[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]
[tex]\begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\dotfill &150\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &35 \end{cases}[/tex]
[tex]A=150\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12\cdot 35}-1} {\frac{0.04}{12}} \right]\implies A= 150\left[ \cfrac{\left( \frac{301}{300} \right)^{420}~~ - ~~1}{\frac{1}{300}} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 137059.64~\hfill[/tex]
Anthony is going to invest in an account paying an interest rate of 4.6% compounded monthly. How much would Anthony need to invest, to the nearest ten dollars, for the value of the account to reach $240,000 in 20 years?
The principal investment required to get a total amount of $240,000.00 from compound interest at a rate of 4.6% per year compounded 12 times per year over 20 years is $95,812.95.
Computation of Compound InterestGiven Data
Interest Rate r= 4.6%
Final Amount A = $240,000
Time T = 20 years
Answer:
P = $95,812.95
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 4.6/100
r = 0.046 per year,
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 240,000.00 / (1 + 0.046/12)^(12)(20)
P = 240,000.00 / (1 + 0.003833333)^(240)
P = $95,812.95
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Find the inverse of the matrix (3, -2)(-10, 9) if it exists.
Answer:
The answer is ' A '
Step-by-step explanation:
:D
The inverse of the matrix will be [tex]\left[\begin{array}{cc}\dfrac{9}{7}&\dfrac{2}{7}\\\dfrac{10}{7}&\dfrac{3}{7}\\\end{array}\right][/tex]. The correct option is A.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of such an object in mathematics. For instance, consider a matrix with two rows and three columns.
Given that the matrix is [tex]\left[\begin{array}{cc}3&-2\\-10&9\\\end{array}\right][/tex]. The inverse of the matrix can be solved as below,
[tex]A^{-1} = \dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]
[tex]A^{-1} = \dfrac{1}{3\times9-20}\left[\begin{array}{cc}9&2\\10&3\\\end{array}\right][/tex]
[tex]A^{-1} = \dfrac{1}{7}\left[\begin{array}{cc}9&2\\10&3\\\end{array}\right][/tex]
[tex]A^{-1}=\left[\begin{array}{cc}\dfrac{9}{7}&\dfrac{2}{7}\\\dfrac{10}{7}&\dfrac{3}{7}\\\end{array}\right][/tex].
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find the side of a cube whose surface area is 216 sq. m
Answer:
6 m
Step-by-step explanation:
Side = x
Surface area = [tex]6x^2[/tex]
[tex]6x^2 = 216[/tex]
[tex]x^2 =36[/tex]
x = 6
The answer is 6m
Hope this helps :)
Have a nice day!
The side length of the cube is calculated as 6m
Data;
Surface Area = 216 sq. medge length = xSurface Area of a CubeThe surface area of a cube is given as
[tex]A = 6x^2[/tex]
This indicates all the six sides in the cube.
Let's substitute the values and solve for x
[tex]A = 6x^2\\216 = 6x^2\\\frac{216}{6} =\frac{6x^2}{6} \\x^2 = 36\\x= \sqrt{36} \\x = 6[/tex]
The side length of the cube is calculated as 6m
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Simplify the expression 6h +(-7.7d) – 16 + 5d - 2.6h.
Answer:
3.4h-2.7d-16
Step-by-step explanation:
Before we even start, we can already simplify some things
For example, in this equation it says +(-7.7d)
We can simplify this to 6h-7.7d-16+5d-2.6h
Now we have to get all of the common variables together
So the d’s and h’s have to be combined together in this equation
This makes a new equation of 3.4h-2.7d-16
That is our answer!
2(x - 10) = 59
What are the steps to come to the correct answer?
Answer:
39.5
Step-by-step explanation:
Open the bracket by multiplying the numbers in the bracket by 2
2x-20=59
collect like terms(-20 crossing over the equal sign will become +20
2x=59+20
2x=79
Divide both sides by 2
[tex]\frac{2x}{2} =\frac{79}{2}[/tex]
x=39.5
[tex] \sf \large↪2(x - 10) = 59[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: ↪2x - 20 = 59[/tex][tex] \: \: [/tex]
[tex]\sf \large \: ↪2x = 59 + 20[/tex][tex] \: \: [/tex]
[tex]\sf \large \: ↪2x = 79[/tex]
[tex] \: \: \: [/tex]
[tex] \sf \large \: ↪x = \cancel \frac{79}{2} [/tex][tex] \: \: [/tex]
[tex]\sf \large \color{purple} ↪39.5[/tex][tex] \: \: \: [/tex]
i need help to solve 4x^2-400=0
Answer:
x = 10
Step-by-step explanation:
Isolate the variable and get x by itself
4x^2 -400 = 0 add 400 to both sides
4x^2 = 400 divide both sides by 4
x^2 = 100. take the square root of both sides
x = 10
What is the bar model for 20-x=6
Answer:
14
Step-by-step explanation:
20-x=6
20-14=6
hope this will help you
David has 400 yards of fencing and wishes to enclose a rectangular area against a pre-existing fence. What equation should David use to help him maximize the area?
A. f(x)=x(400-2x)
B. f(x)=x(400+2x)
C. f(x)=2x(400-x)
D. f(x)=2x(400+x)
Answer: f(x)=x(400-2x)
The equation for the area in terms of x gives the function David should
use to maximize the area.
Response:
The equation that David should use to help him maximize the area is option A.
A. f(x) = x·(400 - 2·x)How can the function for the area be obtained?The given parameter are;
Length of fencing David has = 400 yards
Area to be enclosed = Rectangular area with pre-existing fence (on one side)
Required:
The equation David should use to maximize the area.
Solution:
Let x represent the width of the area (the sides perpendicular to the pre-
existing fence), and let y represent the length of pre-existing fence
We have;
Length of fencing available = Opposite side to pre-existing fence + 2 × Width of the area
Opposite side to pre-existing fence = Length of pre-existing fence
Which gives;
Length of fencing available = Length of pre-existing fence + 2 × Width of the area
400 = y + 2·x
y = 400 - 2·x
Area = Length × Width
Which gives;
Area = y × x
Area as a function of x is therefore;
Area, f(x)= (400 - 2·x) × x
Which gives;
f(x) = x·(400 - 2·x)The correct option is therefore;
A. f(x) = x·(400 - 2·x)Learn more about writing equations here:
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Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples.
How many Golden Delicious apples did Mary buy?
Answer:
Mary bought 9 Golden Delicious apples
Step-by-step explanation:
This can be solved by setting up a system of equations. Based on the information given, the equations would be set up as follows.
[tex].75d+1.25g=21.00\\d+g=22[/tex]
I prefer to solve using substitution, but elimination can be used as well
[tex].75d+1.25g=21.00\\g=22-d[/tex]
We can now plug in this g value to the first equation
[tex].75d + 1.25 (22-d)=21.00\\.75d + 27.5-1.25d=21\\27.5-0.5d=21\\-.5d=-6.5\\d=13[/tex]
This means mary bought 13 delicious apples. She bought 22 apples in total, so the total number minus the amount of delicious apples will give us the amount of golden delicious apples.
22 - 13 = g
9 = g
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
Let me know if you have any questions! Spread the love.
John has some apples, and two brothers, Jack
and Jim.
John eats 3 of his apples and splits the
remainder equally between himself and each
one of his brothers. Jack and Jim both eat half
the apples they have been given. Together the
three brothers have 4 apples left.
How many apples did John start with?
John now has X - 3
and splits the remainder equally between himself and his brothers
Each of the brothers now has (X-3)/3 apples (we have to assume here that Jack and Jim didn't have any apples to begin with).
Jack and John both eat half of the apples they have been given
They now have (X-3)/3/2, or just (X-3)/6
Together the three brothers have 4 apples left
Now we say 4 = (X-3)/3 (Jim) + (X-3)/6 (Jack) + (X-3)/6 (John)
From here it's algebra. A nice trick we can do here is to add (X-3)/6 + (X-3)/6 together first, since they have the same denominator:
4 = (X-3)/3 + (X-3)/3
From there we can do the same trick, since now we have two terms that are both something/3:
4 = 2(X-3)/3
Multiply both sides by 3, divide both sides by 2:
6 = X - 3
Add 3 to both sides
9 = X
Answer:
8 or 9
Step-by-step explanation:
John eats 3 gives brothers and himself the remainder they both eat half and both halves are left making it 1 so add up to how much was eaten 3+1=4 and they have 4 left making it 8. Or just say x-3-1=4 and x=8. It can also be 9 so hopefully, someone else answers because if we add the halves remaining to the altogether it becomes 9 instead. Hope it's right and makes sense.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+2
x+4
Answer:
A=x²+6x+8
Step-by-step explanation:
Answer: A=x²+6x+8
Step-by-step explanation: Since we are looking to find the area of the entire rectangle, we would use the formula. is the length and is width. You would approach this problem like any other area of the rectangle problem, except you are dealing with polynomials instead.
How much sugar syrup what you get by making the following concentration 10% sugar syrup is it 80 g of sugar
Solve
Answer:
800g
Step-by-step explanation:
10% of x = 80 g
x = 80 x 10
x = 800g
Can anyone help me find the missing coefficient?
2n + (7n + 8) = n + 8
Answer:
Step-by-step explanation:
2n + 7n + 8 = n + 8
9n + 8 = n + 8
9n = n
n = 0
Answer:
n = 0
Step-by-step explanation:
2n + (7n + 8) = n + 8
2n + 7n + 8 = n + 8
9n + 8 = n + 8
9n -n = 8 - 8
8n = 0
n = 0
Given two sides of a triangle, find a range of possible lengths for the third side.
4 cm, 17 cm
It takes Skyler 10 hours to rake the front lawn while his brother, Sergio, can rake the lawn in 6 hours. How long will it take them to rake the lawn working together?
To rent a certain meeting room, a collage charges a reservation fee of 49 dollars and an additional fee of 5 dollars and 40 cents per hour. The film club wants to spend at most 81 dollars and 40 cents on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room.
PLEASE HELP WILL GIVE BRAINLIEST
Danny and Delilah were playing a game where they drew digits and placed them on a game board. Danny built the number 247. Delilah built the number 724. How much greater is the value of the digit 2 in Danny's number than the value of the digit 2 in Delilah's number?
Answer:
• This student received Met because the student stated that the 2 in Danny’s number is ten times greater than the 2 in Delilah’s number. The student stated that the 4 in Delilah’s number is one tenth the value of the 4 in Danny’s number. The student stated that the 7 in Delilah’s number is 100 times the 7 in Danny’s number.
This student received Progressing because the student correctly stated that Danny’s number was ten times bigger. The student also stated that the 4 in Delilah’s number is ten times smaller. The student stated the value of the digit 7 without referring to how the values compared.
Step-by-step explanation:
hope this helps :) (:
How do you Solve for x
Answer:
C. x=12
Step-by-step explanation:
Angles in a triangles add up to 180 degrees. We are given that one angle is a right angle which means it's 90 degrees so...
2x+1+5x+5+90=180
Add like terms
96+7x=180
Subtract 96 from both sides
7x=84
Divide both sides by 7
x=12
4. The Lopez family is buying a new home. The price of their home is
$345,800. They also pay for new furniture. In the amount they pay for
new furniture, the digit 5 is exactly 10 times less than it is in the
amount they paid for the house. What is one possible amount that
they could have paid for furniture?
One possible amount the could have paid for furniture is $340,500.
Since the Lopez family pay a price of $345,800 for their new home, and also pay an amount for the furniture in which the digit 5 is exactly 10 times less than it is in the amount they paid for the house.
Amount paid for furnitureSince they paid $345,800 for their home and the digit 5 in this amount is in the thousands place, that is 5000.
In the amount paid for the furniture, the digit 5 is exactly 10 times less than in the amount paid for their home.
So, the place of the digit 5 in the amount paid for the furniture is thus 5000 ÷ 10 = 500.
So, the digit 5 is in the hundreds place.
With that in mind, replacing the 8 in the hunderds place in $345,800, one possible amount the could have paid for furniture is $340,500.
So, one possible amount the could have paid for furniture is $340,500.
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what is the square root of 64?
Help ill give brainliest to the one that works
Answer:
8
Step-by-step explanation:
The square root of 64 is 8
Answer:
8
Step-by-step explanation:
The square root of 64 is 8
8 * 8 = 64
Hope this helps!
PLZ HELP ILL MARK AS BRAINLIEST
Answer:
[tex]2,712 \: {yd}^{2} [/tex]
Step-by-step explanation:
Height of cylinder (h) = 24 yd
radius of cylinder (r) = 6 yd
Lateral surface area of the cylinder
[tex] = \pi {r}^{2} h \\ \\ = 3.14 {(6)}^{2}(24) \\ \\ = 2,712.96 \: {yd}^{2} \\ \\ \approx \: 2,712 \: {yd}^{2} [/tex]
Brainliest if correct
Answer:
w = 3
Step-by-step explanation:
-2 = w -5
Add 5 to both sides of the equation
-2+5=2-5+5
Simplify
w = 3
[RevyBreeze]
Jonathan has 2 solids. One is a right cylinder, and
the other is a sphere. The radius of the base of the
cylinder is the radius of the sphere. The height of
the cylinder is 10 cm. The diameter of the sphere is
12 cm. What is the lateral surface area, in square
centimeters of the cylinder?
O 1847
O 60
O 787
0 120
If you multiply all of them you would get 787 so your answer would be C.
It would be 787
(-4x-9)+(-2x-7) in simplest term
Answer:
-6x-16
Step-by-step explanation:
Combine like terms, (-4x-2x) + (-9-7) = -6x - 16
Step-by-step explanation:
We'll be combining like-terms.
Remove the addition sign, as it has no effect to the expression:
[tex] - 4x - 9 - 2x - 7[/tex]
Combine Like-Terms:
[tex] - 6x - 16[/tex]
-6x - 16 is your simplified expression.
Determine whether the given value is a solution of the equation.
Answer:
84 is a solution.
Step-by-step explanation:
To find out if 84 is a solution or not, we plug in the value and simplify.
(84)/14 = 66 = 6Therefore, 84 is a solution.
Please a genius help me please
Answer:
B, D, and F
They match the graph
Please help!!
-5x+6y=12
y=5/6x+2
Answer:
this is the first answer
Step-by-step explanation:
hope this helps
2. Which of the following expressions is equal to (2g)^3
Answer:
8g³
Step-by-step explanation:
(2g)³ = 2³·g³
A study analyzed the average yearly salt intake in the United States from 2012 thru 2017. The data is summarized in the table:
Year Annual Salt Intake
(grams)
2012 3,554
2013 3,598
2014 3,603
2015 3,655
2016 3,718
2017 3,794
The study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the number of years since 2012 and f(x) is the total amount of salt ingested in grams. Describe the significance of 3,548.
An estimate of the average grams of salt used in 2012
An estimate of the average grams of salt used in 2013
The average amount of salt in grams used in 2012
The average amount of salt in grams used in 2013
Answer:
The answer is A. AN ESTIMATE OOF THE AVERAGE GRAMS OF SALT USED IN 2012.
Step-by-step explanation:
This picture explains everything:
An estimate of the average grams of salt used in 2012.
How the value of x in f(x) is calculated?
Given the values are:
Year Annual Salt Intake
(grams)
2012 3,554
2013 3,598
2014 3,603
2015 3,655
2016 3,718
2017 3,794
Here, we have to find the significance value of 3,548.
f(x) = 52.3x + 3,548
x - number of years
If x = 0,
f(0) = 52.3 (0) + 3,548
= 3,548.
Thus, it is found that it was an estimate of the average grams of salt used in 2012.
So, Option A is the correct answer.
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