After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.
What are equations?The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.
A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.
As in 3x + 5 = 15, for example.
Equations can be of many different types, such as linear, quadratic, cubic, and others.
So, we have the equation:
[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]
Now, solve the following equation as follows:
[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]
[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]
[tex]Inx+Inx^2 = In8^2[/tex]
[tex]In* (x*x^2) In64[/tex]
[tex]x^2 = 64 =4^3[/tex]
[tex]x=4[/tex]
Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.
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Correct question:
What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8
a x = 2
b x = 4
c x = 8
d x = 64
Springfield avenue is 3 miles long. there are 8 sets of stop signs along Springfield avenue. the stop signs are the same distance apart . how far apart are the stop signs
The distance between the stop signs is 0.375 miles or roughly 0.6 kilometers.
distance between stop signs = 3 miles / 8
= 0.375 miles
What is the distance?
While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."
Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
The scalar quantity known as distance measures "how much ground an object has traversed" while moving.
From the question:
We can use the following calculation to calculate the separation between the stop signs:
distance between stop signs = total distance/number of intervals
There are 8 spaces between the stop signs and a total distance of 3 miles in this instance. As a result, we can determine the separation between the stop signs as:
distance between stop signs = 3 miles / 8
= 0.375 miles
As a result, there are 0.375 miles (or 0.6 kilometers) between each stop sign.
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I need help solving theses questions
The value of x is 3 and the sides of given rectangle are 3,3,9,9.
What is Area of rectangle ?
area of rectangle can be defined as product of length and breadth.
From the given figure ,
it is given that ,
perimeter of rectangle = 24 cm
and the sides are ,
x,x,x+6,x+6
so we know that perimeter of rectangle = 2 (l+b)
that is,
24 = x+x+x+6+x+6
24 = 4x + 12
4x = 12
x = 3
Therefore, The value of x is 3 and the sides of given rectangle are 3,3,9,9.
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A plus advertising charges a fee of $24 plus $0. 10 per flyefr to print and delever flyers. Print and more charges $0. 25 per flyer. For how many flyers is the cost at a-plus advertising less than the cost of print andff more
The cost of A Plus Advertising will be less than the cost of Print and More if the number of flyers to be printed and delivered is greater than 160.
Let's assume that the number of flyers to be printed and delivered is "x".
The cost of A Plus Advertising can be represented as:
Cost_A = 0.10x + 24
The cost of Print and More can be represented as:
Cost_P = 0.25x
To find out for how many flyers the cost of A Plus Advertising is less than the cost of Print and More, we need to set up an inequality:
Cost_A < Cost_P
0.10x + 24 < 0.25x
Subtracting 0.10x from both sides, we get:
24 < 0.15x
Dividing both sides by 0.15, we get:
160 < x
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roshan and Isha share a reward of 250 rs. in the ratio 1:4. Find the amount shared by each of them. pls tell the answer. I will mark you as the brainlist
Answer: Roshan: 250/5 = 50 Rs.
Isha: 250 - 50 = 200 Rs.
Step-by-step explanation:
find the perimeter of the given circle
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.
Let r be the radius of the circle. The circumference of the circle will be given as,
C = 2πr units
The diameter of the circle is 28 cm. Then the radius is calculated as,
r = d / 2
r = 28 / 2
r = 14 cm
Then the circumference of the circle is given as,
C = 2 · π · 14
C = 28 × 3.14
C = 87.92 cm
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
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question in the photo please help me im begging lol
Water turning to blood will be the first plague that will be present.
What are plagues?Both humans as well as mammals can contract the plague. The protozoan parasite is the bacterium that causes it. The most common ways for humans to contract the plague are through handling a plague-infected animal or by getting bitten by a rodent bug that is carrying the disease.
The 10 plagues in the correct order are:
Water turning to bloodFrogsLiceFliesTerrible BoilsLivestock dyingHail & fireLocustsThree days of darknessDeath of the firstbornLearn more about plagues, here:
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In Exercises 3-6, find the indicated measure. Explain your reasoning. Show your work
The measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
What are similar triangles?Two triangles are similar if the ratio of their corresponding sides is same and their corresponding angles are equal.
Given are the triangles as shown in the image.
{ 1 } -
We can write -
GH/HJ = GK/KJ
GH/4.6 = 3.6/3.6
GH = 4.6
{ 2 } -
QT/TS = QR/RS
4.7/4.7 = QR/1.3
QR = 1.3
{ 3 } -
AD/DC = AB/BC
AD/AD = AB/BC
AB/BC = 1
5x/4x + 3 = 1
5x = 4x + 3
x = 3
AB = 15
{ 4 } -
UW/UV = DW/DV
7x + 13 = 9x + 1
3x = 12
x = 4
UW = 41
Therefore, the measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
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PLEASE HELP ASAP
Question 2(Multiple Choice Worth 2 points)
(Line of Fit LC)
A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 7 and 3 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 8 and 5 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 2 comma 5 and 4 comma 4
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 4.5 and 2 comma 4.5
The scatter plot indicates that the best graph with a line that fits the data is one with a line passing through approximately 2 comma 5 and 4 comma 4.
What is a scatter plot and how is it solved?Data visualisation that demonstrates the link between various variables is known as a scatter plot. Different data points are positioned between an x- and y-axis to display this data. Each of these data points appears to be "scattered" across the graph, which is how this kind of data visualisation gets its name.
This is because the main trend of the data, which seems to slope downwards, is captured by the line that passes through these places. The other lines don't seem to cover as many points or represent the data trend as effectively.
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The area of a dog kennel is 20 square feet. If the length of the kennel is 4 feet, what is the width of the kennel?
Answer:it would be 25
Step-by-step explanation:
18. Find m/BCA.
(9x + 1)
A
(5x + 12)
B
(10x-37)
C
Answer:
∠BCA 57 degrees
Step-by-step explanation:
∠ABC + (5x + 12) = 180
=> ∠ABC = 180 - (5x + 12)
∠BAC + (9x + 1) = 180
=> ∠BAC = 180 - (9x + 1)
∠BCA + (10x - 37) = 180
=> ∠BCA = 180 - (10x - 37)
∠ABC + ∠BAC + ∠BCA = 180
Substitute to find x
[180 - (5x + 12)] + [180 - (9x + 1)] + [180 - (10x - 37)] = 180
180 + 180 + 180 - 5x - 9x - 10x - 12 - 1 + 37 = 180
564 - 24x = 180
24x = 564 - 180
24x = 384
x = 384/24 = 16
Substitue x = 16
∠BCA = 180 - (10x - 37)
∠BCA = 180 - 10(16) + 37 = 57
Answer:
m∠BCA = 57°
Step-by-step explanation:
To find the measure of angle BCA we must first find the value of x.
The diagram gives expressions for the exterior angles of the triangle.
The exterior angles of a triangle sum to 360°. Therefore, to calculate the value of x, equate the sum of the exterior angles to 360° and solve for x.
⇒ (9x + 1)° + (5x + 12)° + (10x - 37)° = 360°
⇒ 9x + 1 + 5x + 12 + 10x - 37 = 360
⇒ 9x + 5x + 10x + 1 + 12 - 37 = 360
⇒ 24x - 24 = 360
⇒ 24x - 24 + 24 = 360 + 24
⇒ 24x = 384
⇒ 24x ÷ 24 = 384 ÷ 24
⇒ x = 16
Each interior and exterior angle of a triangle form a linear pair.
As the sum of angles of a linear pair is always equal to 180°, to find the measure of angle BCA, equate the sum of ∠BCA and its exterior angle to 180°:
⇒ (10x - 37)° + m∠BCA = 180°
Substitute the found value of x and solve for the angle:
⇒ (10(16) - 37)° + m∠BCA = 180°
⇒ (160 - 37)° + m∠BCA = 180°
⇒ 123° + m∠BCA = 180°
⇒ 123° + m∠BCA - 123° = 180° - 123°
⇒ m∠BCA = 57°
Therefore, the measure of angle BCA is 57°.
URGENT PLEASE HELP 30 POINTS!!!
Answer:
angle 1 will be 32
angle 2 will be 2
hope it helps u mark me BRAINLIST
64200x0.12 with work!
Answer: 7704
Step-by-step explanation:
( see image !)
There are 50 millipedes in an area of rainforest. The number of millipedes is expected to increase by 62% every year compared to the year before.
a) how many millipedes are expected to be in the area of rainforest in 5 years time ?
b) how many millipedes are expected to be in the area of rainforest in 20 years time ? Round your answers to the nearest 100.
There are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.
What is percentage growth rate?
The exponential function with a growth factor has a rate greater than 1
We can use the formula for exponential growth to answer this question:
P(t) = P₀(1 + r)ᵗ
where P₀ is the initial population, r is the annual growth rate as a decimal, t is the number of years, and P(t) is the population after t years.
a) For the first part of the question, we can plug in the given values and solve for P(5):
P₀ = 50
r = 0.62
t = 5
P(5) = 50(1 + 0.62)⁵ ≈ 763
Therefore, there are expected to be about 763 millipedes in the area of rainforest in 5 years time.
b) For the second part of the question, we can plug in the given values and solve for P(20):
P₀ = 50
r = 0.62
t = 20
P(20) = 50(1 + 0.62)²⁰ ≈ 225,000
Therefore, there are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.
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A parallelogram has a height of 2 units. One side of the parallelogram is AB¯¯¯¯¯. The paralleogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment on the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (5, 3) labelled: B.
It is a unique variety of quadrilateral called a parallelogram that has both pairs of opposite sides parallel and equal.
What is quadrilateral?A polygon with has four sides, four angles, and four vertices is called a quadrilateral. The Latin words 'Quadri', which denotes four, and latus, which means side, were combined to form the English word quadrilateral.
Given, Height of the Parallelogram = 2 units
Each segment on the grid is represented as = 1 unit.
So, One side of the Parallelogram = 3 units
Properties of Parallelogram
a. Opposite sides are equal.
b. Opposite sides are parallel.
c. Diagonals Bisect each other.
Also, Every Rectangle is a Parallelogram.
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The Amador family pays $7.50 per thousand cubic feet of natural gas. The total cost, t, varies directly as the number of thousand cubic feet of natural gas, g, used.
The constant of proportionality for the Amador family is obtained as k = 7.50.
What is a COP?The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If the cost t varies directly with the number of thousand cubic feet of natural gas g used, we can write -
t = kg
where k is the constant of proportionality, which represents the cost per thousand cubic feet of natural gas.
Since the Amador family pays $7.50 per thousand cubic feet of natural gas, we have -
k = 7.50
Therefore, the equation relating the total cost t to the number of thousand cubic feet of natural gas g used is -
t = 7.50g
This means that for every thousand cubic feet of natural gas used, the cost is $7.50.
If the Amador family uses 10,000 cubic feet of natural gas, the total cost would be -
t = 7.50(10) = $75
If they use 20,000 cubic feet of natural gas, the total cost would be -
t = 7.50(20) = $150
Therefore, the COP value is k = 7.50.
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please help me out with this and i will give u brainy if u give me the right answer
Question 1
What is the mean of the data set?
684, 615, 648, 598, 654, 612, 606, 621, 642, 689
Answer:
Step-by-step explanation:
The mean is 636.9, I got you brotha
Answer:
636.9
Step-by-step explanation:
684+615+648+598+654+612+606+621+642+689
=6369
6369÷10=636.9
You go out for a long walk. You walk 3/4 mile and then sit down to take a rest. Then you walk 3/8 of a mile. How far did you walk altogether?
*
y = 4* Reflect it across the y-axis, translate it to the right 3 units, and vertically stretch it by a factor of 2
y = -2x + 14
To reflect the equation y = 4 across the y-axis, we need to change the sign of the x-term. Since there is no x-term in the original equation, we can simply add a negative x-term to get the reflected equation: y = -x + 4.
Next, to translate the equation to the right 3 units, we need to subtract 3 from the x-term. This gives us the translated equation: y = -(x - 3) + 4.
Finally, to vertically stretch the equation by a factor of 2, we need to multiply the entire equation by 2. This gives us the final transformed equation: y = 2(-x + 3) + 8.
In summary, the equation y = 4 reflected across the y-axis, translated to the right 3 units, and vertically stretched by a factor of 2 is y = -2x + 14.
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Question content area top
Part 1
In a race, 17 out of the 50 finished in less than 56 minutes. What percent of finished the race in less than 56 minutes? Write an equivalent fraction to find the percent
The percentage of people who participated in the race finished in less than 56 minutes is 34%. This can also be written as the equivalent fraction 34/100
To find the percentage of people who finished the race in less than 56 minutes, we can use the following formula:
percentage = (part/whole) x 100%
where "part" is the number of people who finished in less than 56 minutes, and "whole" is the total number of people who participated in the race.
In this case, we know that 17 people finished in less than 56 minutes, and there were 50 people in total. So we can plug these values into the formula:
percentage = (17/50) x 100%
percentage = 34%
Therefore, 34% of the people who participated in the race finished in less than 56 minutes.
To write an equivalent fraction for this percentage, we can write:
34% = 34/100
This is an equivalent fraction because 34/100 can be simplified to 17/50
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Apparently i got a 40 but i can redo it again, any help?
2- Not J
3- Not B
4- Not F
7- Not 6
8- Not J
9- Not C
2b Every point is in one of the four quadrants. True or False.
2c The abscissa of an ordered pair is always positive. True or false.
Pls help I need this on rsm and get it correct
An abscissa is a line that is drawn perpendicular to the vertical axis, or y-axis, of a graph. It is usually measured in the form of a number, and it is used to determine the position of points, lines, and shapes on a graph. Abscissas are also referred to as the x-coordinates of a graph, and they can be used to plot and analyze data.
What are quadrants?Quadrants are the four sections of a coordinate plane formed by the intersection of the x-axis and the y-axis. Quadrants are labeled I, II, III, and IV, with Quadrant I being the upper right-hand corner, Quadrant II being the upper left-hand corner, Quadrant III being the lower left-hand corner, and Quadrant IV being the lower right-hand corner. Quadrants are commonly used to graph equations and to identify points on a coordinate plane.
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Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=2 ?
The value of z when t=2 is 24
The value of z varies inversely with t, which means that the product of z and t is a constant. We can write this relationship as:
zt = k
Where k is the constant. We are given that z=6 when t=8, so we can plug these values into the equation to find k:
6*8 = k
k = 48
Now we can use this value of k to find the value of z when t=2. Plugging in these values gives us:
z*2 = 48
Solving for z gives us:
z = 48/2
z = 24
Therefore, the value of z when t=2 is 24.
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help me i don't understand
The volume of the fully inflated balloon is [tex]\frac{19652}{3}[/tex]π inch³ and volume of half inflated balloon is [tex]\frac{19652\pi }{6}[/tex].
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Diameter of a fully inflated balloon = 34 inch
Radius is half the diameter.
Radius of fully inflated balloon = 34 / 2 = 17 inches
Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³, where r is the radius.
(a) Volume of fully inflated balloon = [tex]\frac{4}{3}[/tex] π (17)³
= [tex]\frac{19652}{3}[/tex]π inch³
(b) Volume of the half inflated balloon = Half of the fully inflated volume
= ([tex]\frac{19652}{3}[/tex]π / 2) inch³
= [tex]\frac{19652\pi }{6}[/tex] inch³
(c) Volume of half inflated balloon = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] π r³ = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] r³ = [tex]\frac{19652}{6}[/tex]
r³ = [tex]\frac{19652}{8}[/tex]
r = 13.49 inch
Hence the volume and radius are found.
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A professor records the following final grades in one course. Construct a frequency table for the grades.
A
A
A
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
D
D
D
D
F
Complete the table.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Grade Frequency Relative Frequency Cumulative Frequency
A. ____ ____% _____
B ____ _____% ______
C ____ _____% ______
D ____ _____% ______
F ____ _____% ______
TOTAL. ____. 1=100%. _______
The frequency table when constructed is
Grade Frequency Relative Frequency Cumulative Frequency
A 3 12.5% 3
B 8 33.3% 11
C 8 33.3% 19
D 4 16.7% 23
F 1 4.2% 24
Total 25 1 or 100%
How to construct the frequency tableThe grades A to F represent the given parameter
From the given grade, we have the following frequencies
A = 3
B = 8
C = 8
D = 4
F = 1
From the above frequency, we have the relative frequency to be
A = 3/24 = 12.5%
B = 8/24 = 33.3%
C = 8/24 = 33.3%
D = 4/24 = 16.7%
F = 1/24 = 4.2%
From the above frequency, we have the cumulative frequency to be
A = 3
B = 11
C = 19
D = 23
F = 24
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Jamie works twice as many hours on the weekend as he does during the week. He earns $7.75 per hour. This week, he wants to earn at least 279 dollars. Will Jamie meet his goal by working 10 hours during the week? Show your work.
Using algebra, we can conclude that, if Jamie only works 10 hours during the week, he will not be able to meet his goal of earning at least $279, because the total pay he will earn, which is $232.50, is less than the amount he wants to earn.
How to Use Algebra to Solve Problems?The method to use to solve this problem would be algebra. We will use variables to represent the number of hours that Jamie works during the week and on the weekend, and we used equations to express the relationship between the total pay Jamie earns and the number of hours he works.
Let's first find out how many hours Jamie works during the week and on the weekend.
Let's say Jamie works x hours during the week. Then, he works 2x hours on the weekend.
The total amount of money Jamie earns is given by:
Total pay = Pay for week hours + Pay for weekend hours
Pay for week hours = $7.75 per hour * x hours
Pay for weekend hours = $7.75 per hour * 2x hours = $15.50 per hour * x hours
Total pay = $7.75x + $15.50x = $23.25x
Now let's substitute x = 10, since Jamie wants to work 10 hours during the week, to see if he can meet his goal of earning at least $279:
Total pay = $23.25 * 10 = $232.50
Since $232.50 is less than $279, Jamie will not meet his goal by working 10 hours during the week alone. He will need to work more hours during the week and/or on the weekend to reach his goal.
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Does someone mind helping me with this problem? Thank you!
Starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the future amount of the investment after 40 years, we can use the formula for compound interest:
Future Amount = Present Value x (1 + Interest Rate/Compounding Frequency)^(Compounding Frequency x Time)
In this case, the present value (PV) is $500, the interest rate (r) is 15%,
the compounding frequency (n) is 1 (since the interest is compounded every 2 years).
The time (t) is 40 years.
Plugging in the values, we get:
Future Amount = [tex]500 \times (1 + 0.15/1)^{(1 \times 40/2)}[/tex]
Future Amount = [tex]500 \times (1.15)^{20}[/tex]
Future Amount = [tex]500 \times 13.591409[/tex]
Future Amount = $6,795.70 (rounded to the nearest cent)
Therefore, starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
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Adam has 18 counters he gives 10 counters to lesley what fraction of the 18 counters does lesley give your answer in its simplest form
Lesley has 5/9 of the counters that Adam initially had.
What is the fraction?An element of a number or any number of equal parts is represented by a fraction. There is a fraction with an upper value (numerator) and a lower value (denominator) (lower value).
Ten of the 18 counters that Adam had were given to Lesley. Lesley currently possesses 10 counters.
We must divide Lesley's total number of counters by Adam's starting total number of counters in order to determine the proportion of the 18 counters that Lesley has:
Lesley has 10/18 counters, which is her percentage.
By dividing the numerator and denominator by their 2 greatest common factor, we may simplify this fraction:
Lesley has a fraction of the counters she needs: (10 ÷ 2) / (18 ÷ 2) = 5/9
Lesley now owns 5/9 of the counters that Adam started with.
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Find the eigen values and eigen vectors of the matrix A=([2,2,0],[2,1,1],[-7,2,-3]).
The eigen values of the matrix A are 2, -2, and 7, and the corresponding eigen vectors are [1,1,2], [1,-2,0], and [2,1,1].
To find the eigen values and eigen vectors of the matrix A=([2,2,0],[2,1,1],[-7,2,-3]), we first need to find the characteristic equation of the matrix. This is done by finding the determinant of (A-λI), where λ is the eigenvalue and I is the identity matrix.
The characteristic equation is:
|A-λI| = |[2-λ,2,0],[2,1-λ,1],[-7,2,-3-λ]| = 0
Expanding the determinant, we get:
(2-λ)((1-λ)(-3-λ)-2) - 2(2(-3-λ)+7) + 0 = 0
Simplifying the equation, we get:
-λ³ + 6λ² - 5λ - 14 = 0
The eigen values are the roots of this equation. We can use the rational root theorem to find the possible rational roots of the equation, which are ±1, ±2, ±7, and ±14. By testing these values, we find that the eigen values are λ=2, λ=-2, and λ=7.
Now, we can find the eigen vectors by plugging the eigen values back into the equation (A-λI)v=0, where v is the eigen vector.
For λ=2, we get:
([2-2,2,0],[2,1-2,1],[-7,2,-3-2])v = 0
([0,2,0],[2,-1,1],[-7,2,-5])v = 0
The eigen vector for λ=2 is v = [1,1,2].
For λ=-2, we get:
([2+2,2,0],[2,1+2,1],[-7,2,-3+2])v = 0
([4,2,0],[2,3,1],[-7,2,-1])v = 0
The eigen vector for λ=-2 is v = [1,-2,0].
For λ=7, we get:
([2-7,2,0],[2,1-7,1],[-7,2,-3-7])v = 0
([-5,2,0],[2,-6,1],[-7,2,-10])v = 0
The eigen vector for λ=7 is v = [2,1,1].
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Evaluate sin(A-B), if sinA=12/13 where A is in Quadrant II and
cosB= 8/17 where B is in Quadrant IV.
Answer with a fraction. No decimals
Sin(A-B) =
The result of sin (A - B) is 21/221.
To evaluate sin (A - B), we can use the formula:
sin (A - B) = sin A * cos B - cos A * sin B.
We are given that sin A = 12/13 and cos B = 8/17. We need to find cos A and sin B to use the formula.
Since A is in Quadrant II, cos A is negative. We can use the Pythagorean identity, sin²A + cos²A = 1, to find cos A:
cos²A = 1 - sin²A
cos²A = 1 - (12/13)²
cos²A = 1 - 144/169
cos²A = 25/169
cosA = -5/13
Similarly, since B is in Quadrant IV, sin B is negative. We can use the Pythagorean identity to find sin B:
sin²B = 1 - cos²B
sin²B = 1 - (8/17)²
sin²B = 1 - 64/289
sin²B = 225/289
sinB = -15/17
Now we can plug in the values into the formula:
sin (A-B) = (12/13)*(8/17) - (-5/13)*(-15/17)
sin (A-B) = 96/221 - 75/221
sin (A-B) = 21/221
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If S is a vertex matrix, which transformation does S + [\begin{array}{ccc}-1&-1&-1\\-3&-3&-3\end{array}\right] represent? a. translation of 3 units left and 1 unit down b. translation of 3 units left and 1 unit up c. translation of 1 unit left and 3 units down d. translation of 1 unit left and 3 units up
The correct answer is option c. translation of 1 unit left and 3 units down.
The transformation represented by S + [\begin{array}{ccc}-1&-1&-1\\-3&-3&-3\end{array}\right] is a translation of 1 unit left and 3 units down. This can be seen by examining the values in the matrix. The -1 in the first row represents a translation of 1 unit left, while the -3 in the second row represents a translation of 3 units down. Therefore, the correct answer is option c. translation of 1 unit left and 3 units down.
To summarize, the transformation represented by the given matrix is a translation of 1 unit left and 3 units down. This is indicated by the values of -1 and -3 in the matrix.
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