The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.
Explanation:The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.
In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.
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A professor uses a video camera to record the motion of an object falling from a height of 250 meters. The function f(x) = –5x2 + 250 can be used to represent the approximate height of the object off the ground after x seconds. Which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds
(The answer is 5 seconds)
Answer:
B is the answer
Step-by-step explanation:
i just took the test
What is the recursive formula for the sequence 3, 12, 48, 192, 768...?
The given sequence is a geometric sequence. Each term in the sequence multiplies by 4 to obtain the next. Therefore, the recursive formula for the sequence is an = 4 * an-1.
Explanation:The given sequence is: 3, 12, 48, 192, 768, and so on. Looking at the sequence, we can see that each term is multiplied by 4 to get the next term. So, the sequence is a geometric sequence. The recursive formula for a geometric sequence is given by: an = r * an-1, where an is the nth term, r is the common ratio, and an-1 is the previous term. In this case, r equals 4 (since we are multiplying each term by 4 to get the next term). Thus, "the recursive formula for this geometric sequence is: an = 4 * an-1".
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Seven subtracted from the quotient of a number and 2 is -6
18 / n - 7 = 2
18 / n =9
18 = 9n
2 = n
18 / 2 - 7 = 2
9 - 7 = 2
2 = 2
explain one of the theorems that you would use to find the zero of higher degree polynomial
Rational Root Theorem:
If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:
[tex]P(x)=kx^{n}+...+m[/tex]
where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]
1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]
2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:
[tex]P(x)=(x-r)Q(x)[/tex]
3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.
Prove and show your work
cos t (sect -cos t)= sin^2 t
sin 0 cot 0= cos 0
What is the simplified form of the following expression? 10abc^2 sqrt 49a^2b^2c^2
Answer: [tex]70a^2b^2c^3[/tex] will be the answer.
Explanation:
Since Given expression is [tex]10abc^2\sqrt{49a^2b^2c^2}[/tex]
We can write, [tex]10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{7^2a^2b^2c^2}[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{(7abc)^2}[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^27abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10\times7abc^2abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70abc^2abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70a^2b^2c^3[/tex]
1. The simplified form of the expression [tex]10abc^2[/tex] is simply [tex]10abc^2[/tex] itself.
2. The simplified form of the expression [tex]\sqrt{49a^2b^2c^2}[/tex] is 7abc.
1. Since there are no like terms to combine, and no operations to perform, the expression remains unchanged.
2. The expression [tex]\sqrt{49a^2b^2c^2}[/tex] represents the square root of [tex]49a^2b^2c^2[/tex]. To simplify this, we need to find the square root of each term under the radical.
[tex]\sqrt{49a^2b^2c^2} = \sqrt{49} * \sqrt{a^2} * \sqrt{b^2} * \sqrt{c^2}[/tex]
The square root of 49 is 7, and the square root of any variable raised to the power of 2 is simply the variable itself. So, we have: [tex]\sqrt{49a^2b^2c^2} = 7 * a * b * c[/tex]
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PLEASE HELP I NEED SOMEBODY TO PARAPHRASE THIS FOR ME! I'LL MARK BRAINLIEST!! 50 POINTS!!!
if the variables cancel out leaving u with an untrue statement, like 0 = 4 or 2 = 6, then u will have no solutions
if the variables cancel out leaving u with a true statement, like 2 = 2 or 4 = 4, then u will have infinite solutions
if u end up with a variable equaling a number, then u have 1 solution
What is the difference for this question?
What is the IMA of the doorknob shown?
1.5
3
6
15
Answer:
6
Step-by-step explanation:
All at once, pandemonium broke loose. ______________ the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!
Which word best completes the passage above? (5 points)
Anyway
Because
Following
Simultaneously
Answer:
The answer is word SIMULTANEOUSLY.
Step-by-step explanation:
The alternative that fits best is " d.Simultaneously"
All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.
This word maintains the coherence and cohesion of the given text.
Answer:
The alternative that fits best is " d. Simultaneously"
Step-by-step explanation:
Thus, the complete sentence would read: "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"
The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text. The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.
Anyone know the answer to this geometry problem?
1 and 2 are a linear pair, and 2 and 3 are vertical angles. m 2=(5+4 y) and m 3=(6 y-25). what is m 1
18. you work a part-time job earning $6.80/hr with tips that average $2.30/hr. you work 20 hr/wk and your deductions are FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). how much are you allowed in housing expenses per month?
Im asking for help not for you to do it.
Total housing expenses per month allowed will be $168.81.
To calculate how much you are allowed in housing expenses per month, we need to first determine your after-tax income.
You earn $6.80/hr plus tips averaging $2.30/hr, resulting in an hourly wage of
$6.80 + $2.30 = $9.10
Working 20 hours a week gives you a weekly income of
20 hours × $9.10/hr = $182
Monthly, this equates
$182 4 weeks = $728
The deductions are as follows: FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). These deductions total to
7.65% + 8.95% + 6.1% = 22.7%
To get the after-tax income, we calculate
$728 - (22.7% × $728)
≈ $562.69
This is your monthly take-home pay.
Financial experts often recommend spending no more than 30% of your take-home pay on housing. Therefore
$562.69 × 30%
= $168.81 houses expenses per month
Solve the open sentence.
–2 ≤ n + 4 ≤ 7
A. n ≤ 2 and n ≤ 7
B. n ≥ –6 and n ≤ 3
C. n ≥ 6 and n ≤ –4
D. n ≤ –6 and n ≤ 4
point m lies between point L and N on LN
Answer:
64 units
Step-by-step explanation:
Segment addition holds, so we can write ...
LM + MN = LN
(10x +8) +(5x-4) = (12x +16)
15x + 4 = 12x + 16 . . . . . . . . collect terms
3x -12 = 0 . . . . . . . . . . . . . . subtract 12x+16
x-4 = 0 . . . . . . . . . . . . . . . . . divide by 3
x = 4 . . . . . . . add 4
LN = 12x +16 = 12·4 +16 = 48 +16 . . . . . substitute into the expression for LN
LN = 64 . . . . units
Given the three vertices F(-5, 0), G(3, -3), and H(-2, 8), what are the coordinates of I that make quadrilateral FGIH a square
The volume of a cuboid is 1404cm3. The length is 9cm and the width is 130mm. Work out the height of the cuboid in cm.
To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.
To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).
Now, using the formula for volume:
Volume = length x width x height1404cm³ = 9cm x 13cm x heightTo find the height, we divide the volume by the product of the length and width:
height = Volume / (length x width)height = 1404cm³ / (9cm x 13cm)height = 1404cm³ / 117cm²height = 12cmTherefore, the height of the cuboid is 12cm.
john buys a new bedroom set on credit for $2760 and no interest. he pays $115 per month. what is the equation that models the money john owes?
The variable z varies jointly with x and y. also, z = -75 when x = 3 and y = -5. what equation describes this variation?
Answer:
c
5
-10
Step-by-step explanation:
Ginger wanna join a gym.she goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthly fee of $30.if she belongs to the gym for one year then the 12th month is free.how much will a one year membership cost her?
A flagpole stands on a concrete region, as shown. What is the approximate perimeter of the concrete region? Use 3.14 for π.
Thanks!
How many two-digit positive integers can be formed from the digits 1, 5, 6, and 8 if no digit is repeated?
Park rangers released 12 fish into a pond in year 0. Each year, there were twice as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.
Answer: The function would be,
[tex]f(x)=12(2)^x[/tex]
Step-by-step explanation:
Given,
Park rangers released 12 fish into a pond in year 0,
Thus, the initial number of fish = 12,
Also, there were twice as many fish as the year before,
⇒ After 1 year the number of fishes = 2(12) = 12(2),
Similarly,
After 2 years = 2(12(2))= 12(2)²,
After 3 years = 2(12(2)²) = 12(2)³,
................, so on,....
Thus, the number of fishes after x years would be,
[tex]12(2)^x[/tex]
Let f(x) represents the number of fish after x years,
[tex]\implies f(x) = 12(2)^x[/tex]
Which is the required function that the given scenario.
PLEASE HELP URGENT!!!
The price of the land is $2300 per acre ( 1 acre = 4840) how much does the land cost?
Two of the three side lengths are given. To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle. Use the Law of Cosines for this task.
a^2 = b^2 + c^2 - 2ac*cosA
Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or
a^2 = 250000 + 572500 - 750000(-0.1736), or
= 692264
Then a = +sqrt(692264) = 832 yds
Use Heron's Formula to find the area of the land.
First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s
According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )
Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )
I will leave this calculation to you to complete.
Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.
In acres, the area is
1 acre
A* ---------------- = (A/4840) acres
4840 yd^2
How much will this cost? Recall that the unit cost of the land is $2300/acre.
Then the total cost will be:
$2300
(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)
1 acre
1
The relationship between the monthly fee for Brandon’s phone and the price per minute for long distance is modeled by the linear function f (x) = 0.05x + 3, where x is the number of minutes used for long distance. What is the total bill if Brandon used 20 minutes of his long distance service in a month?
the linear function f (x) = 0.05x + 3,
f(x) is the monthly fee and x is the price per minute
Brandon used 20 minutes of his long distance
So x is 20 minutes
We plug in 20 for x
f(x) = 0.05x + 3
f(20) = 0.05(20) + 3 = 4
So total bill is $4 if Brandon used 20 minutes of his long distance service in a month
Which number is irrational? A. square root of 64 B. square root of 256 C. square root of 100 D. square root of 80
When rounding to.the nearest hundred are you to add or subtract?
Answer:
When you round to the nearest hundred:
150 or higher turns into 200, so you'd do add.
But when it's 149 or lower, you simply subtract it by 49.
Step-by-step explanation:
Due tomorrow please help
Anyone know the answer?
the right rectangular prism will be sliced perpendicular to its base along the dashed line. Select from the drop-down menus to correctly describe the cross section formed by the slice.