NO LINKS!! Jacob just won $32000 on the new game show, "The Wall,". He invested his winnings at an interest rate of 4.5%, compounded quarterly.
Answers
Answers:
a) See the table below
b) The equation is [tex]y = 32000(1.01125)^x[/tex]
c) $40,024.02
d) See the graph below
=========================================================
Explanations:
a)
Start with part (b) where I detail how to get the equation.
Once the equation is found, plug in x = 0 to get
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^0\\\\y = 32000\\\\[/tex]
Repeat for x = 1
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^1\\\\y = 32360\\\\[/tex]
Repeat for x = 2, x = 3, x = 4 and x = 20 to get the table shown below.
-----------------------
b)
The template for any exponential equation is [tex]y = a(b)^x[/tex]
a = starting amount = 32000
b = growth factor
The annual interest rate is 4.5%
We compound quarterly, so the quarterly rate is (4.5%)/4 = 1.125% which converts to the decimal form 0.01125; adding one to this leads to the growth factor of b = 1.01125
We go from [tex]y = a(b)^x[/tex] to [tex]y = 32000(1.01125)^x[/tex]
-----------------------
c)
Plug in x = 20 to represent 20 quarters have elapsed (aka 20/4 = 5 years)
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^{20}\\\\y \approx 32000(1.25075052084381)\\\\y \approx 40024.016667002\\\\y \approx 40024.02\\\\[/tex]
The investment would be worth $40,024.02 after five years, aka twenty quarters.
-----------------------
d)
See below for the graph. I'm using GeoGebra to make the graph. Another option is Desmos. It's preferable to use technology than to graph by hand. If you wanted to graph by hand, then you'd plot each of the points found in the table. Then draw a curve through all those points.
Answer:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)n = number of compounding periods per unit of timet = time in decimal years (e.g. 6 months = 0.5 yrs)Given:
P = $32,000r = 4.5% = 0.045n = 4 (compounded quarterly)t = 0.25x[tex]\implies y=32000(1+\frac{0.045}{4})^{4 \times 0.25x}[/tex]
[tex]\implies y=32000(1.01125)^x[/tex]
Part (a)[tex]\begin{tabular}{|c | c |}\cline{1-2} \bf Quarterly & \bf \$ \\\cline{1-2} 0 & 32000.00\\\cline{1-2} 1 & 32360.00\\\cline{1-2} 2 & 32724.05\\\cline{1-2} 3 & 33092.20\\\cline{1-2} 4 & 33464.48\\\cline{1-2} --- & --- \\\cline{1-2} 20 & 40024.02\\\cline{1-2}\end{tabular}[/tex]
Part (b)[tex]y=32000(1.01125)^x[/tex] (where x is the number of quarterly periods)
Part (c)$40,024.02
Part (d)see attached
Related Questions
2. You want to buy some beans. A
7-ounce package costs $2.38. A
15-ounce package costs $5.25. A
26-ounce package costs $8.58. Which
package is the best buy?
Answers
Answer:
Step-by-step explanation:
Remark
If you find out the cost of 1 oz of each of them, that will determine the best buy. The smallest number is the best buy.
Givens
7 oz cost $2.38
15 oz cost $5.25
26 oz cost $8.58
Solution
7 oz7 oz cost $2.38
1 oz cost x This is a proportion. 3 quatities are known. Find x Cross multiply.
7/1 = 2.38/x
7x = 2.38
x = $0.34 dollars
15 oz15 oz cost 5.25
1 oz costs x
15.1/1 = 5,25 x Cross Multiply
15x = 5.25 * 1 Divide by 15
x = 5.25 / 15
x = $0.35
26 oz26 oz cost 8.58
1 oz cost x
26/1 = 8.38/x Cross Multiply
26x = 8.38 Divide by 26
x = 8.38/20
x = 0.32 dollars
Answer
7 oz cost 0.34
15 oz cost 0.35
26 oz cost 0.32
The best buy is 0.32 / oz for 26 ozIn factored form please help
Answers
Answer:
3rd option
Step-by-step explanation:
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] ( factorise numerator and denominator )
3x² - 3 ← factor out 3 from each term
= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 1
= x² - 1²
= (x - 1)(x + 1) , then
3x² - 3 = 3²(x - 1)(x + 1) ← in factored form
--------------------------------
x² - 5x + 4
consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)
the factors are - 1 and - 4 , since
- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then
x² - 5x + 4 = (x - 1)(x - 4)
then
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] = [tex]\frac{3(x-1)(x+1)}{(x-1)(x-4)}[/tex] ← in factored form
Paul wants to order flowers for Mother’s Day and can choose any number of roses and lilies for his mother’s flower arrangement. He has a maximum of $50 to spend. Each stem of lilies costs $3.00, and roses cost $3.50 each. Which inequality represents the situation? Let the number of lilies = x and the number of roses = y.
A. 3.50x - 3y ≥ 50
B. 3x + 3.50y ≤ 50
C. 3x + 50y < 50
D. 3x - 3.50y > 50
Answers
Answer:
b
Step-by-step explanation:
it has to add the two cost of the flowers and it has to be less than or equal to 50 dollars
Faleye Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for an after-tax cost of $19,000, which will generate after-tax cash flows of $6,000 at the end of each of the next 6 years. Alternatively, the company can purchase equipment with an after-tax cost of $13,000 that can be used for 3 years and will generate after-tax cash flows of $6,000 at the end of each year (System B). If the company’s WACC is 10% and both “projects” can be repeated indefinitely, which system should be chosen, and what is its EAA? Do not round intermediate calculations. Round your answer to the nearest cent.
Choose Project
-Select-
, whose EAA = $
Answers
If Faleye Consulting’s WACC is 10% and both “projects” can be repeated indefinitely, the system that should be chosen is System A, and its EAA is $2,866.91.
What is the EAA of a project?The EAA of a project is the Equivalent Annual Annuity. The EAA can be determined using the following formula.
EAA = r x NPV1 - (1 + r)-n
Where the EAA = Equivalent Annual Annuity
r = interest rate per period
n = project duration
NPV = Net present value of project
We can also compute the EAA by using an online finance calculator as follows:
Data and Calculations:System A System B
After-tax cost $19,000 $13,000
After-tax cash flows $6,000 $6,000
Equipment duration 6 years 3 years
WACC = 10%
Annuity factor 4.355 2.487
Present value of cash flows $26,130 $14,922 ($6,000 x 2.487)
NPV $7,130 $1,922 ($14,922 - $13,000)
EAA (an online calculator) $2,866.91 $800.966
Thus, using the EAA rule, the computer system that should be chosen is System A because it has a higher EAA than System B.
Learn more about the equivalent annual annuity at https://brainly.com/question/20566589
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
sinA = 9/41ratio = 9:41Step-by-step explanation:
sin theta = opposite/ hypotenuseac = adjacent
ab = hypotenuse
cb = opposite
= cb/ab
= 9/41
ratio = 9:41HAVE A NICE DAY
STAY SAFE
if this is the answer then pls give BRAINLIST
Answer:
Step-by-step explanation:
Find X exactly. Answer should be in a square root.
Answers
Answer:
7 in <==== no sqrt in the answer
Step-by-step explanation:
x = 7 sqrt 2 * cos 45
= 7 sqrt 2 * sqrt 2 /2
= 7 (2)/2 = 7
At a hardware store 5 hammers and 7 packs of nails costs 62.25 and at the same store, 8 hammers and 3 packs of nails costs 82.30 How much is one hammer and one pack of nails ?
Answers
Maya mailed 3 packages. their weights were 4.5 lbs,2.75 lbs,and 3.4 lbs.
what was the total weight of the 3 packages.
question 2 is explain how u found the answer to the first question (only answer if you know the answer)
Answers
Explanation: Since there is only one number in the hundredth place, i didn’t need to add. Instead i put that number as my hundredth place AKA 5. then i added the tenth place which was 5+7+4 which = 16. i carried the one over. then i added the ones place. 4+2+3= 9. the one i carried over got added to the 9. therefore my final answer was 10.65
What is the formula for the Pythagorean theorem?
Answers
Answer:
a^2 + b^2 = c^2
Step-by-step explanation:
a^2 + b^2 = c^2
Answer:
[tex]\Longrightarrow: \boxed{\sf{A^2+B^2=C^2}}[/tex]
Step-by-step explanation:
In the Pythagorean theorem, the formula is:
[tex]\underline{\text{PYTHAGOREAN THEOREM FORMULA:}}}[/tex]
[tex]\Longrightarrow: \sf{A^2+B^2=C^2}[/tex]
Thus, the Pythagorean theorem's formula is "a²+b²=c²".
I hope this helps. Let me know if you have any questions.
Dan and George share 18
is in the ratio 1:2
How many bananas does Dan get?
Answers
Dan gets 6 bananas and George gets 12 bananas
hope it helps...!!!
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
PQ = 15M = (8.5, 8)Step-by-step explanation:
Given points P(4, 2) and Q(13, 14), you want the length of PQ and its midpoint.
(a) LengthThe length of PQ is given by the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
d = ((13 -4)² +(14 -2)²) = √(9² +12²) = √225
d = 15
The length of PQ is 15 units.
(b) MidpointThe midpoint is halfway between the end points. It is conveniently found as the average of the coordinates of the end points.
M = (P +Q)/2
M = ((4, 2) +(13, 14))/2 = (4+13, 2+14)/2 = (17, 16)/2
M = (8.5, 8)
The midpoint of PQ is M(8.5, 8).
__
Additional comment
The length of PQ is the hypotenuse of a right triangle with side lengths 9 and 12 units. You recognize this ratio as 3:4, so the triangle is a 3-4-5 right triangle, scaled up by a factor of 3. The length PQ is 3·5 = 15.
{3, 4, 5} is one of several Pythagorean triples commonly seen in textbook problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
When used as a diacritic mark, the term dot is usually reserved for the interpunct, or to the glyphs "combining dot above" and "combining dot below" which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese
Find the missing dimension of the triangle.
1.5 in. base
Area = 2 in. squared
h = ? in.
Answers
Answer:
Fraction form:
h = 4/1.5 in
Decimal form:
2.667 in
Step-by-step explanation:
I've attached my work
The formula use is usually use to find the area of a triangle but allowed us to work backward after inputing given values
Hope it helps, Let me know if yoy have any more questions/concerns !
Have a nice rest of your day :)
F is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. F = (z-x)i + xk r(t) = (sin t)i + (Cost) k, 0 <= t <= 2π
Answers
Answer: 177.65
Step-by-step explanation:
its the only accurate answer.........
How many different ways can someone arrange the all letter in AMERICA to make a world
Answers
Answer:
2520 different ways
Solve |2x+5| =15
I need to pass this class, if anyone is interested in helping me with 2 math classes please message me. I need to have them done by may 6th in order to graduate high school. Thank y’all so much!
Answers
Answer:
The answer is x=3 and the extraneous is x=-1
Step-by-step explanation:
The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4.9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground.
10 seconds
20 seconds
15 seconds
5 seconds
Answers
It is found that the time it takes for the projectile to hit the ground would be after 20 seconds.
When does the projectile hit the ground?The projectile would hit the ground when its height h(t), is equal to zero.
The given function that models its height is given by:
[tex]h(t) = -4.9t^2 + 98t.[/tex]
where h is the height in meters and t is the elapsed time in seconds.
Then,
h(t) = 0
[tex]-4.9t^2 + 98t = 0\\-4.9t(t - 20) = 0\\\\t - 20 = 0[/tex]
t = 20
Thus, The projectile hits the ground after 20 seconds.
Learn more about projectile here;
https://brainly.com/question/11422992
#SPJ1
A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual
park is 280 yards long. What is the approximate area of the actual park, in square
yards?
Answers
56000 is the actual park in square yards.
What will happen to the measures of central tendency if the outlier is removed
Answers
1) Which two ratios form a proportion?
A) 1: 3 and 6: 3
B) 1: 3 and 3:6
C) 3: 1 and 9: 3
D) 3: 1 and 3:9
Answers
Option C is correct.
Proportion means two ratios are equal to each other.Option A Option B1 : 3 and 6 : 3 1 : 3 and 3 : 6
1 : 3 and 2 : 1 1 : 3 and 1 : 2
not proportional not proportional
Option C Option D3 : 1 and 9 : 3 3 : 1 and 3 : 9
3 : 1 and 3 : 1 3 : 1 and 1 : 3
proportional not proportional
7) Find x- intercepts
Answers
Answer:
See below:
Step-by-step explanation:
At x axis intercepts, the value of y = 0
0 = -3/5 ( x+7)^2 + 6
-6(-5/3) = (x+7)^2
10 = (x+7)^2
x = -7 +- sqrt (10)
Answer:
[tex] x = -7 \pm \sqrt{10 [/tex]
Step-by-step explanation:
The x-intercepts occur where y = 0.
-3/5(x + 7)² + 6 = 0
-3(x + 7)² + 30 = 0
-3(x² + 14x + 49) + 30 = 0
-3x² - 42x - 147 + 30 = 0
3x² + 42x + 117 = 0
[tex] x = \dfrac{-42 \pm \sqrt{42^2 - 4(3)(117)}}{2(3)} [/tex]
[tex] x = \dfrac{-42 \pm \sqrt{360}}{6} [/tex]
[tex] x = \dfrac{-42 \pm 6\sqrt{10}}{6} [/tex]
[tex] x = -7 \pm \sqrt{10 [/tex]
What is the equation of the line that is parallel to the graph of y = 2x - 5 and passes through the point (4,2)?
Answers
Answer:
[tex]y=2x-6[/tex]
Step-by-step explanation:
A line parallel to another will have the same gradientSo the equation will be [tex]y=2x+c[/tex]We need to find out what c is, so substitute in the values for x and y[tex]2=2\times 4 + c[/tex][tex]2=8+c[/tex][tex]c=2-8=-6[/tex]So your equation is [tex]y=2x-6[/tex]!Answer:
2x-6
Step-by-step explanation:
Have a good day!
Log20x=3 need the answer for algebra 2
Answers
Answer:
x = 50
Step-by-step explanation:
Pls help WILL GIVE BRAINLIST
A person looking out a window, 40 feet above street level can sight the top and
bottom of the building. The angle of elevation to the top of the building is 61 degrees and the angle
f depression to the bottom of the building is 37 degrees. How tall is the building that the person is looking at
Answers
Answer:
135.94 feet
Step-by-step explanation:
Split the problem into two parts :
Distance between viewer and buildingHeight of the top part of the buildingDistance between viewer and building
The lower part of the building is 40 feet, as it is mentioned the viewer is 40 feet above street levelLet the distance be called 'd'Therefore, tan37° = 40/dtan37° = 3/4 = 0.75⇒ 40/d = 0.75⇒ d = 40/(3/4) = 40 x 4/3 = 160/3 = 53.3 feetHeight of the top part of the building
Let the height of the top part be 'h'Therefore, tan61° = h/d = h/53.3tan61° = 1.8⇒ h/53.3 = 1.8⇒ h = 53.3 x 1.8 = 95.94 feetTotal height of building
Lower part + Top part40 + 95.94135.94 feetfind the value of W
Answers
Answer:
answer is equal to 73 degrees
If you get 1620 products every 30 seconds, how much would you get in 60 minutes?
Also,
If you get 450 products every 7 seconds, how many would you get in 60 minutes?
Answers
Answer:
Step-by-step explanation:
Here,
→We get 1620 products every 30 seconds
→We get 1620/30=54 products in every 1 second
→We get 54×60=3240 products in every 60 seconds(1 minute)
As we have
60seconds=1min
60 minutes=60 seconds ×60
Now,
→We get 3240×60=194400 products in every 60 minutes
Also,
→We get 450 products every 7 seconds
→We get 450/7=64.28 products in every 1 second
→We get 64.28×60 products in every 60 seconds
→We get 3856.8×60=231408 products in 60 minutes
I NEED HELP PLEASE MATH
MATH MATH
Answers
Answer:
write a number for t and f
Step-by-step explanation:
Answer:
Cant See
Step-by-step explanation:
Please take a clearer version of this image.
Bill has a farm where he raises pigs and cows. The ratio of cows to total animals on a farm is 5 to 12.
Which number below could be the number of pigs on the farm?
A. 6
B. 20
C. 21
D. 24
Answers
I don't know the answer marked stylish random
Answers
Answer:
A
Step-by-step explanation: i am in math 8
lol
What is the value of 21
Answers
Answer:
Absolute value is the magnitude of a real number regardless of sign. When you take the absolute value of something, it is the positive value of the number being evaluated
|21| = 21
also...
|−21| = 21
Step-by-step explanation:
Hope This Helps
Have A Great Day
~Zero~