The loan option that would allow Charles to pay the LEAST in interest is option A.
What is Compound Interest?Compound Interest is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A=P(1+r\%)^n[/tex]
where A is the value after t period of time, P is the principal amount, and,
r is the rate of interest.
A.) Principle amount = $10,000
Time Period of loan = 2 years
Rate of Interest = 4.75% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0475)^2\\\\= \$10,972.56[/tex]
The interest will be = $10,972.56 - $10,000 = $972.56
B.) Principle amount = $10,000
Time Period of loan = 3 years
Rate of Interest = 4.00% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.04)^2\\\\= \$11,248.64[/tex]
The interest will be = $11,248.64 - $10,000 = $1,248.64
C.) Principle amount = $10,000
Time Period of loan = 4 years
Rate of Interest = 3.75% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.0375)^2\\\\= \$11,586.5[/tex]
The interest will be = $11,586.5- $10,000 = $1,586.5
D.) Principle amount = $10,000
Time Period of loan = 5 years
Rate of Interest = 3.00% per annum
Now, the total amount can be written as
[tex]=P(1+r\%)^n\\\\= \$10,000 \times (1+0.03)^5\\\\= \$11,592.74[/tex]
The interest will be = $11,592.74 - $10,000 = $1,592.74
Hence, the loan option that would allow Charles to pay the LEAST in interest is option A.
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If in total I have 166 students and 32 of them surf, what is their percentage?
If f(x) = x3 – 2x2, which expression is equivalent to f(i)? –2 i –2 – i 2 i 2 – i
Answer:
Answer
d) 2 – i
Explanation
f(x) = x³ – 2x²
When x = i, we proceed as follows.
Note: i =
i² =(√-1)(√-1) = -1
i³ = (√-1)(√-1)(√-1) = -1(√-1) = -1i = -i
f(x) = x³ – 2x²
f(i) = i³ – 2i²
= -i – 2(-1)
= -i + 2
= 2 – i
Step-by-step explanation:
Find the function with x-intercepts (-3, 0) and (5, 0), which also goes through the point (1, 8).
Answer:
y= -0.5x² + 1x + 7.5
Step-by-step explanation:
I graphed the points in Desmos and saw they looked liked a parabola the point (1,8) is in between -3 and 5 for the x-coordinate.
I put the values in a table. and had desmos do a regression
Answer:
f(x) = (-1/2)(x^2 + 8x - 15)
Step-by-step explanation:
Hope this helps
PLEASE HELP ASAP
are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?
Answer:
To find the inverse of:
[tex]f (x)=\dfrac{4}{x-2}-1[/tex]
Set the function to y:
[tex]\implies y=\dfrac{4}{x-2}-1[/tex]
Rearrange to make x the subject:
[tex]\implies y+1=\dfrac{4}{x-2}[/tex]
[tex]\implies (y+1)(x-2)=4[/tex]
[tex]\implies xy-2y+x-2=4[/tex]
[tex]\implies xy+x=2y+6[/tex]
[tex]\implies x(y+1)=2y+6[/tex]
[tex]\implies x=\dfrac{2y+6}{y+1}[/tex]
Swap x and y:
[tex]\implies y=\dfrac{2x+6}{x+1}[/tex]
Change y to the inverse of the function sign:
[tex]\implies f[/tex][tex]\:^{-1}(x)=\dfrac{2x+6}{x+1}[/tex]
Rewrite g(x) as a fraction:
[tex]g(x)=\dfrac{3}{x+2}-2[/tex]
[tex]\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2x-4}{x+2}[/tex]
[tex]\implies g(x)=-\dfrac{2x+1}{x+2}[/tex]
Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other
Store A sells 5 comics for $53.10. Store B sells 3 comics for $31.71. What is the difference in unit rate?
Answer:
Vendor 1 had a higher unit rate.
Step-by-step explanation:
What is the summation notation for the geometric series 5 10 20 40 80?
The summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
Series and sequencesSeries are sum of sequences
Given the following alternating series as shown:
5 - 10 + 20 - 40 + 80
The series is geometrc series with the following parameters
First term "a" =5
ratio= -10/5 = 20/-10 = -2
Since the nth term of geometric sequence is expressed as:
Tn = ar^n-1
Tn =5(-2)^n-1
Hence the summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
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Answer:
A
Step-by-step explanation:
May someone please help I will give 30 points to who can answer fully, no download scam link either
We can write equations by rewriting the important phrases of information using variables. These variables make the equation look neater and it is faster to write a letter instead of constantly repeating 'cost of student tickets', for example.
The important pieces of information lies in the second last sentence of this question.
the tickets of your friend, her mom and her little sister costs a total of $23the tickets of 2 adults and 3 students costs a total of $39Now, let's rewrite them into equations.
Given
x= cost of adult tickets
y= cost of student tickets
Assuming that your friend and her little sister are students, the two equations are:
x +2y= 23 -----(1)2x +3y= 39 -----(2)To convert these equations into slope-intercept form, move all the terms that are not y to the right-hand side of the equation before dividing both sides by the coefficient of y. This is to ensure that the coefficient of y is 1 and that your equation is in y= mx +c, where m is the slope and c is the y-intercept.
From equation (1):
x +2y= 23
2y= -x +23
Divide both sides by 2:
[tex]\bf{y = - \frac{1}{2} x + \frac{23}{2} }[/tex]
From equation (2):
2x +3y= 39
3y= -2x +39
Divide both sides by 3:
[tex]\bf{y= - \frac{2}{3} x + 13}[/tex]
The solution to the system of equations is the point at which the two lines intercept on the graph. I have attached the graph as an image.
The solution is (9, 7).
The x coordinate is the cost of an adult ticket, while the y coordinate is the cost of a student ticket. This means that adult tickets cost $9 and student/ child tickets cost $7.
Hello, I was just doing some practicing for adding integers. I did some problems on my own and I was wondering if I am on the right track.
Answer:
Yes, It looks great! I would suggest moving on to a littler harder problems like dividing integers! You can also look up integers practice and they will give you problems to solvle! If you dont know how to do it yet then you can simply skip but, You are doing wonderful!!! Good job and Good luck!
Step-by-step explanation:
Use the formula a2 – b2 = (a b)(a – b) to factor completely. what are the factors of 36x8 – 49? (9x4 – 1)(4x2 49) (36x4 – 7)(x2 7) (6x4 – 7)(6x4 7) (6x8 – 7)(6x 7)
The factors of 36x^8 – 49 are (6x^4-7)(6x^4+7).
We are given to factor the following polynomial completely:
36x^8 – 49.
We have to find the complete factor of the given polynomial.
Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor
What is the formula for (a^2-b^2)?
The formula for (a^2-b^2)= (a+b) (a-b).
Therefore applying the given formula we have,
[tex]F=(6x^4)^2-7^2[/tex]
[tex]F=(6x^4)^2-7^2\\F=((6x^4)-7)(6x^4)+7)[/tex]
Thus, the required factors are
[tex]F=((6x^4)-7)(6x^4)+7)[/tex]
Therefore,option (C) is correct.
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The factors of 36x^8 – 49 are (6x^4-7)(6x^4+7).
We are given to factor the following polynomial completely:
36x^8 – 49.
We have to find the complete factor of the given polynomial.
Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor
What is the formula for (a^2-b^2)?
The formula for (a^2-b^2)= (a+b) (a-b).
Therefore applying the given formula we have,
b
Thus, the required factors are
b
His balls were 6 feet tall he wanted them to be 20. 4 tall how much does he need to grow {i-Ready} pls help
Answer:
14.4
Step-by-step explanation:
20.4-6 = 14.4
So his balls should grow 14.4 inches/feet/centimeters (whatever measuring tool you're asked to use)
Are you sure it's balls though
Answer:
20.4-6=14.4
since he wants his balls to grow you need to subtract how much he wants them tp grow by how tall the already are
Step-by-step explanation:
oliver bought 7 bags of candy each bags cost 1.50 i need help step buy step
oliver bought 7 bags of candy each bags cost 1.50
Answer-$10.50
Answer:
10.5
Step-by-step explanation:
you take 1.50 and times it by how many bags there are so 7
1.50×7=10.5
a
45°
I’m very confused on this please help me:)
Answer:
45 degrees
Step-by-step explanation:
Since this angle is a right angle (1/4 of a full circle, or 360 degrees) its angle is 90. Since one part of it is 45 degrees. A=90-45=45
If 2^2x = 2^3, what is the value of x?
A 2/3
B 3/2
C 2
D 3
What is the completely factored form of x4 + 8x2 – 9?
(x + 1)(x – 1)(x + 3)(x + 3)
(x + 1) (x minus 1) (x squared + 9)
(x2 – 1)(x + 3)(x – 3)
(x + 1)(x + 1)(x + 3)(x + 3)
Answer:
Hope that the payment picture will help you.Please mark me brilliant
Answer:
Its B
Step-by-step explanation: on edg 2022
Simplify
x + x + y * y
Answer:
2x+y²
Step-by-step explanation:
add the similar terms. since x and x is similar so it'd be
2x + y * y
notice that y and y is also similar so y times y would become
2x+y^2 will be the final answer
What is the average rate of change for this quadratic function for the interval from x = 2 to x = 4? O A. -12 B. 12 C. -6 O D. 6
D. 6.
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6--6}{-2+4}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6+6}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{12}{2}[/tex]
[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
because i am in credit recovery and i had a test on it
Find the degree you of this polynomial
-8x 4 squared
A company orders 27 boxed lunches from a deli for $194.40. Assume each boxed lunch is the same price. If C represents the total cost in dollars and cents of the lunch order for any number,b, of boxed lunches ordered, write a proportional equation for c in terms of b that matches the context
[tex]C = 7.2b[/tex]
Step-by-step explanation:From the question we have that,
27 boxes --------------- $194.40
b boxes --------------- C
Using the Rule of Three we have that,
[tex]27C = 194.40b[/tex]
Since we want a function that represents C in terms of b ( C = f(b) ) we can isolate C on the equation,
[tex]C = \frac{194.40}{27}b = 7.2b[/tex]
PLS HELP I USED ALL MY POINTS ON THIS I NEED HELP ASAP!!!!!!!!!! ʕ •ᴥ•ʔ
Answer:
(12, 6 )
Step-by-step explanation:
locate 12 cups of flour on the x- axis, then go vertically up to meet the line at (12, 6 )
that is 6 cups of sugar would be used with 12 cups of flour.
Identify similar pentagons.
Answer:
P, R
Step-by-step explanation:
If you dilate P, you can find out that P can be the same as R.
Which linear function has the greatest rate of change?
Answer:
D
Step-by-step explanation:
The rate of chnage is the same as the slope.
Slope is x/y. How many y increases/decreases per increase of 1 x
slope for A is
2/500 every 2 x increase, y goes up by 500.
slope for B is
2/500 every 2 x increase, y goes up by 600-100 = 500
slope for C is
1/250
slope for D is
756/3
The greatest one out of these options is D, 756/3
Each of the teams in a mixed volleyball league consists of 5 men and 5 women. there are 9 men and 10 women, including julia, who are trying out for a team. how many possible teams would include julia?
There are 9 men and 10 women, including Julia, who are trying out for a team. so there are 31,752 possible teams that would include Julia.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
Each of the teams in a mixed volleyball league consists of 5 men and 5 women.
There are 9 men and 10 women, including Julia, who are trying out for a team.
The number of combinations for men
= (9 × 8 × 7 × 6 × 5)/(1 × 2 × 3 × 4 × 5)
=126.
The number of combinations for women
= (10 × 9 × 8 × 7 × 6)/(1 × 2 × 3 × 4 × 5)
=252.
The number of the possible team would include Julia
(126 × 252) = 31,752.
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An object was launched from the ground. The graph below shows the path that the object took. Use the graph to answer questions 9-10. What is the domain and range?
Using the concepts of domain and range, it is found that for the function given in the graph:
The domain is [0, 4].The range is [0,64].What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains the values of the horizontal axis.The range of a function is the set that contains all the values of the output. In a graph, it is the set that contains the values of the vertical axis.The graph in this problem gives the height of a projectile after t seconds, hence:
The domain is [0, 4].The range is [0,64].More can be learned about the domain and range of a function at https://brainly.com/question/10891721
Factor x3 – 7x2 – 5x 35 by grouping. what is the resulting expression? (x2 – 7)(x – 5) (x2 – 7)(x 5) (x2 – 5)(x – 7) (x2 5)(x – 7)
The factored expression ofx^3 - 7x^2 -5x +35 is (x^2 - 5)(x - 7)
What is an expression?An expression is an algebraic term used for a mathematical statement that includes addition subtraction multiplication and division
x^3 – 7x^2 – 5x + 35
factor the given equation
x^2(x – 7) – 5(x - 7)
Factor out x - 7
(x^2 - 5)(x - 7)
Therefore, the factored expression is (x^2 - 5)(x - 7)
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Answer:
c. (x^2 - 5)(x - 7)
Step-by-step explanation:
c. (x^2 - 5)(x - 7)
A bee colony produced 0.21 pounds of honey, but bears ate 0.01 pounds of it. How much honey remains?
Answer:0.20 pounds remain .0.21 minus 0.01 = 0.20
Answer:
0.20
Step-by-step explanation:
radius
name 2 chords
diameter
center
central angle
intercepted Arc for Angle EFG
10000 POINTS AND BRAINLIEST SHOW YOUR WORK!!!!!!!!!!
A) = 23.0 miles
B) 14.4 Miles
Step-by-step explanation:A) [tex]distance\ AD= x+y.\\ First\ find\ the\ value\ of\ x\ and\ z,\ then\ use\ the\ value\\ \\ yz\ to\ get\ the\ value\ of\ y\\ cos60\textdegree\ =\frac{21}{hy}=\frac{x}{10}[/tex][tex]sin60\textdegree\ =\frac{opp}{hyp}=\frac{z}{10}[/tex]
[tex]z=10\times sin60\textdegree =10\times 0.8660=8.66\ miles[/tex]
[tex]use\ pythagores\ theorem\ to\ get\ the\ value\ of\ y.\ l,e[/tex]
[tex]y=\sqrt{{20}^2-z^2}=\sqrt{{20}^2-{8.66}^2}=\sqrt{325.0044}[/tex]
[tex]=18.03\ miles[/tex]
[tex]\therefore\ distance\ AD=5+18.03[/tex]
[tex]=23.03\\ 23.0\ miles[/tex]
B) [tex]Ansween\ 14.4\ Miles[/tex][tex]< ABN=\varphi=30\textdegree\ \{Beary\ 4A\ from\ B=360\textdegree\ -60\textdegree\ =300\textdegree\}[/tex]
[tex]AB=y.[/tex]
[tex]\cos{\theta=\frac{ads}{h}p}\\ cos\ G\begin{matrix}0\\0\\\end{matrix}=\frac{x}{25}[/tex]
[tex]x=25\times cos\ 60\textdegree[/tex]
[tex]=12.5\ mle[/tex]
[tex]cos\ 30\textdegree=\frac{xe}{y}=\frac{12.5}{y}[/tex]
[tex]\because\ y=\frac{12.5}{cos\ 30\textdegree}[/tex]
[tex]=14.Fmm'_\mathcal{i}(es[/tex]
I hope this helps you
:)
The cost of a taxi ride is $2 per mile plus an initial charge of $2.75. Sean spent $26.75. Write an equation that represents the situation l. Solve to find the number of miles that Sean traveled.
PLEASE HELP!!
A) 78
B) 145
C) 113
D) 102
Answer:
D
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ BCD is an exterior angle of the triangle , then
∠ BCD = 35° + 67° = 102°
What is the quotient? startfraction 2 m 4 over 8 endfraction divided by startfraction m 2 over 6 endfraction startfraction 24 over (m 2) squared endfraction startfraction (m 2) squared over 24 endfraction two-thirds three-halves
The quotient of the equation is 1.5.
What is the quotient?The quotient is the number that is generated when we perform division operations on two numbers. Basically, it is the result of the division method.
The given equation is;
[tex]\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}[/tex]
By fraction, a quotient is a number obtained by dividing the dividend by the divisor which is a simple division of numerator and denominator.
The solution of the equation is determined in the following steps given below.
[tex]=\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}\\\\=\rm \dfrac{2m+4}{8}\times \dfrac{6}{m+2}\\\\=\rm \dfrac{2(m+2)}{8}\times \dfrac{6}{m+2}\\\\=\dfrac{2\times 6}{8}\\\\=\dfrac{12}{8}\\\\=1.5[/tex]
Hence, the quotient of the equation is 1.5.
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Answer:
2/3
Step-by-step explanation:
What is the quotient?
StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction
StartFraction 24 Over (m + 2) squared EndFraction
StartFraction (m + 2) squared Over 24 EndFraction
Two-thirds
Three-halves