The compound interest on a sum of money in
2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.
Answer:
The difference between the principal and the compound interest in three years is Rs 17,994
Step-by-step explanation:
The compound interest is given according to the following formula;
[tex]C.I. = P \cdot \left ( 1 + \dfrac{r}{n} \right ) ^{n\cdot t} - P[/tex]
The given amount of the compound after 2 years = Rs 5,460
The given amount of the compound after 4 years = Rs 12,066.60
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P[/tex]...(1)
[tex]12,066.60 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{4} - P[/tex] ...(2)
Dividing equation (2) by (1), we have;
[tex]\dfrac{12,066.60}{5,460} = \dfrac{P \cdot \left ( \left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1\right )}{P \cdot \left (\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 \right ) } =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 }[/tex]
[tex]Let \ \left ( 1 + \dfrac{r}{100} \right ) ^{2} = x, we \ get;[/tex]
[tex]\dfrac{12,066.60}{5,460} =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 } = \dfrac{x^2 - 1}{x - 1}[/tex]
∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)
∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)
12,066.60/5,460 = x + 1
x = 12,066.60/5,460 - 1 = 1.21 = 121/100
x = 121/100
[tex]\left ( 1 + \dfrac{r}{100} \right ) ^{2} = x = \dfrac{121}{100}[/tex]
[tex]1 + \dfrac{r}{100} =\sqrt{ \dfrac{121}{100}} = \dfrac{11}{10}[/tex]
We get
[tex]\dfrac{12,066.60}{5,460} =\dfrac{221}{100}[/tex]
[tex]\therefore \dfrac{12,066.60}{5,460} =\dfrac{221}{100} = \left ( 1 + \dfrac{r}{100} \right ) ^{2}[/tex]
[tex]1 + \dfrac{r}{100} = \sqrt{ \dfrac{221}{100} } = \dfrac{\sqrt{221} }{10}[/tex]
[tex]\dfrac{r}{100} = \dfrac{\sqrt{221} }{10} - 1[/tex]
[tex]\dfrac{r}{100} = \dfrac{11}{10} - 1 = \dfrac{1}{10} = 0.1[/tex]
r = 100 × 0.1 = 10%
r = 10%
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P = P \times \left ( 1 + 0.1\right ) ^{2} - P[/tex]
[tex]5,460 = P \times \left ( 1 + 0.1\right ) ^{2} - P = P \times \left (\left ( 1 + 0.1\right ) ^{2} - 1\right) = P \times \dfrac{21}{100}[/tex]
[tex]P = \dfrac{100}{21} \times 5,460 = 26,000[/tex]
The principal = Rs. 26,000
The compound interest in 3 years is therefore;
[tex]CI_3 = 26,000 \times \left ( 1 + \dfrac{10}{100} \right ) ^{3} - 26,000= 8606[/tex]
The difference, 'd', between the principal and the compound interest in three years, is given as follows;
d = P - CI₃
d = 26,600 - 8606 = 17994
The difference between the principal and the compound interest in three years, d = Rs 17,994.
Mr. Velasquez built a playground. It has one section with a slide and another section with a swing set. A pathway connects the two areas. The slide is 2 meters high. The ares and the pathway are covered in asphalt. Mr velasquez want to know how much of the playground is covered in asphalt
Answer:
[tex]A_1 = 24m^2[/tex] -- Swing set
[tex]A_2 = 16m^2[/tex] -- Slide
[tex]A_3 = 5m^2[/tex] --- Pathway
Step-by-step explanation:
Missing part of the question:
Fill in the table above to show the area of each section (see attachment for table)
The area of each section is calculated as:
[tex]Area = Length * Width[/tex]
For the Swing set
[tex]A_1 = 8m * 3m[/tex]
[tex]A_1 = 24m^2[/tex]
For the Slide
[tex]A_2 = 8m * 2m[/tex]
[tex]A_2 = 16m^2[/tex]
For the Pathway
[tex]A_3 = 5m * 1m[/tex]
[tex]A_3 = 5m^2[/tex]
The total area is:
[tex]Area=A_1 + A_2 + A_3[/tex]
[tex]Area = 24m^2 + 16m^2 + 5m^2[/tex]
[tex]Area = 45m^2[/tex]
there are 16 appetizers available at a restaurant. From these, janet is to chose 13 for her party. How many groups of 13 appetizers are possible
Answer:
560
Step-by-step explanation:
The best way to do this is to write it out, but with large ones like this you should use the equation:
C(n,r) = n!/(r!(n-r)!),
where:
C(n,r) is the number of combinations;
n is the total number of elements in the set; and
r is the number of elements you choose from this set.
Having trouble solving this:
Answer:
It's the third option.
Step-by-step explanation:
Because if [tex]\frac{7}{10}[/tex] was converted into a decimal it would be 0.7 plus 666, it would be 666.7
Answer:
it's the 3rd one
20 POINTS AND BRAINLIEST ONLY FOR CORRECT ANSWER
Given square ABCD. Two isosceles triangles ABP and BCQ are constructed with bases AB and BC . Each of these triangles has vertex angle of 80°. Point P lies in the interior of the square, while point Q lies outside of the square. Find the angle measure between PQ and BC
9514 1404 393
Answer:
85°
Step-by-step explanation:
Each of the isosceles triangles PAB and QBC has interior base angles of ...
(180° -80°)/2 = 50°
Then angle PBC is 90° -50° = 40°.
Segments PB and QB are the same length, so triangle PBQ is an isosceles right triangle. This means angle BPQ is 45°. Angle QEB is the sum of the remote interior angles of ∆BEP, so is 45° +40° = 85°.
The acute angle between PQ and BC is 85°.
Im willing to give 20 points maybe even more
A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized that she didn't order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measure tape and paid $178.50.
The system represents the situation
`20c+10m=495`
`8c+1m=178.50`
Find the cost of one calculator and the cost of one measure tape using one of our methods of solving systems.
Answer:
Equations are
20c + 10m = 495..............(1)
8c + 1m = 178.5.................(2)
Now , equation (2) * 10 = 80c + 10m = 1785...........(3)
So, Eq. (3) - Eq(1) =
80c + 10m - 20c - 10m = 1785 - 495
60c = 1290
c= 21.5
********************************************************
Now place the value of c in Eq (2)
So , m =6.5
Mark my answer as brainlist answer
Step-by-step explanation:
Which term has the definition "The value that describes the location of a digit within a number, such
as units, tens, hundreds, etc."?
O Repeating Decimal
O Rational Number
O Terminating Decimal
O Place Value
Answer:
place value is the answer
Answer:
The answer is 'PLACE VALUE'
Step-by-step explanation:
3/8 (2x - 8 / 3x) = 21 solve for x
A -66
B -70
C -84
D -96
Answer:
d
Step-by-step explanation:
Please help:
Find the class width of this graph
Answer:
The biggest one is 32 to 38
Step-by-step explanation:
hope it helps
Solve. Then, rewrite the complete number sentence in decimal form
Step-by-step explanation:
a)
6.9+1.1= 8
b)
9.9+2.45=12.35
[tex]12 \frac{35}{100} [/tex]
c)
2.4+8.9=11.3
[tex]11 \frac{3}{10} [/tex]
d)
6.37+7.7=14.07
[tex]14 \frac{7}{100} [/tex]
In triangle ABC, A is a right angle, and mB = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.
This triangle is called a 45-45-90 triangle, and the side ratio for the sides opposite to the 45-45-90 degree angles respectively are 1-1-sqrt2
Now we know one side is 6 and its opposing the 45 degrees angle and BC is opposing the 90 degrees angle the ratio between the sides are 1:sqrt2
Therefore BC=6*sqrt2=6sqrt2
Thus B is the correct answer!
Hope this helped any questions just leave them in the comments of this answer.
What are the possible measures of the triangle’s sides? Select all that apply.
Answer:
since a whole triangle is 180 you can do 60×3
Answer:
Step-by-step explanation:
Whole triangle = 180°
90 + 60 + 30
A young woman walked into a cafe and asked for a drink of water the man behind the counter suddenly pulled out a gun and pointed it at her a few seconds elapsed and then the women smiled and thanked the man and left
She had hiccups so she ordered a glass of water. The man noticed so he pulled out a gun to give her a scare. Being startled is said to make hiccups stop. Therefore, she thanked him for ending her hiccups and left.
Rectangle A has a length of 6 and width of 4. Rectangle A prime has a length of 9 and width of 6. Find the scale factor of the dilation shown. 1/2 3/2 2 2/3
Answer: The scale factor of the dilation [tex]=\dfrac32[/tex]
Step-by-step explanation:
[tex]\text{Scale factor}=\dfrac{\text{Side in image}}{\text{Corresponding side in preimage}}[/tex]
Given: Rectangle A has a length of 6 and width of 4.
Rectangle A prime has a length of 9 and width of 6.
Scale factor = [tex]\dfrac{9}{6}\ \ \ or \ \ \dfrac{6}{4}[/tex]
[tex]=\dfrac32[/tex]
Hence, the scale factor of the dilation [tex]=\dfrac32[/tex]
Answer:
3/2
Step-by-step explanation:
Please help, will mark brainliest, do not do for points or I will report, explanation please or no brainliest
Multiply.
2y - 1
2y + 1
4y^2 + 1
Answer:
to multiply-----
(2y-1)(2y+1)
2y(2y+1)-1(2y+1)
4y^2+2y-2y-1
=4y^2-1
Help me plz ??? Help
Answer:
16
Step-by-step explanation:
72 paper clips to 63 paper clips
Answer:
72-63=9
9/72=13%
13% IS .13 SO TENTH IS .1
I AM NOT SURE ABOUT THE TENTH
Step-by-step explanation:
Complete the statement. Round to the nearest hundredth if necessary.
0.3 km ≈ ? mi
Answer:
0.186 mile rounded = 0.19
Step-by-step explanation:
the answer is 0.19
What is s??
A 44°
B 35.3°
C. 37.9°
D. 22°
Answer: Choice B) 35.3 degrees
======================================================
Work Shown:
Apply the law of sines
sin(S)/s = sin(R)/r
sin(S)/16 = sin(120)/24
sin(S) = 16*sin(120)/24
sin(S) = 0.57735026918962
S = arcsin(0.57735026918962)
S = 35.2643896827542
S = 35.3
Make sure your calculator is in degree mode.
Grace bought 3 soccer balls for $14 each and 2 pairs of goalie gloves for $9 each. Write an expression for the total cost of the supplies. Then find the total cost. (LABEL)
Answer:
3(14)+2(9) is the equation
$60 is the total cost
Tell me if im right :)
Answer:
T=60
Step-by-step explanation:
Help please !!!! thnk you!!!!
x = 2
The line of symmetry is the line at which the parabola is the same on each side. With the line x = 2 , each side of the parabola is the same.
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
Adam made note of all the bicycles and cars he could see parked or locked on a
certain city block. All the cars had exactly four wheels, and all the bicycles had exactly
two wheels. How many wheels were on the block if there were 15 bicycles and 7 cars?
How many wheels were on the block if there were x bicycles and y cars?
Answer
68 bicycles.
Let there be x bicycles, then there are (93 - x) tricycles.
From the given values:
2x + 3(93 - x) = 211
2x + 279 - 3x = 211
-x = 211 - 279 = -68
x = -68/-1 = 68.
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving. '
Here given that,
Adam made note of all the bicycles and cars he could see parked or locked on a certain city block. All the cars had exactly four wheels, and all the bicycles had exactly two wheels.
Suppose that there are [tex]x[/tex] bicycles, then there are [tex](93 - x)[/tex] bicycles.
So,
[tex]2x + 3(93 - x) = 211\\2x + 279 - 3x = 211\\-x = 211 - 279 = -68\\x = \frac{-68}{-1}\\x= 68.[/tex]
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
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help me.............
Answer:
Step-by-step explanation:
In order to simplify we do the following...
[tex]5y + \frac{5}{14} + 9n + \frac{2}{14} + 2y - 3n = (5y +2y) +(\frac{5}{14}+ \frac{2}{14}) + (9n - 3n) = 7y + \frac{1}{2} + 6n[/tex]
Answer:
This expression can be simplified to 7y + 6n + 1/2
Step-by-step explanation:
You can find this by grouping like terms and adding them together. Starting with the expression we're given:
5y + 5/14 + 9n + 2/14 + 2y - 3n
Let's make it easier by grouping like terms:
(5y + 2y) + (9n - 3n) + (5/14 + 2/14)
Now we'll add them together:
7y + 6n + 7/14
And finally, we can simplify that fraction by factoring 7 out of both the numerator and denominator:
7y + 6n + 1/2
And now we have the final answer.
81 - 4x = 147 please help
Answer: X = -16.5 / -16 1/2 / -33/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Is y=9 a horizontal line or vertical
Answer:
Horizontal
Step-by-step explanation:
Answer:
y = 9 is a horizontal line :)
Step-by-step explanation:
y=9 is the equation of a horizontal line. The slope is 0. This means that for any value of x that is chosen, the y-value is always 9 Hence y=9 .
What's ƒ(g(x)) if ƒ(x) = 3x + 7 and g(x) =6x – 5?
Answer:
ƒ(g(x)) = 18x - 8
Step-by-step explanation:
We're looking for the composition of f and g, in which function g is the input to function f. Literally replace "x: in f(x) with g(x) = 6x - 5:
ƒ(g(x)) = 3(6x - 5) + 7, or, after simplification,
ƒ(g(x)) = 18x - 15 + 7, or 18x - 8
The sum of the first 8 terms of a GP is five times the sum of first 4 terms. Find the common ratio.
Answer:
1Step-by-step explanation:
Sum of nth term of a GP is expressed as;
Sn = a(r^n-1)/r-1
The sum of the first 8 terms of a GP is expressed as;
S8 = a(r^8 - 1)/r-1
The sum of first 4 terms is expressed as;
S4 = a(r^4 - 1)/r-1
If the sum of the first 8 terms of a GP is five times the sum of first 4 terms then
S8 = 5S4
a(r^8 - 1)/r-1 = 5[a(r^4 - 1)/r-1]
r^8 - 1 = 5(r^4 - 1)
r^8 - 1 = 5r^4 - 5
r^8 - 5r^4 = -5+1
r^4(r^4 - 5) = -4
r^4 - 5 = -4
r^4 = -4+5
r^4 = 1
r = 1
Hence the common ratio is 1
A car manufacturer announced that next year the price of a certain model car would increase by 5.5% . This year the price is 19,076. Find the increase and the new price .
Answer
1,049.18 and 20,125.18
Step-by-step explanation:
increase: 19,076*0.055 = 1,049.18
new price: 19,076*1.055 = 20,125.18
beş üzeri üç ekşi otuz bölübeş eksi iki üzeri iki işlemini sonucu aşağıdakilerden hangisidir?
A) 15
B) 78
C) 95
D) 115
cevaplarınızı bekliyorum.
Ce clasă ești sa văd daca te pot ajuta
Graph the image of rectangle EFGH after a reflection over the line x= –1
Answer:
G (1,7)
H (2,7)
F (1,-1)
E (2,-1)
Step-by-step explanation:
The image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
What is a translation?The process of changing the location of the image on the coordinate system will be known as the translation. A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that graph the image of rectangle EFGH after a reflection over the line x= –1. Translated image of the points is attached with the answer below. The translated points are G (1,7), H (2,7), F (1,-1), and E (2,-1).
Therefore, the image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
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