Answer:
We can use a trick here. Let's look at the first few exponents of i to realize this:
i^0 = 1
i^1 = i
i^2= -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
we can see that the pattern (1, i, -1, -i) repeats. Since 82/2 = 41, and 41 is only divisible by 1, i^41 = i, and i^2 = -1. -1*i = -i, so i^82 = -i.
Step-by-step explanation:
Juan invested $3,100 in an account paying an interest rate of 3.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 19 years?
Answer:
A=6143.54( to the nearest dollar A=6144)
Step-by-step explanation:
A=Pe^(r(t))
P=3100 r=0.036 t=19
A=3100e^0.036(19)
A=3100e^(0.684)
There will be $6070 money in the account of Juan after 19 years.
What is Compound Interest?It is the interest on a loan or deposit calculated based on both the initial principal and accumulated interest from previous periods. It is calculated as:
[tex]Amount=P(1+\frac{r}{n} )^{nt}[/tex]
where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of periods elapsed
We have
principal, P= $3100
Rate, r = 3.6%=[tex]\frac{3.6}{100}[/tex]
time, t = 19years
number of times interest compounded per year, n=1
Formula Used:
[tex]Amount=P(1+\frac{r}{n} )^{nt}[/tex]
Substitute the values in the above formula
[tex]Amount=3100(1+\frac{3.6}{100} )^{19}[/tex]
[tex]Amount=[/tex]$6070
Hence, there will be $6070 in account after 19 years.
Learn more about compound interest here:
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Here please help
I will give brainest
Pleaseeeeee helpppppp
Answer:
5,d
6,e
7,b
8,f
9,c
10,a
Hue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that
same length if she gets 15 more chairs. Complete the equation and solve it to find how many chairs are inthat row length. In your equation, use the variable x to represent the number of chairs in each row.
Answer:
8r + 15 = x
Step-by-step explanation:
So being that they can form 6 rows but have 3 left over we know that there are more than three chairs in each row. So for example:
6r + 3 = x
or (x = chairs, r = chairs in the row)
8r + 15 = x
Point (-3,4) is rotated 180° about the origin in a
counterclockwise direction. What are the coordinates of its
image?
Answer:
( 4 , -3)
Step-by-step explanation:
Rate me branliest please :)
An ant travels at a constant rate of 30 cm every 2 minutes
1. At what pace does the ant travel per centimeter
2. At what speed for the ant travel per minute
Answer:
Step-by-step explanation:
1cm every 4 seconds
15 cm per minute
Answer:
15
Step-by-step explanation:
1/15 of a minute per centimeter.
The speed is 15 centimeters per minute.
Find the solution to the equation shown below.
–3.4(x – 2) = 9.8 – 4x
Answer:
X= 5
Explanation (Steps):
Step 1: Simplify both sides of the equation.
−3.4(x−2)=9.8−4x
(−3.4)(x)+(−3.4)(−2)=9.8+−4x(Distribute)
−3.4x+6.8=9.8+−4x
−3.4x+6.8=−4x+9.8
Step 2: Add 4x to both sides.
−3.4x+6.8+4x=−4x+9.8+4x
0.6x+6.8=9.8
Step 3: Subtract 6.8 from both sides.
0.6x+6.8−6.8=9.8−6.8
0.6x=3
Step 4: Divide both sides by 0.6.
0.6x0.6=3/0.6
x=5
PLEASE HELP!
Find four numbers, the
sum of which is 45, so
that if 2 is added to
the first number, 2 is
subtracted from the
second number, the third
number is multiplied by
2, while the fourth
number is divided by 2,
then the four numbers so
produced are all the
same.
45
Step-by-step explanation:
45 +2=47
47-2=45
45×2=90
90÷2=45
The amount of revenue brought in by states from motor vehicle licenses increased at a relatively constant rate of 499.79 million dollars per year from 1990 to 2000. In 2000, the states brought in 15,099 million dollars in revenue from motor vehicle licenses
Answer:
a. the approximate revenue from licenses in 1990 was $10,101.10 million.
b. The function is x = 10,101.10 + 499.79y
c. The revenue from licenses in 1999 is $14,599.21 million.
Step-by-step explanation:
The amount of revenue brought in by states from motor vehicle licenses increased at a relatively constant rate of 499.79 million dollars per year from 1990 to 2000. In 2000, the states brought in 15,099 million dollars in revenue from motor vehicle licenses.
a: what was the approximate revenue from licenses in 1990?
b: write an equation that gives the revenue as a function of the number of years since 1990.
c: find the revenue from licenses in 1999.
a: what was the approximate revenue from licenses in 1990?
This can be calculated using the following function:
x = a + by ............................... (1)
Where;
x = Amount brought in 2000 = $15,099 million
a = Amount brought in 1990 = ?
b = Amount of relative constant rate of increase = $499.79 million
y = Number of years between 1990 and 2000 = 10
Substituting the values into equation (1) and solve for a, we have:
15,099 = a + (499.79 * 10)
a = 15,099 - 4,997.90
a = $10,101.10 million
Therefore, the approximate revenue from licenses in 1990 was $10,101.10 million.
b: write an equation that gives the revenue as a function of the number of years since 1990.
Using equation (1) in part a above, we substitute the values for a and b to obtain an equation that gives the revenue as a function of the number of years since 1990 as follows:
x = 10,101.10 + 499.79y ....................... (2)
c: find the revenue from licenses in 1999.
Since 1999 is 9th year from 1990, we therefore substitute y = 9 in equation (2) as follows:
x = 499.79 + 10,101.10y
x = 10,101.10 + 499.79(9)
x = 10,101.10 + 4,498.11
x = $14,599.21 million
Therefore, the revenue from licenses in 1999 is $14,599.21 million.
14.
The graph shows the decrease in the value, v, of a commercial
jet over time, t, measure in years.
Which equation best represents the graph?
F v(t) = 5.5t + 110
G v(t) = -5.5t + 110
H v(t) = -110 + 110
J v(t) = 11t + 110
Step-by-step explanation:
hugs did ta don't think she knows what that was you baby girl so ti you but I'm not sure what you mean 4buy64g7gugugguvbb Jo is my first year of my first time doing your opinion how are ilocano or so I will get you a quote please let your opinion how much I love sorry na please ❣️❣️ you ❣️❣️❣️❤️ you
Kate is going on a long distance car trip. She begins with 16 gallons of gas in her car and her car burns 3 gallons of gas each hour. If she ends her road trip with 1 gallon of gas left in the tank, how many hours was she driving
9514 1404 393
Answer:
5 hours
Step-by-step explanation:
Starting with 16 gallons and ending with 1 gallon means that Kate has used 15 gallons of gas. Burning 3 gallons per hour means her travel time was ...
(15 gal)/(3 gal/h) = 5 h
Kate was driving for 5 hours.
Solve using elimination. Brainliest for correct answer!!
Answer:
X is 1 and y is 5
Step-by-step explanation:
Please help show work Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
(a) What is the system that models this situation?
(b) Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.
Answer:
A) a ratio system
B)The 4 lb peanuts and the 1 lb mixture because the 4lb added to the 1lb of mixture give the correct percentages.
Step-by-step explanation:
I hope this helps :)
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can someone help me with this I really don't understand
Answer:
No
Step-by-step explanation:
Because the constant of proportionality is not equivalent to 20,13.
Can I have brainliest?
Which expression can be used to determine the slope of the linear function graphed below?
Answer:
Y = 2x-4
Step-by-step explanation:
the anwser is, A
Step-by-step explanation:
-4-0
2-0
Sarah jumps rope to keep in shape. She jumps an average of 20 times in 15 seconds. Which of these describes her jumping rate?
Answer:
80 jumps per minute
Troy needs to complete 45 hours of training. During the fall, Troy completed 12 hours of training, and during the spring he completed twice as many hours as he had during the fall. Which equation can be used to find how many more hours of training (h) Troy needs to complete? Select one:
Answer:
[tex]36 + h = 45[/tex]
[tex]h = 9[/tex]
Step-by-step explanation:
Given
[tex]Total = 45[/tex]
[tex]Fall = 12[/tex]
[tex]Spring = 2 * Fall[/tex]
Required
Determine the equation to find the hours (h) left
The sum of the hours spent during the fall, spring and the hours left must be equal to the total hours.
In other word;
[tex]Fall + Spring + h = Total[/tex]
Substitute 2 * Fall for Spring
[tex]Fall + 2 * Fall + h =Total[/tex]
Substitute values for Fall and Total
[tex]12 + 2 * 12 + h = 45[/tex]
[tex]12 + 24 + h = 45[/tex]
[tex]36 + h = 45[/tex]
The above represents the equation,
Solving further for h
[tex]h = 45 - 36[/tex]
[tex]h = 9[/tex]
Hence, there are 9 hours left
help? i need to due right now
Answer:
200
Step-by-step explanation:
help plzz hurry i didnt study and need help
A one-year membership to Metro Gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. Write an equation to represent what you will pay monthly for the yearlong membership. Write an equation that would help members find how much they pay per month.
Answer: See explanation
Step-by-step explanation:
Let the amount of money to be paid per month be represented by x. The information given in the question can then be formed into an equation as:
$40 + 12x = $460
From the equation, the amount that'll be paid monthly will be:
$40 + 12x = $460
12x = $460 - $40
12x = $420
x = $420/12
x = $35
The amount paid monthly is $35
Rewrite 65% as a decimal number.
Answer:
.65 hope this helps :))
What is the solution to this equation?
6(x - 5) = 4x + 20
A. x= -1
B. x= -5
C. x = 25
D. x = 5
Answer: The answer is 25! :)
Give brainiest?
Pls help me with this!!
W33D
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Assuming the dilatation is centred at the origin.
Then multiply each set of coordinates by the scale factor [tex]\frac{1}{3}[/tex] , thus
(- 12, 3 ) → [tex]\frac{1}{3}[/tex](- 12), [tex]\frac{1}{3}[/tex] (3) ) → (- 4, 1 )
(0, 6 ) → ( [tex]\frac{1}{3}[/tex] (0), [tex]\frac{1}{3}[/tex] (6) ) → (0, 2 )
(3, - 3 ) → ( [tex]\frac{1}{3}[/tex] (3), [tex]\frac{1}{3}[/tex] ( - 3 ) ) → (1, - 1 )
What is the factored form of the expression 5p^3-10p^2+3p-6
Answer: (5p^2+3)(p-2)
Step-by-step explanation:
In this problem, we need to write the factor form of expression .
5p^3-10p^2+3p-6
It can be done as follows :
5p^3-10p^2+3p-6=(5p^3+3p)+(-10p^2-6)
Taking common form the terms as follows :
=p(5p^2+3)-2(5p^2+3)
It can be also written as :
=(5p^2 +3)(p-2)
Hence, the factored form of is
Answer:
(p-2)(5p^2+3)
Step-by-step explanation:
see the image
Will give brainliest
Problem 12
Answer:
44 yards
Step-by-step explanation:
Answer:
wouldn't you just do 14 times 8? If so it would be 112 yards (i might be wrong tho..)
Help me please 12 and f
Answer:
It is not equivalent.
Step-by-step explanation:
You have to expand the brackets :
(x-4)(x+3)
= x(x) + x(3) - 4(x) - 4(3)
= x² + 3x - 4x - 12
= x² - x - 12
Therefore, x² - x - 12 / (x-4)(x+3) is not equivalent to x² - 4x - 12.
What is the momentum of a 2000-kg car traveling at 20 m/s?
a. O kg m'sec
b. 0.001 kg'm'sec
c. 100 kg m sec
d. 40,000 kg m sec
Answer:
D
Step-by-step explanation:
force = mass × acceleration
Answer: D
Step-by-step explanation:
What is the value of the expression 5(23 - 3)? Show your work.
Answer:
100
Step-by-step explanation:
5(23-3)
23-3= 20
5 × 20= 100
five ninths plus four sixths have a nice day Owo
Answer:
Shoyo here!
Step-by-step explanation:
1.22222222222
hehe, that's a long number- have a nice day! <3
find the product of 16 and 24
Answer:
384 16 times 24 is equal to 384
Step-by-step explanation:
You just have to multiply them. 16 times 24 is 384.
Question 1(Multiple Choice Worth 4 points) (04.07A) Two quantities are related, as shown in the table below: x y 2 2 4 5 6 8 8 11 Which equation best represents the relationship? y = 3 over 2x + 2 y = 3 over 2x y = 3 over 2x − 1 y = 3x + 2
Answer:
id say C if not sorry
Step-by-step explanation:
Answer: The answer is C
Step-by-step explanation: Thanks to the person above me I got the question right.