Size of final payment is $6392.43
Given that formula for compound interest is P(1+r/n[tex])^{nt}[/tex]
where P is initial principal
r is interest rate
n is compound times per period
t is time in years
We find all the variables in the formula in order to get our answer.
Initial principal = 96000 less 25%= 72000
interest rate = 9%
number of compound times= 12
time in years =4.25 years (whole period is 4.5 years since number of payments to complete balance will take 54 months)
Hence principal and CI after 4 years and 3 months(the second to last payment)
72000(1+0.09/12)^12x4.25=$105,393.6
We use $105,393.6 as our principal to calculate the whole interest and principal for the period in order to find last payment
105393.6(1+0.09/12)^12x0.25=$107,786.03
interest for the final month = $107786.03-$105,393.6=$2392.43
To get our final payment, we add the principal payment of $4000 to final compounded interest =$6392.43
Colin got a new video game. He scored 31 points on the first level, 31 points on the second level, 31 points on the third level, and 31 points on the fourth level. What kind of sequence is this? both, neither ,arithmetic, geometric
Answer:
Both
Step-by-step explanation:
An arithmetic sequence is given by the next form:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So the given sequence is of the form, because the common difference between terms is 0.
[tex]a_{n} = 31 + (n - 1) 0 = 31[/tex]
A geometric sequence is given by the next form
[tex]ar^0, ar^1, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]
When [tex]r\neq 0[/tex]
In this occasion our [tex]a=31[/tex] and the [tex]r = 1[/tex]
So both sequence represent the given one.
Help help help help help help help help help
Answer:
A'(-2,3) B'(-1,1) C'(-4,0)
Step-by-step explanation:
Translating just means adding whatever numbers to each coordinate. Point A translated from (3,0) to (-2,3) because 3-5 is -2 and 0+3 is 3.
100 points! show work or else i report
A certain microwave requires 1200 watts. How much would it cost to run the microwave for a total of 30 minutes (defrosting chicken) at a cost of $0.20 per kilowatt hour?
[tex]\boxed{\sf E=Pt}[/tex]
E is energy
P is power
t is time in hours
E=1200(0.5h)E=600WhE=0.6KwhCost
0.6(0.2)$0.12Answer:
$0.12
Step-by-step explanation:
Conversions
1000 watts = 1 kilowatt-hour
⇒ 1200 watts = 1.2 kilowatt-hour
60 minutes = 1 hour
⇒ 30 minutes = 0.5 hour
A microwave requiring 1200 watts will use 1.2 kilowatts per hour.
If the microwave is used for a total of 30 minutes, it will use:
⇒ 1.2 × 0.5 = 0.6 kWh
If the cost is $0.20 per kWh, the cost of running the 1200 watt microwave for 30 minutes is:
⇒ 0.6 × $0.20 = $0.12
End is making some pancakes for himself and five friends. The ingredients he needs are shown in the list below.
Pancakes (serves 2)
2/3 milk
3/4 flour
3/2 sugar
1 Egg
a. How many cups of flour will Ed need?
b. How many teaspoons of sugar will Ed need?
Answer:
a. 2 1/4 cup of flour
b. 4 1/2 tsp. off sugar
Step-by-step explanation:
Since the recipe serves 2, the answer given will feed 5 (6) people.
Find the nth term of the geometric sequence.
[tex]a_2 = ar^{2-1} =ar = 6~~ ...(i)\\\\a_4 = ar^{4-1} = ar^3 = 2186 ~~....(ii)\\\\\\(ii)\div (i):\\\\\dfrac{ar^3}{ar} = \dfrac{2186}6\\\\\implies r^2 = \dfrac{2186}6 = \dfrac{1093}3\\\\\implies r = \pm \sqrt{\dfrac{1093}3}\\\\a= \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}}\\\\\text{nth term} = ar^{n-1} = \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( \pm{ \sqrt{\dfrac{1093}3} \right)^{n-1} = \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( { \sqrt{\dfrac{1093}3} \right)^{n-1} \\\\\\[/tex]
[tex]= 6\left(\dfrac{1093}3 \right)^{\tfrac{n-2}2}[/tex]
Answer:
aₙ = (6/19)*19ⁿ⁻¹Step-by-step explanation:
Given:
a₂ = 6a₄ = 2166Equation of nth term of GP:
aₙ = a₁rⁿ⁻¹Substitute for 2nd and 4th terms:
a₂ = a₁r = 6a₄ = a₁r³ = 2166Substitute the value of a₂ into a₄ and find the value of r:
a₁r³ = a₁r * r² = 6r²6r² = 2166r² = 2166/6r² = 361r = √361r = 19Find the first term:
a₁r = 6a₁*19 = 6a₁ = 6/19The equation of nth term is:
aₙ = (6/19)*19ⁿ⁻¹The ratio of the totals of the numbers in box A and box B is 2:3.
Swap two numbers, one from each box, so that the ratio of the totals of the numbers is now 9:11. Show your working.
Please answer asap!! :)
Answer:
Swap 10 from box A and 15 from box B
Step-by-step explanation:
For calculate the ratio between the boxes we find the mean of the box A and the mean of the box B and divide this two results.
For find the mean of a set you use the next formula [tex]\bar{x} = \frac{\text{sum numbers}}{\text{total numbers}}[/tex]
[tex]\bar{A} = \frac{4+5+9+10+12}{5} = \frac{40}{5}= 8\\\bar{B} = \frac{6+7+13+15+19}{5} = \frac{60}{5}= 12[/tex]
Then the ratio is equal to [tex]\frac{\bar{A}}{\bar{B}} = \frac{8}{12} = \frac{2}{3}[/tex]
Know the ask us for a ratio of 9:11 then we know two things about the boxes.
If you swap the numbers between them the total of numbers in the mean not change is always 5 and the sum of all the elements in both boxes is always 100. With this we can state the next equation:
The new mean of [tex]\bar{A}[/tex] is 9 then:
[tex]\frac{\text{sum of elements in box A}}{5} = 9[/tex]
[tex]\text{sum of elements in box A} = 45[/tex]
The new mean of [tex]\bar{B}[/tex] is 11 then:
[tex]\frac{\text{sum of elements in box B}}{5} = 11[/tex]
[tex]\text{sum of elements in box B} = 55[/tex]
Now we know what is the sum of the elements in both boxes, but how we find the elements for swap? Well with the next relation.
When you take out a element from the box A this elements is substracted to the total sum of the elements in the box A and get a new sum of total of elements named [tex]c[/tex] (where [tex]a[/tex] is the element taken):
[tex]40 - a = c[/tex]
And when you sum an element to the box A the current sum of total elements in the box change to (where [tex]b[/tex] is the added element):
[tex]b + c = 45[/tex]
So replace [tex]c[/tex] for the first relation and get:
[tex]b + 40 - a = 45\\b - a = 5[/tex]
From the last equation you can deduct that [tex]b[/tex] is greater than [tex]a[/tex] and the different between both values is 5. So the last step is find a number in the box B that substracted to a number from the box A give us 5. These both numbers are 15 and 10 because 15 - 10 = 5.
Will give brainliest!
We know that a + b + c = 7 and [tex]\frac{1}{a+b} + \frac{1}{b+c} +\frac{1}{a+c} =\frac{7}{10}[/tex]. What is the value of [tex]\frac{10a}{b+c} +\frac{10b}{a+c} +\frac{10c}{a+b}[/tex]?
Answer:
19
Step-by-step explanation:
Note that
[tex]\dfrac{10a}{b+c} + \dfrac{10b}{a+c} + \dfrac{10c}{a+b} = 10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right)[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b}=\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
from [tex]a+b+c=7 \implies a=7-bc; b = 7-a-c; c = 7-a-b[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b} = 7\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}\right)-3[/tex]
because it is not difficult to note that
[tex]$\sum \dfrac a{b+c}=\dfrac a{b+c}+\dfrac b{c+a}+\dfrac c{a+b}$[/tex]
Therefore,
[tex]7\left(\dfrac{7}{10}\right)-3 = \dfrac{49}{10}-3 =\boxed{ \dfrac{19}{10}} = \dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
Finally,
[tex]10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right) = 10 \cdot \dfrac{19}{10} = 19[/tex]
Which equation is linear? y=x4 y=xy –x3 ОООС f(x) = 3х + 1 y=xУ
Answer:
f(x) = 3х + 1
Step-by-step explanation:
Which is the algebraic expression for "two times the sum of a number and four'?
*Someone save me.*
Answer:
2(x+4)
Step-by-step explanation:
Senna was having a party for 15 friends. She bought 3 jars of
pickles for $4.50. What is the cost per jar?
Answer:
it is 1.5
Step-by-step explanation:
if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5
Write an equation with a slope of 2 and a constant of -5
what set of angles can form a line
Answer:
Did u mean triangle? There are no angles on a line.
Or do you mean two angles of 90 degrees?
Step-by-step explanation:
Need help with this question ASAP tysm
Step-by-step explanation:
sorry for my bad handwriting, hope it helps
Louis is comparing the populations of several nearby cities. The population of Liberty Crossing can be written as 49 people, and the population of Harrisburg can be written as 47 people. The population of Glenview is 43 times the population of Harrisburg. Drag the cities to put them in order from least population (top) to greatest population (bottom).
Step-by-step explanation:
Louis is comparing the populations of several nearby cities. The population of Liberty Crossing can be written as 49 people, and the population of Harrisburg can be written as 47 people. The population of Glenview is 43 times the population of Harrisburg. Drag the cities to put them in order from least population (top) to greatest population (bottom).
The order of the cities from least population to greatest population:
Harrisburg
Glenview
Liberty Crossing
Given the information provided:
Harrisburg: This city has a population of 47 people. It's the smallest population among the three cities.
Glenview: The population of Glenview is 43 times the population of Harrisburg.
Since Harrisburg has 47 people, the population of Glenview would be 43 x 47 = 2021 people.
So, Glenview has a larger population than Harrisburg but is still smaller than Liberty Crossing.
Liberty Crossing: The population of Liberty Crossing is given as 49 people, which is the largest population among the three cities.
So, the correct order from least population to greatest population is:
Harrisburg
Glenview
Liberty Crossing
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Malachi ran 8\10 of a mile. Sam ran 3\4 of a mile. How much farther did Malachi run than Sam?
Answer:
1/20
Step-by-step explanation:
Step 1
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 8 by 4, and get 32.
Then we multiply 3 by 10, and get 30.
Next we give both terms new denominators -- 10 × 4 = 40.
So now our fractions look like this:
32/40−30/40
Step 2
Since our denominators match, we can subtract the numerators.
32 − 30 = 2
So the answer is:2/40
Step 3
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
2/40÷ 2 =1/20
Let's try dividing by 2 again...
No good. 2 is larger than 1. So we're done reducing.
There you have it! The final answer is:
1/20
Segments KN and LM are transversals. What is true about the measure of angle N?
Answer:
It is congruent to M
Step-by-step explanation:
Three different maths books are arranged in a line on my table. In how many different orders can these Maths books be arranged.? *
in 5 ways
in 6 ways
in 7 ways
________________________________
that means is it horizontally
vertically
up
down
one by one ?
explain with an example
Answer:
Step-by-step explanation:
Three options for the first position
Two options for the second position
one option for the third position
3•2•1 = 6 ways
their orders could be
1) ABC
2) ACB
3) BAC
4) BCA
5) CAB
6) CBA
Answer:
Would be 6 ways
Step-by-step explanation
3x2=6
The step club made friendship bracelet as a fundraiser and sold them for $1.75 each. The club made a profit of $182. How many bracelets did the step club make?
Answer:
104 bracelets
Step-by-step explanation:
182 ÷ 1.75 = 104
In Mrs. Reed's class, the ratio of boys to girls is 4:1 If there are 15 total students in the class, how many boys are there
Answer:
there are 12 boys
Apply the distributive property to create an equivalent expression
Answer:
3e-3/2f-3/8
Step-by-step explanation:
You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.
PLS ILL GIVE BRAINLIEST!!!!
Answeryawa ka
Step-by-step explanation:
Brainliest to the one thats right
Answer:
Option C is correct.
Step-by-step explanation:
In option C, the fractions are on one side and the constants are on the other. The fractions also have the same denominator. So, Option C is correct.
2.
Fit a quadratic function to these three points:
(−2, 8), (0, −4), and (4, 68)
A. y = −2x2 − 2x − 4
B. y = 4x2 + 2x − 4
C. y = −4x2 − 2x − 4
D. y = −2x2 + 2x − 4
Answer:
It's C.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
just put the x and y values into the equations and see which equation stays true.
for example, point (4, 68) rules out A and C even without detailed calculation, because these 2 expressions can produce for positive x only negative y (and 68 is clearly a positive y).
so, when using this point in B :
68 = 4×4² + 2×4 - 4 = 4×16 + 8 - 4 = 64 + 8 - 4 = 68
correct.
and it is correct also for the other points.
so, B is the right answer.
Mr. And mrs. Samson decide to go with design a and purchase the materials. Their total bill is 356.88. If they pay 220 in cash and charge the remainder, how much did they charge?
Answer:
136.88
Step-by-step explanation:
Subtract 356.88 - 220 = 136.88
Find the sum of 8080,8928 and 7005
Answer:
80,815,933
Step-by-step explanation:
Solve for x. x+12−−−−−√=x√+2
~equality
x + 12 = x√+2
= x + 12 = √2 x
= x = √2 x - 12
= x - √2 x = -12
= (1 - √2)x = -12
= x = -12/1- √2
= x = -(-12(1 + √2))
= x = -(-12 - 12√12)
= x = 12 + 12√2 ✔️
~ nice to help you ^^
1 + 1? (just for fun!)
Answer:
equal 11
Step-by-step explanation:
:>
hmmm wonder what else it would be
Which equation could be represented by the number line?
[tex]Hiya![/tex]
Sokka is here to help!!
I believe it is D..
Hopefully, this helps you!
[tex]Sokka[/tex]
Answer:
I think it is C.
Step-by-step explanation:
It has a starting point. It also has an arrow that is going toward the negatives. It also has a gap of 9 units. So therefore, C is our answer.
Translate this phrase into an algebraic expression.
Five more than the product of 11 and a number
Use the variable n to represent the unknown number.
Answer:
5+(11 x n)
Step-by-step explanation:
I hope this helps
Leah can build a brick wall in 7 hours, while her apprentice can do the job in 10 hours. How long does it take for them to build a wall together
Answer:
70/17 hours or 4 2/17 hours
Step-by-step explanation:
The equation we use is 1/7 + 1/10 = 1/x, x being the time it took them together to build. x works out to 70/17 hours
Leah and her apprentice can build the wall together in 4 2/17 hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Hours required by Leah to build a wall = 7 hours
So , Leah builds ( 1/7 )th of the wall per hour
Hours required by apprentice to build a wall = 10 hours
So , Apprentice builds ( 1/10 )th of the wall per hour
When they are both building the wall together , they build
( 1/7 )th + ( 1/10 )th of the wall together per hour = 1 / x
Therefore , the equation will be
1/x = 1/7 + 1/10
1/x = 17 / 70
Taking reciprocal on both sides , we get
x = 70/17
x = 4 2/17 hours
Hence , Leah and her apprentice can build a wall together in 4 2/17 hours
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