Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
how might the area of a room affect the way the room is used?
Answer:
The more area a room has the more things you can put in it
Step-by-step explanation:
A silo is a storage bin that is a cylinder with a hemisphere on top. A farmer has a silo with a base radius of 30 feet and a storage height of 100 feet. The "storage height" is the part which can be filled with grain - it is just the cylinder. A cubic foot of grain weighs 62 lbs.
One thousand square feet of wheat produces 250 pounds of grain.The farmer's wheat field is 3500 feet by 20,000 feet. Is the silo large enough to hold the grain? By how much? Explain your answer.
para la escuela necesito mucho para mi escuela
I need help. This is due today~
HELP! WILL GIVE BRANLIEST!
Answer:
Z = 80 degrees and X = 8 degrees
Step-by-step explanation:
The reason Z = 80 degrees is because a flat line always has a measure of 180 degrees.
I forget the term, but we know that 6x + 52 is equal to 100 due to some angle theorem. (Once again, I do not remember the term.)
We then subtract 52 from 100 to get the equation 6x = 48. Divide them both by 6 and you get X = 8!
Hope this helped!
Find the value for x and y if x+(xy)^1/2+y=14 and x^2+xy+y^2=84
Answer:
[tex]xy = 4 [/tex]
Step-by-step explanation:
Taking the first equation , we have ,
[tex]\implies x + (xy)^{\frac{1}{2}} + y = 14 \\\\\implies x + \sqrt{xy}+ y = 14 \\\\\implies x + y = 14 -\sqrt{xy}\\\\\implies (x+y)^2 = (14-\sqrt{xy})^2 \\\\\implies x^2+y^2+2xy = 196 + xy -28\sqrt{xy} \\\\\implies x^2+y^2+xy = 196 - 28\sqrt{xy}[/tex]
Now according to second equation,
[tex]\\\\\implies 84 = x^2+xy+y^2 [/tex]
Plug on this value ,
[tex]\implies 84 = 196 -28\sqrt{xy}\\\\\implies -112 = -28\sqrt{xy}\\\\\implies \sqrt{xy}=\dfrac{112}{28}\\\\\implies \boxed{\boxed{ xy = 16 }}[/tex]
On substituting this value in terms of one variable of the equation you can get the values of x and y .
Find the volume of a cone with a base radius of 6 in and a height of 12 in. Write the exact volume in terms of , and be sure to include the correct unit in your answer.
Answer:
we have
radius [r]=6in
height [h]=12in
Volume of cone = 1/3πr²h
Volume = 1/3 ×π × (6)² × 12=144πίn³or 452.38in³ is your answer.
What are the first three terms of the sequence defined by the following equation?
an = 2 • (-3)n - 1.
Answer:
-7, -13, -19
Step-by-step explanation:
plug in 1,2, and 3 into the part of the equation "n".
Answer:
a1 = -7
a2 = - 13
a3 = - 19
Step-by-step explanation:
n = 1
a1 = 2*(-3)*1`- 1
a1 = -6 - 1
a1 = - 7
n=2
a2 = 2(-3)*2 - 1
a2 = -12 -1
a2 = - 13
n3 = 2(-3)*3 - 1
n3 = -18 - 1
n3 = -19
Each term is - 6 away from the previous one.
Help .....................
Answer:
1. 8 is bigger
2. -9 is bigger
3. 12 is bigger
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!
The Expression
12
3+9
is what:
A: Sum
B. quotient
C. difference
Answer:
Sum
Step-by-step explanation:
It needs 2 be 20 characters so dont mind me . . .
wait hol up i took the test again sorry um it quotient
9. Sally works in a cell phone store. She is paid a weekly salary of $80 plus $5.25 for each cel
phone she sells. Which equation can be used to find Sally's total weekly income?
Answer:
y = 5.25x + 80
Step-by-step explanation:
total income = 5.25 * phones + 80 salary
Answer:
y = 5.25x + 80
Step-by-step explanation:
Sathish is going on a 210021002100-kilometer road trip with 222 friends, whom he will pick up 150150150 kilometers after he begins the trip and drop off when there are 150150150 kilometers remaining. The car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter.
Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together.
Answer:
64.80
Step-by-step explanation:
I need a tutor please
Answer:
Ok I can help!
Step-by-step explanation:
I hope this helps! Have a great rest of your day!
what is x equal to? please help
Answer:
147°
Step-by-step explanation:
x+33=180
x=180-33=147°
Which of the following explains why cos60º = sin 30° using the unit circle
Answer:
A I just guested
Step-by-step explanation:
David attended a summer camp last July. He recorded the ages of the camp counselors
here.
Ages: 18, 19, 19, 19, 21, 23, 23, 24, 24, 25, 26
David wants to create a box plot to display the ages he recorded. Which box plot is the best
representation of the information?
( Please help, I need an answer ASAP ;-; )
Answer:
no offence but this David guy sounds like a nerd i mean who would go to camp just to make a graph
Step-by-step explanation:
help anyone like asap plss
Answer: G. (-6,4), (3,5), (2,2) and (-5,1) just look where the dot plot is and you with know the answer.
Step-by-step explanation: Hope this help :)
can someone explain this to me
I need this help me
Step-by-step explanation:
the answer is 2/9
2/9 is .2222222 continuing
2/10 is 0.2
22/1000 is 0.022
2/8 is 0.25
Solve for x - 3 1/2 = 1/2x + 1/2x + x.
-1 1/2
-1 3/4
-5 1/2
Please help
Will give brainly
Answer:
B) -1 3/4
Step-by-step explanation:
Evaluate The expression 3•2^t when t is 1
Answer:
6
Step-by-step explanation:
[tex]2^{1}[/tex] = 2
3 × 2 = 6
Can sumone help me wit this
Answer:
1/9 i think not sure
Step-by-step explanation:
Answer:
1/9
Step-by-step explanation:
Well the chance of picking 3 one time is 1/3
The chance of picking 3 the second time is 1/3
So at first, we've succeeded with probability 1/3 and failed with probability 2/3
We don't care what happens next if we've failed - we already failed.
So we've reached the "picking the second card with hope in our hearts" 1/3 of the time and we again succeed with 1/3 of a chance, so the total probability of success is 1/3 * 1/3 = 1/9
Think of the options:
3 and 3 - probability 1/3 * 1/3 = 1/9
3 and non-3 - probability 1/3 * 2/3 = 2/9
non-3 and 3 - probability 2/3 * 1/3 = 2/9
non-3 and non-3 - probability 2/3 * 2/3 = 4/9
Note that all the options sum to 1 - as probabilities of all options always should.
Helpppppppppppppppppppp
Answer:
Step-by-step explanation:
x=100 (vertically opposite angle)
ye I need some help, please
Answer:
(1,0) (2,1) (4,4)
y<x+1 (for the dashed line)
y≥-2x+2 (for the solid line)
Step-by-step explanation:
A positive angle less than 360 that is coterminal with -725 degrees is
The positive angle is less than 360 which is coterminal with -725 degrees is 85 degrees.
What are Coterminal Angles?Coterminal angles are those with the same beginning side and the same terminal sides. These angles are in the typical position, although their values differ. They have the same sides, are in the same quadrant, and their vertices are identical. The endpoint sides coincide at the same angle when the angles are rotated clockwise or anticlockwise.
An angle that is coterminal with -725 degrees is an angle that has the same initial and terminal sides as -725 degrees, but its measure is between 0 and 360 degrees.
To determine a positive angle less than 360 that is coterminal with -725 degrees, we can add or subtract multiples of 360 from -725 degrees until we get an angle within that range.
In this case, -725 degrees - (2 x 360) = -725-720= -1445.
So, the positive angle less than 360 that is coterminal with -725 degrees is -1445 degrees + 360 = 85 degrees.
To learn more about Coterminal Angles click here:
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PLSSSS HELP AND NOOOO LINKS OR SPAMMERS!!!! Write the equation of the line for the graph shown below.
Answer the question based on the data in the two-way table.
Grades
Gender
Below Above
Average Average
Boy 14 23
Total
37
Girl
16
22
38
Total
30
45
75
Which statement is true?
O A. Aboy above average grades) = P(boy)
B.
Pabove average grades boy) = Pabove average grades)
Ос.
Pboy above average grades) # Pabove average grades)
OD. Pabove average grades| boy) = P(boy)
Answer:
d
Step-by-step explanation:
P(boy above average grades) P(above average grades) is the right answer. The correct option is C.
What is conditional probability?The likelihood that event A will occur provided that event B has already happened is known as conditional probability. It is written as "the probability of A given B" and is indicated by the symbol P(A|B).
We must employ conditional probability in order to respond to this inquiry. We are aware that there are 75 pupils in the class overall, with 37 boys and 38 girls. We also know that 22 girls and 23 boys both have GPAs above the national average.
A. Boy with above-average grades equals a boy.
This claim is untrue. The likelihood of picking a guy at random from the class is 37/75, or P(boy). The likelihood of picking a kid from the class who has above-average grades at random is 23/75, or P(boy with average grades). The odds of these two events are not equal.
B. Boy with above-average grades equals P with above-average grades
This claim is untrue. The chance of picking a student with above-average grades at random from the class is P(above average grades), which is (23+22)/75 = 45/75. The likelihood of picking a kid from the class who has above-average grades at random is 23/75, or P(above-average grades boy). The odds of these two events are not equal.
P (boy with above-average grades) C (boy with above-average grades)
This assertion is accurate. P(boy over average grades) = 23/75 and P(above average grades) = 45/75, respectively, are already known values. The odds of these two events are not equal.
D. P(boy | grades over average) = P(boy)
This claim is untrue. The conditional probability that a student will have above average grades given that they are a boy is P(above average grades | boy), which is 23/37. The likelihood of picking a guy at random from the class is 37/75, or P(boy). The odds of these two events are not equal.
Therefore, the correct statement is C. P(boy above average grades) ≠ P(above average grades).
To know more about conditional probability follow
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Please help Due in 3 Min!
How do I put 4/3 on a fraction number line
Answer:
you would put it as four thirds
Step-by-step explanation:
Answer:
Lets break this down.
4/3 can be simplified as 3/3 and 1/3.
3/3 can also be simplified into 1.
That leaves us with a mixed fraction as 1 1/3.
Now that we know our mixed fraction, we must locate this on a number line.
I drew 3 marks on a number line to demonstrate this, along with a indicator showing where 1 1/3 is.
Since 1 1/3 has one whole, we know that 1 1/3 is greater than 3/3.
We locate 1 on the number line, which is directly in the middle.
Now, we have to move one more to the right, since we have a remaining 1/3.
This leaves us where we are on the photo provided.
Hope this helps! c:
What’s is Arccsc .866 problem
Answer:
arccsc refers to "arc cosecant", or the radian measure of the arc on a circle corresponding to a given value of cosecant. Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions.
what is arccsc equal to? The value of the arccsc function of any argument is an angle in radians whose cosecant function equals the given argument, that is, y = csc-1x if and only if x = cosec(y) for - /2 < y < /2 and y. ˗ˏˋ ❤︎ ࿐
Step-by-step explanation:
Mr. Duval paid $2,730 to rent a home for 6 months. Ms. Phee paid $5,496 to rent a home for 1 year. Which of the following is true?