Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
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Select yes or no for each literal equation.
Answer:
No, Yes, Yes
Step-by-step explanation:
[tex]5x + 2y = 3[/tex]
2y = 3 - 5x
y = (3-5x) / 2
FALSE
[tex] \frac{w + 8}{2} = p[/tex]
2P = w + 8
w = 2P - 8
TRUE
[tex]ax + by = c[/tex]
by = c - ax
y = (c - ax) / b
TRUE
A class has 40 students. Number of boys are 6 more than girls. Find number of boys
and girls in the class.
Basically let's represent the number of girls with x.
There are 6 more boys than girls, so x+6
Let's sum it all up
x+x+6=40
Collect like terms;
2x+6=40
2x=40-6
2x= 34
Divide both sides by 2
x=17
17+6=23
Therefore there are 17 girls in the class and 23 boys.
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Keith plays basketball at a gym. He can get a $20 membership card and pay $2 for every visit, or he can go any time and just pay $5 for each visit. Which two equations represent the two options for his
number of visits with his total ccost?
Step-by-step explanation:
Got it. Hope this will help.
On Mrs. Sean's desk,
there are pink and yellow
markers. The ratio of pink
markers to total markers
is 1:3. If there are 16
yellow markers, then how
many markershare pink?
Since the ratio of pink markers to total markers is 1:3, then there are 8 pink markers.
Number of yellow markers given = 16
Based on the information given, therefore, the pink markers will be half of the yellow markers. This will be:
= 1/2 × 16
= 8 markers
Therefore, the total markers will be:
= 8 + 16 = 24
In conclusion, pink markers will be 8/24 = 1/3. Therefore, the number of pink markers is 8.
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Simplify each expression.
(a^2b^-3/a^-2b^2)2
Answer: a^8/b^10
Step-by-step explanation:in the picture
Frank Camp's regular hourly pay rate is $11.87 an hour. His overtime pay rate is time and-a-half. How much
is Frank paid per hour for overtime work?
Answer:
$17.81
Step-by-step explanation:
11.87 x 1.5 = 17.805
A rectangular solid measures 150cm by 100cm by 200cm calculate the volume, in cm3 and in dm3 show conversion factors
Answer:
3000000cm³
3000dm³
Step-by-step explanation:
150cm x 100cm x 200cm = 3000000cm³
[tex](3000000cm^{3}) (\frac{(10)^{3}(dm)^{3} }{(100)^{3}(cm)^{3} }) = 3000dm^{3} [/tex]
When a truck full of boxes arrives at the Silvergrove Post Office, Miguel unloads the truck by placing the boxes
on a conveyor belt. Miguel's coworkers are impressed with how fast Miguel does his job. Miguel can unload 10
boxes in 5 minutes. How long does it take him to unload 40 boxes?
Answer:
20 minutes
Step-by-step explanation:
If Miguel can unload 10 boxes in 5 minutes, that means that he loads 2 boxes per minute. Assuming he he has a constant unloading speed, it would take him 20 minutes to unload all 40 boxes.
I found this by dividing 40 (boxes) by 2 (min per box)
A sequence is defined recursively by
a1=4
an=34an−1
What is the explicit form of this sequence?
9514 1404 393
Answer:
an = 4×34^(n-1)
Step-by-step explanation:
If your recursive definition is ...
[tex]\begin{cases}a_1=4\\a_{n}=34a_{n-1}\end{cases}[/tex]
this defines a geometric sequence with a first term a1 = 4 and a common ratio of r = 34. The general form of the explicit function is ...
[tex]a_n=a_1\times r^{n-1}[/tex]
For the values shown here, the explicit definition of the sequence is ...
[tex]\boxed{a_n=4\times 34^{n-1}}[/tex]
Hhopppppopppppppohelpppppp
Answer:
gffghjjdfdgfgjgfdgj
Step-by-step explanation:
Find g(x), where g(x) is the reflection across the y-axis of f(x)= –9|x–10|+1.
Answer:
To reflect a graph, f(x) over the x-axis, you take -f(x).
So if f(x)=x^2, then -f(x) is -x^2.
Then g(x)=-x^2 is the reflection of your function f(x) over the x-axis.
Step-by-step explanation:
I need the answer ASAP
Answer:
It would be 120 inches squared.
Step-by-step explanation:
12 x 8 = 96
6 x 4 = 24 / 2 = 12
12 x 2 = 24
96 + 24 = 120 inches squared
Answer: 80 in 2 cm
Step-by-step explanation: so if you add you can find it but add you answer you get 2 times and round to the nearest ten and you have your answer.
given the drawing below what is the difference between angle D and angle B
Answer:
given the drawing below what is the difference between angle D and angle B
Step-by-step explanation:
Which is the correct label for a right angle in the figure? (check picture for options and figure)
Answer:
C
Step-by-step explanation:
Solve for x.
5x−2(x+1)=1/4
Enter your answer as a fraction in simplest form in the box.
x =
Answer:
x=3/4
Step-by-step explanation:
Answer:
X= 3/4
Step-by-step explanation:
Distribute
Combine like terms
Add 2 to both sides of the equation
Simplify
Divide both side s of the equation by the same turm
Simplify
If f(x) is a linear function, what is the value of n?
Х
-4
f(x)
1-25
-10
-1
n
20
2
4
9
Answer:
The value of n is 5.
Step-by-step explanation:
We have been given that f(x) is a linear function and we are asked to find the value of n from the provided table.
x f(x)
-4 -25
-1 -10
n 20
First of all we will find the slope of the given using our given points (-4,-25) and (-1,-10) in slope formula.
m = y2-y1/x2-x1
Upon substituting coordinates of our given points we will get,
m = -10--25/-1--4
m = -10+25/-1+4
m = 15/3
m = 5
Since we know that the equation of a line in slope-intercept form is:
y = mx + b,where, m= Slope and b= y-intercept.
Upon substituting m = 5 in slope-intercept form of equation we will get,
y = 5x + b
Now let us find y-intercept by substituting coordinates of one point in our given line.
-10 = 5(-1) + b
-10 = -5 + b
-10 + 5 = -5 + 5 + b
-5 = b
y = 5x - 5
Now let us find value of n by substituting x = n and y = 20 in our equation.
20 = 5 * n - 5
20 + 5 = 5 * n - 5 + 5
25 = 5 * n
25/5 = 5 * n/5
5 = n
Therefore, the value of n is 5.
Triangle KLM is similar to triangle NOP. Find the measure of side PN. Figures are not
drawn to scale.
Answer:
look at the photo............
Josh wrote 483 out of an expected 500 words for his essay. How would this ratio be expressed in decimal form?
A 0.034
B 0.483
С 0.966
D 4.83
Answer:
b
Step-by-step explanation:
just trust me
Our material handlers make $15 per hour, and it takes them about 15 minutes to complete this process. How much is our handling cost?
Answer: $3.75
Step-by-step explanation: $15x15=225/60= 3.75
Our material handling cost is $3.75.
What is cost?A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels.
How to find the cost per process?Material handlers make $15 per hour
If it takes them about 15 minutes to complete this process then process in an hour is 60/15 =4
The cost per process is 15/4 =3.75.
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1. Scale 1 cm = 250 km
25
Using the scale above, calculate to find how
many km are in the following map distances:
a.) 2 cm =
km
b.) 5 cm
km
c.) 3 cm=
km
Answer:
a= 500km b= 1,250 c= 750
Step-by-step explanation:
a= 250x2=500km
b= 250x5=1,250km
c= 250x3=750km
What is the solution to the following equation? Please help!
Answer :
D
Step By Step Explanation :
Select the correct answer.
What is the equation of the line that has a slope of 1 and passes through the point (1,5)?
Y - 1 = (x + 5)y - 1 = (x + 5)
y - 5 = (x - 1)y - 5 = (x - 1)
y + 1 = (20 – 5)y + 1 = (x - 5)
y + 5 = (x + 1)y + 5 = (1 + 1)
Please I need answer ASAP!! I’ll make you brainliest!!
Answer:b
Step-by-step explanation:
What is the value of k?
help!!!!
Answer:
k = 10°Step-by-step explanation:
[tex] {115}^{o} = {(4k + 5)}^{o} + {(6k + 10)}^{o} \\ [/tex]
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
[tex] {115}^{o} = {(4k + 5)}^{o} + {(6k + 10)}^{o} \\ {115}^{o} = 4k + 5 + 6k + 10 \\ {115}^{o} = 10k + 15 \\ {115}^{o} - 15 = 10k \\ {100}^{o} = 10k \\ \frac{100}{10} = k \\ {10}^{o} = k \\ [/tex]
choose all numbers that round to 30,000 when rounded to the nearest ten thousand
a. 28,5602
b. 20,347
c. 27,563
d. 22,547
Answer:
A & C
Step-by-step explanation:
Caleb wants to rent a kayak. Kayak rentals cost $70.58  for a half hour. If Caleb rents a kayak for 5.0 hours, how much will it cost him?
Step-by-step explanation:
divide each of the following: using the two methods
How do you evaluate -98 - 13
Evaluations can only be done with algebraic equations
Answer:
-111
Step-by-step explanation:
Subtract 13 from -98
9. Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7,0).
Answer:
[tex]x = \frac{1}{28} y^{2}[/tex]
Step-by-step explanation:
parabola equation with vertex (0 , 0) and focus length |f| = 7
4*f*(x - h) = (y - k)²
4*7*(x-0)=(y-0)²
28x = y²
[tex]x = \frac{1}{28} y^{2}[/tex]
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Second-degree, with zeros of −4 and 6, and goes to −∞ as x→−∞.
p(x) =
9514 1404 393
Answer:
p(x) = -x^2 +2x +24
Step-by-step explanation:
When the polynomial has a zero at x=q, it has a factor of (x -q). The zeros of -4 and 6 tell you the factors are (x -(-4)) and (x -6). The end behavior tells you the leading coefficient is negative.
p(x) = -(x +4)(x -6)
p(x) = -x^2 +2x +24
Identify h (x) = [x] + 4
A. Constant function
B. Greatest integer function
C. Direct Variation function
D. Absolute value function
PLEASE HELP ILL MARK BRIANLIEST
Answer:
C
Step-by-step explanation:
The given function h (x) = [x] + 4 as the greatest integer function which is the correct answer would be option (B).
What is the greatest integer function?The greatest integer function takes the greatest integer that is less than or equal to a specified value. The biggest integer less than or equal to a number x is expressed as ⌊x⌋. It will round off the input number to the nearest integer that is less than or equal to the number itself.
Mathematically, the greatest integer function ⌊x⌋ can be defined as follows:
⌊x⌋ = n, where n ≤ x < n + 1 and 'n' is an integer.
According to the given question,
The function is below as
⇒ h (x) = [x] + 4
Here ⌊x⌋ = 4, where 4 ≤ x < 4 + 1 and '4' is an integer.
The given function as the greatest integer function takes the greatest integer that is less than or equal to a value of 4.
Hence, the correct answer would be an option (B).
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Supposed the length of a rectangle is three times the width and the area is 300 ft.² then what is the width of the rectangle in feet
Step-by-step explanation:
the area is
A = length × width.
length = 3 × width
=>
A = 3 × width × width = 3 × width²
300 = 3 × width²
100 = width²
width = 10 ft