The correct option is A.
Vanessa can borrow approximately $6255.57, represented by option A: [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex].
To determine the value of the most money Vanessa can borrow with a monthly payment of $1405 for a 20-year house loan with an APR of 4.8%, compounded monthly, we can use the formula for the monthly payment of a mortgage:
[tex]\[P = \frac{M}{\frac{r}{12} \left(1 - \left(1 + \frac{r}{12}\right)^{-nt}\right)}\][/tex]
Where:
P = Principal amount (the amount she can borrow)
M = Monthly payment ($1405)
r = Monthly interest rate (APR divided by 12, or 0.048/12)
n = Number of times the interest is compounded per year (12 for monthly)
t = Number of years (20)
Now, let's plug in the values and solve for P:
[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-12*20}\right)}\][/tex]
Let's calculate the exponent and simplify:
[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-240}\right)}\][/tex]
Now, we can simplify the monthly interest rate:
[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1.000333333\right)^{-240}\right)}\][/tex]
[tex]\[P = \frac{1405}{0.333333 \left(1 - 0.328624967\right)}\][/tex]
Now, let's calculate the value inside the parentheses:
[tex]\[P = \frac{1405}{0.333333 \times 0.671375033}\][/tex]
[tex]\[P \approx \frac{1405}{0.22487499}\][/tex]
Now, calculate P:
P ≈ 6255.57
So, Vanessa can borrow approximately $6255.57.
The correct expression that represents the value of the most money she can borrow is:
A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]
The complete question is here:
Vanessa can afford a [tex]$\$ 1405$[/tex]-per-month house loan payment. If she is being offered a 20-year house loan with an APR of [tex]$4.8 \%$[/tex], compounded monthly, which of these expressions represents the value of the most money she can borrow?
A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]
B. [tex]$\frac{(\$ 1405)\left((1-0.048)^{240}-1\right.}{(0.048)(1+0.048)^{249}}$[/tex]
C. [tex]$\frac{(\$ 1405)\left((1-0.004)^{200}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]
D. [tex]$\frac{(51405)\left((1+0.048)^{200}-1\right)}{(0.048)(1+0.048)^{240}}$[/tex].
Using the formula for monthly loan payment, we find Vanessa can borrow up to $220,000 with a 20-year loan at 4.8% APR.
To find the maximum amount Vanessa can borrow, we can use the formula for the monthly payment of a loan:
[tex]\[ P = \frac{A \times r}{1 - (1 + r)^{-n}} \][/tex]
Where:
- P = monthly payment
- A = loan amount (the value we want to find)
- r = monthly interest rate (APR divided by 12)
- n = total number of payments (number of years multiplied by 12)
Given:
- Monthly payment ( P) = $1405
- APR ( r ) = 4.8% = 0.048
- Loan term = 20 years
First, we calculate r :
[tex]\[ r = \frac{4.8}{100 \times 12} = 0.004 \][/tex]
Then, calculate n:
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Now, plug the values into the formula and solve for A:
[tex]\[ 1405 = \frac{A \times 0.004}{1 - (1 + 0.004)^{-240}} \][/tex]
Solve for A:
[tex]\[ A = \frac{1405 \times (1 - (1 + 0.004)^{-240})}{0.004} \][/tex]
[tex]\[ A \approx \$220,000 \][/tex]
So, Vanessa can borrow a maximum of $220,000.
The question probable maybe:
Vanessa can afford a $1405-per-month house loan payment. If she is being offered a 20-year house loan with an APR of 4.8%, compounded monthly, What is the value of the most money she can borrow?
Bruce has 97 sports cards. 34 of them are football cards. Which equation can be used to find the number of sports cards y that are not football cards
Answer: 34 + y = 97
Step-by-step explanation:
According to the question,
Total number of sport cards = 97
In which some are foot ball cards and some are non football cards.
Let y be the number of sports cards.
Given, 34 cards are football cards.
Therefore, total number of cards = 34 + y
⇒ 34 + y = 97
Which is the equation that will use to find the number of non football cards.
To find the number of sports cards that are not football cards, you subtract the number of football cards from the total number of sports cards. The equation is y = 97 - 34.
To determine the number of sports cards that are not football cards, you need to subtract the number of football cards from the total number of sports cards.
Step-by-Step Explanation:
The total number of sports cards is 97.
The number of football cards is 34.
The number of sports cards that are not football cards can be found by subtracting the number of football cards from the total number of sports cards: y = 97 - 34.
Therefore, the equation y = 97 - 34 can be used to find the number of sports cards that are not football cards.
neil tried to simplify an expression step by step 5^-6/5^-4
The simplified form of the given expression is 1/25.
The given expression is [tex]\frac{5^{-6} }{5^{-4} }[/tex].
We need to simplify the given expression.
What are exponents and how do solve exponents questions?The exponent of a number shows how many times the number is multiplied by itself. The properties of exponents or laws of exponents are used to solve problems involving exponents. These properties are also considered major exponents rules to be followed while solving exponents.
Using quotient law [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex].
Now, [tex]\frac{5^{-6} }{5^{-4} }[/tex] can be written as [tex]\frac{5^{4} }{5^{6} }[/tex]
By using the quotient rule, we get [tex]\frac{5^{4} }{5^{6} }=5^{4-6}[/tex]
[tex]=5^{-2}=\frac{1}{5^{2}}[/tex]
=1/5×5=1/25
Therefore, the simplified form of the given expression is 1/25.
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angle 0 is in quadrant 1 with sin0 = 2/5. Use the Pythagorean identity, sin^2 0 + cos^2 0 = 1, to calculate the value of cos0 as a radical.
Suppose you have five books in your bookbag. three books are novels
1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals negative 4 x
2.) Which kind of function best models the data in the table? Use differences or ratios.
x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2
3.) Solve the system of equations algebraically. Show all of your steps.
y equals x squared plus two x; y equals three x plus twenty
PLEASE HELP!
To solve the given quadratic equation, we simplified and factored it, yielding solutions x = 0 and x = 17. For the data in the table, an exponential function is suggested by the consistent ratio between y-values. Algebraically solving the system of equations results in two solutions: (5, 35) and (-4, 8).
Formula to Solve the Equation
To solve the equation x squared minus 21 x equals negative 4 x, you'll first want to rewrite it in standard form. Moving all the terms to one side gives us [tex]x^2 - 21x + 4x = 0[/tex], which simplifies to [tex]x^2 - 17x = 0[/tex]. To find the solutions, we can factor out an x, giving us x(x - 17) = 0. This yields two solutions: x = 0 and x = 17.
Model the Data in the Table
Looking at the data given, we see that each y-value seems to be a multiple of the previous y-value. This suggests an exponential function might be a better fit than a linear one. To confirm, you can divide each y-value by the previous y-value and observe if the ratios are consistent. Calculating the ratios between consecutive y-values in the table, we see that the ratio is consistently around 4, confirming that an exponential model is appropriate.
Solve the System of Equations Algebraically
To solve the system [tex]y = x^2 + 2x[/tex]and y = 3x + 20, set the right sides of the equations equal to each other:[tex]x^2 + 2x = 3x + 20[/tex]. Bringing all terms to one side gives us the quadratic equation[tex]x^2 - x - 20 = 0[/tex]. Factoring the quadratic equation we get (x - 5)(x + 4) = 0, which gives us two solutions for x: x = 5 or x = -4. Substituting these back into either original equation provides the related y-values, thus giving us two solutions for the system: (5, 35) and (-4, 8).
Katherine invested $140.she earned a simple interest of 4% per year on the initial investment. If no money was added or removed from the investment what was the amount of interst katherine received at the end of two years?
Find the quotient. Write your answer USING A DECIMAL and ROUNF TO THE NEAREST HUNDREDTH.
8,426÷82
true, false, or open. Explain. 45/x-14=22
What would “x” be ?
Thanks you
Step-by-step explanation:
[tex]cos \: x = \frac{a}{h} \\ cos \: x = \frac{16}{21} = 0.76 \\ cos \: x = 40.36degrees[/tex]
Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? millimeters
Answer:
6 millimeters
Explanation:
The standard deviation is the square root of the variance.
Since the variance is 36, the standard deviation would be
√36 = 6
Answer:6
Step-by-step explanation:
The domain of this graph is {x | x≥−2}.
True.
False.
The doorway into a room is 4 feet wide and 8 feet high. what is the length of the longest rectangular panel that can be taken through this doorway diagonally
How do you find the inverse of y=2x-3
Subtract 3 from each side
y - 3 = 2x
Divide through by 2
y/2 - 3/2 = x
or x = y/2 - 3/2
Now simply switch labels: x↔y
y = x/2 - 3/2
The area of a rectangular knitted blanket is 14 x^2 - 17 x -6. What are the possible dimensions of the blanket? Use factoring.
What are the dimensions of a rectangle that has a perimeter of 26 in the area of 36?
Suppose you want to build a rectangular sandbox where the width is 5 feet less than the length and the diagonal is 5 feet longer than the length. what are the dimensions of the sandbox?
If f(x) = 4x and g(x) = 2x – 1, what is g(f(–2))?
A-17
B-13
C-8
D-5
In spherical geometry, what is the term used for the shortest distance between two points?
need help with algebra 2! but I need the work show
Assuming the cost of cement blocks is $75 per 1,000, how much will it cost for the blocks to build a wall 7ft. tall by 20 ft. long if the block is 6 inches thick and 10 blocks are needed for 1 cubic foot.
You bought 2 pairs of pants at $28.99 each, and one shirt at $21.34. If the tax rate is 5%, what is the total cost of your purchase?
Show how you got the answer
Question 3 options:
$79.32
$58.98
$69.32
$83.29
The total cost of purchase on 2 pants and 1 shirt is $76.986.
Given that, you bought 2 pairs of pants at $28.99 each, and one shirt at $21.34.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Now,
The cost of 2 pairs of pants
= 2 ×28.99
= $57.98
Total cost of two pants and a shirt
= 21.34+51.98
= $73.32
Tax =5% of 73.32
= 5/100 ×73.32
= 0.05 ×73.32
= $3.666
Total cost of purchase =73.32+3.666
= $76.986
Therefore, the total cost of purchase on 2 pants and 1 shirt is $76.986.
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i’m sure this is easy but i'm gonna ask anyway
HIGH AMOUNT OF POINTS! MATH QUESTION! IF YOU DON'T KNOW IT, DON'T ANSWER!
Tracy solved the system of equations by making a substitution for x in the second equation.
What equation did she get as a result of that substitution?
x = –2y – 2
2x + 3y = –6
–2y – 2 = –6
–2y + 1 = –6
–4y – 2 + 3y = –6
–4y – 4 + 3y = –6
The pyramid shown below has a square base, a height of 7, and a volume of 84. what is the length of the side of the base?
The length of the side of the base is 6 units.
What is the volume of the pyramid?The volume of the pyramid is;
[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base[/tex]
The pyramid shown below has a square base, a height of 7, and a volume of 84.
Substitute all the values in the formula
[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base\\\\\rm84 =\dfrac{1}{3}\times height \times 7\\\\Height = \dfrac{84\times 3}{7}\\\\ Height = \dfrac{252}{7}\\\\Height =36[/tex]
The length of the side of the base is;
[tex]\rm Side\ length^2=height\\\\ Side\ length^2=36\\\\Side\ length^2=6^2\\\\Side\ length=6[/tex]
Hence, the length of the side of the base is 6 units.
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In the figure, what is the value of x?
Answer:x=90 °
Step-by-step explanation:
In any circle the exterior angle formed is half of the major arc - minor arc .
Angle formed by tangents or secants = [tex]\frac{1}{2}(Major arc - minor arc )[/tex]
The sum of measure of arcs inany circle is 360°.
Minor arc is given as x°.So Major arc = 360-x.
Substituting the given values in the formula :
[tex]x=\frac{1}{2}(360-x-x)[/tex]
[tex]x=\frac{1}{2}(360-2x)[/tex]
x=180-x
Adding x both sides we have:
2x=180.
Dividing both sides by 2.x= 90.
A TV has a listed price of $ 899.99 before tax. If the sales tax rate is 7.25 % , find the total cost of the TV with sales tax included.
What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.
The solution is, 308π in² is the surface area of the cylinder in terms of pi.
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape. The surface area of a solid object is a measure of the total area that the surface of the object occupies.
here, we have,
from the given diagram , we get,
the cylinder has,
radius = r = 7
height = h = 15
we know that,
Surface Area = 2πr² + 2πrh
so, we get,
r = 7
h = 15
substituting the values, we get,
Surface Area
= 2π(7)² + 2π(7)(15)
= 308π in²²
Answer: 308π in²
Hence, The solution is, 308π in² is the surface area of the cylinder in terms of pi.
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Suppose that in a large company, 30% of the computers are infected by adware. if 6 computers are randomly selected and tested, what is the probability that 2 of the computers are infected by adware?
What is the value of x?
132√ cm
526√3 cm
262√ cm
263√ cm
[tex]\huge \boxed{\sf 26\sqrt{2}\ cm } \\\\\\\sf Using\ trigonometric\ functions \\\\\displaystyle cos \theta = \frac{adj}{hyp} \\\\cos(60)=\frac{adj}{52} \\\\adj=cos(60) \times 52=26 \\\\Using\ the\ Pythagorean\ theorem \\\\x=\sqrt{26^2+26^2} =26\sqrt{2}[/tex]