We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.
The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.
So its growth rate is constant and does not change with time.
The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:
Value after one year
= $500 + 0.06 x $500
= $530
After two years, its value will be:
Value after two years.
= $530 + 0.06 x $530
= $561.80
We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.
The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.
The formula for the value of a continuously compounded bond after t years = $100 x e^(0.04t)
where e is the mathematical constant approximately equal to 2.718.
After one year,
The value of the third bond.
= $100 x e^(0.04 x 1) = $104.08
After two years,
Value after two years
= $100 x e^(0.04 x 2)
= $108.24
We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.
Now,
We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
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1. suppose a point is to be selected at random from the unit square. write the sample space associated with this random experiment.
a) The x-range of a unit square is from o to 1 and y-range is also from 0 to 1
Sample space = {(x, y)} , 0≤x≤1, 0≤y≤1.
So, sample space associated with this random experiment is
{(x, y)} , 0≤x≤1, 0≤y≤1.
b) From the given data,
Sample space for A : {1, 3, 5, 7, 9, 11,...}
Sample space for B: {5, 10, 15, 20, 25,...}
Therefore, the sample space for A∩B will be the set of all odd natural numbers divisible by 5 which is
{5, 15, 25, 35,....}
c) First letter is the capital letter = 26 Possibilities
then four digits = 9*10*10*10
two lower case letters = 26*26
Total possible ways = 26*9*10*10*10*26*26
= 15,81,84,000 ways.
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Complete question:
Suppose a point is to be selected at random from the unit square. Write the sample space associated with this random experiment. 2. Let S = {0, 1, 2, 3, 4, ...), A = the set of odd natural numbers, and B = the set of natural numbers divisible by 5. What is the set An B? 3. A computer password consists of two lowercase letters followed by a capital letter and four digits. Find the total number of possible passwords.
A school ordered `3` large boxes of markers. After giving `15` markers to each of `3` teachers, there were `90` markers left
How many markers were originally in each box?
Answer:
135 markers
Step-by-step explanation:
Let's call the number of markers in each large box "x."
After giving away 15 markers to each of 3 teachers, there were 90 markers left, so:
x - (15 * 3) = 90
Expanding the expression on the right side:
x - 45 = 90
Adding 45 to both sides:
x = 135
So, each large box originally contained 135 markers.
Please help me with this question real quick I didn't understand it if anyone can help please try to
you forgot to put the question
IM BEING TIMED PLS HURRRYYY
Use factoring to write an expression equivalent to
100x^2-49y^2
SHOW UR WORKKK
The equivalent expression is (10x - 7y)²
What are algebraic expressions?They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.
They are also made up of arithmetic operations.
It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.
From the information given, we have that;'
100x^2-49y^2
Find the perfect squares of the values, we have;
(10x - 7y)²
Hence, the expression is (10x - 7y)²
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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Given the quadratic equation:
100x² - 49y²
Factorizing the polynomial:
100x² + 70xy - 70xy - 49y²
= 10x(10x + 7y) - 7y(10x + 7y)
= (10x - 7y)(10x + 7y)
The expression is equivalent to (10x - 7y)(10x + 7y)
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(a) without adding new vertices, add a single edge to the graph so that the new graph will have an euler path. which vertices does your new edge connect?
To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.
In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.
To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.
Let's consider a graph:
A
/ \
B---C
/ \ / \
D---E---F
In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.
A
/ \
B---C
/ \ / \
D---E---F
Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.
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If these two shapes are similar, what is the measure of the missing length h?
In similar triangles, 15.07 miles is the measure of the missing length h .
What does "similarity" for triangles mean?
Triangles are said to be comparable if two of their angles have measurements that are the same as those of two other triangles' angles. In proportion, and with the same measure, are the equivalent sides and angles of identical polygons.
To test whether two triangles are similar, use one of the three triangle similarity theorems, Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS).
35/65 = 28/h
h = 35 * 28/65
h = 15.07 miles
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a rectangular pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex. what is the shape of the cross section?
When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.
To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.
If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.
Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.
In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.
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Clinton borrows a certain amount of money and pays the principle amount and the interest back after 5 years. Calculate the simple interest rate if Clinton pays back double the amount he borrowed
Answer: The simple interest will be 20%.
Step-by-step explanation:
we know the simple interest of borrowed amount is:
S.I.= (P x R x T)/100 ..... (i)
where P⇒ Principal amount
R⇒ rate of interest
T⇒ time
and
total Pays Back amount = Principal amount + S.I.
Hence S.I. = Pays Back amount - Principal amount
Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means
if Principal amount = P
then Pays Back amount = 2P ⇒ S.I.= P
Rate of Interest = R
and Time = 5 years
P= (P x R x 5)/100
R= 100/5
R = 20%
Therefore, the simple interest is 20% annually.
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You attempt an obstacle course five times. The table shows the amounts of time that it takes you to complete the course on your first four attempts. For what values of x will you have a mean time no greater than 120 seconds?
Time (seconds)
118 129 120 114 x
The values of x which have a mean time no greater than 120 seconds is 1
What is mean?The mean (means the arithmetic mean, different from the geometric mean) of a data value is the sum of all values divided by the total number of values.
The most commonly used measure of central tendency and referred to as the “average.”
We are given that;
Time =120sec
Table
118 129 120 114 x
Now,
The mean value of the table entry;
Mean=(118+ 129+ 120+ 114+ x)/5
Mean= 481+x/5
481+x/5<120
481+x<600
x<119
Therefore, the values by the mean will not be grater than 120 will be 1
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Scatter Plot 8 grades, help please!!!
The of association represented in the graph is positive linear association.
option C
What is a positive correlation?
A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.
In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.
The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.
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Simplify. -8/9 - (-2/9)
- 8/9 - (-2/9)
The answer I have gotten is -6/9
Zera has a credit limit of $2,000 on her credit card. Each month, she charges about $200 and makes a payment of $125. Estimate the number of months that Zera can continue this pattern until she reaches her limit?
Answer: 80/3 months
Step-by-step explanation:
Let x be the number of months until Zera reaches her limit.
Then on month x, her charges are 200x, and her payments are 125x.
This leaves her with 200x - 125x = 75x dollars owed.
we need to see when this equals 2000, so she hits her limit:
2000 = 75x
.: x = 2000/75 = 80/3
She can continue her pattern for 80/3 months, (≈26.666667)
if we have four variables, then how many equations will we have in our system of linear equations? 5 2 3
For four variables the required number of system of linear equations are at least option d. 4 equations.
Variable is represented by small alphabets : a , b, x, y , z, m , n ... so on.System of linear equations are set of equation relating variables with degree one. To solve the system of linear equations we need to have number of equations same as the number of variables.If there are two variables then we need to have minimum two system of linear equations .If there are n variables then there should be n system of linear equations.Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.
The above question is incomplete , the complete question is:
If we have four variables, then how many equations will we have in our system of linear equations?
a. 5 b. 2 c. 3 d. 4
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An account earns simple annual interest. $600 at 5% for 2 years
The total amount of interest earned at the end of 2 years is $60.
1. Calculate the interest earned in one year:
Interest = Principal × Rate × Time
Interest = 600 × 0.05 × 1
Interest = $30
2. Multiply the interest earned in one year by the number of years:
Total interest = 30 × 2
Total interest = $60
The total amount of interest earned at the end of 2 years is $60. This amount was earned by taking the principal amount of $600 and multiplying it by the rate of 5%, and then multiplying that product by the number of years, which in this case is 2. This calculation can be expressed as:
Total interest = Principal × Rate × Time
Total interest = 600 × 0.05 × 2
Total interest = $60
the complete question is :
An account earns simple annual interest. $600 at 5% for 2 years. How much interest will be earned on $600 invested at 5% simple annual interest for 2 years?
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\Plot the point (4, −3).
Start at the origin.
Move 4 units
Move 3 units
The point is at ___
Model |
^
On a coordinate plane, point A is 4 units to the left and 3 units up. Point B is 3 units to the left and 4 units up. Point C is 4 units to the right and 3 units up. Pound D is 4 units to the right and 3 units down.
The points A(-4,3) ; B(-3,4) ; C(4,3) ; D(4,-3) are plotted on the graph.
What is meant by a coordinate plane?
Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line which is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.
The given points are
A is 4 units to the left and 3 units up which means A is (-4,3).
B is 3 units to the left and 4 units up which means B is (-3,4).
C is 4 units to the right and 3 units up which means C is (4,3).
D is 4 units to the right and 3 units down which means D is (4,-3).
All these 4 points are plotted on the coordinate plane and the graph is attached below.
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the ratio of 9 minutes and 600 seconds in its simplest form
Answer:
Step-by-step explanation:
600 secs=600/60 mins=10 mins
9 mins= 9 mins
Therefore, 9 mins : 600 secs
=9 mins : 10 mins
=9:10
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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10-1/2x<-18 which inequality represents the solution to this inequality?
The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality is -
10 - 1/2x < -18
Solve the inequality to get the value for x.
First collect all the like terms -
-1/2x < -18 + (-10)
Then use arithmetic operation of addition -
-1/2x < -28
Multiply (-1) to both the sides -
-1/2x × (-1) < -28 × (-1)
1/2x < 28
Then move the coefficient of variable to right hand side of the equation -
x < -1 / (2 × (-28))
Then use arithmetic operation of multiplication and division-
x < 1/56
Therefore, the inequality is 0 < x < 1/56.
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Fatina uses 7.8 pints of white paint and blue paint to paint her bedroom walls 3/5 of this amount is white paint and the rest is blue paint how many pints of blue paint did she use to paint her bedroom walls
Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.
What is a fractional value?A fractional value is a proportional quantity of the whole value.
Fractional values are depicted in decimals, fractions, or percentages.
The total quantity of white and blue paints used on the bedroom walls = 7.8 pints
The fraction of the white paint = 3/5
The fraction of the blue paint = 2/5 (1- 3/5)
2/5 of 7.8 = 3.12 pints
Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.
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Kathy uses 3.12 pint of white paint to paint her bedroom walls
How many pints of blue paint did she use?Total amount of paint ( Blue and white paint)= 7.8 pints
Amount of blue paint=3/5 x 7.8 = 4.68Pints
amount of white paint = Total amount of paint - amount of blue paint
= 7.6 pints - 4.68 pints
=3.12 pint of white paint
In conclusion, she uses 3.12 pint of white paint to paint her bedroom walls
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Anna ate 5/8 of an orange and gave the other 3/8 to her brother.
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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The complete question is
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
What is the standard function of f? F(x)=4(x+6)2+5
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
What is the definition of a function?
A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).
There are several types of functions in mathematics. Here are a few examples:
An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.
Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.
A polynomial function is a function composed of polynomials.
Functions that may be used to inverse another function are known as inverse functions.
Now,
Given function is F(x)=4(x+6)2+5
=(4x+24)2+5
=8x+48+5
=8x+53
hence,
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
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A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
The probability of getting both the marbles to be red will be 4/25.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
Probability = Number of favorable outcomes / Number of samples
Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.
The probability of getting red in the first draw,
P = 2 / 5
Now the marble is returned and again the probability of getting the red marble is,
P = 2 / 5
The probability of getting both the marbles red will be,
Pb = ( 2/ 5 ) x ( 2 / 5 )
Pb = 4 / 25
Therefore, there is a 4/25 chance that both marbles will be red.
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Cool Down: Bacteria Population
The graph shows the bacteria population on a petri dish as a function of the days d since an
antibiotic is introduced.
number of bacteria
1,000,000
Interpreting Exponential Functions
500,000
(0, 1000000)
(1, 900000)
2
(2, 810000)
4
time in days
6
8
00
10
The approximate value of f(4.5) is 550000.
What is the exponential function?Exponents are used in exponential functions, as the name suggests. But take note that an exponential function does not have a constant as its base and a variable as its exponent (A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant).
From the given graph, the coordinate points are (0, 1000000), (1, 900000) and (2, 810000)
We know that, f(x)=mx+c
Here, (0, 1000000) and (1, 900000)
Now, m=(900000-1000000)/(1-0)
m=-100000/(1-0)
m=-100000
Substitute b=-100000 and (x, y)=(0, 1000000) in y=mx+c
1000000=-100000(0)+c
c=1000000
Substitute m=-100000 and c=1000000 in y=mx+c, we get
y=-100000x+1000000
The approximate value of f(4.5)
Now, y=-100000(4.5)+1000000
y=550000
Therefore, the approximate value of f(4.5) is 550000.
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the coordinates of the endpoints of no are n(5,16) and o(19,9). point p is on no and divides it such that np:op is 4:3. what are the coordinates of p?
The coordinates of point P are (12, 12.5).
to put different elements or individuals in a coordinated effort.
To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.
First, we can find the distance between points N and O using the distance formula:
d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)
Next, we can use the ratio of 4:3 to determine the distance between P and O:
d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)
Similarly, we can find the distance between P and N:
d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)
Now, we can use the midpoint formula to find the coordinates of P:
x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12
y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5
So the coordinates of point P are (12, 12.5).
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Farmer Quect started with 110 rews on his farm. Every hour, he destoryed 6 more of them. Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them?
Write a systems of equations in slope intercept form. Farmer's rews (y), hours (x)
The systems of equations in slope intercept form is
y = -6x + 110
y = 9x + 54
What is Slope- intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
As, We know Slope-intercept form is
y = mx + b
where b is the starting value and m is the change per day.
Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.
So, the Equation to show the Situation
y = -6x + 110
and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.
So, the Equation to show the Situation
y = 9x + 54
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Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.
What in mathematics is a similarity?If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.
Two triangles can be seen in the illustration, and their corresponding angles are both equal.As a result, they match the AAA similarity requirement. However, no more details are provided to demonstrate their consistency.Although comparable triangles may not be congruent, congruent triangles are known to be similar.To know more about similarity visit:
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Answer: None
Step-by-step explanation: I Just did it
HELP FOR 15 Points I SUCK AT MATH
The sum Given it can seen that according to the closure property of Rational numbers the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x.
What is Closure Property of Integers ?
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Rational number is defined as a number that can be made by dividing two integers.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number.
using the closure property and based on the sum given, the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x
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I increased a number by 5% twice how much id it increase by in percent.
Answer:
10%
Explanation:
You increased it by 5% twice, which is basically 5+5 or 5x2 which equals 10
15
Determine if lines a and b are parallel, perpendicular or neither.
(1 Point)
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
O parallel, they have the same slope
perpendicular, their slopes are opposite reciprocal
neither
parallel, their slopes are opposite reciprocal
perpendicular, their slopes are the same
Both slope are equal so we can say that both lines are parallel
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
Line a: 2x + y = 10
Line b:
- 6x – 3y = 3
and line
Line a: 2x + y = 10
= slope of line A is
2x + y = 10
y = -2x+10
slope = -2
- 6x – 3y = 3
-3y = 6x +3
x = -2y -1
slope = -2
in this case both slope are equal so we can say that both lines are parallel
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The average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.
Day of June Transaction type Transaction amount (in dollars)
1 Starting balance 1223
10 Deposit 615
15 Withdrawal -63
22 Withdrawal -120
There are 30 days in June.
What is the average daily balance of Elliott's account for the month of June?
Answer: 1583.90
In June it’s 1583.90$
the average daily balance of Elliott's account for the month of June is $902.
calculate the average daily balance for Elliott's account in June. To calculate the average daily balance, we need to determine the balance at the end of each day in June. Starting with a balance of $1223 on June 1st, we can calculate the balance at the end of each day by adding or subtracting the amount of each transaction. The table below shows the daily balances: Day of June - Transaction type - Transaction amount -Balance
1 - Starting balance - 1223 - 1223
5 - Deposit - 615 - 1838
8 - Withdrawal - -632 - 1206
9 - Withdrawal - -120- 1086
10 - 30 - No transactions - 0 1086
The sum of the daily balances is: 01086 × 30 = 32580
The average daily balance is the sum of the daily balances divided by the number of days in June:
average daily balance = 32580 / 30 = 902
Therefore, the average daily balance of Elliott's account for the month of June is $902.
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