It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year
What is Simple InterestSimple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.
The formula of simple interest is given as;
A = P(1 + rt)
where;
A = Simple InterestP = principalr = ratet = time period.In this problem, we have to find the rate first.
The investment doubles after 7 years.
A = p(1 + rt)
2 = 1(1 + r * 7)
2 = (1 + 7r)
2 = 1 + 7r
7r = 2 - 1
7r = 1
r = 1 / 7
r = 0.142
r = 14.2%
The rate is 14.2 %
Now, we can proceed to determine how many years it will take to reach a value of 1000000
Using simple interest formula again;
A = P(1 + rt)
100000 = 1500(1 + 0.142 * t)
1000000 = 1500(1 + 0.142t)
t = 4687.8 years
It will take approximately 4687.8 years
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A survey found the following number of pets in different households.
4, 1, 0, 2, 1, 3, 1
What is the mean absolute deviation for the number of pets?
Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.
Here,
Given:
Mean = 2
Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.
We can determine that at least
100 (1-1k2)% = 100 (1-1/4)% = 75%
is within 2 standard deviations of the mean using Chebyshev's Rule with
k = 2.
The percentage times the sample size yields the equivalent number of households:
=> 75% x 40 = 30
Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
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What will be the mirror image of − 3 − 4 in y-axis?
A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the total area of the two bases
If the Cylinder's height equals to the diameter of its base , then the fraction of the total surface area of the cylinder to the total surface area of the two bases is 1/3 .
The curved surface area of the cylinder with height "h" and radius "r" is written as ⇒ [tex]2\pi rh[/tex] ;
the area of the top and bottom of the cylinder is ⇒ [tex]\pi r^{2} + \pi r^{2}[/tex] = [tex]2\pi r^{2}[/tex] ;
the total surface area of the cylinder will be ⇒ [tex]2\pi rh[/tex] [tex]+2\pi r^{2}[/tex] ....equation(1)
it is given that the height of cylinder is equal to the diameter of the base ,
that means ; [tex]h = 2r[/tex]
Substituting the value [tex]h = 2r[/tex] in the equation(1) ,
we get ,
total surface area of cylinder = [tex]4\pi r^{2} +2\pi r^{2}[/tex] = [tex]6\pi r^{2}[/tex]
So , the required fraction is = [tex]\frac{2\pi r^{2} }{6\pi r^{2} }[/tex] ,
On simplifying ,
we get ,
= [tex]\frac{1}{3}[/tex] .
Therefore , the fraction of two bases to the total surface area is [tex]\frac{1}{3}[/tex] .
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The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?
The side length of the triangle are
33 feet55 feet66 feetHow to find the side length of the triangleA triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is
= a + b + c
where
a, b, and c are the dimensions of the side length of the triangle:
Using the values given in the problem we have
let the ratio be a multiple of x such that
154 = 3x + 5x + 6x
154 = 14x
x = 11
a = 3 * 11 = 33 feet
b = 5 * 11 = 55 feet
c = 6 * 11= 66 feet
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Forming Equations with a given variable
1. The ages of three cats are and. Their total age is
21. Determine.
The value of {a} in the given modelled statement equation is 5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that the ages of three cats are (a) , (a + 4) and (2a - 3). Their total age is 21.
We can model the given equation is -
(a) + (a + 4) + (2a - 3) = 21
a + a + 4 + 2a - 3 = 21
4a + 1 = 21
4a = 20
a = 5
Therefore, the value of {a} in the given modelled statement equation is 5.
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{
Complete question is given below -
The ages of three cats are a, a+4 and 2a-3. Their total age is 21. Determine a.
}
I NEED THIS ASAP ILL GIVE 100 POINTS
1. Gas stations A. B. C, and G are located
along a straight lighway.
Station B is between stations: A
and c The distance frim station A to
station C is 22 miles. BC is 5 miles less than twice AB
Station C is between stations B and C. 4 miles from C. Find AC.
Answer: 3
Step-by-step explanation:You can't start at station 0 or 1, as there is not enough gas to travel to the next station.
Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 0. Your tank = 4 - 3 + 2 = 3
Travel to station 1. Your tank = 3 - 3 + 3 = 3
You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.
Therefore, you can't travel around the circuit once no matter where you start.
30PTS 30PTS don’t explain just answer
Answer:
y = 95°
Step-by-step explanation:
x + 120° = 180°
x = 180° - 120°
x = 60°
25° + y + x = 180°
25° + y + 60° = 180°
y + 85° = 180°
y = 180° - 85°
y = 95°
Given triangle ABC, which equation could be used to find the measure of ∠C?
a
tan m∠C = one half
b
sin m∠C = square root of 5 over 5
c
sin m∠C= square root of 5 over 2
d
tan m∠C = 2
The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2
What is an equation?An equation shows how two or more numbers and variables are related to each other.
On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.
The basic equations of the trigonometry ratios are
sinФ = opposite/hypotenuse; cosФ = adjacent/hypotenusetanФ = opposite/adjacentUsing the above as a guide, and the given triangle:
We have:
tan m∠C = opposite/adjacent
Substitute the known values in the above equation, so, we have the following representation
tan m∠C = 6/3
Evaluate
tan m∠C = 2
Hence, the true equation is (d) tan m∠C = 2
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A line passes through the points (–6,5) and (8,–2). What is its equation in point-slope form?
Answer:
y - (-2 ) = 1\2 ( x- 8)
Step-by-step explanation:
The point slope form equation is y-y₁=m(x-x₁)
( -6 , 5 ) ( 8 , -2 )
( x , y ) (x1 , y1 )
Firstly we need to find the slope
y1 - y -2 - 5
we can find the slope by this equation : ------------- = --------------
x1 - x 8 - (-6)
The slope is 1\2
What is the value calculator?
A value calculator is a tool used to help assess the worth of an asset or investment.
The value calculator is designed to help individuals and businesses determine whether an asset or investment is a good value. The calculator takes into account various types of data, such as the current market value, expected future value, and any associated risk factors.
This data is then used to calculate the present value, which is the amount of money an asset or investment is worth today. The calculator also takes into account inflation and other factors that could affect the current value of the asset or investment.
The value calculator can be used to help individuals and businesses make informed decisions about their financial investments.
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WILL MARK BRAINLIEST: A researcher wishes to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost in the autumn, 8 of the 50 plants in group 1 exhibited damage, and 18 of the 50 plants in group 2 showed damage. Why would the use of z-procedures be questionable value in this situation?
a. We don't know whether the 10% condition has been met.
b. We don't know the standard deviation for either population.
C. d.
Individual plants were not assigned randomly to the two experimental treatments.
We cannot be sure that the Normality condition has been met.
e.
We are collecting results on the entire population of plants, so statistical inference from samples is unnecessary.
Mrs. Katz’s science class has spherical beakers that measure 14 centimeters in diameter. If Mrs. Katz wants to fill the sphere, what is the volume in cubic centimeters that she can fit into the beaker? round your answer to the nearest hundredth.
The volume of the spherical beaker is 1436.76 cubic centimeters
How to determine volume a spherical beaker?
In order to determine the volume the spherical beaker, you need the formula for the volume of a sphere.
The volume of sphere is given by the formula:
Volume of sphere = 4/3 πr³
where r is the radius of the sphere
Since the spherical beaker that measure 14 centimeters in diameter. The radius of the beaker will be:
radius = 14/2 = 7 cm
Volume of the spherical beaker = 4/3 × π × 7³
Volume of the spherical beaker = 1436.76 cubic centimeters
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please help quickly
The polygons are similar. x = ___ Write your answer as a decimal
By using the fact that the two images are similar, we can write and solve a linear equation to get x = 3/2.
How to find the value of x?We know that the two figures are similar, then, if we take the quotient between the adjacent sides for both figures, these quotients should give the same value.
Thus, we can write the equation:
14/10 = (x + 9)/(x + 6)
Now we can solve that equation for x, if we multiply both sides by (x + 6) we will get:
(14/10)*(x + 6) = x + 9
Now we can multiply both sides by 10 to get:
14*(x + 6) = 10*(x + 9)
14x + 84 = 10x + 90
Now we can solve this linear equation for x.
14x - 10x = 90 - 84
4x = 6
x = 6/4
x = 3/2
That is the value of x.
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What is the segment partition formula?
The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints of the segment and the ratio of the desired point from the first endpoint.
The formula is:
Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))
Where x1 and y1 are the coordinates of the first endpoint, x2 and y2 are the coordinates of the second endpoint, and r is the ratio of the desired point from the first endpoint.
The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints and the ratio of the desired point from the first endpoint. The formula is given in the form of Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1)).
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2 + (4-3 (3-6) -4] +12=
Answer: 23
Step-by-step explanation:
Please tell me someone know I have to go back to school tomorrow
An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.
What is a reflection?In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By reflecting the given function across the across the y-axis (y = x), we have the following:
f(x) = x/3 - 6
g(x) = f(-x)
g(x) = -x/3 - 6.
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One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.
(Assume that the computers do not back up at the start of the 24-hour period.)
The number of times which the two computers back up at the same time in twenty four hours as required is; 144.
How many times does the computers back up at the same time in 24 hours?It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.
On this note, the least common multiple of both backup times represents when the two computers back up at the same time.
Hence, since the LCM of 5 and 2 is; 10.
It follows that the two computers back up at the same time after every ten minutes.
Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;
= ( 24 × 60 ) / 10
= 24 × 6
= 144 times.
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The cost to hire a tent consists of two parts. $c + $d per dayThe total cost for 4 days is $27. 10 and for 7 days is $34. 30. Write down two equations in c and d and solve them
The cost to hire a tent consists of a fixed cost of $17.50 and a variable cost of $2.40 per day.
Let's call the total cost of hiring a tent for 4 days as T4, and the total cost of hiring a tent for 7 days as T7.
The first equation is the cost for 4 days:
T4 = c + 4d
The second equation is the cost for 7 days:
T7 = c + 7d
We know the values of T4 and T7 from the problem statement:
T4 = $27.10 and T7 = $34.30
We can now use these two equations and their corresponding values to solve for c and d:
Substitute the value of T4 into the first equation:
$27.10 = c + 4d
Substitute the value of T7 into the second equation:
$34.30 = c + 7d
Now we have a system of two equations with two variables (c and d).
Subtract 4d from both sides of the first equation:
$27.10 - 4d = c
Subtract c from both sides of the second equation:
$34.30 - c = 7d
Now we can substitute the value from step 4 into step 5:
$34.30 - $27.10 + 4d = 7d
7d = $34.30 - $27.10 + 4d
3d = $7.20
d = $7.20 / 3 = $2.40
Now we have the value of d, we can substitute it back into the first equation to find the value of c:
$27.10 = c + 4d
$27.10 = c + 4($2.40)
$27.10 = c + $9.60
c = $27.10 - $9.60
c = $17.50
Therefore, c= $17.50 and d= $2.40
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(a) Write down the value of xº
Given that 2-3 x 2⁹ = 2n
(b) find the value of n
From the equation (2-3 x 2⁹ = 2n), the value of n is -767.
What is the equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.
The word equation and its cognates in various languages may have slightly different meanings. In mathematics, an equation is a formula that uses the equals sign to denote the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Given data :
2-3 x 2⁹ = 2n
= 2n = 2 - 3 .
= 3 . = 1536
= 2n = 2 - 1536
= 2n = -1534
Divide both sides by 2
= 2n/2
= -1534/2
n = -767
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Felix's dinner costs $16.49. Felix pays a $20 bill. About how much change did he receive? Show your work.
Answer: He received $3.51 in change.
Step-by-step explanation:
To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).
It will look like this:
$20.00 - $16.49 = $3.51
Answer:3 dollars and 51 cents
Step-by-step explanation:
A helicopter pad which is in the shape of a circle has a circumference of 62. 48 feet and a diameter of 24 feet. Which expression best represents the value of ?
The expression which represents the value of the area could be the six times the circumference of the circle.
What is area of circle ?
area of circle can be defined as the product of pi(3.14) and square of radius of the circle.
Given,
helicopter pad which is in the shape of a circle has a circumference 72.48
and the diameter of 24 feet.
radius = diameter/2
radius = 24/2
radius = 12
circumference of circle = 72.48
area of circle = π*r*r
area of circle = 22/7 * 12 * 12
area of circle = 452.5
area of circle is approximately 6 times the circumference of circle.
Hence , The expression which represents the value of the area could be the six times the circumference of the circle.
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plsss answer for brainliest
Answer:
answer is below
Step-by-step explanation:
1.
Two lines from right angles.
The lines are perpendicular
2.
x + 20 = 32
x =12
3.
You are a third year high school student.
You are a junior high school student.
4.
An angle measures 20°.
The angle is acute.
5.
A figure is square.
The figure is quadrilateral.
How do you find the dilation of a function?
Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. The scale factor is equal to the ratio of these distances.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A graph's form is altered by dilations, frequently leading to "movement" in the process. In the figure above, the green curve has been "transformed" into the red curve. It has been three times "dilated" (or stretched) horizontally. A dilatation is an axial stretching or contraction brought on by multiplication or division.
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There are 8 employees on The Game Shop's sales team.
Last month, they sold a total of g games. One of the
sales team members, Chris, sold 17 fewer games than
what the team averaged per employee.
How many games did Chris sell?
Write your answer as
an expression.
games
According to the solving the team average is g/17 and Chris sold (g/8) - 17 games.
What do you mean by average?The term "Average" refers to a value that should be used to describe the sample as a whole. The average is determined by dividing the total number of values in a set by the total number of values. also known as the arithmetic mean.
How do you calculate the mean?Average A collection of integers are added, their count is divided, and the sum is used to determine the arithmetic mean.
According to the given information:average game sold = g/8
since Chris sold 17 games less than average
hence, Chris sold games
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What is the slope of the linear regression prediction equation if a person with 12 years of schooling
On solving the provided question, we can say that the e slope of the linear regression prediction equation if a person with 12 years of schooling is 1.
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
the e slope of the linear regression prediction equation if a person with 12 years of schooling
a. 1(correct)
b. 12
c. 13
d. 1,500
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HELP THIS IS MY LAST PROBLEM
A store bought a set of speakers for $82.86
and sold it for $195.82. What was the markup percentage? Round your answer to the nearest tenth.
Answer:
142%
Step-by-step explanation:
How I got this solution is made it as a ratio, "82.86:195.82".
I then simplified the balance by dividing 82.86 into both sides.
It then equaled around 0.42 (or 42%). Including itself, it got a markup percentage of 142%
Please help!!!
if 7^9/7^n = 7^3 then n is ___?
Answer:
n= 6
Step-by-step explanation:
7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3
Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum fo a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72
Work out the value of Dylan's initial investment
The amount invested by Dylan will be £1200.
What is simple interest?Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.
Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.
The amount of money invested will be calculated as,
SI = ( P x R x T ) / 100
72 = ( P x 3 x 2 ) / 100
7200 = 6P
P = 7200 / 6
P = £1200
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convert the following decimals into mixed fraction. a) 4.444
Answer:
4444/1000
You take the number of decimal points and turn them into zeros for the denominator
Please just write the numerical value of the volume of the prism.
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the prism in the attached figure is calculated to be
672 m³
How to find the volume of the prismIn the given problem, the formula used for volume of prism is
= area of base * height
Assuming a triangular base
area of triangular base = 1/2 * base * height
where
base = 12 m
height = 14 m
area of triangular base = 1/2 * 12 * 14
area of triangular base = 84 m²
The volume of the prism with a triangular base
volume of the prism = area of triangular base * height
where
area of triangular base = 84 m²
height = 8 m
volume of the prism = 84 * 8
volume of the prism = 672 m³
The volume of the prism is solved to be 672 m³
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