On a scale drawing, the height of a tree is 3 inches. If the scale of the drawing is 1 in:50 ft , how tall is the tree?
A triangle plot of land has one side along a straight road measuring 324 feet. A second side makes a 68Degree angle with the road and the third side makes a 54 degree angle with the road. How long are the other two sides?
The missing dimensions of the triangular plot of land are:
i. b = 2.45
ii. A = 69.5
iii. C = 75.5^o
What is a cosine rule?A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.
Cosine rule states that;
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B
To determine the missing values of the triangle in the attached diagram, we have;
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B
= 4^2 + 7^2 - 2(4*7)Cos35^o
= 16 + 49 -2(36*0.8192)
= 65 - 58.9824
= 6.0176
b = (6.0176)^1/2
= 2.4531
b = 2.45
From sine rule,
a/ Sin A = b/Sin B = c/ Sin C
a/ Sin A = b/Sin B
4/Sin A = 2.45/ Sin 35
Sin A = 4* Sin 35/ 2.45
= 0.9365
A = Sin^-1 0.9365
= 69.47
A = 69.5
So to determine the value of C, we have;
A + B + C = 180^o
69.5 + 35 + C = 180
104.5 + C = 180
C = 180 - 104.5
= 75.5
C = 75.5^o
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On a certain hot summer's day, 539 people used the public swimming pool. The daily prices are $ 1.50 for childten and $ 2.25 for adults. The receipts for admission totaled $1017.00. How many children and how many adults swam at the public pool that day?
If the daily prices are $ 1.50 for children and $ 2.25 for adults, a total of 284 children and 255 adults swam at the public pool that day.
Let's assume that the number of children who swam in the pool is x, and the number of adults who swam in the pool is y.
From the problem statement, we know that the total number of people who swam in the pool is 539. Therefore, we can write:
x + y = 539
We also know that the total receipts for admission are $1017.00. The price for a child is $1.50 and the price for an adult is $2.25. Therefore, the total revenue can be expressed as:
1.5x + 2.25y = 1017
Now we have two equations with two variables. We can solve for x and y by using any method of solving linear equations. For example, we can use the substitution method to solve for x and y:
x + y = 539 → x = 539 - y
Substituting this value of x into the second equation, we get:
1.5(539 - y) + 2.25y = 1017
Simplifying and solving for y, we get:
y = 255
Substituting this value of y into the equation x + y = 539, we get:
x = 539 - 255 = 284
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What kinda transformations does this make y=3^(x-2)-4
The function is transformed by horizontal translation to the right is applied first, followed by the vertical translation downward
Given data ,
Let the parent function be represented as f ( x )
Now , the value of f ( x ) is
y = 3ˣ
Let the transformed function be f' ( x )
y' = 3⁽ˣ⁻²⁾ - 4
Horizontal Translation: When compared to the basic function, y = 3x, the function's "(x-2)" inside the exponent of 3 causes a horizontal translation to the right of 2 units.
This results in a 2 unit shift along the x-axis of the function's graph.
Vertical Translation: In comparison to the base function y = 3x, the "-4" at the end of the function causes a vertical translation downward of 4 units.
This results in a 4 unit downward shift of the function's y-axis graph.
Hence , the function is transformed
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Math:
Please very urgent, I’ll give brainliest if it’s correct
(a) [2 marks] The function
p(t) = 20 sin 360t + 100 models a
person's blood pressure while resting, where p(t) represents the blood pressure, in millimeters of mercury, and t is the time, in seconds. Sketch a graph of this function for 0
(b) [2 marks] Find the period of the function in part {a), and describe what the period represents.
(c) [4 marks] The function
p(t) = 20 sin 720t + 100 models a
person's blood pressure while exercising.
Sketch a graph of this function for 0 < t < 3.
(d) [2 marks] Find the period of the function in part (c), and describe what the period represents.
(e) [2 marks] Find the amplitude of each function, and describe what the amplitude represents.
A bag contains 9 red marbles, 6 white marbles, and 6 blue marbles. You draw 3 marbles out at random,
without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
Submit Question
Step-by-step explanation:
a it be 3/21 to get red which is 0.143
b to get not red if u don't replace red would be 12/18 so it be 0.6666 but if u replace it then it would be 0.517
Please help I have been wasting all my points for no answer. After consulting with his broker, Bruce Sowder purchased 100 shares of a computer company stock at $44.41 per share. He also purchased 600 shares of a second company’s stock at $19.08 per share. Sowder’s online broker charges $0.04 per share. What is the total cost of the stock including the commission?
the total cost for the company including commission is $15,917
what is commission?The commission is a sum of money that an employer pays as a fee or a percentage to an employee for completing a certain task or for generating new business by promoting the company's products or services. Incentives or sales commissions are other names for it. In general, anyone can earn a commission; it's not just for salespeople. The commission comes on top of the wage.
The company's policy, which ensures basic compensation and commission over a specific number of deal closures, determines the proportion of commission.
How do you define share?Equity ownership in a corporation is represented by shares. Shares are a type of financial asset that some businesses use to guarantee an equitable dividend distribution of any declared residual profits.
according to question,
total cost of 100 shares = 100*44.41 = $4441
total cost of 600 shares = 600*19.08 = $11448
broker charges for all 700 shares = 700*0.04 = $28
total cost acquired by the company is = $4441+$11448+$28
= $15917
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A(n) __________ is an amount returned after purchase or deducted from the purchase price.
Step-by-step explanation:
A(n) discount is an amount returned after purchase or deducted from the purchase price.
Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFractionWhich statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFractionWhich statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction
The statement that describes the behavior of the function f(x) is: The graph approaches 0 as x approaches infinity.
The correct answer is an option (b)
Consider the function [tex]f(x) = \frac{2x}{1-x^2}[/tex]
Consider the limit of function f(x) as x approaches infinity (x → ∞)
[tex]\lim_{n \to \infty} f(x)\\\\= \lim_{n \to \infty} \frac{2x}{1-x^2} \\\\= \lim_{n \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ = \lim_{n \to \infty} \frac{-2}{x}[/tex]
= 0
This means that when x approaches infinity the term x² grows rapidly
So, 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator.
We can say that the function approaches zero.
Thus the correct statement is: The graph approaches 0 as x approaches infinity.
The correct answer is an option (b)
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The complete question is:
Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?
a) The graph approaches –2 as x approaches infinity.
b) The graph approaches 0 as x approaches infinity.
c) The graph approaches 1 as x approaches infinity.
d) The graph approaches 2 as x approaches infinity.
James bought 16 bolts at the hardware store for a total of $6.00/ Some were 3-inch bolts that cost 36 cents each and the others were 4-inch bolts that cost 42 cents each. How many 3-inch did James buy
Let's use the variable "x" to represent the number of 3-inch bolts that James bought.
We know that he bought a total of 16 bolts, so the number of 4-inch bolts he bought would be 16 - x.
The cost of the 3-inch bolts is 36 cents each, so the total cost of the 3-inch bolts would be 0.36x dollars.
Similarly, the cost of the 4-inch bolts is 42 cents each, so the total cost of the 4-inch bolts would be 0.42(16 - x) dollars.
We know that the total cost of all the bolts was $6.00, so we can set up the following equation:
0.36x + 0.42(16 - x) = 6.00
Simplifying and solving for x, we get:
0.36x + 6.72 - 0.42x = 6.00
-0.06x = -0.72
x = 12
Therefore, James bought 12 of the 3-inch bolts.
SHOW WORKINGS PLEASE.
The MNC must pay a 25% tax on remitted funds, and the stable exchange rate is C$1.02 per US$ over the next two years and a rate of C$1.025 per US$ in year 3.
All cash flows are remitted to the parent and there is no tax on salvage.
Required:
i) Calculate the after-tax operating cash flows that will be remitted to the parent
company each year.
ii) Calculate the Net Present Value of the project.
iii) Explain whether or not the MNC should accept the project?
iv) Flagstaff Corp. is a U.S.-based firm with a subsidiary in Mexico. It plans to reinvest its earnings in Mexican government securities for the next 10 years since the interest rate earned on these securities is so high. Then, after 10 years, it will remit all accu- mulated earnings to the United States. What is a drawback of using this ap- proach? (Assume the securities have no default or interest rate risk.).
i) The after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, 110.30 and USD 146.34.
ii) The Net Present Value of the project are USD 66.85, USD 91.90 and USD 107.50.
iii) The MNC may want to consider other investment opportunities or reassess the assumptions used in this analysis.
iv) As per the subsidiary, the firm may be better off remitting earnings on a regular basis to minimize exchange rate risk and invest in a diversified portfolio of assets to mitigate other types of risks.
i) To calculate the after-tax operating cash flows that will be remitted to the parent company each year, we need to first calculate the operating cash flows in CAD and then convert them to USD while taking into account the tax on remitted funds. Let's assume the operating cash flows for each year are CAD 100, CAD 150, and CAD 200, respectively.
In year 1, the CAD 100 operating cash flow is remitted to the parent company in USD. Using the exchange rate of C$1.02 per US$, this is equal to USD 98.04. However, the MNC must pay a 25% tax on this amount, so the after-tax cash flow is USD 73.53.
In year 2, the CAD 150 operating cash flow is remitted to the parent company in USD. Using the same exchange rate of C$1.02 per US$, this is equal to USD 147.06. After the 25% tax on remitted funds, the after-tax cash flow is USD 110.30.
In year 3, the CAD 200 operating cash flow is remitted to the parent company in USD. However, the exchange rate has changed to C$1.025 per US$, so the CAD 200 is now equal to USD 195.12. After the 25% tax on remitted funds, the after-tax cash flow is USD 146.34.
Therefore, the after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, USD 110.30, and USD 146.34, respectively.
ii) To calculate the Net Present Value (NPV) of the project, we need to discount the after-tax operating cash flows back to their present value using a discount rate that reflects the riskiness of the project. Let's assume a discount rate of 10%. Using this rate, we can calculate the present value of each year's after-tax cash flow as follows:
Year 1: USD 73.53 / (1 + 0.10)¹ = USD 66.85
Year 2: USD 110.30 / (1 + 0.10)² = USD 91.90
Year 3: USD 146.34 / (1 + 0.10)³ = USD 107.50
iii) Based on the calculated NPV, the MNC should not accept the project. The negative NPV indicates that the project is not expected to create value for the MNC's investors. Additionally, the after-tax operating cash flows that will be remitted to the parent company each year are not sufficient to compensate for the investment's costs and the 25% tax on remitted funds.
iv) The drawback of Flagstaff Corp.'s approach of reinvesting earnings in Mexican government securities for 10 years before remitting accumulated earnings to the United States is that it exposes the firm to exchange rate risk. Over the course of 10 years, exchange rates between the Mexican peso and the U.S. dollar could fluctuate significantly, potentially eroding the value of the accumulated earnings when they are finally remitted. Additionally, there is no guarantee that the Mexican government securities will continue to provide a high interest rate over the entire 10-year period.
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Please help me ASAP………
The simplified expression is given as follows:
7/x³.
Where the coefficients are:
c = 7.e = 3.How to simplify the expression?The expression in this problem is defined as follows:
x³(1/4 x³)(28x^-9).
To obtain the coefficient c, we must multiply the coefficients of each expression, as follows:
c = 1 x 1/4 x 28
c = 7.
When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:
3 + 3 - 9 = -3.
The negative exponents goes in the denominator, hence the simplified expression is given as follows:
7/x³.
Meaning that the exponent is of e = 3.
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Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
Answer:
The correct answer is D. purchase price: $117, advertised price: $293.
Step-by-step explanation:
Hailey goes to a store an buys an item that costs a dollars. She has a coupon for 35%
off, and then a 8% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hailey paid at the register.
Hailey goes to a store an buys an item that price of a dollars, so the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.
The amount of discount that Hailey receives is 35% of the original price, which is 0.35a. Therefore, the discounted price she pays is a - 0.35a = 0.65a.
The amount of tax that is added to the discounted price is 8% of the discounted price, which is 0.08(0.65a) = 0.052a.
So the total amount that Hailey paid at the register is the discounted price plus the tax:
total amount = discounted price + tax
total amount = 0.65a + 0.052a
Simplifying this expression, we get:
total amount = 0.702a
Therefore, the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.
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Please help stuck on this question!
Answer:
Step-by-step explanation:
To solve this problem, we need to use the distance formula to find the length of each side of the triangle, and then apply the Pythagorean theorem to determine whether the triangle is a right triangle.
Let's label the three vertices of the triangle as A, B, and C, and their coordinates as follows:
A = (-2, 5)
B = (3, -1)
C = (1, 3)
The length of AB is:
AB = sqrt((3 - (-2))^2 + (-1 - 5)^2) = sqrt(25 + 36) = sqrt(61)
The length of AC is:
AC = sqrt((1 - (-2))^2 + (3 - 5)^2) = sqrt(9 + 4) = sqrt(13)
The length of BC is:
BC = sqrt((1 - 3)^2 + (3 - (-1))^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)
Now, we need to check whether the triangle is a right triangle. We can do this by checking whether the sum of the squares of the two shorter sides (AB and AC) is equal to the square of the longest side (BC). If it is, then the triangle is a right triangle.
AB^2 + AC^2 = 61 + 13 = 74
BC^2 = (2sqrt(5))^2 = 20
Since AB^2 + AC^2 is not equal to BC^2, the triangle is not a right triangle.
Therefore, the answer is: "The triangle is not a right triangle."
help qiuckly math homework
Angle or arc HGJ is measured at 275 for given figure.
What does arc of circle stands for?Arcs may be created from the circumference of a circle. It is referred to as the curved line that connects two locations on a circle's perimeter and splits it into segments. The length of an arc is inversely proportional to the angle it makes at the centre of the circle.
When the central angle rises, so does the arc's length, and vice versa. Arcs are commonly used to depict and compute measurements of circles and circular objects in geometry, trigonometry, and physics.
For given problem,
mHGJ= 360° - mJH = 360°-( mJl + mlH ) = 360°-(30°+55°)
= 360°-85° = 275°
Hence, arc or angle HGJ= 275 degrees
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If coto = 13 on top
6 on bottom
Then what is Seco
Remember to simplify and rationalize all answer
Answer:
√(205)/13
Step-by-step explanation:
You want sec(θ) when cot(θ) = 13/6.
Trig relationsSome calculators can figure this directly as ...
[tex]\sec{(\cot^{-1}\dfrac{13}{6})}=\boxed{\dfrac{\sqrt{205}}{13}}[/tex]
Others need to make use of the trig relations ...
tan(θ) = 1/cot(θ)
sec(θ) = √(tan²(θ) +1)
or
sec(θ) = 1/cos(θ)
ApplicationThe tangent of the angle is
tan(θ) = 1/cot(θ) = 1/(13/6) = 6/13.
Then the secant is ...
sec(θ) = √((6/13)² +1) = √(6² +13²)/13
sec(θ) = √205/13
A calculator can get there from ...
sec(θ) = 1/cos(arctan(6/13)) = √205/13
suppose you want to double the area of the patio shown at the right. find the increase x of both the length and width of the patio
The New Area based on the information will be 168ft
How to calculate the areaExpanding the above equation, we get:
120ft² + 22x + x² = 240ft²
Rearranging and simplifying, we get:
x² + 22x - 120 = 0
Since the increase cannot be negative, we take the positive value of x:
x = 2
Therefore, the increase in both the length and width of the patio should be 2ft to double its area.
New Length = 10ft + 2ft = 12ft
New Width = 12ft + 2ft = 14ft
New Area = 12ft x 14ft = 168ft²
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Kenny, Marcus, and Sean each ate 1/5 gallon of ice cream from a
I-gallon tub. When they were done, how much ice cream was left?
If they wanted to eat 3/5gallon each, how much ice cream would
they need?
Planes T and X are parallel. Plane T contains line a. Plane X contains line b.
Planes T and X are parallel. Plane T contains line a and plane X contains line b.
Answer:
Step-by-step explanation:
1
Consider the regular hexagon shown below. What is the area of the hexagon? (attached image)
A. 64.5 cm^2
B. 30cm^2
C. 21.5 cm^2
D. 10.75 cm^2
ANSWER ASAP PLEASE
Question content area top Part 1 An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d).
If the normally distributed heights have mean as 69, then the probability that he can fit through the doorway without bending is 0.9938.
In "Normal-Distribution", probability refers to the likelihood of a continuous random variable falling within a certain range of values
We first convert the height of the doorway and the height of the male passenger to z-scores by using z = (x - μ) / σ,
where:
x = height (doorway height or male passenger height)
μ = mean of the male height,
σ = standard deviation of male height,
For the doorway height:
⇒ [tex]Z_{doorway}[/tex] = (76 - 69.0)/2.8 = 2.50,
For a male passenger:
⇒ [tex]Z_{male}[/tex] = (x - 69.0)/2.8,
To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the proportion of the "male-population" that has a height less than or equal to the height of the doorway;
⇒ P([tex]Z_{male}[/tex] ≤ [tex]Z_{doorway}[/tex] ) = P([tex]Z_{male}[/tex] ≤ 2.50) and
We know that the value of P(z ≤ 2.50) is 0.9938,
Therefore, the required probability is approximately 0.9938.
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The given question is incomplete, the complete question is
An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in,
If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
What is the solution to the following system of equations?
4x + 2y = 18
x − y = 3
(−4, −1)
(1, 4)
(−1, −4)
(4, 1)
pls help me
2. Write an equation that
gives your own "recipe" for
making a skateboard.
The equation is Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization.
What is the equation for making a skateboard?
Here's an equation that outlines my "recipe" for making a skateboard:
Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization
Explanation of the equation:
Deck: The wooden or composite board that serves as the main body of the skateboard. It is typically made from layers of plywood or other materials, and its dimensions (length, width, concavity, etc.) can be customized based on personal preference.
Grip Tape: A sandpaper-like material that is applied to the top of the deck to provide traction for the rider's feet. It is usually made of adhesive-backed paper or fabric and comes in various designs and colors.
Trucks: Metal T-shaped components that are mounted on the underside of the deck and serve as the axle and suspension system of the skateboard. They consist of a baseplate, hanger, kingpin, bushings, and hardware, and are responsible for allowing the board to turn and pivot.
Wheels: Typically made of urethane or other durable materials, skateboard wheels come in various sizes, shapes, and hardness levels (durometer). They are attached to the trucks and provide smooth rolling and maneuverability.
Bearings: Small, round metal or ceramic components that fit inside the wheels and allow them to spin freely on the axle. They are crucial for reducing friction and enabling the wheels to roll smoothly.
Hardware: Nuts, bolts, and screws used to attach the trucks to the deck and assemble the skateboard. They are typically made of metal and come in different sizes and lengths.
Assembly: The process of putting together all the skateboard components to create a functional skateboard. It involves attaching the trucks to the deck using the hardware, installing the wheels and bearings, and applying the grip tape.
Personalization: This refers to any additional customization or personal touches that a skateboarder may choose to add to their skateboard, such as stickers, artwork, or modifications to the deck shape or truck settings, to make it unique and suited to their individual style.
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Solve the system using the method of your choice.
3x+y=−12x−y=−8
Answer: x=-5,y=3
Step-by-step explanation: Add the 2 equations together, 3x+x=4x, y+(-y)=0, and -12-8=-20. This leaves us with 4x=-20, so x=-5. Plug x back into the equation, so -5-y=-8, add 5 to both sides so -y=-3, and y=3.
Help math homework will brainlist
Answer:
? = 13.7
Step-by-step explanation:
Right triangle equation A^2 + B^2 = C^2
7.6^2 + 11.4^2 =
57.76 + 129.96 = 187.72
find the square root of 187.72 by putting it in the calculator
187.72 = 13.70109485^2
Estimate = 13.7^2
Hello everyone please Can u help
Answer:
the second one is x= -1
*this stuff is genuinely easy. I'm in 10th grade and all you have to do is put it in the calculator. If you have a tinspire like me you could make the x into a 1 in the calculator, put the whole thing in graph and it'll trace the answer for you. If your teacher wants to see work then maybe don't do that but let me know and I'll send the work for you.
mathematics
please click the image, and answer. show your solution please.
thank you po!!
Answer:
1) 35%
2) 73%
3) 23%
4) 57%
5) 13%
6) 37%
Step-by-step explanation:
The general solution is to grab the total, which is 100%, and subtract the percentage of the given problems to find the solution. In some problems you have to add some percentages togheder to finish the problem.
So, in the first problem you subtract the percentage of girls to the whole class percentage: 100%-65%=35%.
In the second, whole package minus the red ones: 100%-27%= 73%
In the third, group of children minus swimmers: 100%-78%=22%
In the fourth, 100%-43%= 57%.
In the fifth, there is won percentage, loss percentage, and the remaining percentage you need to add to make 100% is the tie percentage.
So if we do the reverse (subtracting both win and loss percentage to have the tie percentage): 100%-45%-42%=13%.
In the sixth, it's the same thing as the fifth problem: subtracting the basketball and hockey from the whole children percentage that chose the sport: 100%-35%-28%=37%.
I hope this helped
Melissa deposited $5000 into an account with a 4.8% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $5960?
Assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.
How to find how long will it take for the investment to grow to $5960To answer this problem, use the compound interest formula:
A = (1 + r/n)(n*t).
We're looking for t so we can rearrange the formula to find it:
n = (log(A/P) / log(1 + r/n))
When we substitute the provided values, we get:
12.63 t = (log(5960/5000) / log(1 + 0.048/12))
Hence, assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.
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Consider the quadratic equation x2 + 9x + 10 = 0. Which of the following is the correct form after substituting a, b, and c into the
Quadratic Formula?