(a) The monthly payment for a 36-month plan is $704.41, and for a 60-month plan is $488.08.
(b) The interest charges for the 36-month plan are $1,459.07, and for the 60-month plan are $3,369.10.
For a)
To calculate the monthly payment for a car loan, we need to use the formula for monthly payments:
M = [tex]P[r(1+r)^n / ((1+r)^n - 1)][/tex]
where M is the monthly payment, P is the principal (the loan amount), r is the monthly interest rate (the annual interest rate divided by 12), and n is the number of months over which the loan is to be repaid.
For the 36-month plan, the principal is 75% of $28,000, or $21,000. The monthly interest rate is 6% / 12, or 0.005. The number of months is 36. Plugging in these values, we get:
M = $[tex]21,000[0.005(1+0.005)^{36} / ((1+0.005)^{36} - 1)][/tex] = $704.41
For the 60-month plan, the principal, monthly interest rate, and a number of months are the same, but we change the number of months to 60:
M = $21,000[0.005[tex](1+0.005)^{60[/tex] / ([tex](1+0.005)^{60[/tex] - 1)] = $488.08
Therefore, the monthly payment for a 36-month plan is $704.41, and for a 60-month program is $488.08.
For b)
To calculate the total interest charges for the loan, we need to subtract the principal (the amount of the loan) from the total amount paid and round to the nearest cent:
For the 36-month plan, the total amount paid is $25,459.07 (36 x $704.41), so the interest charges are:
$25,459.07 - $21,000 = $4,459.07, rounded to $1,459.07
For the 60-month plan, the total amount paid is $29,284.80 (60 x $488.08), so the interest charges are:
$29,284.80 - $21,000 = $8,284.80, rounded to $3,369.10
Therefore, the interest charges for the 36-month plan are $1,459.07, and the 60-month plan are $3,369.10.
Learn more about Interest Rates:
https://brainly.com/question/29415701
#SPJ4
Find the equation of L
[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]
Explination:
Y-intercept is -6, (0,-6)
The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.
Write an equation to describe the relationship between t, the number of tickets, and c
, the total cost of tickets
The relationship between t, the number of tickets, and c, the total cost of tickets is: c = 55t
Relation between two variables, i.e, total cost and number of tickets:
The statistical relationship between two variables is called their correlation. The correlation can be positive, which means that the two variables move in the same direction, or negative, which means that when the value of one variable increases, the value of the other variable decreases.
Based n the Question:
Since there is no processing fee and the ticket price remains the same, we know that the fee will be proportional to the number of tickets purchased. The general form of the equation expressing the proportional relationship between the cost (c) and the number of tickets (t) is:
c = kt
where k is the constant of proportionality (the cost per ticket).
We can find k by using any of the data points given in the table. Using the first point, we have :
110 = k·2
Dividing the equation by 2:
110/2 = k = 55
Then using this value for k, the desired equation can be written:
c = 55t
Complete Question:
Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),
Learn more about Number:
https://brainly.com/question/17429689
#SPJ4
Which of the filling best describes the expression 6(y+3)
Answer: 6y+18
Step-by-step explanation:
6 x y=6y
6 x 3= 18
Answer:
The product of a constant factor of six and a factor with the sum of two terms.
Step-by-step explanation:
Since we have given that
6(y+3)
It has sum of two terms i.e. y and 3.
Mathematically, it is expressed as
y+3
And the product of constant factor of six and a factor with the sum of two terms.
Mathematically, it is expressed as
6(y+3)
Hence, The product of a constant factor of six and a factor with the sum of two terms.
19. INVESTMENTS Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account
that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year.
a. Write an expression that represents the amount of money invested in the traditional account.
b. Write a polynomial model in simplest form for the total amount of money T Kent has invested after one year.
(Hint: Each account has A + IA dollars, where A is the original amount in the account and I is its interest rate:)
c. If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?
Part a: Expression for conventional account: $(5000-x) at 5%pa.
Part b: polynomial model: T = 5250 - 0.01x
Part c: Sum of investments in retirement account: T= $5245.
Explain about the bond account?When they need to raise money, governments and businesses issue bonds.
a. Create an expression to show how much money is invested in the conventional account.
Back $(5000-x) at 5%pa
b. Construct a polynomial model in its simplest form to represent the entire sum of investments made by T. Kent after a year (possibility: thus every account has A + iA dollars, in Which a is the account's initial balance and I is the interest rate).
The bond will increase to after a year to : x + 0.04x
= x(1+0.04)
= 1.04x ...eq 1
So, after the time of one year this traditional account growth will be-
(5000-x) + 0.05(5000-x)
= 5000 - x + 0.05*5000 - 0.05x
= 5000 - x + 250 - 0.05x
= 5250 - 1.05x ..eq 2
From eq 1 and eq 2
T = 1.04x + 5250 - 1.05x
T = 5250 - 0.01x
c. If Kent invested $500 in bonds, how much will he have in the retirement account in a year?
x=500
T= 5250 - 0.01*500
T= 5250 - 5
T= $5245
Know more about the bond
https://brainly.com/question/16868705
#SPJ1
PLEASE HELP
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
Answer: 64πa^2-192πa+144
Step-by-step explanation:
Area of a circle: π •r^2
So then the area would be: 4•π(4a-6)^2
FOIL (4a-6)(4a-6) and get 16a^2-48a+36
Plug it in and get 4•π(16a^2-48a+36)
Distribute pi sign and get 4•(16πa^2-48πa+36π)
Distribute the 4 and you get 64πa^2-192πa+144
Answer: 64πa^2-192πa+144
A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
Answer:
There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).
Step-by-step explanation:
i thought of a number. four times the number increased by 30 equals 70 decreased by the number. what was my number?
Answer:
number is 8
Step-by-step explanation:
let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30
70 decreased by the number means subtracting n fro 70 , 70 - n
then
4n + 30 = 70 - n ( add n to both sides )
5n + 30 = 70 ( subtract 30 from both sides )
5n = 40 ( divide both sides by 5 )
n = 8
the temperature at 12 noon was 10 degree Celsius above zero .if it decreases at the rate of 2 degree Celsius per hour until midnight ,at what time would the temperature be 8 degree Celsius below zero? what would be the temperature at midnight?
Answer:
The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.
Write a phrase in words for each algebraic
expression.
22. m+83_
23.42s
24. 9/d
25. t - 29
26. 2+g
27. 11x
28. h/12
29. 5- k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
what is expression ?An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.
given
The sum of m and 83.
Forty-two times s.
Nine divided by d.
t decreased by 29.
Two more than g.
Eleven times x.
h divided by twelve.
Five minus k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
help
I need this asap
Answer: natural number=11
integer= -4
irrational= pi, 0.1010010001.....,root 5
rational= 0.1212...., -3/5,0.3,2 1/4
Step-by-step explanation:
Consider parallelogram ABCD below. Point E is the intersection of diagonals AC and BD.
Progress: 0/2
Part 1 of 2
4(-2,2)
D(-2,-10)
(a) Find the area of AABE.
cm
2
B (8.2)
C(8.-10)
How is the distributive property used when finding the product of two polynomials?
DUCK is a rectangle. Solve:
X=
UDK=
For the rectangle, the value x will be 14 and angle UDK will be 35°.
What exactly is a rectangle?
A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.
Now,
As we know all angles of a triangle are 90°.
then 5x-15+2x+7=90
7x=98
x=14
and in triangle UDK
sum of all angles = 180°
∠UDK+90+5x-15=180
∠UDK=180-145
∠UDK=35°
Hence,
the value x will be 14 and angle UDK will be 35°.
To know more about rectangles visit the link
brainly.com/question/29123947
#SPJ1
please help quick
6d = 54
answer
6 divided by 54 is equal to 9
therefore
answer = d=9
A quadrilateral has opposite sides with the same slopes and consecutive sides with slopes that are reciprocals. What is the most precise classification of the quadrilateral?
Quadrilateral
Rectangle
Parallelogram
Trapezoid
The most precise classification of the quadrilateral with opposite sides having the same slopes and consecutive sides having slopes that are reciprocals is a Rectangle.
1. Opposite sides with the same slopes imply that these sides are parallel.
2. Consecutive sides with slopes that are reciprocals mean that they are perpendicular.
3. Parallel opposite sides make the quadrilateral a parallelogram.
4. Perpendicular consecutive sides make it a rectangle, as all angles are 90 degrees.
So, the quadrilateral is a Rectangle.
More On Quadrilateral:https://brainly.com/question/23935806
#SPJ11
The following table gives the probability distribution of a random variable X
X 1 2 3 4
P(x) ¼ C ½ 1/8
a) Find the value of the constant C
b) Find
The value of the constant C is 3/4.
Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is a measure of the likelihood that a specific event will occur, expressed as a value between 0 and 1
The sum of the probabilities for all possible values of X should equal 1
P(1) + P(2) + P(3) + P(4) = 1
Substituting the given values, we get:
C/4 + 1/2 + 1/8 + C/4 = 1
Simplifying the equation, we get:
C/2 + 5/8 = 1
Move 5/8 to right hand side of the equation
C/2 = 3/8
C = (3/8) x 2
C = 3/4
Learn more about probability here
brainly.com/question/11234923
#SPJ4
maurice is buying a house that has 1,200 square feet on the main, a vaulted entry, and 650 square feet on the top level, plus a 335-square-foot garage. what's included in the livable square feet?
The livable square footage of the house is 1,850 square feet.
To determine the livable square footage of the house, we need to exclude areas that are not considered living spaces. The main level of the house has 1,200 square feet and is considered livable space.
The top level has 650 square feet, but since it is not clear if the entire space is livable or if there are non-livable areas (such as an attic), we cannot assume that the entire space is livable.
Therefore, we will exclude the top level from our calculation of livable square footage. The garage is also not considered livable space, so we will exclude the 335 square feet of the garage as well.
Thus, the livable square footage of the house is 1,200 square feet (main level) + 0 square feet (top level) + 0 square feet (garage) = 1,200 square feet. Therefore, the total livable square footage of the house is 1,850 square feet.
To know more about square feet refer here:
https://brainly.com/question/30678567#
#SPJ11
help pls its too much
Answer:
24.13
Step-by-step explanation:
165. 1% of 384. 7. Round to the nearest thousandth
Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.
In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:
Step 1: We make the assumption that 384.7 is 100% since it is our output value.
Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.
Step 3: In the same sense, x% = 165.1.
Step 5: Now, we have a pair of simple equations:
100% = 384.7 --(1).
x% = 165.1 ---(2).
Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.
Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7
=> x = ( 165.1/384.7) × 100
=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.
For more information about percentage, visit :
https://brainly.com/question/28398580
#SPJ4
Select ALL the set of numbers that are possible values for x in the inequality, x<-3
The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)
To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.
{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.
{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.
Learn more about Inequality:
https://brainly.com/question/25275758
#SPJ4
Complete Question:
Select all the sets of numbers that are possible values for x in the inequality, x<-3.
{5,7,9}{-9, -7, -5}{-33, -22, -11}{-5,0,5}The price of a 6-minute phone call is 1. 80. What is the price of a 18-minute phone call?
Answer:
5.40
Step-by-step explanation:
let X represent the price of a 18 minute phone call
X=18 ×1.80
6
= 5.40
does the line ever match up perfectly? can the lines ever have the same slope? can the lines ever have the same y-intercept? why or why not?
No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.
No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.
If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.
To learn more about equation of the line link is here
brainly.com/question/21511618
#SPJ4
Evaluate. Write your answer as a fraction or whole number without exponents.
6^–3 =
Answer:
i'm pretty sure it's 33
Step-by-step explanation:
6^= 36
36-3= 33
PLEASE HELP WITH EXPLANATION PLEASE PLEASE PLEASE NO SCAMMING FOR THE COINS OR I WILL REPORT YOU
The correct solutions for the given equation is given by table in option 3.
Explain about the solution of linear equation?A straight line is produced when a linear equation, which is a two-variable equation, is graphed. The intersection of corresponding values which satisfy the equation results in the line.
The variables x and y are most frequently used in linear equations, hence the associated values can be shown as (x,y) on the coordinate plane, pairs. A collection of two maybe more linear equations is known as a system of linear equations.
The given equation is-
y = x - 6
Put the value of 'x' from the options and check for 'y', if its correct.
The option are the solution of the equation.
option 1:
y = x - 6
x = --5
y = -5 - 6 = -11 (incorrect)
option 2:
y = x - 6
Put x = -8
y = -8 - 6 = -14 (incorrect)
option 3:
y = x - 6
Put x = -7
y = -7 - 6 = -13 (correct)
Thus, the correct solutions for the given linear equation is given by table in option 3.
Know more about the linear equation
https://brainly.com/question/2030026
#SPJ1
Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
To learn more about sequence visit: https://brainly.com/question/30262438
#SPJ11
There are 36 students in the school choir. The ratio of girls to boys in the choir is
5:4. Two girls are absent from practice on Monday. What is the ratio of girls to
boys at choir practice on Monday?
A 3:4
C 9:8
B 5:2
D 10:7
Answer:
C 9:8
Step-by-step explanation:
total students = 36
5+4=9
5:4 = 20:16
20-2=18
ratio for monday = 18:16
=9:8
a coffee distributor needs to mix a(n) kenya coffee blend that normally sells for $8.20 per pound with a breakfast coffee blend that normally sells for $14.00 per pound to create 10 pounds of a coffee that can sell for $9.36 per pound. how many pounds of each kind of coffee should they mix?
The coffee distributor should mix 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend to make 10 pounds of a coffee blend that can sell for $9.36 per pound.
We can use the idea of weighted averages to overcome this issue. Assume that 10 pounds of the desired blend require x pounds of Kenya coffee blend and y pounds of morning coffee blend.
The price of the Kenya coffee mix per pound is $8.20, while the price of the morning coffee blend per pound is $14.00. The required combination costs $9.36 per pound. On the basis of the weighted average, we can construct the following equation:
8.20x + 14.00y = 9.36(10) (10)
When we simplify this equation, we obtain:
8.20x + 14.00y = 93.60
Given that we are producing 10 pounds of the ideal blend, we also know that x + y = 10. To get the values of x and y, we can use substitution or elimination to solve this system of equations.
Use substitute now. We can find x from the second equation by solving in terms of y:
x = 10 - y
Substitute this into first equation, we get:
8.20(10 - y) + 14.00y = 93.60
82 - 8.20y + 14.00y = 93.60
5.80y = 11.60
y = 2
We obtain x = 8 by substituting y = 2 into x = 10 - y. Hence, to manufacture 10 pounds of a coffee mix that can be sold for $9.36 per pound, we'll need 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend.
Learn more about pounds here:
https://brainly.com/question/29181271
#SPJ4
according to census 2000, asians in the united states represent about what percent of the total population? question 1 options: 16.2 percent 10.5 percent 3.6 percent
Answer: 4.2 percent
Step-by-step explanation: Your welcome
Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
To learn more about conversion factor click here
brainly.com/question/28770698
#SPJ4
when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
To know more about center of gravity:
https://brainly.com/question/17409320
#SPJ11