Tony Peyton, age 20, would like to have $1,000,000 by the time he is 65 years of age. If Tony could earn 6.9% annual interest compounded monthly, how much must he invest now to have $1,000,000 by the time he is 65?
Using compound interest, it is found that he must invest $45,225 now.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem:
He wants to have $1,000,000 in 65 - 20 = 45 years, hence [tex]t = 45, A(t) = 1000000[/tex].6.9% annual interest, hence [tex]r = 0.069[/tex].Compounded monthly, hence [tex]n = 12[/tex].Then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]1000000 = P\left(1 + \frac{0.069}{12}\right)^{12(45)}[/tex]
[tex]P = \frac{1000000}{(1.00575)^{540}}[/tex]
[tex]P = 45225[/tex]
He must invest $45,225 now.
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Answer:
He must invest $45,225
Tell whether the ordered pair is a solution to the system.
(-1, -2) 3x + 5y = 3
-9x - 8y = -9
no
yes
Answer:
no
Step-by-step explanation:
no. substitute -1 for x and -2 for y.
the first one is -1 - 10
this equals -11 not 3
What is the value of r in the equation −4/3r − 1 = −2 ?
Answer:
r = 3/4
Step-by-step explanation:
A movie theater sold a total of 50 tickets. 23 of the tickets were child tickets, and the rest were adult tickets. What is the ratio of the number of adult tickets to the total number of tickets?
Write your answer as a fraction. Use a slash ( / ) to separate the numerator and denominator.
27/50
Step-by-step explanation:
You would have to subtract 50 and 23 to find out how many adult tickets there was
solve the inequality and graph its solution.
Answer:
D
Step-by-step explanation:
Hope this helped! :D
A student's bank account is represented in the table shown.
1. Create a linear regression equation that can be used to model the amount of money in the account (the balance), y, based on the time (in weeks), x. Round all values to the nearest hundredth.
2. What is the slope of your linear regression equation? What does it mean in the context of the situation (time and $).
3. Use the model to approximate the amount in the account after 15 weeks. Round to the nearest hundredth.
4. Use the model to approximate how long it would take to have $50.00 in the account.
The desmos link is in the reply section below...
1.) y = 1.56x + 1.29
2.) the slope is 1.56
As the weeks are increasing, the student's balance is growing about 1.56 per week.
3.) y = 24.69
4.) 50 = 1.56x + 1.29
50 - 1.29 = 1.56x + 1.29 - 1.29
48.71 =1.56x
48.71 / 1.56
31.2
Meredith is 3 times as old as Adam. Six years from now, she will be twice as old as Adam will be then. How old is Adam now
Answer:
A=6
Step-by-step explanation:
M=3A
M+6=2(A+6) M+6=2A+12 M=2A+6
System of equations:
M=3A Subtract
M=2A+6
0=A-6
A=6
Verizon charges a $100 initial contract fee, then $70 a month for a basic cell phone plan.
What is the rate of change or slope in this problem?
Write the equation y=mx+b that would fit this problem.
Using a linear function, it is found that the slope of the problem is of $70.
A linear function for a cost is modeled by:
[tex]C(t) = C(0) + at[/tex]
in which:
C(0) is the fixed cost.a is the monthly cost, which is the slope.Verizon charges a $100 initial contract fee, then $70 a month for a basic cell phone plan, then:
[tex]C(t) = 100 + 70t[/tex]
Then, the slope of the problem is of $70.
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Select the correct answer from each drop-down menu.
Consider triangles PQR, MNO, and STU, which have resulted from rotating, reflecting, and translating triangle XYZ.
Answer:
Not Similar because they don't have equivalent angles.
Step-by-step explanation:
First one is D
Second one is A
The Triangle XYZ is Congruent to PQR by ASA congruence, the Triangle XYZ is Congruent to MNO by SSS congruence, the Triangle XYZ is Congruent to STU by SAS congruence
What is a Triangle?A triangle is a polygon with three sides, they are classified as acute angle triangle, right angle triangle, obtuse angle triangle on the basis of angles subtended by the vertices.
The triangles PQR, MNO, XYZ, STU can be seen in the figure
Triangles PQR, MNO, and STU, which have resulted from rotating, reflecting, and translating triangle XYZ.
The Triangle XYZ is Congruent to PQR by ASA congruence
From the image
XY = PQ
∠YXZ= ∠QPR
∠YZX = ∠PQR
The Triangle XYZ is Congruent to MNO by SSS congruence
From the image
XY= MN
YZ=ON
ZX=OM
The Triangle XYZ is Congruent to STU by SAS congruence
XY = ST
∠YXZ=∠TSU
XZ= SU
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PLLSSS HELP MEEEE!!
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.
Number of tiles Bruce used: 5x + 2
Number of tiles Felicia used: 5x + 5
Answer:
No it is not possible for Bruce and Felicia to have used the same number of tiles.
Step-by-step explanation:
Bruce would have used 10x of tiles and Felicia used 7x of tiles.
No, it is not possible that Bruce and Felicia to have used the same number of tiles
The expression which shows the difference is (n² - 2)/2n, the correct option is B.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Number of tiles Bruce used: 5x + 2
Number of tiles Felicia used: 5x + 5
On equating the two expressions
5x+2 = 5x+5
There is no solution
At any value of x, Bruce would have always used 3 tiles less than Felicia.
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A patio measures 120 cm long and 70 cm wide. If a tile measures25 cm. How many tiles will be needed to cover the patio?
Answer:
So, multiply 120 by 70 cm for the area which is 8,400. Divide that by 25 cm which would be 336. That would be your final answer. (A tip for these problems is to draw it because it makes it easier sometimes.)
Thanks Mark As Brainlist
Jason's new business will start making a profit when he sells more than 20 items. Which graph best represents this situation?
Answer:
I- where is the graph
Step-by-step explanation:
Answer:
It's A the first graph
Step-by-step explanation:
7.
Which of the following is a prime number between 80 and 90?
OA. 85
B.
86
O C. 81
OD
83
HELP!!
Answer:
D) 83 is the answer. this is because it doest divide more then 2wice like the rule
Answer:
D TRUST ME
Step-by-step explanation:
what inequality does the number line graph represent
Answer: what number line
Step-by-step explanation:
anyone can have few minutes to help!!
Answer:
i am not sure
Step-by-step explanation:
if i have decent grades, but miss a lot of school
will they fail me???
3q+3.97=7.57 please help im stuck on ixl
Answer:
1.2
Step-by-step explanation:
3q+3.97=7.57
3q=7.57-3.97
3q=3.6
q=3.6/3
q=1.2
Solve the inequality
4x - 19 ≥ -27
The answer is X>-2. I uploaded a picture of the steps below. Hope this helps. :)
HURRRYYYY! I ONLY HAVE 3 MINUTES.
2/5 of a kiddy pool was filled with water. After pouring out 5/7
of the amount of water in the pool 62 liters of water was needed to fill the pool completely. Find
the amount of water needed to fill up the empty
pool.
Answer:
The question is asking what is the volume of water in the full pool. It is 70 liters.
Step-by-step explanation:
Let P represent the volume of a full pool.
"2/5 of a kiddy pool was filled with water" can be written as:
(2/5)P.
"After pouring out 5/7 of the amount of [I assume from the 2/5P] water in the pool" can be written as:
(2/7)(2/5)P, or (4/35)P [This represents the amount of water remaining in the pool after the above shenanigans.]
The we are told that when 62 liters are added back to the pool, it is full. That can be written as:
62 + (4/35)P = P [Add 62 liters to what was remaining. ((4/35)P), and we'll have P, a full pool, for a cool fool. [sorry]
62 = (31/35)P
P = 62(35/31)
P = 70 liters
what is the modulus of the complex number -4+3i
The modulus of the complex number -4+3i is 5.
Complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit,
A complex number is a number of the form a + bi, where a and b are real numbers.
The modulus (z) of a complex number x + iy is given by:
z = √(x² + y²)
The modulus of the complex number -4+3i is:
[tex]z=\sqrt{(-4)^2+3^2} =\sqrt{25}=5[/tex]
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find the some of -3x^2-x-10 and 10x^2+x-10
Answer:
( X - 2 )(3x + 5) For 3x^2-x-10
Step-by-step explanation:
For which value of x does each expression make sense
[tex]\text{If you want the domain of this function then it is}~x\leq 0 ~ \text{or} ~ (-\infty ,0][/tex]
If f(x)=-4x+1, what is f(-x/2)?
Answer:
[tex]f(-\frac{x}{2})=-2x+1[/tex]
Step-by-step explanation:
[tex]f(x)=-4x+1[/tex]
[tex]f(-\frac{x}{2})=-4(\frac{x}{2})+1[/tex]
[tex]f(-\frac{x}{2})=-2x+1[/tex]
2. Daniel orders sushi from the sushi restaurant. The total bill is $80. He tips the sushi chef 20%.
How much money does the sushi chef get?
Answer:
16
Step-by-step explanation:
(20/100) * 80=16
Answer:
16
Step-by-step explanation:
$20.43 is how much tip was
27% >>> .27
.27 * 75.68 = 20.43 tip
Bonus: $96.11
the bold word are tip but your answer is 16
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HELPPPPPP PLLSLLSLSLLSSS!!!
Cereal is on sale this week. Is it a better buy to get the 10-ounce box for $1.95 or the 14-ounce box for $2.81?
Answer:
It is better to buy the 10-ounce box for $1.95
Step-by-step explanation:
1.) Set up a ratio to represent this problem.
Ounces : Price
10 : 1.95
14 : 2.81
2.) Find the unit price for the first ratio.
10 : 1.95
/10 /10
1 : 0.195
This means that a one-ounce box of cereal will cost $0.12
3.) Find the unit price for the second ratio.
14 : 2.81
/14 /14
1 : 0.20071428571
This means that a one-ounce box of cereal will cost $0.20
4.) Compare prices
$0.12 < $0.20
Therefore, it is better to buy the 10-ounce box for $1.95.
Can someone explain how to do this:
If you put 10 in to the function f(x) = 2x, what would be the output?
--
Im so lost-
Answer:
It would be 2 (10)
Step-by-step explanation:
If you replace x with 10 then you have a multiplacation problem and the output of the answer is 20
you travel 90 miles in 1.5 hours. find the speed you travel.
Answer:
60 mph
Step-by-step explanation:
what is the area of the square units ? W (11,2), X (11,8), Y (14,8), Z (14,2)
Answer:
18 units²
Step-by-step explanation:
Find the side lengths then multiply the length and width to find the area.
Shane is following an English recipe for scones. The recipe calls for 1.2 kilograms of flour. How many pounds of flour, to the nearest tenth of a pound, does he need?
Answer:
Bilemedim fotoğrafını çeksen daha iyi olur kankacim çok güzel birisin
There are 2.6 pounds of flour.
What is Measurement unit?
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The recipe calls for 1.2 kilograms of flour.
Now,
Since, The recipe calls for 1.2 kilograms of flour.
We know that;
⇒ 1 kg = 2.2 pounds
So, 1.2 kg = 1.2 × 2.2 pounds
= 2.6 pounds
Thus, There are 2.6 pounds of flour.
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