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.
To begin a bacteria study, a petri dish had 2500 bacteria cells. Each hour since, the number of cells has increased by 4.6%.
Let ( be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and
Answer:
Amaxesha amnandi ukuba unexesha elimnandi enkosi kuThixo ukuba unexesha elimnandi enkosi kuThixo ngokuba nexesha elimnandi enkosi kuThixo ngokuba nexesha elimnandi bulela uThixo ngokuba nexesha elimnandi
-4x(5x +1)
this needs to be written in polynomials
Answer:
-20x^2-4x
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.
The weatherman predicted the high temperature for today to be 52 degrees. The actual high temperature was 50 degrees. What was the percent of error?
Answer:
Weatherman on top of them out to replace the temperature is currently 0° has been followed at the constantWeatherman on top of them out to replace the temperature is currently 0° has been followed at the constant Weatherman on top of them out to replace the temperature is currently 0° has been followed at the constant rWeatherman on top of them out to replace the temperature is currently 0° has been followed at the constant raWeatherman on top of a mountain reports the temperature is currently 0° has been falling at the constant rate of 3° per hour what was the temperature three hours ago
Step-by-step explanation:
Find a slope for each line (each block is one unit):
X, Y and Z form the vertices of a triangle with area 59.7cm2. If XZ = 21.5cm and XY = 13.5cm, work out the acute angle ∠YXZ. Round to 1 DP.
Answer: The acute angle ∠YXZ = 24.3°.
Step-by-step explanation:
If in triangle ABC, C is the angle included between sides a and b then
Area of triangle = [tex]\dfrac12a\cdot b\cdot sin C[/tex]
here, XZ = 21.5cm and XY = 13.5cm are sides that includes acute angle ∠YXZ..
Area of a triangle = 59.7cm²
then, as per given, we have
[tex]59.7=\dfrac12(21.5)(13.5)\ \sin X\\\\\Rightarrow\ 59.7=145.125\ \sin X\\\\\Rightarrow\ \sin X = \dfrac{59.7}{145.125}\\\\\Rightarrow\ \sin X =0.41137\\\\\Rightarrow\ X = \sin ^{-1}(0.41137)\approx24.3^{\circ}[/tex]
Hence, the acute angle ∠YXZ = 24.3°.
Find the sum by first finding the equivalent fractions so both of the fractions have common
denominators.
Answer:
3x3/8x2 = 9/16
9/16+7/16 = 16/16
=1
What is the surface area of the cone in terms of pi
15 m 8 m
Answer:
Multiply po ba yan? Or hindi po?
Basahin niyo po yung comment ko hehehe
PLZ HELP ME I NEED HELP ASAP
Answer:
75 I hope this helped and brainliest please!
Step-by-step explanation:
The equation for surface area for a square pyramid is A=a squared + 2a times the square root of (a squared over 4) + height squared. Since everything is 5 yd, the answer is 75.
Other option
B: 74.9
C: 15.1
D: 15.7
Step-by-step explanation:
cosine of B = adjacent/hypot
to find hypotenuse use a^2+b^2 = c^2
which is 5 (it's a 3,4,5 triangle so it's easy)
Cosine B= 4/5
A line that intersects a circle in exactly one point.
a. secant
b. tangent
c. segment of a circle
d. sector of a circle
YEAR 9 MATHEMATUCS ALGEBRA
Answer:
Your answer is :
B. 6a^2 + 3ab
Markn my answer as brainlist . Follow me for more answer.
Step-by-step explanation:
Use the slope formula to find the slope between the given two points.
(-4, -1) and (-2, -5)
Answer:
y2 -y1 over x2 - x1
Step-by-step explanation: plz mark brainliest
A car travels 45 miles on one gallon of gas.The car uses 10 gallons of gas.How many miles does it travel
Answer:
69
Step-by-step explanation:
A car travels 45 miles on one gallon of gas.The car uses 10 gallons of gas.How many miles does it travel
Answer:
it travels 450 miles on 10 gallons of gas.
Step-by-step explanation: Can I get the brainliest answer if it's correct.
Cand someone please help me with this assignment!!!
Answer:
1. 3
2. 4
3. 2
4. 1
5. 1
7. 3
8. 10?
thats all i know because thats my answers hope it helps
(Easy) PLEASE HELP! I REALLY NEED TO GET THESE QUESTIONS RIGHT!
1. For the given equation, find the value of M when x=5. x + 3M = 14
2. What is the standard form for an exponential equation? Explain how you know if an exponential equation show’s growth or decay
What is an equation of the line that passes through the point (- 7, 0) and is parallel to the line x + y = 1
Answer:
y = -x - 7
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is x + y = 1.
First, let's put this into standard form.
x + y = 1
y = -x + 1
Now we have an equation in standard form. Its slope is -1. A line parallel to this one will also have a slope of -1.
Plug this value (-1) into your standard point-slope equation of y = mx + b.
y = -x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-7, 0). Plug in the x and y values into the x and y of the standard equation.
0 = -1(-7) + b
To find b, multiply the slope and the input of x (-7)
0 = 7 + b
Now, subtract 7 from both sides to isolate b.
-7 = b
Plug this into your standard equation.
y = -x - 7
This equation is parallel to your given equation (y = -x + 1) and contains point (-7, 0)
Hope this helps!
Help me please answer thanks
a student has a savings account with $475 in in it. She deposits $125 of her paycheck into the account every week. Her goal is to save 7,000 for college. How long will it take her to reach her goal of $7000?
Answer:
52.2 weeks
Step-by-step explanation:
7000 - 475 = 6,525
6525 ÷ 125 = 52.2
Answer:
It will take her 53 weeks to get her goal of 7,000$
Step-by-step explanation:
I subtracted 475 from 7,000 to see how much she needed to save for. I got 6525. I multiplied 125 times 52 and got 6500. To get to her goal she needs 25 more dollars so, she'll have to work another week to get to that goal.
:)
I’m confused about this problem
x= arctan (114/180)
=32.34744..
rounded to the nearest tenth =32.3
Step-by-step explanation:
Which graph represents an exponential growth function?
Answer:
Graph 1 or A
Step-by-step explanation:
The graph is gradually getting bigger as it starts at the left (0,-10) and gets bigger and bigger until it hits the end of the chart, increasing endlessly. That is exponential growth.
The cost of 9 scarves is $56.25. What is the unit price?
Answer:
6.25
Step-by-step explanation:
Diane looked out the window in the store parking lot and said, “There are 13 motorcycles and cars in the lot.” Steve looked out the window and said, “I see 42 wheels.”
Question: How many motorcycles and how many cars are in the parking lot?
Answer:
There are 5 motorcycles and 8 cars in the parking lot.
Step-by-step explanation:
Set variables X to represent the number of cars and Y to represent the number of motorcycles. You will get the following equations:
X + Y = 13 (Total number of motorcycles and cars)
4X + 2Y = 42 (Total number of wheels)
Combine the two equations together and solve for Y and X
4(13 - Y) + 2Y = 42 note: X = 13 - Y
52 - 4Y + 2Y = 42
-2Y = -10
Y = 5
X + 5 = 13
X = 8
Need help ASAP
48 ÷ 2 (9 + 3) = ?
Answer:
I think the answer is 288
Step-by-step explanation:
I think this because 48/2=24 and 9+3=12 (parentheses means multiply) 24x12=288
Find the 11th term of the geometric sequence 10,-40,160, ...
Answer: The 11th term is 6144
Step-by-step explanation: luv ya boo thang
1)y=4
2)y=4x
3)y=4x+4
4)x=4
Answer:
I think number letter shape 14
Answer:
I am pretty sure that the answer is y=4x
Im giving brainiest to the person who answers it first. Thank you!
Answer: Oscer
Step-by-step explanation:
Evaluate the expression
27²
⁻⁻⁻⁻
27^4/3
Answer:
The answer is 9
Step-by-step explanation:
27^2 =729
729/27^4/3
Factor the GCF: 6x^2 + 3x + 9 *
Answer:
3(2x² + x + 3)
Step-by-step explanation:
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the sum of the three terms consecutive terms of an ap is -6 and the product is 64, find the terms. using a, a + d, a + 2d
Answer:
-8, -2 and 4
Step-by-step explanation:
Let the terms of the AP be a-d, a and a+d
If the sum is 6, then;
a-d+a+a+d = -6
3a = -6
a = -6/3
a = -2
Hence the first term is 6
If the product is 64
(a-d)(a)(a+d) = 64
-2(a²-d²) = 64
-2(4-d²) = 64
4-d² = -64/2
4-d² = -32
-d² = -32-4
-d² = -36
d² = 36
d = 6 or -6
The first term is a-d = -2-6 = -8
second term is a = -2
third term is a+d = -2+6 = 4
Hence the required AP is -8, -2 and 4
What can be concluded if ∠EJS and ∠SJV form a linear pair?
Answer:
They are supplementary.
Step-by-step explanation:
A linear pair consists of two opposite angles whose non-common sides create a straight line. If a linear pair consists of two angles, then they are supplementary
