Answer: There is a difference of $ 1.0228.
Explanation: Given, initial amount or principal = $ 1000,
Time= 5 years and given compound rate of interest = $3.7%
Now, Since the amount in compound continuously,
[tex]A= Pe^{rt}[/tex] , where, r is the rate of compound interest, P is the principal amount and t is the time.
Here, P=$ 1000, t=5 years and r= $3.7%,
Thus, amount in compound continuously , [tex]A=1000e^{3.7\times5/100}[/tex]
⇒[tex]A=1000e^{18.5}=1000\times 1.20321844013=1203.21844013[/tex]
Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013
now, Since the amount in compound quarterly,
[tex]A=P(1+\frac{r/4}{100} )^{4t}[/tex], where, r is the rate of compound interest, P is the principal amount and t is the time.
Thus, amount in compound quarterly, [tex]A=1000(1+\frac{3.7/4}{100} )^{4\times5}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A= 1202.19567617[/tex]
Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617
So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228
A 3-lb force acting in the direction of the vector (3,-1) moves an object just over 9 ft from point (0,5) to (6,-2). Find the work done to move the object to the nearest foot-pound
Answer: The Work done to move the object is [tex]=23.15 \text { foot pounds }[/tex]
Step-by-step explanation:
Given;
Force F=3 [tex]l b s[/tex]
Vectors of F= (3,-1)
Moves object to a distance=9 [tex]f t s[/tex]
Let A and B be the displacements Vectors
A= (0,-5)
B= (6,-2)
To Find:
Work done in foot-pounds
Solution:
Work done [tex]W=F \times D[/tex]
Direction of force vector= (3,-1) (i, j)
=3i-j
Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]
[tex]=\sqrt{9+1}[/tex]
Force vector=(Force/Unit Vector)Direction of force vectors
F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]
Direction of motion vector= (B-A)
= (6,-2)-(0,-5) x i,j)
=(6-0),(-2-5) x (i, j)
=(6,-7) x (i, j)
=6i-7j
Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]
[tex]=\sqrt{36+49}[/tex]
[tex]=\sqrt{85}[/tex]
Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)
[tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]
Workdone [tex]W=F \times D[/tex]
[tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]
[tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j) \times(6i-7j)][/tex]
[tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]
[tex]= [0.94867 \times 0.97619] \times [18+7][/tex]
[tex]=23.15 \text { foot pounds }[/tex]
Result:
Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]
Answer:
[tex]W = 25.617\,lbf\cdot ft[/tex]
Step-by-step explanation:
The work done to move the object is:
[tex]W = F \cdot s \cdot \cos \alpha[/tex]
The angle of the force with respect to change in the position vector is:
[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]
[tex]\alpha \approx 18.415^{\textdegree}[/tex]
The magnitude of the work done is:
[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]
[tex]W = 25.617\,lbf\cdot ft[/tex]
Can someone show me how to do this?
16! / 4! 12!
Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
Help on homework! Which of the following can have a negative effect on your credit score?
A. Getting a promotion at work
B. Late payments on a car loan
C. Paying credit card balances in full
D. low debt-to-income ratio
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?
Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
What is the answer to the jones family plans a trip to the amusement park...
Solve for x in the image below
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
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At a high school 7 student volunteer for a committtee how many different 5 person committees can be chosen
Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.
To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:
C(n, k) = n! / [k! * (n - k)!]
where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.
Applying this to the given problem, we have:
C(7, 5) = 7! / [5! * (7 - 5)!]
This simplifies to:
C(7, 5) = (7 * 6) / (2 * 1)
Therefore, C(7, 5) = 21.
There are 21 different 5-person committees that can be formed from 7 students.
Help please??????????
Please help me idk this
Answer:
1 13/20
Step-by-step explanation:
You want the total of distances walked to be the length of the hike:
2 1/10 + 1 1/4 + (left to walk) = 5
Then the amount left to walk is the difference ...
left to walk = 5 - 2 1/10 - 1 1/4
___
You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.
5 - 2 1/10 - 1 1/4
= (5 -2 -1/10) - 1 1/4
= 2 9/10 - 1 1/4
= (2 -1) + (9/10 -1/4)
= 1 + (9/10 -1/4)
= 1 + (18/20 - 5/20)
= 1 13/20 . . . miles left to walk
___
Using a calculator:
5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20
Your job pays 6$ per hour write a variable expression for your pay in dollars for working h hours what is your Pay if you work 32 hours
On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?
Answer:
Nick's car can travel 384 miles using a full tank of gas.
Step-by-step explanation:
Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
Learn more about trigonometric functions here:
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please help no will mark brainlyst
Explain how you would find 90% of 120.
What are the coordinates of the vertex of the table? Is it a minimum or a maximum?
x y
0 1
-1 -2
-2 -3
Question 1 options: A.(-4, 1); minimum B.(-2, -3); maximum C.(-2, -3); minimum D.(1, 0); maximum.
In how many different ways can the letters of the word china be arranged
Kali invests $3516 in a savings account with a fixed annual interest rate of 7% compounded 3 times per year. What will the account balance be after 7 years
PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS
Expand the number 1800 into its corresponding exponential form.
2^3 · 3^2 · 5^2
9^2 · 100
8 · 9 · 25
2^2 · 3^3 · 5^2
Select expression equal to ^3√320
4
4^3√5
5^3√4
5^3√5
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
A travel website reports that in a particular city, the probability of rain on any day in April is 40%. What is the expected number of rainy days in this city during the month of April?
**MARKING BRAINLIEST IF RIGHT AND IF YOU SHOW WORK**
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.
My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.
Jesse earns $420 a week, and he works 5 days a week. What is his daily wage?
A. $84
B. $415
C. $60
D. $425
Which path is a Hamiltonian circuit?
Silvia wants to retire at 65 and live on $40,000 a year. How much does she need to save to ensure that her retirement funds last until she is 85?
Select the best answer from the choices provided.
$800,000 because she will need to save for 20 years times $40,000
more than $800,000 because taxes and inflation will increase the value of her savings
less than $800,000 because returns will continue to increase the amount in her savings even after retirement
more than $800,000 because compound return will reduce her savings
Answer:
$800,000 because she will need to save for 20 years times $40,000
Step-by-step explanation:
Silvia wants to retire at 65 and live on $40,000 a year.
She wants to live till 85 and retire at 65 years.
So, number of years to save = [tex]85 -65= 20[/tex]
And she needs to save [tex]40000\times20=800000[/tex]
Hence, she must save 800,000.
please help with this??
A die is thrown twice. What is the probability that:
1. Neither a doublet ordered pair nor a total of 10 will appear?
2. Neither a multiple of 2 on the first throw nor a total of 6 will appear?
A. 7/9
B. 5/12
Answer:
1.)- B. 5/12
2)- A. 7/9
Step-by-step explanation: