The time needed to pay the compound interest of Rs 6,305 is given as follows:
3 years.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 40000, A(t) = 40000 + 6305 = 46305, n = 1, r = 0.05.
Hence the time is obtained as follows:
[tex]40000(1.05)^t = 46305[/tex]
[tex](1.05)^t = \frac{46305}{40000}[/tex]
[tex]t = \log{\left(\frac{46305}{40000}\right)}{\log{1.05}}[/tex]
t = 3 years.
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The price of a home is $170,000. The bank requires a 15% down payment. The buyer is offered two mortgage options: 15-year fixed at 10% or 30-year fixed at 10%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 15-year option? Use the following formula to determine the regular payment amount.
Answer:36000
Step-by-step explanation:
He saves 36000 dollars
A math quiz has 3 multiple choice questions and 2 true/false questions. Each multiple choice questions has 4 answer options: A, B, C, D.
Find the number of possible outcomes.
Answer:
The total number of possible outcomes for the math quiz is 16
Step-by-step explanation:
Can someone help me please
After using Gauss-Jordon elimination method, the solution for the system of equation is as follows;
[tex]\left[\begin{array}{cccc}1&0&0&-1\\0&1&0&-3\\0&0&1&-2\end{array}\right][/tex]
How do you find the solution for the system of equation using the elimination method by Gauss-Jordon?To solve the system of equation, its needs us to use the Gauss-Jordon elimination method. Therefore, the matrix
- 5 7 7 -30
1 -4 4 3
2 -4 6 -2 will be reduced to its echelon form as follows;
R₁ ÷ 5 R₂ - R₁ R₃ - 2× R₁
1 −1.4 −1.4 6 1 −1.4 −1.4 6 1 −1.4 −1.4 6
1 −4 4 3 0 2.6 5.4 -3 0 2.6 5.4 -3
2 −4 6 −2 2 −4 6 −2 0 −1.2 8.8 −14
R₂ ÷ -2.6 R₃ - 1.2 R₂
1 −1.4 −1.4 6 1 −1.4 −1.4 6
0 1 -2.077 1.154 0 1 -2.077 1.154
0 −1.2 8.8 −14 0 0 1 -2
R₁ - 1.4R₃ R₂ - 2.077R₃ R₁ - 1.4R₂
1 -1.4 0 3.2 1 -1.4 0 3.2 1 0 0 -1
0 1 -2.077 1.154 0 1 0 -3 0 1 0 -3
0 0 1 -2 0 0 1 -2 0 0 1 -2
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(When a side has a measurement that is a mixed number, what do you need to do to use it in the formula: area = length x width?)
The sides of the rectangle should be in improper fractions, to calculate the area.
When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.
Then, you put the result over the original denominator.
Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.
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Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
The remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] is
[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
To find the remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3),[/tex] we can use polynomial long division.
The dividend is[tex](10m^8 + 4m^6 + 10m^5)[/tex] and the divisor is [tex](2m^2 + 5m^6 + 4m^4 + 10m^3).[/tex]
Starting with the highest degree term, we divide ([tex]10m^8[/tex]) by ([tex]2m^2[/tex]) which gives us [tex]5m^6[/tex].
Next, we multiply the entire divisor [tex](2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] by [tex]5m^6[/tex], which gives us ([tex]10m^8 + 25m^{12} + 20m^{10} + 50m^9[/tex]).
We then subtract this product from the original dividend:
[tex](10m^8 + 4m^6 + 10m^5) - (10m^8 + 25m^{12} + 20m^{10} + 50m^9)[/tex] =[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
We repeat the process with the new dividend ([tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex]) and the divisor ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]).
Continuing the long division process, we eventually find the remainder to be: [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
Therefore, the remainder when dividing ([tex]10m^8 + 4m^6 + 10m^5[/tex]) by ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]) is [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex].
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Note the full question is:
Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
What is the reminder
a. If this trend continues, predict the percent of U.S.house- holds with an Internet subscription in 2025. graph it
b.Explain any issues with your answer to part c.
The requried, predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
To find the number of subscriptions in the year 2020, we need to find the value of y when x = 10 (since x is the number of years after 2010).
Substituting x = 10 into the equation y = 1.56x + 72.7, we get:
y = 1.56(10) + 72.7
y = 15.6 + 72.7
y = 88.3
Therefore, the predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.
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If Richard's monthly deposit fee is R69, 95 per R100 what would be the total bank charges for R4200?
Whats the probability either event will occur?
Answer: 0.68
Step-by-step explanation:
A researcher wants to know the mean weight of all garbage being discarded per household in Gallup, NM. A random sample of n = 9 households is selected and the garbage weighed. The following data is obtained: 10.8, 17.2, 23.1, 27.8, 27.9, 31.0, 33.3, 37.6, 44.5.
Find a) the sample mean________. b) the sample median ________. c) the sample mode ________. d. the sample standard deviation (hint: divide by n -1) __________e) the sample variance _________. f) the sample range ______
Operating at the 90% confidence level:
g) what is the Margin of Error E (show work)
h) Find the 90% confidence interval for the mean weight of all garbage discarded per household in Gallup, NM. (show work)
i) What is the probability that the true population mean lies outside the interval in h) ______.
Operating at the 98% Confidence Level
k) What is the Margin of Error E (show work)
m) Find a 98% confidence interval for the mean weight of all garbage discarded per household in Gallup, NM.
o)What is the probability that the true population mean lies outside the interval in m) _____
Answer: what subject, and i got you.
Step-by-step explanation:
HELP ME QUICK. paul is thinking of a number. ⅖ of this number is 14 what is the number??
Answer:
Step-by-step explanation:
If we know that 2/5 of the number is 14, 5/5 must be the answer Paul is thinking of.
= (14/2) x 5 <---- This is 1/5 of the number
= 35
∴, the number Paul is thinking of if 35
The triangular prism below has a height of 13.4 units3 and a volume of 536 units
Find the area of one of its bases.
Answer: 40
Step-by-step explanation:
5. Sketch rectangles with whole number dimension with perimeters that range from 12 to 16 units. a) For each perimeter, what are the dimensions of the rectangle that give the greatest area? b) For each perimeter, what are the dimensions of the rectangle that give the least area? 6. Draw a figure made from square tiles where adding an additional tile decreases the perimeter. 7. A student claims that perimeter is a 2-dimensional measure because one needs to know length and width (or base and height) in order to measure it. How would you respond to this student? 8. Compare a square, equilateral triangle, and circle that each have perimeter of 12 cm. Which has the greatest area? Which has the least area?
The solution to all parts are shown below.
a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.
For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.
For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.
For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.
For a perimeter of 16 units, the dimensions are 4 units by 4 units.
b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.
For a perimeter of 13 units, the dimensions are 1 unit by 6 units.
For a perimeter of 14 units, the dimensions are 2 units by 5 units.
For a perimeter of 15 units, the dimensions are 2 units by 6 units.
For a perimeter of 16 units, the dimensions are 2 units by 7 units.
6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.
If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.
7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.
8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.
To see this, we can use the formulas for the perimeter and area of each shape:
A square with a perimeter of 12 cm has side length 3 cm.Its area is (3 cm)² = 9 cm².
An equilateral triangle with a perimeter of 12 cm has side length 4 cm.Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.
Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².
A circle with a perimeter of 12 cm has circumference 12 cm.Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.
Thus, r = 6/(2π) cm, which is approximately 0.955 cm.
The area of the circle is πr², which is approximately 2.87 cm².
Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.
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Nam asked his mother's permission to go buy toys to give to Tuan's friend on the occasion of his birthday. Men buy two toys with list prices of VND 45,000 and VND 25,000 respectively and receive a 10% discount. how much does the male have to pay to buy those two toys?
Answer:
The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.
Step-by-step explanation:
The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.
Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.
Nam will have to pay VND 63,000 to buy the two toys after the discount.
Can someone please help me with this? I’ll give brainlist!!
Answer:
12) x = 6. 13) not tangent
Step-by-step explanation:
12) x² - 5 = 31 (since they are both tangents)
x² = 31 + 5 = 36
x = ±6
x = +6 (has to be positive since it's a length).
13) if it was tangent, angle BAC would be 90°.
that would also mean AB² = BC² - AC²
= 15² - 5²
= 225 - 25
= 200
AB = √200 ≠ 14.
Since the values are different, AB is not a tangent to the circle
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 58° and AB = 9.3.
Calculate the length of BC rounded to 3 SF.
Answer:
To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.
Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.
Using the sine function, we can find the length of BC:
sin(∠BCA) = BC / AB
Rearranging the formula, we have:
BC = AB * sin(∠BCA)
Substituting the given values:
BC = 9.3 * sin(32°)
Using a calculator or trigonometric table, we find:
BC ≈ 9.3 * 0.529 = 4.917
Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.
Step-by-step explanation:
Can you Please calculate this:
Answer:
14
Step-by-step explanation:
used a calculator to check the answer
determine unkown side length in a right triangle. round to nearest tenth.
side 1= 9
side 2= 3
Step-by-step explanation:
If side 1 and side 2 are LEGS of the triangle, then hypotenuse is found by
hyp^2 = 9^2 + 3^2 using pythagorean theorem
hyp^2 = 90
hyp = sqrt 90 = 3 sqt 10 =9.5 units
If hyp is 9 and 3 is one leg:
9^2 = 3^2 + L^2
L = 6 sqrt 2 =8.5 units
A line has a slope of 7 and includes the points (-5,-5) and (-3,w). What is the value of w?
The value of w is 9.
We can use the slope formula to find the value of w.
The slope formula is:
m =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
where m is the slope of the line and [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are two points on the line.
We know that the slope of the line is 7, and the two points on the line are (-5, -5) and (-3, w). So we can plug in these values into the slope formula and solve for w:
7 = (w - (-5)) / (-3 - (-5))
Simplifying the right-hand side, we get:
7 = (w + 5) / 2
Multiplying both sides by 2, we get:
14 = w + 5
Subtracting 5 from both sides, we get:
w = 9
Therefore, the value of w is 9.
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Annabel's water bottle holds 6 cups of water. How many fluid
ounces does it hold?
The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.
How to find the volume of water in fluid ounces?Annabel's water bottle holds 6 cups of water. Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:
Therefore,
1 cup = 8 fluid ounces
6 cups = ?
cross multiply
Hence,
number of fluid ounces of water the water bottle can hold = 8 × 6
number of fluid ounces of water the water bottle can hold = 48 fluid ounces.
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Tick the box to show where the hyphen is needed in the sentence below.
Answer:
I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?
For the following stock investment, find (a) the total
purchase price, (b) the total dividend amount, (c) the
capital gain or loss, (d) the total return, and (e) the
percentage return. Ignore broker and SEC fees.
(a) What is the total purchase price?
4
Number of shares
Purchase price per share
Dividend per share
Sale price per share
60
$40
$2
$87
Answer:
can you be more clear
Step-by-step explanation:
what exactly does question need
el area de la base de un cilindro es de 40 pi m2. expresa el volumen en funcion de la altura
The volume of the cylinder, when expressed as a function of the height of same cylinder, is V ( h ) = 40 h ft ³.
How to express the volume of the cylinder ?The volume V of a cylinder is given by the formula:
V = Area of the base of the cylinder x height of the cylinder
Given that the area of the base A is 40 ft², you can substitute this into the formula to express the volume as a function of height:
V ( h ) = 40 ft ² x h
V ( h ) = 40h ft ³
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Help pleaseee is just one problem
The matrices after the row operations are given as follows:
a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
How to obtain the resultant matrices?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]
When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.
Hence the resulting matrix after we multiply row 3 by 2 is given as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
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You roll a 6-sided die.
What is P(odd or less than 2)?
Answer:
50%.
Step-by-step explanation:
If the die is perfectly balanced, the probability of rolling an odd number is 3 out of 6, or 50%.
Which of the following algebraic steps will solve the equation 3x/4=7/3 what is the solution
The solution to the equation is x = 28/9
Given data ,
To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:
Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:
(4) (3x/4) = (4) (7/3)
3x = (4/1) (7/3)
Step 2:
Simplify the right side of the equation:
3x = 28/3
Step 3 :
Divide both sides of the equation by 3 to isolate x:
(1/3) (3x) = (1/3)(28/3)
x = (28/3) / 3
Step 4 :
Simplify the right side of the equation:
x = 28/9
Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9
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The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm.
The bank has found that for all personal checking accounts the mean of all the daily balances is $ 900 and the standard deviation is $175.
In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.
what the answer for this?
Please help me with these questions
The value of each angle 6x + 7 and 4x + 3 will be 55° and 35°, respectively.
Given that:
Angles, ∠1 = 6x + 7 and ∠2 = 4x + 3
Two angles are said to be complementary angles if their sum is 90 degrees.
The equation is given as,
∠1 + ∠2 = 90°
6x + 7 + 4x + 3 = 90°
10x + 10 = 90°
10x = 80°
x = 8
The value of each angle is calculated as,
∠1 = 6 * 8 + 7
∠1 = 55°
∠2 = 4 * 8 + 3
∠2 = 35°
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A company is making concrete blocks. The blocks are in the form of right trapezoidal prisms and have the dimensions shown. What is the volume of one block? Show your work
Please help I give 40 brainly
Answer:
9180 (cm³)
Step-by-step explanation:
area of cross-section (trapezium) = 0.5 X (12 + 22) X 9
= 0.5 X 34 X 9 = 153 cm²
then multiply that by the length (60)
153 X 60 = 9180 (cm³)
name the leading coefficient and degree of the polynomial 4xy^8
(a) The leading coefficient is 4
(b) The degree is 8
How to determine the leading coefficient and the degree of the expressionFrom the question, we have the following parameters that can be used in our computation:
4xy⁸
Consider an expression ax where the variable is x
The leading coefficient of the variable in the expression is a
Using the above as a guide, we have the following:
The leading coefficient is 4
Consider an expression axⁿ where the variable is x
The degree of the variable in the expression is n
Using the above as a guide, we have the following:
The degree is 8
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