Answer: 9/80
Step-by-step explanation:
1/8 = 10/80
1/10 = 8/80
9/80 is fraction between 1/8 and 1/10
Have A Good Day :)
5. An art teacher mixed 3 cups of blue paint with 2 cups of red
paint to make some purple paint. How many cups of purple paint did
the art teacher make?
A) 62 cups
12
C) 5-
51712 cups
B) 5-½ cups
D) 672 cups
Answer: C - 5 cups
Step-by-step explanation:
Hello! The art teacher mixes 3 cups of blue paint with 2 cups of red paint. Since the art teacher combines the two, you have to add the two. 3 + 2 = 5, which should be your answer. Hope this helps!
in an elcetion there four candidates,j k l and m. teri is drawing a pie chart to show the results. the sectors for j and k have been drawn. twice as many people votes for l as voted for m. a) work out th angle that needs to be used to draw sector l b) altogether, 15 840 people voted. how many voted for j
The angle that needs to be used to draw the sector for L will be 60°. Then the number of people who voted for J will be 5,280.
What is the pie chart?A circular data visual with slices illustrating numerical proportions is called a pie chart. Each slice's angle in a pie chart corresponds to the material it represents.
In an election there were four candidates, J, K, L, and M. Teri is drawing a pie chart to show the results. The sectors for J and K have been drawn. Twice as many people voted for L as voted for M.
Let 'x' be the number of people who voted for L and M. Then the number of people who voted for J and K will be 2x.
The angle that needs to be used to draw the sector for L will be given as,
⇒ 360° × [x / (2x + 2x + x + x)]
⇒ 360° × [x / 6x]
⇒ 360° × 1/6
⇒ 60°
Altogether, 15,840 people voted. Then the number of people who voted for J will be given as,
⇒ [(2x) / (2x + 2x + x + x)] × 15,840
⇒ (1/3) × 15,840
⇒ 5,280
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assume a member is selected at random from the population represented by the graph. find the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
Remember that
z =(x - μ)/σ
where
μ=509
σ=121
so
Find out the value of Z for x=200
Z =(200 - 509)/121
Z=-2.5537
Find out the value of Z for x=450
Z=(450-509)/121
Z=-0.4876
Hence, 0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
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The x and y -intercepts of a line are -5/3 and 3/5 respectively. What is its equation?
The equation of the line whose x and y -intercepts are -5/3 and 3/5 respectively is [tex]9x - 25y + 15 = 0\\[/tex] .
Given,
The x-intercept of a line = -5/3
The y-intercept of a line = 3/5
by substituting values in the intercept form of a line:
[tex]-\frac{3x}{5} + \frac{5y}{3} = 1\\[/tex]
On multiplying the equation by 15 both L.H.S. & R.H.S.
[tex]-9x + 25y = 15[/tex]
⇒ [tex]9x - 25y + 15 = 0\\[/tex]
Therefore, the Equation of line is [tex]9x - 25y + 15 = 0\\[/tex] .
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1
Which of the following lists the terms in
x^2-7x + 11?
A. x, 7, 11
B. x², -7x, 11
C. x, -7x, 7, 11
D. x, x², 7, -7x, 11
The equation is x² - 7x+11 is in form of quadratic equation ax²+bx+c where a = x² , b = -7 and c = 11 .
Option B is correct.
How do quadratic equations work?Quadratic equations are second-degree algebraic expressions with the form ax² + bx + c = 0. The word "quadratic" comes from the word "quad," which means square. To put it another way, an "equation of degree 2" is a quadratic equation. Numerous situations call for the use of a quadratic equation.
Evaluating :Factoring x²-7x+11
The first term is, x² its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is 11
x² - 7x + 11 = 0
Why do we use quadratic equations?When two things are multiplied together and both depend on the same variable, quadratic equations are frequently used. A quadratic equation is used, for instance, when working with area when both dimensions are written in terms of the same variable.
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|x+3|=7
solve
pls show work
Answer: x=4
Step-by-step explanation:
Firstly, x+3 is in absolute value and absolute value basically turns that into positive, which brings us to x+3=7. Now, use your basic algebra skills to subtract 3 form both sides and get x=4. Hope this helps!
Answer:
Two roots: -10 and 4
Step-by-step explanation:
Since the expression inside the modular brackets can be positive or negative, the equation can have two different roots. And it is solved for the positive and negative options.
Positive option:
x+3=7
x=7-3
x=4
Negative option:
x+3=-7
x=-7-3
x=-10
please explain what comparison you can state about the two angles and explain how you can draw that conclusion
The conclusion about angles B and C is that the angles are equal angles
How to determine the true statement?
The given parameters are:
Angle A and Angle B are supplements
Angle A and Angle C are supplements
Supplementary angles add up to 180 degrees.
This means that
A + B = 180
A + C = 180
Subtract the two equations
So, we have
A - A + B - C = 180- 180
Evaluate the like terms
So, we have
B - C = 0
Add C to both sides
B = C
Hence, both angles are congruent angles
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the three interior angles of a triangle measure x°, (x+5)°, and (x+25)°, which is the measure of the three angles
* 45°
* 65°
* 70°
* 50°
Answer:
*50
Step-by-step explanation:
Sum of the interior angle
(n - 2) 180
From the question n is 3.
=(3 - 2) 180
=(1) 180
=180
The value of x
x + (x + 5) + (x + 25) 180
=x + x + x + 5 + 25 = 180
=3x + 30 = 180
=3x = 180 - 30
=3x = 150
=3x/3 = 150/3
x = 50
Therefore the value of x is 50.
rewrite 9x2 + 3xy + 15x + 5y in factored form. (3x + 3)(5x + y) (3x + 5)(3x + y) (3x + 5y)(3x + 1) (3x + y)(5x + 3)
The given equation 9x2 + 3xy + 15x + 5y in factored form is[tex](3 x+y)(3 x+5)$$[/tex]
What is factored form?The factored form of a quadratic expression is one in which the quadratic expression is the product of two factors, each of which is a linear expression. By extending it, which entails multiplying out the factors, a factored expression can be restated in standard form. Y=12(x-6)(x+2) is an illustration of a factored quadratic function. The graph's x-intercepts and vertex can both be determined by analyzing this form. The four primary methods of factoring are the Grouping method, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factor (GCF).
Factor [tex]$9 x^2+3 x y+15 x+5 y:[/tex]
Steps
[tex]& 9 x^2+3 x y+15 x+5 y \\[/tex]
[tex]& =\left(9 x^2+3 x y\right)+(15 x+5 y)[/tex]
Factor out 3 x from [tex]$9 x^2+3 x y: \quad 3 x(3 x+y)$[/tex]
Factor out 5 from[tex]$15 x+5 y: \quad 5(3 x+y)$[/tex]
[tex]$$=3 x(3 x+y)+5(3 x+y)$$[/tex]
Factor out common term[tex]$3 x+y$[/tex]
[tex]$$=(3 x+y)(3 x+5)$$[/tex]
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Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.
The categories include,
8th grade: left-skewed unimodal
Unimodal and symmetric birth weight
Computer count is unimodal and skewed to the right.
Bimodal adult weight distribution
Describe the histogram?A graph called a histogram shows the frequency distribution of a few data points for a single variable. Data is frequently divided into a number of "bins" or "range groups" by histograms, which count the number of data points in each bin.
While bar charts show categorical factors, histograms display numerical or quantitative data. In most situations, a histogram's numerical data will be continuous (having infinite values). To attempt to plot a continuous variable's possible values on an axis would be absurd.
Based on the frequency distribution, there are four different types of histograms.
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The complete question is: Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.
Draw rectangle HIJK, if HI = 3x + 7 and JK = 6x − 11,
find the value of x.
pls i need it
Answer:
x = 6
Step-by-step explanation:
Vertices of a rectangle are normally listed so that adjacent vertices are connected by edges. Therefore, the edges of rectangle HIJK are HI, IJ, JK and KH.
As the opposite sides of a rectangle are congruent:
HI = JK and IJ = KHTherefore, to find the value of x, set the given expressions for HI and JK equal to each other and solve for x:
[tex]\implies \sf HI=JK[/tex]
[tex]\implies 3x+7=6x-11[/tex]
[tex]\implies 3x+7-7=6x-11-7[/tex]
[tex]\implies 3x=6x-18[/tex]
[tex]\implies 3x-6x=6x-18-6x[/tex]
[tex]\implies -3x=-18[/tex]
[tex]\implies -3x \div -3=-18 \div -3[/tex]
[tex]\implies x=6[/tex]
30 divided by 0.25?????????????????? I need step by step explanation!!!!
Answer:
120
Step-by-step explanation:
This is simply because 0.25 is 1/4 and 30 ÷ 1/4 is the same as 30 × 4/1 which equals to 120
Answer:
120
Step-by-step explanation:
multiply 100 in the numerator and denominator to remove the decimal point.2
30×100/0.25×100
=3000/25
=120
What is a good claim for this question?
Is democracy the best form of government
Answer:
Democracy is the best form of government because it promotes equality and representation of all citizens, protects individual rights and freedoms, and encourages participation and accountability in the political process.
Which expression shows the first step in evaluating
2+7.12-3²?
6
A 2+84-3²
6
B 9.12-3²
C 2+7.122
1.12-9
6
D 2+7.2-3²
The first step in evaluating 2+7. 12/6-3² is to substitute the values for the numbers and calculate the sum of 2+7, which is 9.
What is evaluating?Evaluating is the process of making judgments about something based on a set of criteria. It involves analyzing and assessing a subject and making a determination of its value or worth. This can be done for a variety of things, such as an essay, a project, an individual or group, or a product. Evaluation is a crucial part of the decision-making process and involves a careful consideration of all relevant information and factors. It helps to identify strengths and weaknesses, and determine the effectiveness of something. Evaluating is also used to measure performance, identify areas for improvement, and make comparisons.
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let $x$ be a real number selected uniformly at random between 100 and 200. if $\lfloor \sqrt{x} \rfloor
The value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.
Let x be the random variable denoting the real number selected uniformly at random between 100 and 200.
The square root of [tex]$X$, $\sqrt{X}$,[/tex] will be a real number between 10 and 14. The floor function, [tex]$\lfloor \sqrt{X} \rfloor$[/tex] will take the integer less than or equal to[tex]$\sqrt{X}$.[/tex]This means that the value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.
For example, if [tex]$X = 150$[/tex], then [tex]$\sqrt{X} = 12.25$[/tex], so [tex]$\lfloor \sqrt{X} \rfloor = 12$[/tex]
In summary, for any real number selected uniformly at random between 100 and 200, the value of[tex]$\lfloor \sqrt{X} \rfloor$[/tex] is any number between 10 and 13.
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assume the following data for a country: total population, 500; population under 16 years of age or institutionalized 120; not in labor force 150 (besides under 16); unemployed 23; part-time workers looking for full-time jobs 10.
Given:
Total Population = 500 millions
Population Under 16 Years of Age or Institutionalized = 120 millions
Not in Labor Force = 150 millions
Unemployed = 23 millions
Now,
A) Labor force
= Total population – Population under 16 years of age – Not in labor force
= 500 – 120 – 150
= 230 millions
B) Unemployment rate [tex]$=\frac{\text { Unemployment }}{\text { Labor force }} \times 100 \%$[/tex]
or
Unemployment rate [tex]$=\frac{23 \text { million }}{230 \text { million }} \times 100 \%$[/tex]
or
Unemployment rate [tex]$=10 \%$[/tex]
The complete question is,
Assume the following data for a country:
Category Number of People (in Millions)
Total Population 500
Population Under 16 Years of Age or Institutionalized 120
Not in Labor Force 150
Unemployed 23
Part-Time Workers Looking for Full-Time Jobs 10
A) What is the size of the labor force (in millions)?
B) What is the official unemployment rate (in percentage)?
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Lizzy made 10 cups of strawberry jam and divided the jam equally among 6 containers. How much jam went into each container?
Answer:
1 2/3 went in each container
Step-by-step explanation:
10 divided by 6 is 1.666666666677777777777 which equals to 1 2/3 multiply it by 6 and you will get 10.
A rectangular field measures 63.9m by 104.6metres find the minimum number of poles to be Erected for fencing if they are to be at most 2.4meters apart.
71 poles are needed to fence the rectangular field.
What are the dimensions of the rectangle?
A rectangle is a two-dimensional shape with four sides that has opposite sides that are parallel and equal in length. The length and width of a rectangle are its dimensions. The sides that are equal in length are called the "long sides" or "length," and the sides that are shorter are called the "short sides" or "width."
The total length of the fence required to enclose the rectangular field is the sum of the lengths of all four sides. To find this, we multiply the length and width of the field and then add twice:
Total length = 2 * (63.9m + 104.6m) = 2 * 168.5m
Next, we need to determine the number of poles required to fence the rectangular field. To do this, we divide the total length by the maximum distance between poles (2.4m):
Number of poles = Total length / 2.4m
= 168.5m / 2.4m
= 70.21 poles
Since we can't have a fractional number of poles, we round up to the nearest whole number. This means that we need at least 71 poles to fence the rectangular field.
Hence 71 poles are needed to fence the rectangular field.
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PLEASE HELP ME WITH THIS
statistics math
Make a Mosaic plot
(Image above)
I’ll give you brainlist answer
The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.
What is percentage?A percentage is a number or ratio in mathematics that represents a fraction of 100. It is one of several methods for representing a dimensionless relationship between two numbers; others include ratios, fractions, and decimal.
The symbol "%" written after a number is commonly used to represent percentages. They can also be indicated by adding "percent" or "pct" to the end of the number. 35%, for example, is represented by the decimal 0.35, as well as the fractions 35/100 and 7/20.
Total boys = 23 + 40 + 15
= 78
Win percentage in basket ball = 23/78 × 100
= 29.49%
Win percentage in baseball = 40/78 × 100
= 51.28%
Win percentage in fencing = 15/78 × 100
= 19.23%
Total girls = 18 + 10 + 25
= 53
Win percentage in basket ball = 18/53 × 100
= 33.96%
Win percentage in baseball = 10/53 × 100
= 18.87%
Win percentage in fencing = 25/53 × 100
= 47.17%
Thus, The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.
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The distanse between Toronto and sudbury is 418km. Terry leaves Sudbury on his motocycle and drives 310km towards Toronto. Damon leaves Toronto at the same time on his motocycle and drives 303km toward Sudbury. How far apart are Terry and Damon?
Using mathematical operations, the distance that differentiates Terry and Damon is 7 kilometers.
What are mathematical operations?Mathematical operations are the computation of values using mathematical operands (÷, ×, +, -, etc), and mathematical operators like addition, subtraction, division, and multiplication.
In this situation, we use the subtraction operation to determine the difference or the distance between Terry and Damon.
The total distance between Toronto and Sudbury = 418 km
The distance covered by Terry from Sudbury to Toronto = 310 km
The length yet to be covered by Terry = 108 km (418 - 310)
The distance covered by Damon from Toronto to Sudbury = 303 km
The length remaining for Damon = 115 km (418 - 303)
The distance apart between Damon and Terry = 7 km (115 - 108)
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it take nadia 4/9 h to complete her language arts homework and 2/9 h to complete her mathematic homework.Which takes longer? How much longer?
Mathematic homework takes longer. It takes 2/3 h longer than language arts homework. Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator.
Language arts homework: 4/9 h
Mathematic homework: 2/9 h
We can compare these two fractions by converting them to the same denominator.
Language arts homework: 4/9 h = 8/18 h
Mathematic homework: 2/9 h = 4/18 h
Mathematic homework takes 2/3 h longer than language arts homework.
Mathematic homework takes longer than language arts homework, by 2/3 h.
Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator. Language arts homework takes 4/9 h, or 8/18 h, while mathematic homework takes 2/9 h, or 4/18 h. Mathematic homework takes 2/3 h longer than language arts homework. This means that mathematic homework takes more time to complete than language arts homework, by 2/3 h.
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Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = sin(x), y = 0, 0 ≤ x ≤ ????; about y = −5
The upper limit of y is not given, the integral cannot be evaluated at this point.
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line can be determined by the following integral:
V = ∫-5^y [π(y-sin(x))^2]dx
The integral is set up by breaking the region up into slices that are perpendicular to the y-axis. The width of each slice is equal to dy and the height of each slice is equal to the area of the cross-section of the solid, namely π(y-sin(x))^2. The integral is then evaluated from the lower limit of y=-5 to the upper limit of y, which is determined by the equation of the given curve, y=sin(x). As the upper limit of y is not given, the integral cannot be evaluated at this point.
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(a) Express the general solution of the given system of equations in terms of real-valued functions. (b) Also draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as - 8?
the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.
Lx + My = N ---------(1)
Ax + By = C ---------(2)
System 2 :
(L - A)x + (M - B)y = N - C -------(3)
Lx + My = N ---------(4)
If we subtract equation (2) from equation (1),
(Lx + My) - (Ax + By) = N - C
Lx - Ax + My - By = N - C
(L - A)x + (M - B)y = N - C
Which is similar to equation (3) of the system 2.
And equation (1) of the system (1) is similar to the equation (4) of the system (2)
Therefore, equation (3) of the system 2 is the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.
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Ready
How do you find the distance between
the points shown?
Add the distance between
each point and the y-axis.
What is the distance between
point A and point B?
units
A(-8,-4)
B (2,-4)
Answer:
10 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
To find the distance between two points, substitute the given points into the distance formula and solve for d.
Given points:
A (-8, -4)B (2, -4)[tex]\begin{aligned}\implies d&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-8))^2+(-4-(-4))^2}\\&=\sqrt{(10)^2+(0)^2}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
However, as the y-values of the two given points are the same, we can simply find the difference between the x-values of the two points to find the distance between point A and B:
[tex]\begin{aligned}\implies \textsf{Distance}&=x_B-x_A\\&=2-(-8)\\&=2+8\\&=10\end{aligned}[/tex]
Therefore, the distance between point A and point B is:
10 unitsMs. Morales bought the kiddie pool shown below for her children. pleas help thank you
A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
Responses
A)5,832π in.3
B) 6,561π in.3
C) 7,776π in.3
D) 8,748π in.3
The water Ms. Morales put in the pool in terms of π is [tex]\pi[/tex]6561inch^3
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given;
Diameter= 54 in.
Height of pool= 12ft
Now,
3/4 th height of pool;
3/4 x 12= 9inch
Volume= [tex]\pi r^{2}h[/tex]
=[tex]\pi[/tex]27x27x9
=[tex]\pi[/tex]6561inch^3
Therefore, the volume of pool will be [tex]\pi[/tex]6561inch^3
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Lines L and M are perpendicular to each other. Line L has an undefined slope. Find the possible equation of line M.
y=7 is One of line M's potential equations.
Let L and M be two lines that are perpendicular to each other. Slope of line is given by m=x 2 −x 1/ y 2 −y 1
If the denominator is zero, or if the value of the x-coordinate is the same at all points, the value of m is undefined. Every point lying on L has the same value of the x-coordinate because L has an undefined slope.
L is a vertical line because it is parallel to the Y-axis.
Lines that are vertical and horizontal are perpendicular to one another.
∴ Line M will be parallel to the X-axis since it is perpendicular to line L.
Every point located on M will have a constant y-coordinate.
∴ m=0 for M.
Thus, y=7 is one of line M's potential equations.
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table values for the equation
xy=5
The table of values for the equation xy =5 are
x y
5 1
10 1/2
15 1/3
20 1/4
25 1/5
What is table of values?The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can use this pattern to forecast things.
In the problem, the equation to derive the table of value is xy = 5, this is re written to be y = 5/x
The values of y are solved as follows
For x = 5, y = 5/5 = 1
For x = 10, y = 5/10 = 1/2
For x = 15, y = 5/15 = 1/3
For x = 20, y = 5/20 = 1/4
For x = 25, y = 5/25 = 1/5
Table of values
x y
5 1
10 1/2
15 1/3
20 1/4
25 1/5
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a cube has edge length 2. suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. then find the percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed.
The total surface area is 28 square units.
Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.
The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.
This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.
Therefore, The total surface area is 28 square units.
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next piece of fruit out of the bag will be an apple is ²/₃.
What is the probability?The probability is the chance that an expected outcome occurs out of many possible outcomes.
Probability is a fractional value that is obtained as the quotient of the expected outcome over the total events.
The number of apples = 4
The number of peaches = 3
The number of plums = 2
Total number = 9
The number of fruits taken out = 3 (2 plumbs and 1 peach)
The remaining fruits in the grocery bag:
The number of apples = 4
The number of peaches = 2 (3 - 1)
The number of plums = 0 (2 - 2)
Total number = 6
The probability of picking an apple out of the remaining fruits = 4/6 = 2/3
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(a) If you invest Po dollars at 7% annual interest and the future value is computed by continuous com- pounding, how long will it take for your money to double?
(b) Suppose you invest Po dollars at r% annual interest and the future value is computed by continuous compounding. If you want the value of the account to double in 2 years, what is the required interest rate?
(c)A rule of thumb used by many people to determine the length of time to double an investment is the rule of 70. The rule says it takes about t = 70/r years to double the investment. Graphically compare this rule to the one isolated in part b. of this problem.
(a) It will take approx 10.2 years to double your principal at 7% interest.
(b) The required rate of interest to double our income in 2 years is approx 44%
(a) Given,
Annual rate of interest = 7%
Let the principal be [tex]x[/tex].
Formulae for compound interest :
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Substituting the value of [tex]P , r , n[/tex] in above formulae.
[tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{0.07}{1})^{1t}\\\\2 = 1.07^{t} \\\\t=\frac{ln(2)}{ln(1.07)\\}\\\\t = 10.244768[/tex]
Therefore, it took approx. 10.2 years to double your principal at 7% interest.
(b) Given,
The annual rate of interest = [tex]r[/tex]%
Let the principal be [tex]x[/tex].
Formulae for compound interest :
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
we want our money to double in 2 years
[tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{r}{1})^{2}\\\\2 = (1+r)^{2} \\\\\sqrt{2} = 1 + r\\\\r=0.44[/tex]
Therefore, the required Rate of interest is approx 44%.
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