interest you earn on interest is known as compound interest. This can be demonstrated with simple math: if you have $100 and it earns 5% interest per year, you will have $105 at the end of the first year. You'll have $110.25 at the end of the second year. Compound interest accelerates the growth of your money because interest is calculated on both the accumulated interest over time and the original principal. Compounding can cause a snowball effect, in which the initial investments and the income earned from those investments grow in tandem.So, Teresa borrowed $8,000 at a rate of 15.5%:
(Refer to the table given below)
Owe in 3 years: $12.519.69Rounding off: 12.520Teresa will owe $12.520 in 3 years.Therefore, Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.
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Related Questions
Polygon ABCDE is reflected across the
line x = -2. Graph and label the image
A'B'C'D'E'. Is mLA = mLA'? Explain.
Answers
The labeled graph showing ABCDE, A'B'C'D'E', and the line of reflection x = -2 is shown. Also, m∠ A = m∠ A'.
In the question, we are given that the polygon ABCDE is reflected across the line x = - 2.
We are asked to graph and label the image A'B'C'D'E'. Also, we are asked if m∠ A = m∠ A'.
When the polygon ABCDE is reflected across the line x = - 2, all the coordinates on it are reflected across the line x = -2.
The reflection of any point with coordinates (x, y) on reflection across the line x = a, results in a point with coordinates (-x + 2a, y).
The coordinates of the vertices of the given polygon are:
A (-4, 4), B (-3, 3), C (-3, 2), D (-5, 1), and E (-5, 3).
Reflecting these points across the line x = - 2, we get:
A (-4, 4) → A' ( -(-4) + 2(-2), 4) = A' (0, 4).
B (-3, 3) → B' ( -(-3) + 2(-2), 3) = B' (-1, 3).
C (-3, 2) → C' ( -(-3) + 2(-2), 2) = C' (-1, 2).
D ( -5, 1) → D' ( -(-5) + 2(-2), 1) = D' (1, 1).
E (-5, 3) → E' ( -(-5) + 2(-2), 3) = E' (1, 3).
Plotting ABCDE, A'B'C'D'E', and the line x = -2 has been shown on the graph.
The angles m∠ A and m∠ A' are equal since ABCDE is reflected to make A'B'C'D'E' which makes the two figures congruent. And in congruent figures, the corresponding angles are equal.
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A supermarket wants to send code for $.25 off a bag of chips to its rewards members. Each coupon will have one digit followed by four letters the letters D and E, and the digits 0, 5and 8 will not be used so there are 24 letters and 7 digits that will be used assume that the letters can be repeated how many such coupons can be generated.
Answers
There are 2322432 coupons generated .
According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as
code = D L L L L where D and L represent the digits and letters.
Now total digits we have is = 7
total number of letters we have = 24
So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.
Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways = 24⁴
Therefore the number of coupons that can be generated from the combination are :
7*24⁴ = 7*331776
= 2322432
Hence the number of coupons generated are 2322432.
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rectangle PQRS with vertices (5,15) Q(15,15) R(15,10) and S(5,10): k=4/5
Answers
The vertices of the rectangle are:
P'(4,12)
Q'(12,12)
R'(12,8)
S'(4,8)
Given,the vertices of the rectangle are:
P(5,15), Q(15,15), R(15,10) and S(5,10)
also k= 4/5 to find the new vertices, that is:
P' = P×k
P' = P × 4/5
P' = (5×4/5 , 15×4/5)
P' = (4,12)
similarly:
Q' = Q×k
Q' = Q × 4/5
Q' = (15×4/5 , 15×4/5)
Q' = (12,12)
R' = R×k
R' = R × 4/5
R' = (15×4/5 , 10×4/5)
R' = (12,8)
S' = S×k
S' = S × 4/5
S' = (5×4/5 , 10×4/5)
S' = (4,8)
Hence we get the required points, for which we plot the graph.
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A bookstore manager purchased a case of
40 paperback books and a display stand
that cost $8.00. He paid $108.00 for the
total purchase. If each book cost the same
amount, how much did he pay per book?
A
B
C
D
$0.34
$2.50
$2.70
$100.00
Answers
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 3 comma negative 2 up to the right through the point 1 comma 0
R colon open bracket y is an element of all real numbers close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 2 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to 1 close bracket
Answers
Greetings from Brasil...
The range will be the region of the Y axis comprised by the function. Looking at the graph, we conclude that:
Range = {Y ∈ ℝ/Y ≥ - 2}NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+106t+206.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after
seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at
meters above sea-level.
Answers
If the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
Given that the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206.
We are required to find the time after which the rocket will splash down into the ocean and the time after which the ocean will get its peak and the height of the rocket.
The rocket will splash down when the height of the rocket is 0.
-4.9[tex]t^{2}[/tex]+106t+206=0
4.9[tex]t^{2}[/tex]-106t-206=0
t={106±[tex]\sqrt{(106)^{2} -4*4.9*(-206)}[/tex]}/2*4.9
t=(106±[tex]\sqrt{15273.6}[/tex])/9.8
We have to ignore the negative sign because the time is always shown in positive signs.
t=(106+123.59)/9.8
t=229.59/9.8
t=23.43 seconds
Rocket will be at its peak when the slope of the equation is 0.
[tex]h^{I}[/tex](t)=-9.8t+106
-9.8t+106=0
-9.8t=-106
t=-106/-9.8
t=10.82 seconds
To find the height we need to use t=10.82 in the equation.
h(10.82)=[tex]-4.9*(10.82)^{2} +106*10.82+206[/tex]
=-573.65476+1353.92
=779.26524 meters.
Hence if the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
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Refer to the number line. Find the coordinate of point K that is 4/5 of the distance from A to F.
Answers
Point K coordinate from the given number line is; -1²/₃
How to Partition a Line Segment?Partitioning of a line segment means dividing the line segment in the given ratio. The two numbers in the ratio must add up together to equal the total number of partitions of the line segment. For example: If a line segment AB is divided into a ratio of 2:3, it shows that the line segment can be divided into 5 equal sections. Hence, there are 5 parts in total, in which 2 parts will be before the desired point and 3 parts will be after the desired point.
We are given a line segment A F divided into different parts of points B, C, D and E.
Now, we want to find the point K such that it divides Line segment A F in the ratio 4:5.
Now, from the number line, line A F measures 12 units. Thus;
Point K = (4/5) * 12 = 5¹/₃ from point A
Thus, point K coordinate = -7 + 5¹/₃
Point K coordinate = -1²/₃
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For the point P(-20,7) and Q(-13,12), find the distance d(P,Q) and the
coordinates of the midpoint M of the segment PQ.
Answers
Distance
[tex]d(P,Q)=\sqrt{(-20-(-13))^2+(7-12)^2} \\ \\ =\sqrt{49+25} \\ \\ =\boxed{\sqrt{74}}[/tex]
Midpoint
[tex]M=\left(\frac{-20-13}{2}, \frac{7+12}{2} \right)=\boxed{\left(-\frac{33}{2}, \frac{19}{2} \right)}[/tex]
a bakery has six bags of flour. they are are asked to make four loaves of bread
the first two loaves each require two bags and quarter of another bag
the next loaf requires one bag and two thirds of another bag
the final loaf requires a half bags of flour
write a calculation,using brackets ,to work out how much flour the bakery will have left the bakery will have left after making these loaves
Answers
The bakery is short on half a bag of flour.This problem can be solved using fractions . So, first loaf of bread requires 2bags of flour and a quarter which can be written as 2[tex]\frac{1}{4}[/tex]second loaf of bread also requires the same amount which is 2[tex]\frac{1}{4}[/tex]
the third loaf of bread requires one bag and two third of another bag which can be written as 1[tex]\frac{2}{3}[/tex]
And the final loaf of bread requires half bag of flour which is [tex]\frac{1}{2}[/tex]
the total requirement of flour for making the four loaves of bread is
= 2[tex]\frac{1}{4}[/tex] + 2[tex]\frac{1}{4}[/tex]+ 1[tex]\frac{2}{3}[/tex]+[tex]\frac{1}{2}[/tex]
=[tex]\frac{9}{4}[/tex] +[tex]\frac{9}{4}[/tex] + [tex]\frac{5}{3}[/tex] + [tex]\frac{1}{2}[/tex]
= [tex]\frac{27}{12}[/tex]+ [tex]\frac{27}{12}[/tex] +[tex]\frac{20}{12}[/tex] +[tex]\frac{6}{12}[/tex]
= [tex]\frac{80}{12}[/tex]
To work out how much flour the bakery will have left after making these loaves we need to reduce the total requirement with total flour we have = 6 -[tex]\frac{80}{12}[/tex]
=[tex]\frac{72}{12}[/tex] - [tex]\frac{80}{12}[/tex]
=- [tex]\frac{6}{12}[/tex] or- [tex]\frac{1}{2}[/tex]
therefore the bakery is short on half a bag of flour
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Yuki was curious if △ A B C △ABCtriangle, A, B, C was congruent to △ F E D △FEDtriangle, F, E, D, so she tried to map one triangle onto the other using transformations: A coordinate plane. The x- and y-axes both scale by one. A pre-image Triangle A B C has point A at two, two, point B at five, four, and Point C at eleven, two. Another triangle D E F has point D at three, twelve, point E at nine, ten, and point F at twelve twelve. Triangle A B C is translated four units to the right and six units up to form the image Triangle A prime at six, eight, B prime at nine, ten, and C prime at fifteen, eight. E E D D F F A A B B C C A coordinate plane. The x- and y-axes both scale by one. A pre-image Triangle A B C has point A at two, two, point B at five, four, and Point C at eleven, two. Another triangle D E F has point D at three, twelve, point E at nine, ten, and point F at twelve twelve. Triangle A B C is translated four units to the right and six units up to form the image Triangle A prime at six, eight, B prime at nine, ten, and C prime at fifteen, eight. Yuki concluded: "It's not possible to map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D using a sequence of rigid transformations, so the triangles are not congruent." What error did Yuki make in her conclusion? Choose 1 answer: Choose 1 answer: (Choice A) A One more transformation — a rotation — would map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D. So the triangles are congruent. (Choice B) B One more transformation — a reflection — would map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D. So the triangles are congruent. (Choice C) C There is no error. This is a correct conclusion.
Answers
Answer:Nose
Step-by-step explanation:Q es eso
(√14 + √10i)(√14 - √10i)
Answers
Answer:
24
Step-by-step explanation:
You want the value of the product ...
(√14 + √10i)(√14 - √10i)
Difference of squaresThe factoring of the difference of squares is ...
a² -b² = (a +b)(a -b)
Here, we have a=√14 and b=√10i. The product of the sum and difference of these values is ...
(√14 + √10i)(√14 - √10i) = (√14)² -(√10i)²
= 14 -(10(-1)) = 24
The product is 24.
f(x)= -x^2 + 4x +5 and g(x)= -f(x) + k. find the values of k so that g(x) = 0 has no real roots
Answers
According to the given quadratic equation the values of k = -1.
In mathematics, what is quadratic equation?A quadratic equation seems to be a second-order polynomials equation with a single variable x ax2+bx+c=0. Ta he fundamental theorem of algebra assures that it has at least one solution because it is second-order polynomial equation.
According to the given data:g(x)= -f(x) + k. given
Putting the value of f(x).
g(x)= - -x^2 + 4x +5 + k
= x^2 - 4x - 5 + k
= 0
When g(x) = 0 has no real roots, Δ < 0 a quadratic equation of one variable has no real roots.
So,
16 - 4(5 + k) = 0
16 - 20 -4k < 0
-4 -4K < 0
4K> -4
k>-1
According to the given quadratic equation the values of k = -1.
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Solve the system of linear equations by graphing.
Answers
By using a graphing tool, the point of intersection of the two lines is (x, y) = (7, 0).
How to solve a system of linear equations by graphic approach
In this question we have a system of two linear equations with two variables, which can be represented on Cartesian plane. By geometry it is known that a line can be constructed after knowing the location of two distinct points.
First, we find two distinct points from each line:
x + y = 7: (7, 0), (0, 7)
- x + y = - 7: (7, 0), (0, - 7)
Second, set each pair of points and construct the lines on a Cartesian plane.
Third, mark the point of intersection of the two lines. The result is shown in the image attached aside. The point of intersection of the two lines is (x, y) = (7, 0).
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a duck spends about .45 of a day sleeping. how much hours does a duck sleep each day
Answers
Answer:
10.8
Step-by-step explanation:
24 * .45 = 10.8
Write the following in simplest form
in parenthesis negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end parenthesis
three over 6 times x plus 8
three over 6 times x plus negative 20
negative five sixths times x plus eight
negative five sixths times x plus negative 8
Answers
The simplest form in parenthesis is option C which is negative five sixths times x plus eight (- 5x/6 + 8)
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
WE have Given equation as; parenthesis negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end parenthesis,
( -2/3 * x - 6 ) - ( -14 + 1/6 * x)
Now solving the equation will gives;
= ( -2/3 * x - 6 ) - ( -14 + 1/6 * x )
= ( -2x/3 - 6 ) - ( -14 + x/6 )
= -2x/3 - 6 + 14 - x/6
Now collecting like terms;
= -2x/3 - x/6 - 6 + 14
= - 5x/6 + 8
Therefore the correct answer is option C; negative five sixths times x plus eight (- 5x/6 + 8)
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-4x + y = 5. Solve for y
A. y = -4x + 5
B.y = 4x + 5
C. y = 4x - 5
D. y = -4x - 5
Answers
Answer:
y = 4x + 5
Step-by-step explanation:
-4x + y = 5
-4x + 4x + y = 5 + 4x
y = 5 + 4x
Hope this helps! :)
What is the answer ? How do you work this problem out ?
Answers
Check the picture below.
At the end of spring break, Mary left the beach and drove back towards home, driving at a rate of 51 mph. A friend of Mary left the beach for home 0.5 hour later, and drove 66 mph. How long did it take Mary's friend to catch up to Mary?
Answers
Answer:
2.2 hours or
2 hours and 12 minutes they will meet.
Step-by-step explanation:
Givens
Mary's speed = 51 mph
Friend's speed = 66 mph
Mary will be on the road for t hours
Her Friend will be on the road t - 0.5. Why minus? Because she was on the road 1/2 hour less than Mary was. Any time you see More or Less in a question, pay attention. usually it is the key to the question.
Equation
d_Mary = d_friend
d = rate * time
Solution
51 * t = 66*(t - 0.5) Remove the brackets.
51*t = 66*t - 66*0.5
51*t = 66*t - 33 Subtract 66t from both sides. Be careful
51t - 66t = - 33 Combine
- 15t = - 33 Divide by - 15
t = - 33/-15
t = 2.2 hours or 2 hours and 12 minutues
Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest tenth of a percent. Original: 90 New: 160
Answers
Answer:
Since the quantity started at 90 and then changed to 160, there was clearly an increase in its value.
Step-by-step explanation:
Amy has three times as many Star Wars toys as Carly. Total they have 232 Star Wars toys. How many Star Wars toys does Amy have?
Answers
Answer:
174
Step-by-step explanation:
Since we don't know how many toys Carly has, we'll use a variable (x). The equation would then be:
x+3x=232
We can then combine like terms, and the new equation would be:
4x=232
Now, we have to get x by itself. To do this, divide both sides by 4, and you get:
x=58
But, remember, x is how many Carly has. Amy has three times that, so:
58*3=174
Amy has 174 toys.
Hope this helps!
whats the answer for?(9.6x103)x(6.7x102)
Answers
Answer:
675,745.92
Step-by-step explanation:
(9.6 × 103) × (6.7 × 102)
(988.8) × (683.4)
= 675,745.92
I hope this helps!
partial products
16x29?
Answers
Step-by-step explanation:
464
first u will multiply 16 with 29
after u get that number that will be your answer
Answer:
29
× 16
54
120
90
+ 200
= 464
Points E, D, and H are the midpoints of the sides of ΔTUV. UV=110, TV=140, and HD=110. Find HE.
Answers
The required value of HE is 55 units.
What is proportion?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.
Now it is given that Points E, D, and H are the midpoints of the sides of ΔTUV.
UV = 110,
TV = 140, and
HD = 110
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
HD/HE = TV/(TV/2)
Put the values we get,
110/HE = 140 / 70
⇒ HE = 110*70/140
⇒ HE = 55 units
Thus, the required value of HE is 55 units.
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A kite is flying 9.75 feet above a lamp post that is 84 2/3 feet tall. How high is the kitchen flying?
Answers
The kite is flying at the height of 94 5/2 feet.
Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
= 9.75 +84 2/3 { 9+0.75 = 9.75 84 2/3}
= 9 + 0.75 +84 2/3 { a+b+c+d = a+c+b+d}
= 9 + 84 + 3/4 + 2/3
=93 + 3*3 / 4*3 + 4*2 / 4*3
= 93 + 9/12 + 8/12
= 93 + 17/12
= 93 + (1 + 5/12)
= 94 + 5/12
=94 5/12 feet
{kite height = (post height + the height of the kite above the post)
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Find the value of X.
Answers
Answer:
It's x+10=5+2x+6=>x=-1
July, May, March, what comes next?
Answers
Answer:
January
Step-by-step explanation:
subtract 2 from each numbe(month)
7-2=5-2=3-2=1
7: July
5: May
3: March
1: January
The diameter of a gold atom is approximately 144 trillionths of a metre. The diameter of an oxygen atom is approximately 0.074 billionths of a metre. Which is larger? How many times larger is it than the other?
Answers
The diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
What is a diameter?The diameter of a shape (usually a round shape) is a line that divides the shape to equal parts
Which is larger?The diameters are given as:
Diameter of a gold atom = approximately 144 trillionths of a meter
Diameter of an oxygen atom = approximately 0.074 billionths meter
Using a calculator, we convert the above numbers to scientific numbers
So, we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
The number with the higher exponent is greater than the other number
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom
How many times larger is it than the other?In (a), we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
Calculate the difference
d = 1.44 x 10^-10 - 7.4 x 10^-11
Evaluate the difference
d = 7 x 10^-11
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
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Write the following in exponential form:
log3y=x
Answers
the equation rewritten in exponential form is:
y = 3^x
How to rewrite the given expression?
Here we start with.
Log₃(y) = x
Remember that we can rewrite:
Log₃(y) = ln(y)/ln(3)
Then we can simplify so we get:
ln(y) = ln(3)*x
Now we just apply the exponential function to both sides:
exp(ln(y)) = exp(ln(3)*x)
y = (e^(ln(3))^x = 3^x
y = 3^x
That is the equation rewritten in exponential form:
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What’s 6 and 2/3 divided by 8
Answers
Answer: 5/6
Step-by-step explanation:
Answer:
6 divided by 8 is 3/4 (.78)
2/3 divided by 8 is 1/12 (0.083)
6 2/3 divided by 8 is 5/6 (0.83)
If the two lines below are perpendicular and the slope of the red line is -,
what is the slope of the green line?
-5
01
A
5
5
Answers
We get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.
We are given that the red line is perpendicular to the green line.
Also, we are given that the slope of the red line is - 5 / 2
m₁ = - 5 / 2
Now, we need to find the slope of green line.
Let the slope of the green line be m₂
We know that, when the lines are perpendicular, then the relationship between their slopes is given by:
m₁ × m₂ = - 1
Substituting the values, we get that:
- 5 / 2 × m₂ = - 1
m₂ = - 1 × - 2 / 5
m₂ = 2 / 5
Therefore, we get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.
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