Answer:
n = 16
Step-by-step explanation:
The slope from the origin to each point must be equal
(0,0) and (n, 8)
m = 8/n
(0, 0) and (32, n)
m = n/32
Set the slopes equal
8/n = n/32
cross multiply
256 = n²
Take the square root of both sides
n = 16
John finances his daughter's college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16th through the 19th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero. Calculate X.
Answer:
Monthly payment = 241.925
Step-by-step explanation:
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
Solving, we have i = 0.6434% monthly approximately
To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18. We therefore conclude that the "future values" fall on the same day, and that they are equal.
We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts. By the end of the operations, one will balance the other (they are equal).
We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.
F(A,i,n) = A*((1+i)^n-1)/i
Step 1:
calculate the future value of the withdrawals
A = W = 25000 (annual withdrawal)
i = 8% (effective annual interest)
n = 4 years (beginning of 16,17,18,and 19th years)
F(A,i,n) = A*((1+i)^n-1)/i
= 25000( (1+0.08)^4 - 1)/(0.08)
= 112652.80
This is also the total deposit after eighteen years.
Step 2:
calculate the future value of the annual deposits D
A = D (total of annual deposits)
i = 8% (effective annual interest)
n = 18 years
Future value of deposits
F(A,i,n) = A*((1+i)^n-1)/i
= D( (1+0.08)^18 -1 ) / 0.08
= 37.45024373981167D
Since this must equal the total withdrawal, we equate the two to calculate D.
37.45024373981167D=112652.80
and solve for D
D = 112652.80 / 37.45024373981167
= $3008.0659
Step 3
Calculate monthly deposit, X
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
The actual monthly interest rate is therefore
i = 1.08^(1/12)-1
Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by
D = X*((1+i)^n-1)/i
3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)
or the monthly amount
X = $3008.0659 / ( 1.08^(1/12)-1)
= 241.925 per month.
=
Mary has 2 blouses (1 Red and 1 blue) and 3 pair of slacks (1 yellow and 1 white and 1 green).
If Mary choose 1 blouse and 1 pair of slacks at random , what is the probability that the outfit she chooses will include a pair of green slacks?
Answer:
1/3, the information with the blouses is there to distract you
I need help.
The question is in the picture
Answer: In attached
Step-by-step explanation:
Use the given functions to set up and simplify
Attachment has your answer.
I’m not good at typing functions on this app so this image is all I could give.
Answer:
there you go..........
30. A model train is 4 inches long. If the
scale factor is 1 in : 48 it, what is the
actual length of the train?
F 192 feet
H 12 nches
G 12 feet
s 192 inches
grade 7 work please help
there is 2 questions 5 and 6
Answer:
For 5 the yellow square stays the same, while the blue adds 2 each time.
5. 1(2x) something like that.
6. 3 is 6 4 is 7 5 is 8
I have gotten too old for this, my bad somethings just dont make sense anymore.
Answer:
5.
a. 2 blue blocks added
b. 2 blue blocks are added on the top blue blocks
c.y = 2x +3
6.
a.
1,4
2,5
3,6
4,7
5,8
b. starting off with 4 triangles and ending with a bottom triangle a triangle is added first from the top, then the bottom for each increase (increment)
c. y = x+4
Step-by-step explanation:
all the answers are up
Please help me with this question!!
Answer:
ok so for g times h you would have to foil it and then you would multiply it by f of X
The Solution to a system of linear equations is the _____
of their graphs.
please help me with this .
Answer:
20:1
Step-by-step explanation:
every 20 dollar she spends she save 1 dollar
On a coordinate plane, a line goes through points (1, negative 1) and (2, 4). This graph displays a linear function. What is the rate of change? Rate of change =
Answer:
5
just took the test
Answer:
Step-by-step explanation:
its 5
Question 1 of 5 Shelley has a bag containing three balls: one red, one yellow, and one green. All balls are equally likely to be chosen. Shelley will choose one ball without looking in the bag. What is the probability that Shelley will choose the yellow ball out of the bag?
Answer:
1/3=33 1/3%
Step-by-step explanation:
Since there is 3 balls.
What are the measures of
∠
1
and
∠
2
? Show your work or explain your answers.
Answer:
Step-by-step explanation:
angle 2 is 75 degree because angle 2 and 75 dgeree are corresponding angles corresponding angles are always equal.
angle 1 + angle 2 = 180 degree (being linear pair)
angle 1 = 180 - 75
angle 1 = 105 degree
∠1 = 105° and ∠2 = 75°
What are parallel lines?"These are the lines in the same plane that are at equal distance from each other and never meet."
What is transversal?"It is a line that passes through two lines in the same plane at two distinct points."
What are corresponding angles?"The angles which are formed in matching corners or corresponding corners with the transversal when the transversal intersects two parallel lines."
For given question,
Line c and line d are parallel lines.
These parallel lines are intersected by a transversal.
We can observe that ∠2 and the angle that measures 75° are corresponding angles.
We know that the corresponding angles are congruent.
⇒ ∠2 = 75°
Also, the sum of all angles on either side of the line is 180°
⇒ ∠1 + ∠2 = 180°
⇒ ∠1 + 75° = 180°
⇒ ∠1 = 105°
Therefore, ∠1 = 105° and ∠2 = 75°
Learn more about parallel lines and transversal here:
https://brainly.com/question/17432060
#SPJ3
what is the answer to
2/3x = − 1/2x + 5
Answer:
x = 30/7
Step-by-step explanation:
2/3x = − 1/2x + 5
multiply by 6 to clear the fractions
4x = -3x + 30
add 3x to both sides
7x = 30
Divide both sides by 7
x = 30/7
Alan recorded the points he scored on the basketball court in ms2 school yard. What is the mean absolute deviation of his scores
Answer:
The mean absolute deviation is: 7.44
Step-by-step explanation:
Given
[tex]Scores: 98, 78, 84, 75, 91[/tex]
Required
The mean absolute deviation
First, calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{98+78+84+75+91}{5}[/tex]
[tex]\bar x = \frac{426}{5}[/tex]
[tex]\bar x = 85.2[/tex]
The mean absolute deviation (M) is:
[tex]M = \frac{1}{n}\sum|x - \bar x|[/tex]
So, we have:
[tex]M = \frac{1}{5}(|98 - 85.2|+|78 - 85.2|+|84 - 85.2|+|75 - 85.2|+|91 - 85.2|)[/tex]
[tex]M = \frac{1}{5}(|12.8|+|-7.2|+|-1.2|+|-10.2|+|5.8|)[/tex]
Remove absolute brackets
[tex]M = \frac{1}{5}(12.8+7.2+1.2+10.2+5.8)[/tex]
[tex]M = \frac{1}{5}*37.2[/tex]
[tex]M = 7.44[/tex]
Find the circumference of a circle with radius, r = 6.5m.
Give your answer in terms of pie
Answer:
13π m
Step-by-step explanation:
circumference of a circle = 2πr
=2*π*6.5
=13π m
Answer:
13[tex]\pi[/tex] m
Step-by-step explanation:
The formula for circumference is 2r[tex]\pi[/tex], so...
2r[tex]\pi[/tex]
2(6.5)[tex]\pi[/tex]
=13[tex]\pi[/tex]
Please help me i'm struggling!
Answer:
c
Step-by-step explanation:
Answer:
x is greater than or equal to 3
So it is the first answer.
Part A
Whose scatter plot matches the data, and what is wrong with the incorrect scatter plot?
Answer: hello your question has some missing data attached below is the missing data
answer:
The second scatter plot
Step-by-step explanation:
The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot
Answer:
Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.
Step-by-step explanation:
If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.
(in other words the other person who answered is correct)
NEED HELP ASAP
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 1/3. What is the equation of function g?
Substitute a numerical value for k into the function equation.
Step-by-step explanation:
x' = ⅓ x => x = 3x'
f'(x) = 7(3x')+1
= 21x' + 1
so g(x) = 21x + 1
Wendy has $17 to buy seed for her birdfeeders. Each bag of seed costs $2. How many bags of seed can she buy?
Answer:
It depends if there is tax or not, if there isn't she can buy 8 of them.
Step-by-step explanation:
$17 is the total so we need to see how many $2 fit in $17.
8×2=16, and 16 is the closest number we can get to.
what is nine times a number x, in algebraic expression?
Answer:
Not possible to answer.
calculate the amount that will be in the bank after 4years if R3500 was invested at 9% p.a. simple interest
Answer:
4760
Step-by-step explanation:
Simple interest= principal× time ×rate/100
=3500×4×9/100
= 1260
Amount that will be in the bank after 4years= 3500+1260
=4760
Xavier shoots a basketball in which the height, in feet, is modeled by the equation, h(t) = -4t^2+10t +18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
h = 24.25 feet
Step-by-step explanation:
Xavier shoots a basketball in which the height, in feet, is modeled by the equation.
[tex]h(t) = -4t^2+10t +18[/tex] ....(1)
For maximum height,
Put dh/dt=0
So,
[tex]\dfrac{dh}{dt}=\dfrac{d}{dt}(-4t^2+10t +18)\\\\=-8t+10[/tex]
So,
-8t = -10
t =1.25s
Put t = 1.25 s in equation (1)
[tex]h(t) = -4(1.25)^2+10(1.25) +18\\\\=24.25\ feet[/tex]
So, the maximum height of the basketball is equal to 24.25 feet.
Find the surface area plzzzzzz
Answer:
184 m²
Step-by-step explanation:
Surface Area = 2(10*2) + 2(10*6) + 2(2*6)
Surface Area = 2(20 + 60 + 12)
Surface Area = 2(92)
Surface Area = 184 m²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
how many solutions are there to the system of equations graphed below if the lines are parallel ?
A. Zero
They're parallel so they will never intersect therefore: no solutions :]
What is the equation of the line that passes through the point (−4,−8) and has a slope of 4?
Answer:
i hatee maths thank u
Step-by-step explanation:
For each steak, lobster, or chicken dinner in a restaurant, you have a choice of french fries or mashed potatoes. You get a choice of Water or Iced Tea to drink. If all combinations are equally likely to be ordered, find the sample space of the possible outcomes.
Please help I’ll give brainliest
Answer:
B. $1650
Step-by-step explanation:
the middle share = 3/(2+3+5) × $5500
= 3/10 × $5500 = $1650
Which linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
Answer:
y minus 9 = negative 2 (x + 1)
Step-by-step explanation:
i put it onto desnos graphing calculater and thats what i got
Answer:
A
Step-by-step explanation:
bannana
Find the value of x
Answer:
X+6+2x=180
6+3x=180
3x=172
x=57 1/3
Using the equation
[tex] \sqrt{x + 7} + 5 = x[/tex]
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.
Given:
The equation is:
[tex]\sqrt{x+7}+5=x[/tex]
To find:
Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.
Solution:
We have,
[tex]\sqrt{x+7}+5=x[/tex]
Subtract 5 from both sides.
[tex]\sqrt{x+7}=x-5[/tex]
Taking square on both sides, we get
[tex]x+7=(x-5)^2[/tex]
[tex]x+7=x^2-10x+25[/tex]
[tex]0=x^2-10x+25-x-7[/tex]
[tex]0=x^2-11x+18[/tex]
Splitting the middle term, we get
[tex]x^2-2x-9x+18=0[/tex]
[tex]x(x-2)-9(x-2)=0[/tex]
[tex](x-2)(x-9)=0[/tex]
[tex]x=2,9[/tex]
Now, substitute [tex]x=2[/tex] in the given equation.
[tex]\sqrt{2+7}+5=2[/tex]
[tex]\sqrt{9}+5=2[/tex]
[tex]3+5=2[/tex]
[tex]8=2[/tex]
This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.
Substitute [tex]x=9[/tex] in the given equation.
[tex]\sqrt{9+7}+5=9[/tex]
[tex]\sqrt{16}+5=9[/tex]
[tex]4+5=9[/tex]
[tex]9=9[/tex]
This statement is true. So, 9 is a solution of given equation.
Therefore, 2 is an extraneous solution and 9 is a solution of given equation.
Find the area of the triangle on problem #7 and what statement in true for the triangle on #8
Answer:
Step-by-step explanation:
Using the pythagorean theorem, a^2+b^2=c^2
32/2=16, 20 would be the hypotenuse, so it would be 20^2-16^2=a^2 because we want to find the middle line. 400-256=144. sqrt(144) = 12.
Then since it is an isosceles triangle, we can simply do 12*16=192
The answer for 7 is 192ft^2
For #8, the answer is short leg * sqrt(3) = long leg
On another note, you can find the hypotenuse of a 30-60-90 triangle by doubling the shortest leg