The stemplot gives a correct comparison of eastern and western states’ expenditures as The eastern states have, on average, a higher per-pupil expenditure than the western states.
What does the stemplot show?The Eastern States have expenditure per pupil which are higher in number and in quantity. For instance, they have per-pupil expenditure of $153, $154, $155, and $156. They also have $191, and $190.
When compared to the western states therefore, the eastern states seem to on average, spend more per-pupil.
Options for this question include:
The western states exhibit more variability in their expenditures than the eastern states. The eastern states have, on average, a higher per-pupil expenditure than the western states. The distribution of per-pupil expenditures in the eastern states is more symmetric than the distribution of the western states. The distribution of the western states' per-pupil expenditure is skewed left, while the distribution of the eastern states' per-pupil expenditure is skewed right. Valid conclusions comparing the distributions cannot be made, since there is a different number of states in each group.Find out more on stemplots at https://brainly.com/question/11320163
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1. What is the y intercept that connects all of the data points?
2. What does the y intercept represent in the context of this problem?
3. If your friend says he can get a dozen DVD's from this website for $90, is he correct?
4. How much would it cost to buy 50 DVD's from this website?
Giving Brainliest to whoever gives the correct answer
1. The y-intercept is: 12.
2. The y-intercept represent the initial cost that excluding the cost per DVD.
3. Your friend is incorrect. A dozen DVD's is gotten for $84.
4. 50 DVD's from the website would cost: $312.
How to Interpret the Y-intercept of a Line?The y-intercept is the value of the y-coordinate of the point where the line intercepts the y-axis.
The y-intercept is referred to as the starting value or initial value. At this point, x = 0.
1. First, find the slope (m) of the line using two points, (1, 18) and (2, 24):
Slope (m) = change in y/change in x = (24 - 18)/(2 - 1) = 6/1
Slope (m) = 6
Substitute m = 6 and (x, y) = (1, 18) into y = mx + b to find the y-intercept, b:
18 = 6(1) + b
18 - 6 = b
b = 12 (y-intercept)
Substitute m = 6 and b = 12 into y = mx + b:
y = 6x + 12
The y-intercept that connects all the data points is: 12.
2. The y-intercept in this context represents the initial cost that excludes the charge for each DVD.
3. Substitute x = 12 into y = 6x + 12 and solve to see if y equals 90:
y = 6(12) + 12
y = 84 [not equal to $90)]
Thus, your friend is incorrect. a dozen DVD's can be gotten for $84.
4. Substitute x = 50 into y = 6x + 12:
y = 6(50) + 12
y = 312
It would cost $312 to get 50 DVD's from the website.
The graph for the points (1, 18), (2, 24) , and (3, 33) is shown below.
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Question 16 of 35
Henri earned $1030 a week last year. What was his yearly salary?
OA. $54,600
OB. $53,560
OC. $52,800
OD. $49,440
SUBMIT
2. The translation (x, y) → (x + 3, y-7) maps TUVW onto T'U'V'W'. What translation maps
TU'V'W' onto TUVW?
O(x,y) → (x+3, y-7)
O(x,y) → (x-7, y + 3)
O(x,y) → (x+7,y-3)
O(x,y) → (x-3, y+7)
The mapping of T'U'V'W' onto TUVW is translated as follows:
(x, y) → (x - 3, y + 3)The translation:The backward translation of the mapping T'U'V'W' onto TUVW is the mapping TUVW onto TUVW.
The coordinates of the -axis move by units in the right direction during the translation (x, y) → (x - 3, y + 3), while the coordinates of the y-axis move by 3 units downward.Therefore, we must return to our original position for the mapping of T'U'V'W' onto TUVW.Reversing the mapping involves the steps listed below.
As was previously mentioned, moving all x-coordinates by 3 units in the right direction is the opposite of moving them in the opposite direction. As a result, x-3 would be the translation for the x-axis.Earlier, all y-coordinates were moved by 3 units downward; the inverse of this is an upward 3 unit move for all y-coordinates. As a result, y+3 would be the translation for the x-axis.Therefore, the mapping of T'U'V'W' onto TUVW is translated as follows:
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The complete question is given below:
The translation (x,y)(x+3,y-3) maps TUVW onto T'U'V'W. What translation maps T'U'V'W onto TUVW?
(x,y)(x+3,y-7)
(x,y)(x-7,y+3)
(x,y)(x+7,y-3)
(x,y)(x-3,y+7)
how to do this question ¨a motorcycle travels 340 miles on 4 gallons of gas¨ and use rates and unit rates.
For one gallon of gas, it travels 85 miles.
Given a motorcycle travels 340 miles on 4 gallons of gas
We have to find the unit rate that means for one gallon of gas how much this travel.
This is known as the Unitary method.
Unitary method:
The unitary method is the method in which we need to solve the problem by first finding the value of a single unit, then we can multiply that single unit value by the necessary amount that we need.
So, given 340 miles on 4 gallons of gas per gallon, it should be
= 340/4
= 85 miles
Therefore, It travels 85 miles on one gallon of gas.
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Someone pleaseeeeee help me :
What measurement is represented on the x-axis and what unit is it measured in?
Answer:
It looks like the chart says time and hours.
Step-by-step explanation:
Using the axis title we found that the time is the measurement represented on the x- axis and and time is measured in hours
What is Axis Title in a graph?The axis title is a title in the form of words or numbers that describes the entire axis . The title that describes that what quantity varies along x-axis is called x-axis title and the title which describes what quantity varies along y- axis is called y- axis title.
Some times units of the quantities measured along the respective axis is also mentioned in the title of the axis in a bracket.
From the Given graph in the question we can see that a Distance vs Time graph is given
And the title of the x- axis is Time (hours )
Therefore , the measurement along the x- axis is of time and unit of time is hours.
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Part 4:
7. What is the point slope equation of line that passes throug
point (2,-3) and has the same y intercept as y = 5x + 2?
to get the equation of any straight line, we simply need two points off of it, hmmm let's take a peek at the y-intercept of the line above
[tex]y = 5x \stackrel{\stackrel{b}{\downarrow }}{+2} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \stackrel{y-intercept}{(0~~,~~2)}[/tex]
so we're really looking for the equation of a line that passes through (2 , -3) and (0 , 2)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}} \implies \cfrac{2 +3}{-2} \implies -\cfrac{ 5 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{2}) \implies y +3= -\cfrac{ 5 }{ 2 } (x -2)[/tex]
Given the matrices A =
2
2
3
4
B=
0
4
2
-3
C=
4
6
5
6
the matrix X in the equation (x-4b)a=c
Answer:
Hello,
Step-by-step explanation:
[tex]A=\begin{bmatrix}2 & 2 \\3 & 4 \end{bmatrix}\\\\\\B=\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}\\\\\\C=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}\\\\\\(X-4B)*A=C\\\\X-4B=C*A^{-1}\\\\X=C*A^{-1}+4B\\[/tex]
[tex]\begin{array}{|cc|cc|}A&&A^{-1}&\\---&---&---&---\\2&2&1&0\\3&4&0&1\\---&---&---&---\\1&1&\frac{1}{2}&0\\0&1&\frac{-3}{2}&1\\---&---&---&---\\1&0&2&-1\\0&1&\frac{-3}{2}&1\\---&---&---&---\\\end {array}\\\\[/tex]
[tex]X=C*A^{-1}+4B=\begin{bmatrix}4 & 6 \\5 & 6 \end{bmatrix}*\begin{bmatrix}2&-1\\\frac{-3}{2}&1\end{bmatrix}+4*\begin{bmatrix}0 & 4 \\2 & -3 \end{bmatrix}[/tex]
[tex]X=\begin{bmatrix}-1 & 2 \\1 & 1 \end{bmatrix}+\begin{bmatrix}0 & 16 \\8 & -12 \end{bmatrix}\\\\\\X=\begin{bmatrix}-1 & 18 \\9 & -11 \end{bmatrix}\\[/tex]
HELPPPP ME NOWWWW PLEASEE
Solve using the Quadratic Formula. 3 x²+9 x=27
The correct answer of the question is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .
The given quadratic equation is 3 x²+ 9 x=27
To begin, we must transform the equation in the form
ax² + bx + c = 0, then apply the quadratic formula i.e.
x = {-b±√(b²- 4ac)}/ 2a .
Now,
3 x²+ 9 x=27
⇒ 3 x²+ 9 x - 27 = 0
⇒ 3(x²+ 3 x - 9 )= 0
⇒ x²+ 3 x - 9 = 0
Here, a = 1, b = 3 and c = --9
Now, applying quadratic formula
{-b±√(b²- 4ac)}/ 2a
= {-3±√(3²- 4 × 1 × -9)}/ (2 × 1)
= {-3±√(9 + 36)}/ 2
= {-3±√45}/ 2
= {-3±3√5}/ 2
= 3{-1 ±√5}/ 2
= 3{-1+√5}/ 2 or 3{-1-√5}/ 2
Therefore, the ultimate answer to the given equation is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .
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Sequences of congruence transformations:
Triangle T'U'V' is the image of triangle TUV under a rotation followed by a reflection across the y-axis.
The transformation rules for the given figure are as follows:
Rotation: (x,y) -> (-y, x).Reflection: (x,y) -> (-x,y).What is a transformation in a function?A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
From Triangle TUV to Triangle T'U'V', the complete rule is given by:
(x,y) -> (y, x).
The rule for a reflection over the y-axis is:
(x,y) -> (-x,y).
Hence the rotation rule was given by:
(x,y) -> (-y, x).
Hence the rules are:
Rotation: (x,y) -> (-y, x).Reflection: (x,y) -> (-x,y).More can be learned about transformations at https://brainly.com/question/4521517
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I NEED HELP YALL- ASAPPPP!
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time. f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t). d(t)=t squared +11t+4
a.Write a function w(t) to represent the amount of water in the pool using the two functions.
b. Use the new function to determine if the pool will leak all of the water
c. If the pool will drain of all water, how much time will it take?
d.Will f(t) and d(t) intersect on a graph? Explain what it means if they do.
e. What is the domain of f(t), d(t), and w(t)? Explain your answer.
Step-by-step explanation:
so, if I understand you correctly and nothing was left out :
f(t) = t² + 8t + 9
d(t) = t² + 11t + 4
just by looking at the 2 functions, it is clear that d(t) creates larger functional values for higher values of t.
because t² = t², but 11t > 8t. and the constants in the end are irrelevant for larger numbers.
so the pool will drain.
a.
w(t) = f(t) - d(t) = t² + 8t + 9 - t² - 11t - 4 = -3t + 5
b.
yes, it will completely drain, as -3t will drive it to 0, and if it was physically possible into the negative ask the way to -infinity.
c.
-3t + 5 = 0
5 = 3t
t = 5/3
it will be completely drained after
1 2/3 hours = 1 hour 40 minutes.
d.
to intersect they need to create the same result for a value of t :
t² + 8t + 9 = t² + 11t + 4
8t + 9 = 11t + 4
-3t + 5 = 0
t = 5/3 or 1 hour 40 minutes.
that means that the filling and the draining are only equal, when there is no water in the pool.
that also means that f(t) is actually calculating how much water there is in the pool, if there would not be no drain, with a starting value of 9.
e.
the domain is the interval or set of all valid input values (here for t).
negative t (hours) don't make any sense for any of the 3 functions.
but f(t) can go on theoretically forever. but usually it's limited by the size of the pool (once it reaches the top, there is no more filling). we just don't know anything about that.
so, the domain for f(t) is
0 <= t < +infinity
d(t) could go on and on as well, as long as there is water in the pool.
so, the domain for d(t) is also
0 <= t < +infinity
but w(t) based on its meaning and definition makes only sense between the start (t = 0) and until the water is fully drained by the combination of f(t) and d(t).
so, the domain of w(t) is
0 <= t <= 5/3
we could define w(t) as segmented function
w(t) = -3t + 5 0 <= t <= 5/3
= 0 t > 5/3
THEN the domain would be again
0 <= t < +infinity
Please help and explain the picture is down below.
It should be noted that in order to measure the value, the measurement has to be in the same unit.
How to illustrate the information?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
Measurement is crucial in establishing connections across different branches of mathematics. For instance, it gives the use of math abilities and spatial concepts a rich and meaningful context. Measurement also establishes connections between mathematics and other academic disciplines.
From the information, it was illustrated that the boys all had measurements of trees taken. Therefore, it should be noted that since they are in different units, it cannot be done.
In this case, the reason is that in order to measure the value, the measurement has to be in the same unit. This will make it easier to do the calculation.
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Which of the following transformations best describes how to sketch the graph of (look at picture)
The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the y-axis.
The types of transformation.Generally, there are different types of transformation and these include the following:
RotationTranslationDilationReflectionWhat is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In conclusion, we can reasonably and logically deduce that the order of transformation which best describes how the graph of h(x) = ∛1 - x should be sketched is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one unit, and then reflect the graph about the y-axis.
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Complete Question:
Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?
A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the y-axis.
B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one unit, and then reflect the graph about the y-axis.
C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one unit, and then reflect the graph about the x-axis.
D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one unit, and then reflect the graph about the y-axis.
A spherical water tank holds 9000 ft³ of water. What is the diameter of the tank? (Hint: (¹/₆ d³ π=V)
The diameter of the tank is 25.8 feet.
We are given the volume of water tank. Also, we are provided the formula relating volume and density.
Rewriting the formula -
V = 1/6×π×d³, where d represents the diameter. Taking the value of π as 3.14
Rewriting the formula according to diameter -
d³ = 6V/π
Keep the values in formula to find the value of diameter of water tank
d³ = 6×9000/3.14
Performing multiplication and division to find the value of diameter
d³ = 54000/3.14
Performing division to find the value of diameter of water tank
d³ = 17197.45
d = ∛17197.45
Taking square root to find the value of diameter of water tank
d = 25.8 feet
Hence, the diameter of tank is 25.8 feet.
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To the nearest tenth, what is the percent of Container A that is empty after the pumping is complete?
After pumping all of container A into container B there will remain empty space in B = 78.5 ft³
The percentage for this empty space is of the entire volume is = 3.4 %
What is volume of cylinder?
Volume of cylinder is calculated as;
v = π r² h
Since, Container A has a diameter of 18 feet and a height of 9 feet.
Then, Radius = 18/2 = 9 ft
Hence, Volume of Container A = π r² h
= 3.1416 * 9 * 9 * 9
= 2,290.22 ft³
Since, Container B has a diameter of 16 feet and a height of 11 feet.
Then, Radius = 16/2 = 8 ft
Hence, Volume of Container B = π r² h
= 3.1416 * 8 * 8 * 11
= 2,211.68 ft³
After pumping all of container A into container B there will remain empty space in B = 2,290.22 - 2,211.68 = 78.5 ft³
And, The percentage for this empty space is of the entire volume is,
78.5/2,290.22 = 0.03427 *100 = 3.4 %
So, After pumping all of container A into container B there will remain empty space in B = 78.5 ft³
The percentage for this empty space is of the entire volume is = 3.4 %
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The first term of an arithmetic sequence is 10 and the common difference is 5. Find the value of the 30th term
Answer:
Step-by-step explanation:
First term of the sequence is 10 and common difference is 3.
a
1
= 10 and d = 3
Next term = a
2
=a
1
+d=10+3=13
a
3
=a
2
+d=13+3=16
Thus, first three terms of the sequence are 10, 13 and 16.
Let 100 be the nth term of the sequence.
a
n
=a
1
+(n−1)d
100=10+(n−1)3
90=(n−1)3
n−1=30
n=31, which is a whole number.
Therefore, 100 is the 31
st
term of the sequence.
A publisher sells 106 copies of a new book. Each book has 102 pages. How many pages total are there in all of the books sold?
Write the answer using exponents.
Answer:
10812
Step-by-step explanation:
books sold=106
number of pages=102
106 × 102=10812
Answer:
106^102
Step-by-step explanation:
Because there are 106 copies of the book and each book has 102 pages
Solve the system of equations.
y = 3x
y=x-4
Step-by-step explanation:
y=3x
y=x-4
3x=x-4
2x=4
x=2
y=3*2
y=6
(2,6)
x=2
y=6
What are the best anime jobs that use geometry? i need at least 5
Cinematic layout lead, Technical Assistant, Game Artist, 2D Artist, and Game Producer are the best anime jobs that use geometry.
There are many opportunities for animators to get anime jobs that use geometry as well. In order to demonstrate how an object is rotated or shifted to be made larger or smaller—for the process of producing movement—animators must comprehend the geometrical characteristics of figures and apply linear algebra.
Due to their work with moving and changing objects, animators frequently use a number of mathematical techniques, including geometry, linear algebra, and others. The ability to utilize linear algebra to demonstrate how a certain figure or object is shifted or rotated with the intention of making it smaller or larger is crucial for animators. Movement is produced by this mechanism.
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.
Answer: hello frawn
Step-by-step explanation:
free point dootie head
3x+2y−z=82x+2z=−4x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer: (1/14, 10/7, -13/14)
Step-by-step explanation:
3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations
3x+2y−z=4
82x+2z=4
−4x+3y=4
(3x+2y−z=4)*2
6x+4y−2z=8 ==> add this equation
82x+2z=4 ==> add this equation
88x+4y=12 ==> add the top 2 equations
(−4x+3y=4)*4
-16x+12y=16
(88x+4y=12)*3 ==> multiply by 3 to get 12y
264x+12y=36
-16x+12y=16
264x-(-16x)=36-16
264x+16x=20
280x=20
280x/280=20/280
x=1/14
−4x+3y=4
−4(1/14)+3y=4
-4/14 + 3y=4
-2/7 + 3y=4
(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions
-2+21y=28
21y=30
y=30/21
y=10/7
3x+2y−z=4
3(1/14)+2(10/7)−z=4
3/14 + 20/7 - z=4
(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions
3 + 20*14/7 - 14z=56
3 + 280/7 - 14z=56
3+40-14z=56
43-14z=56
43-43-14z=56-43
-14z=13
z=-13/14
Answer: (1/14, 10/7, -13/14)
Which length of time is between 1.45 pm and 3.10 pm ?
Answer:
Step-by-step explanation: its 1.45-3.10 and then its =1.35
ez
have a good day
HELP!!!
6) Solve for x. show steps. (Lesson 1.06)
6x − 10 ≤ 8 or 1/3x + 6 > 12
The solution for x in the compound inequality is 18 < x ≤ 3
How to solve for x in the compound inequality?The compound inequality is given as
6x − 10 ≤ 8 or 1/3x + 6 > 12
Add or subtract the constant to both sides of the compound inequality
So, we have
6x ≤ 18 or 1/3x > 6
Divide both sides of the compound inequality by the coefficient of x
So, we have
x ≤ 3 or x > 18
Rewrite as
x > 18 or x ≤ 3
Combine both inequalities
18 < x ≤ 3
Hence, the solution for x in the compound inequality is 18 < x ≤ 3
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If Harry travels 10 and 4/10 of a mile in 5 hours on his broomstick. How far will he travel in 1 hour?
Group of answer choices
5 and ½ miles per hour
2 and 2/25 miles per hour
52 miles per hour
2 and ½ miles per hour
Answer:
2 and 2/25 miles per hour.
Step-by-step explanation:
Harry's speed = distance / time
= 10 4/10 / 5
= 104/10 * 1/5
= 104/50
= 2 4/50
= 2 2/25
What is the solution to the equation+=+
x=
10
0x = //
0x = 1/5/2
0x = 1/
Ο r
Calculator
2
?
The value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.
We are given the equation:
x² - 2 x + 5 = 2
We need to solve the equation to find the value of x.
For this, we will first subtract 2 from both the sides:
x² - 2 x + 5 - 2 = 2 - 2
x² - 2 x + 3 = 0
Now, we will solve for the value of x:
D = b² - 4 ac
D = (- 2)² - 4 (3)(1)
D = 4 - 12
D = - 8
√D = 2 i √2
Now putting it in quadratic formula, we get that:
x = (- b ± √D) / 2 a
x = (2 ± 2 i √2) / 2 (1)
x = 1 ± i √2
Therefore, the value of x in the equation x² - 2 x + 5 = 2 is 1 ± i √2.
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Your question is incomplete. Please refer the content below:
What is the solution to the equation for x:
x² - 2 x + 5 = 2
What are the slope of the two lines?
Answer:
AB has the slope of 4/3
CD has the slope of 3/2
Step-by-step explanation:
CD I chose the points (0,2) and (3,0)
[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 2}{3 - 0} \\ m = \frac{ - 2}{3} [/tex]
AB I chose the points (0,6) and (8,0)
[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 6}{8 - 0} \\ m = \frac{ - 3}{4} [/tex]
A college bookstore marks up the price that it pays the publisher for a book by 35%. If the selling price of a book is $60.00, how much did the bookstore pay for this book?
The college bookstore paid $44.4 for the book
How to calculate the price paid for the book ?A college store marks up the price it pays the publisher for a book by 35%
The selling price of the book is $60.00
Therefore the amount paid by the bookstore can be calculated as follows
( 35/100 + 1) x = 60
0.35+1x= 60
1.35x= 60
Divide both sides by the coefficient of x which is 1.35
x= 60/1.35
x= 44.4
Hence the book store will pay $44.4 for the book
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A theater holds a total of 2,013 chairs. 197 chairs are in the VIP section. How many chairs are not in the
VIP section?
Answer:1,816
2,013 minus 197 equals 1,816
Suppose you invest a dollars to earn an annual interest rate of r percent (as a decimal). After t years, the value of the investment with interest compounded yearly is A(t)=a(1+r) t . The value with interest compounded continuously is A(t)=a . e rt
c. For each situation find the unknown quantity, such that continuous compounding gives you an $ 1 advantage over annually compounded interest. Show your work.
- How much must you invest for 1 year at 2 % ?
- At what interest rate must you invest $ 1000 for 1 year?
- For how long must you invest $ 1000 at 2 % ?
The sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.
What exactly is a continuous compounding formula?The continuous compounding formula should be used when an issue expressly states that the amount is "constantly compounded."This formula makes use of the mathematical constant "e," which has a value of approximately 2.7182818.The continuous compounding formula is as follows:
A = Pe^rtWhere P represents the starting sum, A represents the total sum, r represents the interest rate, t represents time, and e is a mathematical constant.So,
According to the first point, we know that atr = 0.02, and t = 1.
a(e^rt) - a(1+r)^t = a[ e^(0.02) - 1.02]= 0.00020134 aThus for advantage > 1$ we need is as follows:
0.00020134 a > 1a > 1/ 0.00020134a~4966.7According to the second point, we got that:
t1= 1, a= 1000Then,
1000[e^r-1-r]> 1>> e^r-1-r > 0.001>>e^r-1-r - 0.001 > 0 ......(1)Now we hold that r > 0.04439:
r~ 0.04439 r~ 4.439%According to the third point, we got to know that:
a = 1000, r = 0.02,1000[e^0.02t - (1.02)^t] > 1>>e^0.02t - (1.02)^t > 1 ......(2)Now 2nd equation holds t > 4.621.
Therefore, the sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.
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What does |-5| + |7| equal?
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
|-5|+|7|
|-5|=5
|7|=7
=5+7
=12
hope this helps u ; )
In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001 , an earthquake of magnitude 6.8 shook Washington state. How many times more intense was the 1995 earthquake than the 2001 earthquake?
The earthquake in 1995 was 1.2 times than the 2001 earthquake .
In 1935, American geologist Charles Richter (1900-1984) predicted the magnitude M of an earthquake is given by [tex]M=log(\frac{I}{S} )[/tex] where 'I' is the intensity of the earthquake (measured by the amplitude of the seismometer 100 km from the epicenter), 'S' is the "standard" seismic intensity whose (amplitude is 1 micron = 10 -4 cm). Standard earthquake magnitude is 0.
It is given that in 1995, an earthquake in Mexico registered 8.0 on the Richter scale and earthquake of magnitude 6.8 in Washington state.
If [tex]I_1[/tex]and [tex]I_2[/tex] are the intensities of the Mexico and Washington earthquakes, then we are required to find [tex]\frac{I_1}{I_2}[/tex]. To relate this to the definition of magnitude, we divide numerator and denominator by S
[tex]log(\frac{I_1}{I_2})=log\frac{\frac{I_1}{S} }{\frac{I_2}{S} }[/tex]
Using property of logarithm [tex]log\frac{a}{b} =loga-logb[/tex] , we get
[tex]log(\frac{I_1}{I_2})=log{\frac{I_1}{S} -log{\frac{I_2}{S} \\\\\\[/tex]
[tex]log(\frac{I_1}{I_2})=8.0-6.8\\\\log(\frac{I_1}{I_2})=1.2[/tex]
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