well, first off, let's see how much each one costs per month.
so, hmmm if she goes with the Bank loan at 9% for 3 years
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ A=9000[1+(0.09)(3)] \implies \boxed{A = 11430}[/tex]
now, that's for 36 months, so she'd be owing the Bank per month [tex]\cfrac{\stackrel{total}{11430}}{\underset{months}{36}}~~ = ~~\text{\LARGE 317.5}[/tex]
now let's take a look at the Credit Card's loan at 18% for 7 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9000\\ r=rate\to 18\%\to \frac{18}{100}\dotfill &0.18\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases} \\\\\\ A=9000\left(1+\frac{0.18}{12}\right)^{12\cdot 7} \implies A \approx \boxed{31433.31}[/tex]
now, in 7 years there are 84 months, thus [tex]\cfrac{\stackrel{total}{31433.31}}{\underset{months}{84}}\approx \text{\LARGE 374.21}[/tex]
so, the Bank will give her a better deal per month, and to be honest altogether.
The plan with simple interest will give the lowest monthly repayment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
Option C is the correct answer.
What are simple interest and compound interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
We have,
Simple interest:
Principal = $9000
Rate = 9%
Time = 3 years
Simple interest:
= P x R x T / 100
= 9000 x 9 x 3 / 100
= 2430
Amount = simles interest + principal
A = 9000 + 2430 = $11430
3 years = 36 months
Monthly payment = 11430 / 36 = $317.5
Compound interest:
Principal = $9000
Rate = 18%
Time = 7 years
A = P [tex](1 + \frac{18}{100}) ^{7}[/tex]
A = 9000 [tex](1 + 0.18) ^{7}[/tex]
A = 9000 x3.19
Amount = $28,710
7 years = 84 months
Monthly payment = 28710 / 84 = $341.78
Thus,
The plan with simple interest will give the lowest monthly repayment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
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Identify the vertex, axis of symmetry, and direction of the graph of each function. Compare the width of the graph to the width of the graph of f(x)=x^2
===================================================
Explanation:
Compare the equation
[tex]y = (x-2)^2 - 4[/tex]
to the vertex form
[tex]y = a(x-h)^2 + k[/tex]
we have:
a = 1h = 2k = -4The vertex is located at (h,k) = (2, -4). Nice job on getting the correct answer for the vertex.
The axis of symmetry is x = 2 since the axis of symmetry goes through the vertex. It's the vertical mirror line.
Because a = 1 is positive, the parabola opens upward. It forms a bowl shape. The vertex is the lowest point.
If a < 0, then the parabola would open downward and have a highest point.
What ratio is equivalent to 18:3 and 6:1
Answer:
12:2
Step-by-step explanation:
THIS IS TRUE AND EASY
Answer:
12:2
24:4
30:5
36:6
42:7
find the intersection of the three sets: A={-2,7,8,11}, B={-2,7,11}, C={-2,8,11}
The intersection of three sets A,B and C is {₋2 , 11}.
Given set A = {₋2,7,8,11}
set B = {₋2,7,11}
set C = {₋2,8,11}
we need to find A∩B∩C.
The components shared by all the sets A, B, and C are given by the intersection of A and B as a set. A ∩ B ∩ C is a notation that can be used to indicate the intersection of A, B, and C.
To obtain A intersection B intersection C, first determine the common elements of sets A and B, or A ∩ B. Then determine the common elements of sets B and C, or B ∩ C. Finally, compute the common elements of these two results.
we first find:
A∩B = {₋2,7,8,11} ∩ {₋2,7,11}
= {₋2,7,11}
then B ∩ C = {₋2,7,11} ∩ {₋2,8,11}
= {₋2 , 11}
now (A∩B) ∩ (B∩C) = {₋2,7,11} ∩ {₋2 , 11}
= {₋2 , 11}
hence we get the intersection of three sets as {₋2 , 11}
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X - 2(X + 10) = 12
What is this??!?!!?
Answer:
-32
Step-by-step explanation:
Pal, it's M A T H
Answer:
-32
Step-by-step explanation:
x-2x-20=12
-x=32
x=-32
.....................
translate the following statement into an equation and solve for x: the number 80 is the product of "-10" and x
The value of x is -8 in the equation.
How to calculate the equation?It should be noted that the information is that the number 80 is the product of "-10" and x.
This will be represented as:
-10 × x = 80
-10x = 80
Divide both side by -10
-10x/-10 = 80/-10
x = -8
Therefore, the value of x is -8.
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8/7 x 4 6/7 help plssss
Answer:
272/49
Step-by-step explanation:
hope this helps :)
solve 2x + 6 < 10 or 2x + 8 > 20.
Answer:
Step-by-step explanation:
the answer you end up getting is D
2x/2 > 12/2x > 6
Because x is greater than 2
Evaluate the expression 5•5-1•3
5 * 5 - 1 * 3
Since multiplication goes before addition in PEMDAS, we do the multiplication first.
25 - 3
2
Answer:
22
Step-by-step explanation:
5•5-1•3
(5 x 5) - (1 x 3)
25 - 3
22
You would multiply both separately and then subtract.
Remember PEMDAS
:)
11 Write as a power of 5
125²
21
Starting with the letter A and counting left
to right,
B
C
I
J
P Q
write the fifth letter
write the eighth letter
write the third letter
A
H
O
D
K
E
L
RS
CND
G
F
M
T U
Answer:
fifth letter: E
eighth letter: H
third letter: C
Im not sure
Johnathan worked 4 hours on Monday, 4 hours on Tuesday, 4 hours on Wednesday, 4 hours on Thursday, and 4 hours on Friday. He makes $12.125 an hour. What is his total pay?
Answer:
$242.50
Step-by-step explanation:
The total of number of hours = 20
Hourly pay = 12.125
20*12.125
Total pay= 242.50
Point N is the midpoint of segment FG. If FN = 2z2 + 4z +3, write the expression below that represents FG.
The center of segment FG is located at point N. Write the formula that expresses FG if FN = 2z2 + 4z + 3.
Since O represents the midway, both FO and OG must be equal.
3x + 17 = 7x - 15
Add 3x to both sides and subtract:
17 = 4x -15
To both sides, add 15:
32 = 4x
Subtract 4 from both sides:
x = 32/4
X = 8
Now that you know the value of X, find the lengths:
FO = 3x +17 = 3(8) +17 = 24 +17 = 41
OG = 7x -15 = 7(8) -15 = 56-15 = 41
Total length would be 41 + 41 = 82
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If AB and CD intersect at point E, m measure of all four angles.
The all four angles are ∠AEC=40o, ∠BEC=140o, ∠AED=140o, ∠BED=40o.
What are vertically angles?
Vertical angles are formed when two lines cross at a point. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.
Given that
∠BOC+∠AOC=280o (AB and CD intersect at point E)
we know that, ∠AED and ∠BEC are vertically opposite angles ∠AED=∠BEC
we know that, ∠AED=∠BEC
so it can be written as
∠AED+∠AED=180o,
2∠AED=280o,
∠AED= 140o,
∠AED=∠BEC=140o
we know that ∠AEC and ∠AEC form a linear pair
So it can be written as
∠AEC+∠AED=180
substituting the values
∠AEC+140o=180o
∠AEC=40o
we know that ∠AEC and ∠BED are vertically opposite angles
∠AEC=∠BED=40o
Therefore, ∠AEC=40o, ∠BEC=140o, ∠AED=140o, ∠BED=40
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point b is between A and C. if AC = 3x+3, BC = 2x-1, and AB = 11. Find the length of BC
==================================================
Work Shown:
AB+BC = AC
(11) + (2x-1) = 3x+3
2x+10 = 3x+3
2x-3x = 3-10
-x = -7
x = 7
which is then use to find:
BC = 2x-1 = 2*7-1 = 13AC = 3x+3 = 3*7+3 = 24As a check,
AB+BC = 11+13 = 24 = AC which confirms the answer.
Please help me with this
Answer:
2.7 miles
Step-by-step explanation:
0.5 + 1.3 + 0.9 = 2.7
Segments AD and BC intersect at point O.
Prove that AC = BD,
m∠ABC=m∠BAD.
Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.
How to prove Congruent Angles?
In ΔOAC and ΔODB, we have the following observations
CO = DO because it is shown that they are congruent
∠AOC = ∠BOD because vertical angles are congruent
∠ACO = ∠BDO because we are given that they are congruent
Now, the congruency theorem that we can use here is ASA which means Angle - Side - Angle. This implies that 2 corresponding angles and the included side are congruent.
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by Angle - Side - Angle congruence theorem.
Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.
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Does the figure below appear to have line symmetry if so how many lines of symmetry
A vinyl decal shop charges a set-up fee of $25.00 and $5.00 for each decal printed. donna is ordering one decal for each of the 6 cheerleaders. if x decals are ordered, the total cost of the set-up fee and decals can be represented by f\left(x\right)=5x+25f(x)=5x+25. what are the range values for this situation?
The range of the situation is 30 to 55.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used when you do not know the exact number in a calculation.
Given:
A vinyl decal shop charges a set-up fee of $25.00
$5.00 for each decal printed.
as, f(x)=5x+25 represents the total cost of the set-up fee
we have 6 cheerleaders
put x= 1
5x+25 = 5+25 = 30
and x=6
5x+25= 5*6+25= 30+25= 55
Hence, the range is 30 to 55.
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Are 5y and 5x like terms?
Answer:
No. They include 2 different elements that are unrelated, being x and y, making them unlike terms.
Answer:no
Step-by-step explanation:in order for them to be like terms they would have to have the same variables
A $44,200.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account? Round to the nearest cent.
The balance amount at the end of 4 years in the account will be $53275
Principal amount= $44200
Rate of interest = 5% compounded annually
Number of years amount is invested for: 4 years
The formula for compound interest is given by:
A = P(1 + r/100)^n
where A = Final amount
P = principal amount invested
r = Rate of interest annually
n = number of years amount is invested
Putting the values in the formula we get:
A = 44200(1 + 5/100)^4
= 44200(1.05)^4
=44200*1.21
Amount at end of 4 years= 53725.37 or 53725
So, the balance amount at the end of 4 years in the account will be $53275
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Simplify: (2 3/5)+(-3 3/4)
Answer:
-23/20
Step-by-step explanation:
Givin h(x) =-x-2 , solve for x when h(x)= 3.
Answer:
-5
Step-by-step explanation:
h(x)=3
3=-x-2
3+2=5
3=-(-5)-2
negatives cancel
3=5-2
Given f(n) = 7n - 5
Evaluate f(-2)
Answer:
[tex]{ \tt{f(n) = 7n - 5}} \\ { \tt{f( - 2) = 7( - 2) - 5}} \\ { \tt{f( - 2) = - 14 - 5}} \\ { \tt{f( - 2) = - 19}}[/tex]
HELP PLEASEEEI’ll
Make you brainlist
Answer:
Step-by-step explanation:
0,5 0.6 and 0.5 again? sorry i might be wrong if i am my apologies
Help me out to get the answer please
Answer:
21
Step-by-step explanation:
1+6=7
7+4=11
11+11=21
Answer:
m=7
Step-by-step explanation:
it's in the picture
the left got cut out but there's a bracket at the end of the first line
A function is shown in the table.
x g(x)
−2 2
−1 0
0 2
1 8
Which of the following is a true statement for this function? (5 points)
Group of answer choices
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = −1 to x = 0.
The function is increasing from x = 0 to x = 1.
The function is increasing from x = −2 to x = −1.
Answer:
The function is increasing from x = 0 to x = 1.
Step-by-step explanation:
The value of g(0) is less than g(1), meaning g(x) increased from x=0 to x=1.
PLEASE HELP ASAPPP !! WILL GIVE BRAINLIEST AND 5 STAR RATINGGG
Answer: C
Step-by-step explanation:
A negative times a negative equals a positive.
shae used the product of rule to prove that 7 to 0 power is equal to 1
Answer:
yes a product of any number to 0 is equal to 1
Smallest
437.55
437.49
437.15
437.5
437.05
Largest
Answer:
smallest to largest will be:
437.05 , 437.15, 437.49, 437.5, 437.55
Step-by-step explanation:
an easier method i use is to simply check the 1st digit rhat comes after the decimal point if the whole numbers are similar.
in a case where there is only one number after the decimal while the rest have 2, for example 437.5, simply add a 0 to make it even as the rest
If there are 52 weeks in a year, how many more hours does a squirrel sleep in a year than a rabbit?
The squirrel sleeps 2548 hours more than the rabbit.
Difference of the numbers
Difference of the numbers means the result of subtracting one number from another.
Given,
If there are 52 weeks in a year,
Then we need to find how many more hours does a squirrel sleep in a year than a rabbit.
First, we have to find the sleeping pattern of squirrel and rabbit.
A squirrel spends up to 60% of its day asleep, which means that an average squirrel sleeps for almost 15 hours each day.
Similarly, the rabbits are sleep six to eight hours each day.
So for one day,
Rabbit = 8 hours per day
Squirrel = 15 hours per day.
Then the sleeping hours for one week is
Rabbit = 8 x 7 = 56 hours
Squirrel = 15 x 7 = 105 hours
So, for 52 weeks, they spend
Rabbit = 56 x 52 = 2912
Squirrel = 105 x 52 = 5460
So, the difference is
=> 5460 - 2912
=> 2548
Therefore, the squirrel sleeps 2548 hours more than the rabbit.
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