a) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 7% APR, your employer contributions should be $190.49.
b) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 4% APR, your employer contributions should be $423.03.
What is the future value?The future value represents the amount expected to be the balance in the investment account after a period.
The future value can be used to determine the periodic payments required to meet the target balance, using an online finance calculator.
Periodic Deposits at 7%:N (# of periods) = 480 months (40 years x 12)
I/Y (Interest per year) = 7%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $190.49
Sum of all periodic payments = $91,435.07
Total Interest = $408,564.93
Periodic Deposits at 4%:N (# of periods) = 480 (40 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $423.03
Sum of all periodic payments = $203,052.33
Total Interest = $296,947.67
Thus, the periodic deposits to meet the future value will depend on the interest rate.
Learn more about periodic deposits at https://brainly.com/question/13031679
#SPJ1
sin 0 = 5/13 find tan 0 A 13/12 B 12/5 C 5/12 D 12/13
Answer: C.5/12
Step-by-step explanation:
A truck can be rented from Company A for $150 a day plus $0.50 per mile. Company B charges $60 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
At 300 miles the rental costs for Company A and Company B are the same.
What is meant by an equation?An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.
Given :
Vehicle A: 150 + 0.5m = Cost A
Cost B = 60 + 0.8m for truck B.
Given that a one-day scenario was required by the challenge, the two equations are as follows:
Price B =60+0.8m Price A =150+0.5m
By combining the two equations, we get
150 + 0.5m = 60 + 0.8m.
150-60=0.8m-0.5m
90=0.3m
m=90/0.3
m=300 miles
Consequently, there are 300 miles in a day.
To know more about equation, visit:
https://brainly.com/question/13911876
#SPJ1
Write an equation of the line that goes through (-2,7) and (4,7)
Answer:
y=7
Step-by-step explanation:
y is always the same and it is 7
A swordfish is 400 centimeters long. A swordfish is __ meters long.
Answer:
400
Step-by-step explanation:
1 centimeter = 0.01 meter
400 centimeters = 4 meters
Kyle invests in an account earning 4.5% interest compounded continuously. How long will it take to double his investment?
Doubling time in years =
let's take from the basic of one dolla!!! how long for a buck to turn into two bucks at 4.5%?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 2=1e^{0.045\cdot t} \implies \log_e(2)=\log_e(e^{0.045t})\implies \log_e(2)=0.045t \\\\\\ \ln(2)=0.045t\implies \cfrac{\ln(2)}{0.045}=t\implies 15.4\approx t\qquad \textit{about 15 years and 146 days}[/tex]
if grocery price increases 1% per month for a whole year, how much would groceries that cost $100 at the beginning of the year cost at the end of the year
Answer: it's still $100 because the beginning of the year hasn't started yet so you need to wait for the year to end so the 1 percent can be added
Step-by-step explanation:
If 15 out of 24 students enjoyed math
yesterday, what percentage of students
did not enjoy math yesterday?
Answer: 37.5
Step-by-step explanation: 9 students didn't fw math, divide 9 by the total (24) n u get 37.5%
Answer:
Below
Step-by-step explanation:
9 out of 24 did NOT
9/24 = .375 = 37.5 %
Using Function Notation
State if the following are functions or not.
The following given table with input and output is a function.
What is function?A relation between a domain and range is called a function when each value in the domain only has one value in the range. This notion is violated by relations that are not functions. They have at least one domain value that corresponds to two or more range values.
Write names of type of functions.Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
To learn more about function visit the link:
https://brainly.com/question/28193995
#SPJ1
The following given table with input and output is a function.
What is function?
A function is a self-contained block of code that performs a specific task. It is a logical grouping of instructions and operations that can be used multiple times throughout a program. Functions help to keep code organized and modular, making it easier to debug and maintain. They also allow for code reuse, which can result in faster development times and greater efficiency. Furthermore, functions can be used to pass data between different parts of a program, making it easier to share information and reduce the need for redundant code.
Write names of type of functions.
Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
To learn more about function visit the link:
https://brainly.com/question/28793267
#SPJ1
determine the range of the following graph
The required range of the given function is -4 < y < 6.
What is the range?Range, it is the set of values that come out to an outcome for certain mathematical operations.
Here,
A graph of a function is shown,
From the graph, it has been determined that,
The function is defined for domain -11 < x < -3.
As every value on the y- axis for the respective domain represents the element of range so,
The respective domain range of the function on the graph is -4 < y < 6.
Thus, the required range of the given function is -4 < y < 6.
Learn more about the range here:
https://brainly.com/question/12239390
#SPJ1
The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in Model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is ____, and the value of b is ____.
The value of a is 71°, and the value of b is 109°.
What is a parallel line?A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.
When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;
Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.
That is 180 - 71 = 109°
Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.
Learn more about parallel lines here:
https://brainly.com/question/24607467
#SPJ1
if the first term in a geometric system is six and the constant multiple is 3÷4 list out the first five terms in the sequence.
The first five terms in the sequence are 6, 4.5, 3.375, 2.53125 and 1.8984375
How to list out the first five terms in the sequence?The first term of the sequence is given as
First term= 6
The constant multiple is given as
constant multiple = 3/4
These parameters can be represented as
a = 6
r = 3/4
The nth term of a geometric sequence is represented as
A(n) = a(r)ⁿ⁻¹
So, we have the following equation
A(n) = 6(3/4)ⁿ⁻¹
For the first term, we have
A(1) = 6
For other terms, we have
A(2) = 6(3/4) = 4.5
A(3) = 6(3/4)² = 3.375
A(4) = 6(3/4)³ = 2.53125
A(5) = 6(3/4)⁴ = 1.8984375
Hence, the other terms are 4.5, 3.375, 2.53125 and 1.8984375
Read more about sequence at
https://brainly.com/question/6561461
#SPJ1
Simplify the expression (-3r^2+13)+2r(r-6)-4r
Answer:
A potential energy function is given by U(x) = (3.6)x + (1.2)x3. What is the force function F(x) that is associated with this potential energy function
Step-by-step explanation:
A water tank initially contained 105 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute How many minutes have passed, m. when the tank contains 181 liters? Round to the nearest hundredth
Answer:
8.44 minutes
Step-by-step explanation:
The tank initially contained 105 liters so the amount of water needed is 181 - 105 = 76 litters
if the rate is 9 L/min then the number of minutes is
76/9 = 8.44 minutes
Write an equation to show that 68 is 8 times an many as 6.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
What is meant by an equation?An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.
Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
To know more about equation, visit:
https://brainly.com/question/10413253
#SPJ1
Many of the strongest earthquakes in the world take place off the coast of Alaska in the Andreanof Islands or in Prince William Sound. In 1957, a 9.1 magnitude earthquake hit this area. What was the
intensity of that earthquake? (Round your answer to two decimal places.)
cm
Answer:
1,258,925,411.79cm
Step-by-step explanation:
earth quake is measured with the Richter Scale,
R (Magnitue) = log (I / I°)
where I° is the base intensity to the Richter Scale and will be taken as 1
9.1 = log I
10^9.1 = I
thus,
intensity I = 1,258,925,411.79 cm
what is capacity . please explain
Answer:
Step-by-step explanation:
the ability to hold, receive, store, or accommodate. : a measure of content : the measured ability to contain : volume. a beaker with a capacity of one liter.
Answer:
Capacity is the maximum amount that something can contain; Volume, or the amount that something can produce.
Capacity is a noun
Hope this helps
You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary? (round to the nearest tenth, if needed)
The percent change in your salary is = 6%
Initial earning per hour = $12.50
New earning per hour after the raise = $13.25
The formula that we will be using to solve this question is -
= %change = [final value - initial value] ÷ [initial value] × 100
First, find the difference between the initial value and the final value
= $13.25 - $12.50
= $0.75
Divide the difference by the initial ( $12.50) value
= $0.75 ÷ $12.50
= 0.06
Convert the quotient into a percentage
= 0.06 x 100
= 6%
Therefore, the percentage change in your salary is = 6%
To learn more about percentage questions,
https://brainly.com/question/28158528
For the job paying $12.50 per hour, the percent change in your salary after the raise is 6%.
What is the percent change in your salary after a raise?Given data:
Hourly salary after the raise = $13.25Hourly salary before the raise = $12.50Hourly increase:
= Hourly salary after the raise - Hourly salary before the raise
= $13.25 - $12.50
= $0.75
The percent increase is:
= (Hourly increase / Hourly salary before the raise) * 100
= ($0.75 / $12.50) * 100
≈ 6%.
Read more about percent change
brainly.com/question/1053881
#SPJ2
Liseta has $8 to buy blank CDs. If each CD costs $0.26, how many can she buy?
Answer:
she can buy 30
Step-by-step explanation:
8/0.26 = 30.7
round to 30 because you need a whole number.
Find the slope of the line that goes through the given points.
(-5, -10) and (-6, -1)
Answer:
-9
Step-by-step explanation:
(y2-y1)/(x2-x1)
[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9
Answer:
slope m=-9
Step-by-step explanation:
m=−1−−10−6−−5
m=9−1
m = -9
a. 5.2
b. 8.5
c. 7.4
d. 6.3
Answer:
c.7.4
Step-by-step explanation:
<BDE=90°
Now,in RT.angled triangle BDE,
BD=√(BE)²-(DE)²
or, BD=√64-9
or,BD=√55
:.BD=7.41
Answer please thank you!
After performing division on the given expression the quotient is x + 3 and the remainder is -16.
What is an arithmetic operation?
The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
x + 3) x² - 7 ( x + 3
x² + 3x
= 3x -7
3x + 9
= -16 (Remainder)
Hence, the quotient obtained after division is x+3.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ1
This question is based on a time when people needed to log in to email servers to write emails. Assume that Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. The times that his emails are sent can be modeled by a Poisson process with a rate
λ A
/
hour. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam. The time that her emails are sent also can be modeled by a Poisson process with a rate
λ B
/
hour. (a) (6 points) Let
Y 1
, and
Y 2
be the times at which Adam's first and second emails were sent. Find
E[Y 2
∣Y 1
]
(b) (8 points) Similar to the last question, let
Y 1
and
Y 2
be the times at which Adam's first and second emails were sent. When Brianna logs in to the server, you are told that Adam has sent exactly one email so far. (b.1) (4 points) What is the conditional expectation of
Y 1
given this information? (b.2) (4 points) What is the conditional expectation of
Y 2
given this information? (c) (8 points) Find out the PMF of the total number of emails sent by two of them together during the interval of
[0,2]
(which means in the first two hours). (d) (8 points) Given that a total of 10 emails were sent during the period of
[0,2]
(the first two hours), what is the probability that exactly four emails were sent by Adam? (e) (10 points) Suppose that
λ A
=4
. Use Chebyshev's (4 points) and Markov's (4 points) inequality to find upper bounds on the probability that Adam sent at least five emails during the time interval [0, 1 ]. Which one provides a better bound ( 2 points)?
The upper bounds on the probability that Adam sent at least five emails during the time interval is [0, 1].
in math upper bound refers a number that is greater than or equal to any number in a set
Here we have given that, Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam.
And we need to find the upper bounds on the probability that Adam sent at least five emails during the time interval.
While we looking into the given question, we have identified that Adam Poisson process with a rate λ A/hour and Brianna Poisson process with a rate λ B/hour.
Here let us consider that Y1 and Y2 be the times at which Adam's first and second emails were sent.
Here we know that the Brianna logs in to the server, you are told that Adam has sent exactly one email so far.
So, here the upper limit while logging is 1. So, the lower limit is 0.
Because these is the real life scenario so the negative value is not applicable.
Therefore, the resulting interval is [0, 1].
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
(b) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
From the given matrices, the values w,x,x and z are 5,-8,4 and -3 respectively.
How to solve matrix equations?Matrices is the rectangular arrangement of numbers and letters in rows and columns
An equation is defined as a mathematical expression showing the equality of two sides of the statement
The given matrices are;
[tex]2\left[\begin{array}{ccc}w&2&\\5&z&\/\end{array}\right] -3\left[\begin{array}{ccc}2&x&\\-2&-6&\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]
Opening the brackets in the matrices
[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] -\left[\begin{array}{ccc}6&3x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]
Adding the Left hand side
[tex]\left[\begin{array}{ccc}2w-6&4-3x\\16&2x+18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y12&6\\\end{array}\right][/tex]
Equate Left hand side with Right hand side to form linear equations
2w-6=16
2w=10
w=5
4-3x=28
-3x=28-4
-3x=24
x=-8
16=4x
4=x
2z+18=12
2x=12-18
2x=-6
x=-3
These are how the various values are gotten
Learn more about solution to matrix equations on https://brainly.com/question/2253966
#SPJ1
What is the exact value of tan 75°?
A.
OB.
O c.
D.
1-
1+
3
1+
1-4
1+√3
1-v3
1+√3
The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))
What are trigonometric identities?Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.
The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;
tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))
tan(75°) = tan(45° + 30°)
tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))
tan(30°) = √3/3
tan(45°) = 1
tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)
tan(75°) = (1 + √3/3)/(1 - √3/3)
The correct option is therefore option B
[tex]tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } [/tex]
Learn more about trigonometric identities here:
https://brainly.com/question/14421002
#SPJ1
3(4.1x-3.9y)-5= (Simplify your answer. Use integers or decimals for any numbers in the expression.)
The value of the expression 3(4.1x - 3.9y) - 5 is 12.3x - 11.7y - 5.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, it should be noted that the expression is illustrated as:
3(4.1x - 3.9y) - 5
Open the parentheses
12.3x - 11.7y - 5
Therefore, the value of the expression is 12.3x - 11.7y - 5.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Help please!!!!!! Which table represents a linear equation that has a y-intercept of -3?
Answer: A
Step-by-step explanation:
A y-intercept is a point where a function (i.e a line) intercepts the y-axis.
Every point on the y-axis has a x value of 0.
The ordered pair will look like this (0,y)
In answer a, you have an x value of 0 with a corresponding y value of 3.
This point is (0,3).
You could also graph the points and look for where the function crosses the y-axis.
If 2x-4 = 6, what is the value of 3x + 2?
When 2x-4 = 6, the value of 3x + 2 is 17.
What is the value of 3x + 2?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
When 2x - 4 = 6, the value of x will be:
2x - 4 = 6
2x = 6 + 4
2x = 10
Divide
x = 5
Therefore, 3x + 2 will be:
3x + 2 = 3(5) + 2
= 15 + 2
= 17
The value is 17.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Inequalities in the real world
Pls help
The number line which describes the the measure of third side of the triangle must be greater than 10 cm is the second figure.
What is Number line?Number line is a straight horizontal line on which numbers are written in a certain intervals.
We can use number line for basic mathematical operations like addition, subtraction, division and multiplication.
Here the situation described is that measure of the third side of the triangle must be greater than 10 cm.
The inequality sign is '> 10'.
Since the inequality sign does not contain the equal to (≥) sign, the point 10 does not belong to this set.
So we will mark an open circle at the point 10 and draw a line afterwards.
Hence the second number line describes the situation that the third side of the triangle must be greater than 10 cm.
To learn more on Number line, click on the link:
https://brainly.com/question/13425491
#SPJ1
how to solve 4 divided by 3
Answer:
1.33333 , it just keeps going
Step-by-step explanation:
divide 4/3 you can use a long division or a calculator.
Hope this helps!!
Let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = integral^x_1, (t) dt. Find the values of g(2) and g(-2). For each of g'(-3) and g"(-3), find the value or state that it docs not exist. Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. For -4 < x < 3, find all values of v for which the graph of g has a point of inflection. Explain your reasoning.
a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2
b) The value of g'(x) = 2 The value of g''(x) =1
c) g has neither a relative maximum nor a relative minimum at x= 1
d) the graph of g has a point of inflection at each of x=-2 , x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
There are several types of functions in maths. Some important types are:
Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
To know more about functions visit: brainly.com/question/21145944
#SPJ4