Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.
Calculation of monthly withdrawFirst, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = A * (((1 + r)^n – 1) / r) ................................. (1)
Where,
FV = Future value of the amount after 20 years =?
A = Monthly deposit = $235.15
r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667
n = number of months = 20 * 12 = 240
Substituting the values into equation (1), we have:
FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41
The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:
P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)
Where;
P = Monthly withdrawal or payment = ?
PV = Present value = FV calculated above = $78,910.41
r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667
n = number of months = 10 * 12 = 120
Substitute the values into equation (2), we have:
P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27
Therefore, the amount that can be withdrawn each month for 10 years is $769.27.
Learn more about the present value of an ordinary annuity here: https://brainly.com/question/17112302.
#SPJ4
The answer is A: $769.27
-----------------------------------------------------------------
Have a great day and God bless! :D
19-42 evaluate the integral.
23. [tex]\int_{0}^{2}(2 x-3)\left(4 x^{2}+1\right) d x[/tex]
Expand the integrand:
[tex](2x - 3) (4x^2 + 1) = 8x^3 - 12x^2 + 2x - 3[/tex]
Then integrate using the power rule:
[tex]\displaystyle \int (8x^3-12x^2+2x-3) \, dx = 2x^4 - 4x^3 + x^2 - 3x + C[/tex]
By the fundamental theorem of calculus, the definite integral has a value of
[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=2} - \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=0}[/tex]
[tex]\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = 32 - 32 + 4 - 6 = \boxed{-2}[/tex]
What is the value of x in this figure?
O x= 30
O x = 40
O x = 60
O I don't know.
Answer:
i guess you know its 40 now. :p
Step-by-step explanation:
What transformations would result in the image shown?
Δ ABC is reflected over both axes.
Δ ABC is reflected over the y-axis and translated down 5 units.
Δ ABC is reflected over the x-axis and translated right 5 units.
Δ ABC is translated right 5 units and down 5 units.
step right up for a brainilest
Answer:
0, 2/5, 1/6,-3/4,-7/10
Step-by-step explanation:
this is just what i think i didint understand the no spaces or no commas or negatives thing but here you go i hope its right
A person invests 8000 dollars in a bank. The bank pays 6.25% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 10800 dollars
Answer:
4.8 years
Step-by-step explanation:
10 800 = 8000 e^(i t) i = decimal interest per year t = years
10800/8000 = e^(.0625 t) ln both sides
.300 = .0625 t
t = 4.8 years
The longest length of a sail on Jessica's sailboat is 12v40 feet long. Which number is equivalent to this length?
O 24140
O 4840
O 247/10
O 48V/10
Answer:48V/10
Step-by-step explanation:
I got it right from Khan Academy
A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons. One crayon is chosen at random. Write each probability as a fraction, a percent, and a decimal
The probability of getting black crayons is 0.3, blue crayons 0.2, red crayons 0.25, yellow crayons 0.15, and white crayons 0.1.
What is the probability?
Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons.
One crayon is chosen at random.
The total number of crayons = 20
The probability of getting black crayons
= 6/20
= 0.3
The probability of getting blue crayons
= 4/20
= 0.2
The probability of getting red crayons
= 5/20
= 0.25
The probability of getting yellow crayons
= 3/20
= 0.15
The probability of getting white crayons
= 2/20
= 0.1
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
jhon and jack divided their math homework, jhon solved twice as many problems as jack
Answer:
If this is your question: john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?
Answer:
John: 19
Jack: 9
Step-by-step explanation:
Hope it helps! God bless!
Please solve this in a few mins! :)
Answer:
The answer is greater than or equal to 15 which is the third answer.
Envision Math 4th grade topic 16-1
Race drivers must complete 200 laps in the Daytona 500. if Ticky Bobby only completed 57% of the race, how many laps did he complete?
Answer:
114 laps
Step-by-step explanation:
Multiply 200 x 57% :
200 x 57%200 x 57/1002 x 57114 lapsA scanner scanned 72 photos in 8 minutes. If it scans photos at a constant rate, it can scan ___ photos in 23 minutes.
Answer:207
Step-by-step explanation:
First divide 72/8 to find how many photos the scanner scans per minute which is 9
Then you multiply 9 by 23 = 207
Solve for x: 2x² - 7x - 30 = 0
Answer:
x=-10
Step-by-step explanation:
2x²-7x=0+30
2x²-7x=30
4x-7x=30
-3x=30
x=-10
Answer:
Step-by-step explanation:
(2x + 5)(x - 6) = 0
2x + 5 = 0
x = -5/2
x - 6 = 0
x = 6
You have a job that pays $25.00 for each day you show up, plus $19.00 per hour. Which expression shows the amount you make in one day if you work for h hours?
H E L P PLEASE ASAP
Answer:
19.00 x h + 25.00 =
What you make in a day if you work for h hours.
Step-by-step explanation:
You automatically make $25.00 when you show up.
So the equation is asking for how many hours. If you get $19 per hour
then it would be $19.00 x h (how many hours you worked) + $25.00.
Example:
If you worked for 5 hours and one day, then the equation would be
19.00 x 5= 95
95 + 25 (for showing up that day) = 120
So if you worked 5 hours for one day you would make 120
(This was just an example to further explain how the equation worked)
Hope this helped!
Have a great day!!
#83 will give brainliest with best response!
Answer:
[tex]\frac{31x-159}{168y}[/tex]
Step-by-step explanation:
[tex]\frac{x-4}{7y}[/tex] - [tex]\frac{x+7}{8y}[/tex] + [tex]\frac{x+3}{6y}[/tex]
the LCD of the denominators is 168y , then
[tex]\frac{24(x-4)-21(x+7)+28(x+3)}{168y}[/tex] ← distribute and simplify numerator
= [tex]\frac{24x-96-21y-147+28x+84}{168y}[/tex]
= [tex]\frac{31x-159}{168y}[/tex]
Answer:
[tex]\frac{31x - 159}{168y}[/tex]
Step-by-step explanation:
First we need to find a common denominator between 7y, 8y, and 6y. And the smallest common denominator is 336y, which I got by multiplying 7*8*6 and since they all share y, we can just keep the y without multiplying it.
Now, we need to multiply each fraction by the correct number on the top and bottom to reach 336. When we do this, we get [tex]\frac{x-4}{7y} (\frac{48}{48} ) - \frac{x+7}{8y}(\frac{42}{42}) + \frac{x+3}{6y}(\frac{56}{56})[/tex]. OMG. Well, now we need to expand the numerators...[tex]\frac{48x - 192}{336y} - \frac{42x + 294}{336y} + \frac{56x + 168}{336y} = \frac{62x - 318}{336y}[/tex]. Another OMG. But now we need to simplify...so we get [tex]\frac{31x - 159}{168y}[/tex]. Done.
Hope this helps! :)
Which statements about the cone are true? check all that apply. the radius is double the diameter. the radius is 9 mm. the base area is calculated using the radius. the volume is one-third the volume of a cylinder with the same height and diameter. the volume of the cone is 297 pi millimeters cubed.
To solve this problem, we have to understand and establish some basic mathematical facts on a cone.
The answer to this question are option b and c only.
ConeThis is a solid figure that has the base of a circle and the top is made up round triangle.
The formula of volume of a cone is given as
[tex]v = \frac{1}{3}\pi r^2 h[/tex]
where;
r = radiush = heightIn the given question, the first fact given is if the radius doubles the diameter and that false.
[tex]diameter = 2 * radius[/tex]
If we have the value of the the radius, we can calculated the base area using area of a circle
[tex]area = \pi r^2[/tex]
The volume of a cone is actually one-third the volume of a cylinder
we can only calculate the volume of the cone is we have the value of the height of the cone.
The answer to this question are option b and c only.
Learn more on volume of a cone here;
https://brainly.com/question/12004994
#SPJ4
Answer:
B, C, D, E
Step-by-step explanation:
Got it wrong the first time.
Which two numbers on the right will you use to calculate 3 x 9?
Answer:
3×9=27 the two numbers right to use is 2and7
write the smallest and greatest 5 digit number 6,8,9,5,3 digit
Answer:
Smallest- 35689
Greatest- 98653
Answer:
35689 =- least
98653 = greatest
Step-by-step explanation:
this is because we want the bigger numkbners to be at the end for the smaller number and vise vera for the greater number,
Why is cereal is packaged in rectangular boxes?
Answer:
A rectangular solid offers more volume while still maintaining a width acceptable to be gripped by one hand. Considering the average grip width available to humans is a couple inches wide, cereal boxes conform to this to allow one handed pouring.
Step-by-step explanation:
Try writing this on your own words if you want :)
solve the system of equations. {2y=6x
x^2+y=4
Answer: (1,3)and (-4,-12)
Step-by-step explanation:
find the dot product of the pair of vectors and determine whether they are normal. (4,-3) and (-3,-4)
Answer:
normal
Step-by-step explanation:
Dot Product of Vectors
Multiply x-values with x-values and same for the y-values4(-3) + (-3)(-4)-12 + 120As the dot product of the vectors equals 0, the vectors are normal.
What is the average rate of change of the function over the interval x = 0 to x = 4? f(x)=2x−13x 5 enter your answer, as a fraction, in the box.
The average rate of change of the function over the interval x = 0 to x = 4 is: 61/400.
What is the Average Rate of Change of a Function?Average rate of change = f(b) - f(a) / b - a
Given the function, f(x) = 2x - 1 / 3x + 5.
a = 0, f(a) = 2x - 1 / 3x + 5 = 2(0) - 1 / 3(0) + 5 = -1/5
b = 4, f(b) = 2x - 1 / 3x + 5 = 2(4) - 1 / 3(4) + 5 = 7/17
Average rate of change = 7/17 - (-1/5) / 4 - 0 = 61/400
Learn more about average rate of change on:
https://brainly.com/question/11627203
#SPJ4
What is h(-8) for h(x) = x²
2
-x² +7x?
Answer:
8
Step-by-step explanation:
Re-write the equation:
h(x) = x² * 2 - x² -7x
If X is equal to -8, then we can re-write the equation as:
h(-8) = (-8)² * 2 - (-8)² - 7(-8)
Following P.E.M.D.A.S. we must first solve for the exponents:
h(-8) = (64) * 2 - (64) - 7(-8)
Then we need to solve the multiplication.
h(-8) = (128) - (64) - (-56)
Now, we solve for the addition/subraction.
h(-8) = (128) - (120)
Lastly...
128 - 120 = 8
This means that if h(-8), then H = 8
I think?
I have 60 balls, 12 of them are blue, 34 of them are green and 14 of them are yellow. What is the probability that I get a blue one
Answer: As a fraction it is 1/5 but as a percent 20%
Step-by-step explanation:
this is because 12/60=1/5 or 20%
answer is 20%
heres why
ok so if there is 60 balls all together out of all the color and you want to get a blue ball but the blue has less balls out of all the other colored balls so there is would be a less percent of getting a ball of that color out of 100%
you would need to take the blue color of balls and put in a fraction with the amount of balls together
so that would be 12/60
you half 12/60 and you would need to get the percent which is 20% so you have a 20% of getting a blue colored ball
These points are linear. Find the slope.
Answer:
8
Step-by-step explanation:
Concepts
The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These points represent the x- and y-coordinates of the points.
Application
To find the slope of these points, we need to take two points and use the aforementioned formula. Let's take (0, 8), and (1, 16).
Solution
[tex]\frac{(16)-(8)}{(1)-(0)}[/tex] [tex]\frac{8}{1}[/tex] [tex]8[/tex]Therefore, the slope is 8.
Answer:
slope = 8
Step-by-step explanation:
Take 2 points from the given table:
[tex]\textsf{let}\:(x_1,y_1)=(0,8)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(-1,0)[/tex]
Use the slope formula to find the slope:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-8}{-1-0}=\dfrac{-8}{-1}=8[/tex]
express one hour in seconds,in standard form
Answer:
Hi! There are 3600 seconds in one hour.
Step-by-step explanation:
60 min. = one hour
60 seconds = one minute
:)
Nan wrote each letter in the word ILLINOIS on a separate slip of paper. She put
the slips in a bag. What is the probability of her drawing a slip that is labeled
with a vowel?
A 1/8
B. 218
C. 3/8
D. 4/8
E. 5/8
Answer:
D. 4/8
Step-by-step explanation:
To find probability, you simply divide what you are looking for over the total. In the word, ILLINOIS, you have 4 vowels, and 8 letters total, so the probability of finding a vowel would be 4/8.
A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate.
Which of the following would be an appropriate procedure for this experiment?
A)The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.
B)The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients.
C)The doctor needs to let the 30 patients choose which medication they are going to take through use of a survey to determine whether they want to participate in the experiment.
D) The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.
Answer:
B)The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients.
OR
D) The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:1,024
Step-by-step explanation:
We will use the formula hint it gives:
[tex]\displaystyle {1^{st}\;term} * \text{common ratio}\,^{(\text{desired term -1})}[/tex]
[tex]-1 * -4^{6-1}[/tex]
[tex]-1 * -4^{5}[/tex]
[tex]-1*-1,024[/tex]
[tex]1,024[/tex]
The 6th term in the sequence is 1,024.
Carl is wrapping present in the box shown. How much wrapping paper doe she need not including overlap
Answer:
164 [tex]in^{2}[/tex]
Step-by-step explanation:
We find the areas of all the faces
30 [tex]in^{2}[/tex]
30[tex]in^{2}[/tex]
40[tex]in^{2}[/tex]
40[tex]in^{2}[/tex]
12[tex]in^{2}[/tex]
12[tex]in^{2}[/tex]
add them all up to get 164[tex]in^{2}[/tex]
:)