(a) the future value after 9 years is $7254.76 .
(b) the effective rate of interest is 3.769% .
(c) the time required to reach $10000 is 1.77 years .
The Continuous Compounding formula for the principal P , rate of interest r , and time t is
A = P×[tex]e^{rt}[/tex]
In the question ,
it is given that
Part(a)
the amount deposited (P) = $5200
rate percent (r) = 3.7% = 3.7/100 = 0.037
time = 9 years
Amount = 5200×[tex]e^{0.037\times9}[/tex]
= 7254.76
the future value after 9 years is $7254.76 .
Part(b)
the effective rate is calculated using the formula
effective rate = [tex]e^{r}[/tex] - 1
effective rate = [tex]e^{0.037}[/tex] - 1
= 1.03769 - 1
= 0.03769
= 3.769%
Part(c)
the time to reach $10000 is calculated using the formula
10000 = 5200[tex]e^{0.037\times t}[/tex]
[tex]e^{0.037\times t}[/tex] = 10000/5200
[tex]e^{0.037\times t}[/tex] = 100/52
taking ㏑both the sides , we get
0.037×t×㏑(e) = ㏑(100/52)
0.037t = 0.65392
t = 0.65392/0.037
t = 1.76735
t ≈ 1.77 years
Therefore , (a) the future value after 9 years is $7254.76 .
(b) the effective rate of interest is 3.769% .
(c) the time required to reach $10000 is 1.77 years .
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Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto: $30,000 Estimated life: 5 years Residual value: $800 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 $30,000 A B C D E 2 $30,000 F G H I J 3 $30,000 K L M N O
The table is completed as follows using the double-declining-balance method of depreciation:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
The double-declining-balance approach is what?
The double-declining-balance method is one of the depreciation techniques in use, however it adds additional costs in the first years of an asset's life.
In this depreciation method, the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2, is twice.
At the conclusion of each year, the leftover balance for the depreciation charge is adjusted using the double rate.
The difference between the closing balance from the previous year and the residual value is used to determine the depreciation charge for the most recent year.
Auto = $30,000
Estimated useful life = 5 years
Residual = $800
Depreciable amount = $30,000 - $800 = 29,200
Straight-line depreciation rate = 100/5 = 20%
Double-declining depreciation rate =20% x 2 = 40%
Depreciation Expense:
1st year = 30,000 x 40/100 = 12,000
2nd year = 18,000 x 40/100 = 7,200
3rd year = 10,800 x 40/100 = 4,320
4th year = 6,480 x 40/100 = 2,592
5th year = 3,888 x 40/100 = 1,555
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
4 $30,000 $23,520 $6,480 $2,592 $26,112 $3,888
5 $30,000 $26,112 $3,888 $1555 $27,667 $2,332
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h(x) = |x + 10|, find h(-17).
Work Shown:
h(x) = |x+10|
h(-17) = |-17+10|
h(-17) = |-7|
h(-17) = 7
Find the sum of those four-digit numbers which are constructed by the digits 1, 2, 3, 4 (and the digits are not repeated).
The sum of four digits numbers constructed by the digits 1, 2, 3, and 4 is 10
How to find sum of the digitsThe sum of the digits is achieved by adding the digits
The sum will be same no matter how the numbers are placed and as long as the numbers are not repeated.
The property that is useful here is the commutative property of addition
adding the digits
= 1 + 2 + 3 + 4
= 10
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Drag and drop the cards in order from least to greatest on the number line.
-10
1
- 31
1
0
8
14
218
I
816
9
The order of cards on number line are in main body.
What is number line?
In elementary arithmetic, number line could be a image of a graduated line that is visual illustration of the important numbers. each purpose of range|variety} line is assumed to correspond to a true number, and each complex number to a degree.
Main body:
According to question we need to arrange numbers in ascending order ,
so the order will be as
-31/ 3 = -11.33
-10
-9/8 = -1.125
0
1/4 = 0.25
1
9/8 = 1.125
8
hence the order is as -31/3< -10< -9/8 < 0< 1/4 < 1 < 9/8< 8
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How many permutations can you make using the word TRANSFORMED?
There is 19958400 Number of permutations can be made using all letters.
What is permutation?
The term "permutation" describes a mathematical calculation that counts all possible arrangements of a given set. The term "permutation" simply refers to the variety of possible arrangements or orders. The arrangement's order matters in permutations.
Given Word is TRANSFORMED.
Total Number of letters = 11
Number of times Letter T repeating = 1
Number of times Letter R repeating = 2
Number of times Letter A repeating = 1
Number of times Letter N repeating = 1
Number of times Letter S repeating = 1
Number of times Letter F repeating = 1
Number of times Letter O repeating = 1
Number of times Letter R repeating = 1
Number of times Letter M repeating = 1
Number of times Letter E repeating = 1
Number of times Letter D repeating = 1
Number of permutations that can be made using all letters
= 11!/(1! * 2! * 1! * 1! * 1! * 1! * 1! * 1!) = 39916800/(2*2*2) = 39916800/2 =
19958400
Thus, there is 19958400 Number of permutations can be made using all letters.
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Gina Wilson unit 4 linear equations Homework 2 Slope intercept and standard form
All the answers to the given questions are mentioned below -
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given are six graphs as shown in the image.
PART [1]The equation of graph [1] -
m = (- 2 - 4)/(2 - 0)
m = -6/2
m = -3
Equation : y = -3x + 4
The equation of graph [2] -
m = (0 + 1)/(2.5 - 0)
m = 1/2.5
m = 10/25
m = 2/5
Equation : y = 2x/5 - 1
The equation of graph [3] -
Equation : y = 4
The equation of graph [4] -
Equation : x = 2
PART - [2][1] : 2x - y = - 7
y = 2x + 7
[2] : 5x + 3y = 12
3y = -5x + 12
y = -5x/2 + 4
[3] : x - y = 1
y = x - 1
[4] : x - 3y = - 15
3y = x + 15
y = x/3 + 5
[5] : 8x - 10y = 20
8x - 20 = 10y
y = 4x/5 - 2
[6] : 14x + 6y = 36
6y = -14x + 36
y = -7x/3 + 6
Therefore, all the answers to the given questions are mentioned above.
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[REFER TO IMAGE FOR QUESTION]
Which of the following shows that the two composite figures cover the same area?
For both figures, A=12+4+2+2+2=22 units²
For both figures, A=6+4+2+2+1=15 unit.²
For both figures, A=6+4+3+2+1=16 units.²
For both figures, A=6+4+3+3+2=18 units²
the Answer: A
Step-by-step explanation:
"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height according to information given is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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What word sentence represents this inequality?
A number is at least as large as 8.9
A number is no more than 8.9
A number is greater that 8.9
Answer:
a number that is at least as large as 8.9
Step-by-step explanation:
the line under the greater than sign makes it equal to or greater than
Find the Difference.
3.) 99-5.87
Answer:
93.13
Step-by-step explanation:
8 9 10 This is to show the work
99.00
- 5.87
------------
93.13
Triangle ABC has the following angle measures:
mLA = (x + 6)°, mzB = (3x - 15)°, mzC = (5x +36)°
What is m/C?
The value of ∠C: 121°
What is Triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.
Given this,
There is an ABC triangle.
m∠A = (x + 6)°
m∠B = (3x - 15)°
m∠C = (5x + 36)°
The size of C must be determined.
Having said that,
A triangle's total number of angles equals 180 degrees.
As a result, we can say,
∠(A) + ∠(B) + ∠(C) = 180
(x + 6)° + (3x - 15)° + (5x + 36)° = 180°
(x + 3x + 5x) + (6 - 15 + 36) = 180°
9x + 27 = 180°.
9x = 180 - 27
9x = 153 degrees
x = 153/9 degrees
17 = x.
Hence,
The ∠C is expressed as
∠C = 5x + 36
= 5*17 + 36
= 85 + 36
∠C = 121.
Thus, ∠C = 121.
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SOMEBODY HELP PLEASEEEE
The values of a, b and c when comparing ⁷√(6³) with [tex]a^\frac{b}{c}[/tex] are 6, 21 and 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
⁷√(6³)
Applying the law of exponents gives:
= √[(6³)⁷]
= √[6²¹]
[tex]=6^\frac{21}{2}[/tex]
Given the form [tex]a^\frac{b}{c}[/tex], the values of a, b and c are 6, 21 and 2
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Please help me on these two
they appear answered but their not.
1) The equivalent fraction is 27/8, so the correct option is A.
2) The value of the exponent in the right side must be y = 2, the correct option is C.
How to find an equivalent fraction?1) First we want to find an equivalent fraction to (2/3)^(-3)
Remember that a negative exponent means that we nee to take te inverse, we can write:
(2/3)^(-3) = (3/2)^3
Now we can just distribute the exponent along the numerator and denominator.
(3/2)^3 = (3^3)/(2^3) = 27/8
The correct option is A.
2) How to find the value of y?
Here we have the equation:
(3^3)^2/9^2 = 3^y
If we move the denominator to the right side, we can write:
(3^3)^2 = 9^2*3^y
Now, remember that:
9 = 3^2
Then we can write the right side as:
(9^2)*3^y = (3^2)^2*3^y = 3^(2*2)*3^y = 3^(4 + y)
Replacing that in the original equation we get:
(3^3)^2 = 3^(4 + y)
The exponent in the left side can be rewritten as:
(3^3)^2 = 3^(3*2) = 3^6
The the equation becomes:
3^6 = 3^(y + 4)
This is only true if:
6 = y + 4
6 - 4 =y
2 = y
The correct option is C.
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E = mc^2 True or False question
Answer:
False.
Step-by-step explanation:
E = mc² shows the relationship between mass and energy.
Which statements are true about the ordered pair (7, 19) and the system of equations? {2x−y=−5x+3y=22 Select each correct answer. Responses The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair 1 comma 19 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair 1 comma 19 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair 1 comma 19 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (7, 19) is a solution to the system because it makes both equations true.
The true statement about this system 2x - y = 0 and 5x + 3y = 22 is
The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x,y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given are two equations 2x - y = 0 and 5x + 3y = 22.
The ordered pair (7, 19) is not a solution to this system as these two equations do not intersect each other at (7, 19).
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Answer:
the answers are 2 choices
1- The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
2- The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
Step-by-step explanation:
i took the k12 test and got these as the answers correctly
A rectangular table is 22.5 inches wide and 31 inches
Answer: area = 697.5 area
If $1000 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 2 years
(b) 4 years
(c) 12 years
yeah bc the answer is 4 yrs
Answer:
3.5 years
Step-by-step explanation:
If 2 sweaters cost $18.72, how much would 6 sweaters cost?
Answer:
£56.16
Step-by-step explanation:
do 2 divided by 18.72 which is 9.36 then do 9.36×6 which is 56.16
Given: FC bisects ACD,
XACD is a straight angle
Prove: ACF is a right angle
If FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle
The ∠ACD is a straight angles
We know the angles on a straight line add up to 180 degree
Therefore,
The measure of angle ACD = 180 degrees
Here it is given that the line FC bisects angle ACD
Therefore, The angle ACF is equal to Angel DCF
Angle ACF = Angel DCF
Angle ACF + Angle DCF = 180 degrees
Then,
Angle ACF = Angel DCF = 90 degrees
Hence, if FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle
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A delivery truck drove 32 miles per hour. It took 4 hours to travel between two towns. What is the distance between the two towns? Use the equation d=rt, where d is distance, r is rate, and t is fine.
As per the given equation, the distance between the two towns is 128 miles.
Equation:
Equation defined as the mathematical statement that is made up of two expressions connected by an equal sign.
Given,
A delivery truck drove 32 miles per hour. It took 4 hours to travel between two towns.
Here we need to find the distance between the two towns.
Here we know that, the equation
d=rt,
where
d is distance,
r is rate, and
t is fine.
Through the given question we have identified that the value of r (rate) is 32 miles per hour and the value of t (fine) is 4 hours.
So, the distance is,
d = 32 * 4
d = 128.
Therefore, the distance between the two towns is 128 mile.
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Simplify the ratio [tex]\frac{8 ft}{12 in}[/tex] Use the conversion 12 in. = 1 ft.
A. [tex]\frac{8}{1}[/tex]
B. [tex]\frac{2}{3}[/tex]
C. [tex]\frac{1}{18}[/tex]
D. [tex]\frac{96}{12}[/tex]
The answer is A ([tex]\frac{8}{1}[/tex])!
The simplified form of the ratio using the conversion 12 in = 1 ft as required in the task content is; Choice A; 8/1.
What is the simplified form of the ratio as given in the task content?It follows from the task content that the simplified form of the ratio 8 ft / 12 in is to be determined.
Since the given ratio whose simplified form is to be determined is; 8 ft / 12 in.
However, recall that according to the conversion; 12 in = 1 ft.
On this note, 8 ft = 8 × 12 in.
Therefore, the equivalent ratio can be written as;
(8 × 12in) /12in.
The required simplified ratio is therefore; 8/1.
Ultimately, the correct answer choice is; Choice A; 8/1.
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I need assistance with this math assignment
Answer:
46.6 m/sec.
Step-by-step explanation:
A country has a goal to build 12,000 bus stop shelters in 48 months if the country builds 215+ shelters each month will it reach at school explain one way to estimate the answer
If it reaches 250 bus stop shelters per month, then only the country can achieve their goal of 12000 bus stop shelters in 48 months.
Given,
The number of bus stop shelters a Country should built = 12,000
Time period for achieving the goal = 48 months
The average bus stop shelters the country can build in a month = more than 215
We have to explain that if they follow the above given format, will they achieve the goal in 48 months.
We can find it by using division operation;
Lets see;
Number of bus stop shelters they should build in one month = 12000/48 = 250
Here,
They are building more than 215 bus stop shelters per month.
If it reaches 250 bus stop shelters per month, then only the country can achieve their goal of 12000 bus stop shelters in 48 months.
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a fibonacci sequence begins: 1,1,2,3,5,8...
what is the 7th number in the sequence?
Begining with the third term, each term of the sequence is the sum of the preceding two.
1+1 = 21+2 = 32+3 = 53+5 = 85+8 = 13Bert has 100 cards.
There is a whole number from 1 to 100 on each card.
No cards have the same number.
Bert puts a star on every card that has a multiple of 3 on it.
He puts a circle on every card that has a multiple of 5 on it.
Work out how many cards have both a star and a circle on them.
The picture is right here
Estimate the average by first rounding to the nearest 100:
120, 230, 455, 175
Answer:
250.
Step-by-step explanation:
First we need to round to the nearest 100:
120 rounded to the nearest 100 is 100.
230 rounded to the nearest 100 is 200.
455 rounded to the nearest 100 is 500.
175 rounded to the nearest 100 is 200.
So, we have the numbers 100, 200, 500, and 200.
To find the average of numbers, we need to add them up and divide the number we get by how many numbers we added:
100 + 200 + 500 + 200 = 1,000
Since we added 4 numbers, we divide by 4:
1,000 divided by 4 = 250.
We don't round to the nearest 100 for 250 because the question said to only round for the original numbers. But, if i am wrong somehow, 250 rounded is 300.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The linear function m = 200 − 50v represents the amount m (in dollars) of money that you have after buying v video games. a. Interpret the terms and coefficient in the equation. b. Find the domain of the function. Is the domain discrete or continuous? Explain. c. Graph the function using its domain.
a. The terms are
200 is to buy the games50 is what it cost for a gamev is the number of gamesm is the total amount on gamesb. The domain of the function is given as 1 ≤ x ≤ 4. The graph is a discrete graph
How to solve for the graphThe term in the linear function m = 200 − 50v interpreted as
200 = money set aside for buying video games
50 = cost per video game
v = number pf video games
m = total amount spent on video games
b. How to find the domain of the functionThe number refers to all the possible input values, this value as regard this context is when the money left for video game is finished.
the input value is v, the domain is solved as follows
200 - 50v = 0
50v = 200
v = 200/50
v = 4
The maximum number is 4 while the minimum is just above 0 or from 1 hence the domain is
1 ≤ x ≤ 4
the graph is attached
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The movie theater is offering a deal on Friday. Every 12th customer will receive a free movie ticket, and every 15th customer will receive a free small popcorn.
What customer will be the first to receive both a free movie ticket and a free small popcorn?
A.180th customer
B.120th customer
C.60th
D.3rd customer
A pizzeria sells three sizes of pizza: small, medium, and large. The pizzas sell for $9, $13, and $15, respectively. One evening they sold 28 pizzas and received $320. If they sold 9 more small than large pizzas, how many of each size did they sell?
Answer:
Step-by-step explanation:
so if you find the quadratic formula of 3 and multiply it by 82 you get 16. Then if you add 16 and 9 you get 25 this means that they sold 67 large pizzas. Your welcome
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x)=x²-440x+64,948. What is the minimum unit cost?
Do not round your answer.
