Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT = (R% of P)T
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).
Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,
6.5% of x + 9% of ($50,000 - x) = $3625
0.065x + 0.09(50,000 - x) = 3625
0.065x + 4,500 - 0.09x = 3,625
0.065x - 0.09x = 3625 - 4500
0.025 = 875
x = 875/0.025
x = 35,000
Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.
Learn more about Simple Interest here:
https://brainly.com/question/2793278
#SPJ4
Hassan's soccer team is trying to raise $688 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $43 for the breakfast. How many people need to attend their breakfast in order to raise $688?
Answer: 182
Step-by-step explanation:
What is the slope of the line that passes through the points (4, -6) and (-2, 3)?
Write your answer in simplest form.
Answer:
-3/2
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (3 - (-6))/(-2 - 4)
slope = (3 + 6)/(-6) = 9/(-6)
slope = -3/2
Answer:
Step-by-step explanation: 3/-2
17. the amount a of money in an account after simple interest has been earned is given
by the formula a = p + prt where p is the principal, r is the annual interest rate
in decimal form, and t is the time in years.
a. solve the formula for r
b. the amount of money in an account after interest has been earned is $1080, the
principal is $1000, and the time is 2 years. what is the annual interest rate?
c. solve the formula for p.
pl
a) the formula for r is r = (a/p - 1)/r
b) The interest rate for the principal is $1000, the time is 2 years and simple inters $1080 is 0.04
c) The formula for p is p = a/1+rt
Simple Interest:
Simple interest is the process of multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given,
the amount a of money in an account after simple interest has been earned is given by the formula
=> a = p + prt
where
p is the principal,
r is the annual interest rate in decimal form, and
t is the time in years.
Here we need to find the following:
a. solve the formula for r
b. the amount of money in an account after interest has been earned is $1080, the principal is $1000, and the time is 2 years. what is the annual interest rate?
c. solve the formula for p.
a) The formula for r is calculated by moving the other elements and hold on r.
Then, the given formula,
=> a = p + prt
=> a = p (1 + rt)
=> a/p = 1 + rt
=> a/p - 1 = rt
=> r = (a/p - 1)/r
b) The given values are
p = $1000
t = 2
a = $1080
Now apply the values on the formula r to find the value of it,
=> r = ([1080/1000] - 1)/2
=> r = (1.08 - 1) /2
=> r = 0.08/2
=> r = 0.04
c) The formula for p can be derived as follows:
=> a = p + prt
=> a = p(1+rt)
=> p = a/1+rt
To know more about Simple Interest here.
https://brainly.com/question/25845758
#SPJ4
Natalie is paid for writing numbers on pages of a book. She is paid for writing each digit of the number. If she wrote 702 digits, how many pages is the book?
Answer:
I think 1,000??
HELP NEED ANSWERS ASAP!''!!!!!!!!!!!!!!!
By using subtraction, Brenda needs an additional amount of $ 182.75 for the school trip.
How much money does Brenda need to save for her school trip?
In this question we notice that Brenda is aware of how much money she needs to make her school trip and besides we find a table with all the money saved during a 4-month period. Lastly, we must determine if the amount of money saved by Brenda is sufficient or not.
The money needed for the school trip is:
y = $ 197 + $ 230 + $ 85
y = $ 512
And the money saved by Brenda is:
x = $ 67 + $ 30.50 + $ 160 + $ 71.75
x = $ 329.25
Then, the additional money needed for Brenda is found by subtacting the second result from the first result:
z = y - x
z = $ 512 - $ 329.25
z = $ 182.75
Brenda needs an additional amount of $ 182.75 for the school trip.
To learn more on subtraction: https://brainly.com/question/1927340
#SPJ1
Complete the table of values for f(x) = -3|x+1|-4 using the table of values for g(x) = |x|
f(x)>=-7
Functions:
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x
Given :
f(x) = -3|x+1|-4
using the table of values for g(x) = |x|
Solution :
f(x) = -3|x+1|-4
f(x) = -3|g(x)+1|-4
f(x) = -3||x|+1|-4
which means |x| is always positive |x|>0
f(x) = -3||x|+1|-4
f(x) = -3x-3-4
f(x) = -3x-7
f(x)>=-7
For more details: brainly.com/question/18071485
#SPJ9
0.6x +0.5=0.8x - 1.1
Answer:
8
Step by step :
0.6x = 0.8x-1.1-0.5
0.6x-0.8x = -1.6
-0.2x = -1.6
x = -1.6/-0.2
x = 8
Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (let |a| = 26 lb a
Magnitude of the resultant vector = 31.3 lb and Angle of the resultant vector = 23.3o are the magnitude of the resultant force and the angle .
what is magnitude of forces?
The amount that encapsulates the force's strength is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude can be thought of as simply the "value" or "amount" of any physical quantity.a = 26 lb
Angle made by the vector 'a' = θ1 = 45o
Component of vector 'a' in the X-direction = ax = aCosθ1 = (26)Cos(45) = 18.38 lb
Component of vector 'a' in the Y-direction = ay = aSinθ1 = (26)Sin(45) = 18.38 lb
b = 12 lb
Angle made by the vector 'b' = θ2 = 30o
Component of vector 'b' in the X-direction = bx = bCosθ2 = (12)Cos(30) = 10.39 lb
Component of vector 'b' in the Y-direction = by = -bSinθ2 = -(12)Sin(30) = -6 lb
Let the resultant vector be 'c'
Component of vector 'c' in the X-direction = cx
cx = ax + bx
cx = 18.38 + 10.39
cx = 28.77 lb
Component of vector 'c' in the Y-direction = cy
cy = ay + by
cy = 18.38 + (-6)
cy = 12.38 lb
c=104)2 + (cy)
c= (28.77)2 + (12.38)2
c = 31.3 lb
Angle made by vector 'c' = θ
Tanθ =
Tanθ = 12.38 28.77
θ = 23.3o
a) Magnitude of the resultant vector = 31.3 lb
b) Angle of the resultant vector = 23.3o
Learn more about magnitude
brainly.com/question/18485448
#SPJ4
THE COMPLETE QUESTION IS -
Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 26 lb and b = 12 lb. Round your answers to one decimal place.)
Why is nobody ANSWERING ME PLS MAth HELPPPPPP 12 points
Answer:
Step-by-step explanation:
Lets see here, this question is a bit confusing to understand, But Ill work at it for you ^^
So at that first line that says ones, you are going to want the middle lint horizontal on that vertical line to be labeled 5.
Slightly above that, more near to the top you are going to want to write 85.
On the second Line drawn you are going to want to label the middle horizontal line 4
Above that, near the top write 854
The rounded number of 8.546 Would Be 9, Because since the tens place is a 5, you round up a number.
for question 3. a
the answer would be 18.4 if you round to the tenths, or 18.39
This is because the number in the thousands place is a 6, and thats 5 or above so you round the hundreths up 1 to become 9, and 9 is 5 or above so the 3 would become a 4(only if rounding to the tenths!!)
For question 3. b
1 meter = 100 centimeters, so we would multiply 18.386 by 100
That would shift the decimal point to the right 2 places (if you don't want to have to do the multiplying, rule of thumb is one 0 shifts one place to the right, you shift however many places as there are zeroes)
This would give us 1838.6 centimeters.
And I cant read question 4(sorry)
Hope this helps!!
The granite sample has a
mass of 24. 31 g and a volume
of 9. 35 cm3. What is the
density of the granite?
d = [?] g/cm3
Find the value of x in the given diagram.
Answer:
The value of x is 125°.==================================
We see the exterior angle measures given with one unknown.
Recall the sum all exterior angles of a polygon is 360°.
Set up equation and find the unknown value:
70 + 65 + 60 + 40 + x = 360235 + x = 360x = 360 - 235x = 1254. If C.P of a product is E950 and loss percentage is 6%, then find the S.P of the product.
So S.P of the product is 10.4% .
We have been given C.P of a product is E950 and loss percentage is 6%,.
So the starting price is the the price for which something actually sells.
And the cost price represents the specific value that represents unit price purchased. This value is used as a key factor in determining profitability, and in some stock market theories it is used in establishing the value of stock holding.
A saving account has a rate of interest of 10 denoted by our which we can write equal to 0.1 in decimal form and we have to calculate the effective annual yield yield if the interest is calculated quarterly, that means we have the number of compounds per year denoted by M equal to four. The effective yield denoted by capital Y is given by the formula one plus are divided by M. Hold raised to the Power M -1. After putting in the values of R and M we get one plus 0.1 divided by four. Hold raised to the Power 4 -1, equal to one plus 0.25 raised to the power four minus one which is equal to 1.025 raised to the Power 4 -1. On simplifying this further, we get the value equal to 0.1038. Now this value is in the decimal form to convert it into percentage. We will multiply this value by 100. That means we have like 0.1038 multiplied by 100 Which gives us 10.38. And after rounding it off to one decimal place, we get the value 10.4%.
Know more about cost price and sell price at brainly.com/question/26536051
#SPJ9
What is the area of the semicircle? Use 3.14 for pi. 22cm
hi
area of circle is π* radius²
as radius is half diameter, and as diameter is 22 , so radius is 22 /2 = 11 cm
so area is 11²π and 11² = 121 then area is 121π
as it is say to use 3.14 for pi , then 121*3.14 = 379.94
but 379.94 is the area of the whole circle , and we only have half.
so : 379.94 / 2 = 189.97
area of semi circle is 189.97
Find the equation of the line shown.
Answer:
The x is 2 and the y is 1. So, it's 1/2
Step-by-step explanation:
x = 2
y = 1
Slope goes y,x,
please help!
Given an arithmetic progression -8, -3, 2,.... Determine three consecutive terms in this progression which sum up to 111.
Answer:
9th, 10th and 11th terms; 32, 37 and 42=============================
Given AP:
-8, - 3, 2, ...We observe that:
The first term is a = - 8,The common difference is d = -3 - (-8) = 2 - (-3) = 5.Let the three terms be aₙ, aₙ₊₁, aₙ₊₂.
Use nth term formula:
aₙ = a + (n - 1)d = - 8 + (n - 1)*5 = - 8 + 5n - 5 = 5n - 13The following two terms are:
aₙ₊₁ = 5n - 13 + 5 = 5n - 8aₙ₊₂ = 5n - 8 + 5 = 5n - 3Their sum is 111, set an equation and solve for n:
5n - 13 + 5n - 8 + 5n - 3 = 11115n - 24 = 11115n = 135n = 135/15n = 9The three terms are 9th, 10th and 11th terms and they are:
5*9 - 13 = 45 - 13 = 3232 + 5 = 3737 + 5 = 42Three red cards are numbered 1, 2, and 3 and the other three green cards are also numbered 1, 2, and 3. All of them are in a box. Randomly pick 2 cards one by one with returning before the second pick. Find the probability that they have the same number or the same color.
Answer:
Step-by-step explanation:
According to the information, first pick with returning make the question easy, it means that fist pick and second pick are independent events, we want to calculate the probability of same number or same color so 'or' means the addition method in statistics, from above second card has same number or same color decide the probability, not the first picked card,
P = P(same number) + P(same color) = 1/3 + 1/3 = 2/3
Or you can draw a tree diagram
The ages of three friends are represented by three consecutive odd integers. If the youngest of
the three is represented by m, express the sum of the ages of the three friends.
Solving the Question
We're given:
m is the smallest age.This means that the consecutive odd integers will be m + 2 and m + 4.
If we add all their ages, it will look like this:
[tex]m+(m+2)+(m+4)\\= m+m+2+m+4\\= 3m+2+4\\= 3m+6[/tex]
Answer[tex]3m+6[/tex]
What steps would you take to approximate the total amount Gwinnett
County must pay teachers for the whole year?
The steps that you should take to approximate the total amount that Gwinnett County must pay teachers for the whole year are:
Find out the average wages paid to teachers in Gwinnett County.Find out the number of teachers in Gwinnett County.Multiply the number of teachers with the average wages paid. How to find the approximate amount paid to teachers?The approximate amount that is paid to teachers in will be based on the average wages that is paid to teachers in Gwinnett County. You can find this out by conducting an anonymous survey of different levels of teacher salaries in Gwinnett County or you can find it from the relevant Gwinnett County government department.
Then, look for records to show the number of teachers in Gwinnett County.
Multiply these two figures and you will then get the approximate the total amount that Gwinnett County needs to pay its teachers.
Find out more on finding the approximate amount at https://brainly.com/question/201331
#SPJ1
To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment? The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan. The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment. The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.
A plan which would give Genesis the lowest monthly payment is: C. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
How to determine the plan with the lowest monthly payment?In order to determine the plan which would give Genesis the lowest monthly payment, we would calculate the simple interest earned over each of the time period.
Mathematically, the simple interest earned can be calculated by using this formula:
A = P(1 + rt)
Where:
A represents the future value.P represents the principal or original value.r represents the interest rate.t represents the time.Substituting the given parameters into the formula, we have;
A = 9000[1 + (0.09 × 3)]
A = 9000[1 + 0.27]
A = 9000 × 1.27
Future value, A = $11,430.
Next, we would calculate the monthly payment over a period of 36 months as follows:
Monthly payment = Future value/Time
Monthly payment = 11,430/36
Monthly payment = $317.50.
Similarly, we would calculate the compound interest earned on the credit card by using this formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾
A = 9000[1 + 0.015]⁸⁴
A = 9000 × 1.015⁸⁴
A = 9000 × 3.49258954
Future value, A = $31,433.31.
Next, we would calculate the monthly payment over a period of 84 months as follows:
Monthly payment = Future value/Time
Monthly payment = 31,433.31/84
Monthly payment = $372.21.
In this context, we can reasonably infer and logically deduce that the plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan.
Read more on monthly payment here: https://brainly.com/question/27447530
#SPJ1
Answer:
C
Step-by-step explanation:
got 100% on exam
Please help with algebra!
Answer: x=-10
Step-by-step explanation:
LMN=LMF+FMN
125=x+48+x+97
125=2x+48+97
125=2x+145
2x=-20
x=-10
write an equation of the line
Which choice shows 17+14+ 13 rewritten correctly using the commutative
property and then simplified correctly?
Answer:
Could I see the available choices?
Step-by-step explanation:
Answer:
didnt have the choices but any that would have it as the same problem different order
Step-by-step explanation:
17+14+13=13+14+17=14+13+17=14+17+13=17+13+14=13+17+14
The midpoint of a line segment ab is (1, 2). point a coordinates are (3,-3)
and point b coordinates are (x, 7). find the value of x.
The value of x in (x,7) is -1
Mid Point of a line segment is defined as the point which divides the line segment in equal ratio that means divides in two equal parts.
Let one end point of line segment be A(a,b) and other end be B(c,d)
then its mid point X(x,y) will be given by [tex]x=\frac{a+c}{2} , y=\frac{b+d}{2}[/tex]...….(1)
Given the points A(3,-3) and B(x,7) and the midpoint X(1,2)
The mid point [tex](1,2)=(\frac{3+x}{2} ,\frac{-3+7}{2} )[/tex]...............using (1)
On comparing the x coordinate we get
[tex]1=\frac{3+x}{2}[/tex]
On cross multiplying we get
[tex]2=3+x[/tex]
On solving further
[tex]x=-1[/tex]
Therefore , the value of x in (x,7) is -1.
Learn more about Midpoints here https://brainly.com/question/25831290
#SPJ4
f(x) = 12x + 10 is a function which can used to to calculate a person's daily paycheck.
Which would be a reasonable domain for this function?
A: all real numbers
B: 0
C: 0
D: 0
This shows that a reasonable domain for this function is x > -5/6
Domain of a functionThe domain of a function is a value of the independent variable of the function for which it exists.
Given the equation below:
f(x) = 12x + 10
Since the function represents the expression used calculate a person's daily paycheck, then the function f(x) must be greater than zero;
12x + 10 > 0
12x > -10
x > -10/12
x > -5/6
This shows that a reasonable domain for this function is x > -5/6
Learn more on domain of a function here: https://brainly.com/question/26098895
#SPJ1
Which number would be found on the number line between 0 and -1
Answer: -.5 OR -.1, -.2, -.3, -.4, -.5, -.6,-.7,-.8,-.9
Step-by-step explanation: The simple answer is -.5, it is right in the middle of 0 and -1. The answer number is everything in between.
Current trends in math instruction are likely to lead to graduates who are able to?
Current trends in math instruction are likely to lead to graduates who are able to "find precise answers quickly by consulting texts and tables."
What is math instruction?A analysis of studies on mathematics instruction encompassing students with educational disabilities discovered a variety of behavioral, cognitive, & metacognitive approaches that have been shown to improve both mathematical computation & mathematical solving problems in students with LD.
Some key features regarding the math instruction are-
The majority of metacognitive instruction has indeed been combined with really explicit instructional strategies in which students are taught and then given ample practice opportunities.Metacognitive strategy training research has revealed the effectiveness of these training across a wide range of tasks and training types. Recent research on explicit solving problems, including the growth to higher-level math including algebra, and research on affectively oriented self-instruction, has piqued the interest of many.Some points regarding the importance of the math instruction are-
encourage students to learn the math facts, concepts, computational skills, as well as strategies needed to solve a variety of problemspromote the creation of efficient and adaptable problem-solving approaches; and instill adaptive arithmetical behaviors and beliefs in students.To know more about the computational skills, here
https://brainly.com/question/28032366
#SPJ4
Write an equation in standard form of a line that is parallel to y=4x-3 and passes through the point (7, 10).
The equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
What is the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10)?Given that;
Equation of line: y = 4x - 3Point: ( 7,10 )First, we determine the slope of the line using the slope intercept form.
y = mx + b
m is slope and b is y-intercept.
y = 4x - 3
Comparing with the slope intercept form equation,
Slope m = 4
Now, to determine the the equation of line parallel, the slopes must equal.
We find the line using the point slope formula.
y - y₁ = m(x - x₁)
Plug in m = 4, x₁ = 7, y₁ = 10 and simplify.
y - 10 = 4(x - 7)
y - 10 = 4x - 28
-10 + 28 = 4x - y
4x - y = -10 + 28
4x - y = 18
Therefore, the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
Learn more about slope formular here: https://brainly.com/question/23754615
#SPJ1
The pressure, p (in lbs/ft2 ), in a pipe varies over time. five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. the pressure at t = 0 is 90.
The value of P(t) is p(t) = -70 cos(10xπ t) + 165.
What is pressure?Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).
range of pressure = low of 90 to a high of 230
As, Pressure oscillating ten times every hour. So period n = .0.2 min.
Now, P = f(t) = Acos(Bt) + D
Amplitude = (HP - LP / 2
= (230- 90) / 2
= 140/ 2
= 70
Period B = 2xpi / 0.2 = 10xπ
and, D= (Ph + Pl) / 2
= (230+ 90) / 2
= 330/ 2
= 165
Hence, p(t) = -70 cos(10xπ t) + 165.
Learn more about this pressure here:
https://brainly.com/question/9104240
#SPJ4
a statistical procedure for analyzing the results of multiple studies to reach an overall conclusion.
A "meta-analysis" is a statistical procedure for combining the findings of multiple studies to reach a single conclusion.
What is meant by meta-analysis?Meta-analyses are more rigorous and quantitative than both kinds of reviews.
Some main points related to meta-analysis are-
These papers, in addition to providing an overview, provide a quantitative assessment of how effectively a treatment works or an evaluate of how significantly more likely a person is to grow a disease if they engage in a certain behavior.Meta-analyses are performed so that research from multiple studies with differing data can be combined to make more informed decisions about effectiveness of a medication on the a person's risk of developing a disease than a Magic 8-ball.The research question is defined first in meta-analyses. A well-defined research topic identifies the population impacted by the intervention as well as the potential treatment outcome(s).To know more about the meta-analysis, here
https://brainly.com/question/14723190
#SPJ4
Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.
Both functions are the solution to the given Laplace solution.
Given Laplace's equation: [tex]u_{x x}+u_{y y}=0[/tex]
We must determine whether a given function is the solution to a given Laplace equation.If a function is a solution to a given Laplace's equation, it satisfies the solution.(1) [tex]u=e^{-x} \cos y-e^{-y} \cos x[/tex]
Differentiate with respect to x as follows:
[tex]u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x[/tex]
Differentiate with respect to y as follows:
[tex]u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x[/tex]
Supplement the values in the given Laplace equation.
[tex]e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0[/tex]
The given function in this case is the solution to the given Laplace equation.
(2) [tex]u=\sin x \cosh y+\cos x \sinh y[/tex]
Differentiate with respect to x as follows:
[tex]u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y[/tex]
Differentiate with respect to y as follows:
[tex]u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y[/tex]
Substitute the values to obtain:
[tex]-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0[/tex]
The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
Know more about Laplace's equation here:
https://brainly.com/question/14040033
#SPJ4
The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)