[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]
Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]
Answer:
[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus (Line Integrals)
Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]
Div and Curl:
[tex]\displaystyle \text{div \bf{F}} = \nabla \cdot \textbf{F}[/tex][tex]\displaystyle \text{curl \bf{F}} = \nabla \times \textbf{F}[/tex]Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]
Step-by-step explanation:
*Note:
Your question is incomplete, but I have defined the missing portions of the question below.
Step 1: Define
Identify given.
[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]
[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]
Step 2: Find Flux Pt. 1
[Vector Field] Find div F:Step 3: Find Flux Pt. 2
[Flux] Define:We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]
[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]
∴ [tex]\displaystyle \Phi = \boxed{6875}[/tex]
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Topic: Multivariable Calculus
Unit: Stokes' Theorem and Divergence Theorem
A city in the country determines public servants different than usual. The city asks citizens to rank candidates and the person with the highest point total wins. First place votes get 4 points, second place votes get 2 points and third place votes get 1 point. If John Tyler received 867 first place votes, 301 second place votes and 432 third place votes, how many total points did he obtain?
A) 1600
B) 2467
C) 3370
D) 4502
First Place Vote: 4x867= 3468
Second Place Vote: 2x301= 602
Third Place Vote: 1x432= 432
3468+602+432= 4502.
Your answer is therefore D.
I hope this helps! :)
Answer:
D) 4502
Step-by-step explanation:
It is given that,
Points for first place = 4 points
Second place = 2 points
Third place = 1 point
Thus, First Place Vote : 4 × 867 = 3468
Second Place Vote: 2 × 301= 602
Third Place Vote: 1 × 432= 432
Thus, Total Points = 3468 + 602 + 432 = 4502.
Hence, last option is correct.
20. what is the missing value to the nearest hundredth
tan _ = 15
• 0.97°
• 0.27°
• 88.09°
• 86.19°
Answer:
86.19°
Step-by-step explanation:
Let x represent the missing value.
The given trigonometric equation becomes:
[tex]\tan x=15[/tex]
We take the inverse tangent of both sides to obtain:
[tex]\tan^{-1}(\tan x)=\tan^{-1}(15)[/tex]
This implies that;
[tex]x=\tan^{-1}(15)[/tex]
We use at least a scientific calculator to evaluate this and obtain:
[tex]x=86.18592517\degree[/tex]
To the nearest hundredth, the missing value is [tex]x=86.19\degree[/tex]
Mahmoud spent 1/6 of the day working in the flower bed Mahmoud spent 2/3 of that time adding mulch to the flower bed what fraction of the day did Mahmoud spend adding mulch?
Answer: 5/6
Step-by-step explanation:
Add both of the fractions.
1/6+ 2/3
Need to make the denominator the same for both fractions.
Denominator would be 6. Multiply by 2 up and down for 2/3
1/6+4/6
5/6
Harold moves no more than 43 of his sheep and goats into another field. Fewer than 22 of his animals are goats.
Let s represent the number of sheep and g represent the number of goats identify two inequalities that represent this situation.
A. g<22
B. s>22
C. s+<43 with the line under
D. s-g<45 with the line under
Answer:Options 'A' and 'C' are correct.
Step-by-step explanation:
Let the number of sheep be 's'.
Let the number of goats be 'g'.
According to question, we have given that
the number of sheep and goats are not more than 43.
The number of goats are fewer than 22.
So, the inequalities would be
[tex]g<22\\\\and\\\\s+g<43[/tex]
Hence, Options 'A' and 'C' are correct.
The two inequalities for Harold's sheep and goats situation are A. g < 22 and C. s + g ≤ 43.
To represent the situation described about Harold's sheep and goats, we need to set up two inequalities based on the given information:
A. g < 22: This inequality indicates that the number of goats (g) is fewer than 22.C. s + g ≤ 43: This inequality means that the total number of sheep and goats combined (s + g) is at most 43.Using these inequalities, we can help Harold determine how to distribute his sheep and goats in the new field.
Solve the equation of e^x-2=(1/e^6)^x+3.
Answer:
x = -16/7
Step-by-step explanation:
The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...
x ≈ 1.60945071137
_____
Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...
e^(x-2) = (1/e^6)^(x+3)
x -2 = -6(x +3) . . . . . . . . take the natural log of both sides
x -2 = -6x -18 . . . . . . . . . eliminate parentheses
7x -2 = -18 . . . . . . . . . . . add 6x
7x = -16 . . . . . . . . . . . . . add 2
x = -16/7
HELPPPPPPP Consider the equation 3/4 y = 2.4x. Solve the equation for y. What is the constant of proportionality?
1.8y is the answer because first you do 3/4y into a decimals number and then it’s 0.75 then I times it by 2.4 which is 1.8y
To solve the equation 3/4 y = 2.4x for y, we multiply both sides of the equation by 4/3 to eliminate the fraction. Simplifying the equation gives us y = 3.2x. The constant of proportionality in this equation is 3.2.
Explanation:To solve the equation 3/4 y = 2.4x for y, we need to isolate y on one side of the equation. First, we can multiply both sides of the equation by 4/3 to eliminate the fraction:
3/4 * y = 2.4x
y = (2.4x)/(3/4)
Next, we can simplify the equation by multiplying the numerator and denominator of the fraction by the reciprocal of 3/4, which is 4/3:
y = (2.4x) * (4/3)
y = (9.6x)/3
y = 3.2x
Therefore, the equation 3/4 y = 2.4x can be solved for y to give the expression y = 3.2x. The constant of proportionality in this equation is 3.2, which indicates that y is directly proportional to x with a scale factor of 3.2.
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Amir pitches a baseball at an initial height of 6 feet, with a velocity of 73 feet per second. If the batter misses, about how long does it take the ball hit the ground?
Hint: Use H(t) = −16t2 + vt + s.
4.64 seconds
2.94 seconds
2.28 seconds
0.08 second
Answer:4.64
Step-by-step explanation: I took the test on this and it was correct
Answer:
4.64
Step-by-step explanation:
bcuz sir ghost said so
Jesse wants to go skydiving. Each skydive is 14,000 feet high. Jesse wants to do 2 jumps which will cost him $400. In addition, Jesse must pay a $100 training fee. What is the price per foot of skydive if the training fee is added to the final price?
Answer:
Price per foot of skydive is 31.11 repeated, or 31 1/9
Step-by-step explanation:
Jesse is going on 2 jumps, which is 14000*2=28000.
Each Skydive is $400, and two jumps would be $800. Plus a $100 training fee, it would cost $900 for 2 jumps.
28000/900=31.1111 repeated.
Jada,Elena,and lin walked a total of 37 miles last week. Jada walked 4 more miles than Elena, and Lin walked two more miles than jada.
What is your question??
Identify the surface area of the composite figure. HELP PLEASE!!
The total surface area for the figures aee;
1) 128 m²
2) 714 in²
How to find the surface area?1) To find the surface area, we need to find the area of each surface that makes up the object and add together.
Thus:
T.S.A = 4(4 * 4) + (4 * 4) + 4(½ * 4 * 6)
T.S.A = 128 m²
2) The total surface area here is;
T.S.A = 2(15 * 10) + 2(10 * 7) + 2(15 * 7) + 4(4 * 4)
T.S.A = 714 in²
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The volume of a rectangular prism is 3 25/36 cubic units, and the base area of the prism is 3 1/6 square units. The height of the rectangular prism is a. 1 1/6units b. 1 1/2 units c. 3 1/6 units d. 3 1/3 units. The number of cubic blocks, each with a volume of 1/36 cubic units, needed to fill the rectangular prism is a. 7 b. 19 c. 133 d. 152. ?
Answer:
The height of the prism is [tex]1\frac{1}{6}[/tex] units ⇒ answer a
The number of blocks needed is 133 ⇒ answer c
Step-by-step explanation:
* Lets explain how to solve the problem
- The volume of a rectangular prism is
→ V = Area of the base × its height
- The volume of the rectangular prism is [tex]3\frac{25}{36}[/tex] units³
- The area of its base is [tex]3\frac{1}{6}[/tex] units²
- Substitute the values of the volume and area of the base in the rule
∴ [tex]3\frac{25}{36}=3\frac{1}{6}*h[/tex]
- Divide the two sides by [tex]3\frac{1}{6}[/tex]
∴ [tex]h=\frac{7}{6}=1\frac{1}{6}[/tex] units
* The height of the prism is [tex]1\frac{1}{6}[/tex] units
- The volume of each cubic block is [tex]\frac{1}{36}[/tex] units³
- The number of blocks = volume of the prism ÷ volume of the block
∵ The volume of the prism is [tex]3\frac{25}{36}[/tex] units³
∵ The volume of each block is [tex]\frac{1}{36}[/tex] units³
∴ The number of blocks = [tex]3\frac{25}{36}[/tex] ÷ [tex]\frac{1}{36}=133[/tex]
∴ The number of blocks = 133
* The number of blocks needed is 133
Answer:
1st one is 1 1/6
2nd one is 133
I did the test on Plato and this was right :)
Write the equation of the circle in general form. Show all of your work.
Answer:
x^2 + y^2 + 6x - 8y + 21= 0.
Step-by-step explanation:
The center of this circle is (-3, 4) and the radius id 2.
So in Standard form, the equation is:
(x + 3)^2 + ( y - 4)^2 = 2^2
Converting to General form we have:
x^2 + 6x + 9 + y^2 - 8y + 16 = 4
x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0
x^2 + y^2 + 6x - 8y + 21= 0.
During a weekend sale, a store sold 85 DVDs for $19 each. What is the total amount of money, rounded to the nearest hundred, the store made by selling DVDs?
Answer:
$1615.00
Step-by-step explanation:
In a game a die numbered 9 through 14 is rolled. What is the probability that the value of a roll will be a multiple of two or ten?
Answer:
Step-by-step explanation:
This is a special die. Its six sides bear the numbers {9, 10, 11, 12, 13, 14}.
There are three possibilities for getting a multiple of two: {10, 12, 14}, and
there is only one possibilities for getting a multiple of ten: {10, 12, 14}
The probability here of getting a multiple of two is 3/6, and that of getting a multiple of ten is 1/6. But one of the outcomes is found in both result sets: 10. Getting a multiple of 10 is already included in the event that the outcome is a multiple of two. My answer here would be 3/6, or 1/2.
the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.
The probability of rolling a multiple of two or ten on a die numbered 9 through 14 can be calculated as follows:
Numbers that are multiples of two in the given range are 10, 12, and 14, which are 3 possibilities.Numbers that are multiples of ten in the given range are 10, which is 1 possibility.Therefore, the total favorable outcomes are 3 (for multiples of two) + 1 (for a multiple of ten) = 4. The total possible outcomes from 9 through 14 are 6.Hence, the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.\
16.4
19.6
10.6
21.2
question 45
Answer: FIRST OPTION
Step-by-step explanation:
You need the formula for calculate the arc lenght:
[tex]arc\ length=2\pi r(\frac{C}{360})[/tex]
Where "r" is the radius and and "C" is the central angle in degrees.
You know that the radius is:
[tex]r=7.5[/tex]
And the central angle ∠CAT is:
[tex]C=\angle CAT=125\°[/tex]
Then, you need to substitute these values into the formula [tex]arc\ length=2\pi r(\frac{C}{360})[/tex] to calculate the length of CT.
Then, this is:
[tex]arc\ length=CT=2\pi (7.5)(\frac{125\°}{360})[/tex]
[tex]arc\ length=CT=16.4[/tex]
What is the five-number summary for the data set?
76, 100, 88, 83, 97, 94, 90, 99, 82, 86, 95, 81, 79, 95
Enter your answers in the boxes.
Minimum:
First quartile:
Median:
Third quartile:
Maximum:
Answer:
Min: 76
Q1: 82
Med: 89
Q2: 95
Max: 100
Step-by-step explanation:
First arrange the data set 76, 100, 88, 83, 97, 94, 90, 99, 82, 86, 95, 81, 79, 95 in ascending order:
76, 79, 81, 82, 83, 86, 88, 90, 94, 95, 95, 97, 99, 100
The minimum number is 76 and the maximum number is 100. There are 14 numbers, the median is the average of two middle terms:
[tex]Med=\dfrac{88+90}{2}=89[/tex]
The middle term of first 7 numbers is 82 and the middle term of the second seven numbers is 95, so the five-number summary is
Min: 76
Q1: 82
Med: 89
Q2: 95
Max: 100
A football team lost a total of 56 yards in their first game. Which expression results in an integer that represents the team's average per quarter? IF YOU DON"T KNOW THE ANSWER PLEASE DON'T ANSWER! AND PROVIDE AN EXPLANATION IF YOU CAN!
F. \frac{-56}{4}
G. -56 Divided by 25
H -56 divided by (-4)
J. \frac{56}{-25}
Answer:
F
Step-by-step explanation:
You have to divide the the total number of yards lost (so 56) by 4 quarters. We know that lost yards are negative so therefore -56 divided by 4 is the answer
Question 6 Gradpoint Math Question Please Help
Answer:
The right answer is 3a - 11 ≤ 7 ⇒ 4th answer
Step-by-step explanation:
* Lets study the problem
- From the figure
# The blue line started from 6 and the point is bold that means
the inequality sign is ≤ or ≥
# The blue line started from 6 and moved to the negative numbers
that means the inequality is less than or equal
∴ a ≤ 6
* Now lets look to the answers
- There is only one answer has the sign ≤ , the last answer
* Now lets solve it to be sure
∵ 3a - 11 ≤ 7 ⇒ add 11 to the both sides
∴ 3a ≤ 18 ⇒ divide the both sides by 3
∴ a ≤ 6
* The right answer is 3a - 11 ≤ 7
A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per second. The equation h = ?16t2 + 40t + 30 models the projectile's h height at t seconds. How long will it take for the projectile to hit its target on the ground? (to the nearest tenth of a second)
Answer:
t = 3.1 seconds
Step-by-step explanation:
Set the equation h = -16t^2 + 40t + 30 equal to 0 (0 represents ground level).
Then h = -16t^2 + 40t + 30 = 0
Applying the quadratic formula with a = -16, b = 40 and c = 30,
-40 ± √( 1600 - 4[-16][30] )
t = -----------------------------------------
2(-16)
-40 ± √ 3520
t = -------------------------
-32
-40 - 59.33
Only the positive t value makes sense. It is t = ------------------
-32
t = 3.1 seconds
The sum of two numbers is equal to 63 and their difference is equal to 12. Find the numbers.
Answer:
a + b = 63
a - b = 12
So, a - b = 12 which can also be written as a = b + 12
Then use substitution and plug in (b + 12) for a in the first equation
(b+12) + b =63
-12 -12
---------------------
2b = 51 so b=25.5
Now, you know b which can be used to find a
63- 25.5= 37.5
So, a = 37.5 and b = 25.5
Answer:
25.5 and 37.5
Step-by-step explanation:
37.5-12=25.5
25.5+37.5=63
Which of the following is equal to sqrt. (50(a^6) (b^7))
Answer:
5 · a³ · b³ · √5b
Step-by-step explanation:
Start with √(50a^6b^7). Rewrite 50 as the product of the largest possible perfect square and a multiplier: 50 = 25 · 2. Then √50 = 5√2.
a^6 is already a perfect square, so find its square root: √a^6 = a^3.
b^7 = b · b^6, so √b^7 = b^3√b
Now rewrite (50(a^6) (b^7)) as √(50a^6b^7).
Then rewrite √(50a^6b^7) as 5√2 · a³ · b³ · √b.
This latter result can be simplified to 5 · a³ · b³ · √5b
This matches possible answer #1.
Please answer fast!!! Will give brainliest!!!
given: m∠EYL= 1/3 m arc EHL Find: m∠EYL.
Answer:
The measure of angle EYL is [tex]45\°[/tex]
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
Let
x-----> the measure of arc EVL
y----> the measure of arc EHL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
[tex]m<EYL=\frac{1}{3}(y)[/tex]
so
[tex]\frac{1}{3}y=\frac{1}{2}(x-y)[/tex]
Multiply by 6 both sides
[tex]2y=3x-3y[/tex]
[tex]3x=5y[/tex]
[tex]x=\frac{5}{3}y[/tex] -----> equation A
[tex]x+y=360\°[/tex] -----> equation B ( is a complete circle)
substitute equation A in equation B
[tex]\frac{5}{3}y+y=360\°[/tex]
[tex]\frac{8}{3}y=360\°[/tex]
[tex]y=(360\°)*(3)/8=135\°[/tex]
Find the value of x
[tex]x=\frac{5}{3}(135\°)=225\°[/tex]
Find the measure of angle EYL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
substitute the values
[tex]m<EYL=\frac{1}{2}(225\°-135\°)=45\°[/tex]
What are the domain and range of the piecewise function below? HELP ASAP
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
[tex](-\infty,6)\cup(6,\infty) = \mathbb{R}\setminus\{6\} = \{x \in \mathbb{R}\ :\ x\neq 6\}[/tex]
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is
[tex](-\infty,-2)\cup[0,\infty) = \mathbb{R}\setminus [2,0) = \{x \in \mathbb{R}\ :\ x\geq 0\ \lor\ x<-2\}[/tex]
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is
If the volume of a rectangular prism is 1440cm, width is 5cm length is 2cm what is the height
Answer:144
Step-by-step explanation: 144 since width times length times height equals volume. so 5 times 2 times ? equals 1440. So 10 times ? equals 1440. So next 1440 divided by 10 equals 144. So the answer is 144.
Answer:
Step-by-step explanation:
144 cm.
jason answered 12 questions correctly on a test worth 150 points. each question was worth 10 points. what percent did jason earn on the test?
Answer:
He earned 120% out of 150%.
Step-by-step explanation:
The test is work 150 points, while each question being 10 points each, so we can divide this and we will get 15 questions. Then we can just multiple, 10 by 12 and get 120, this means he got 12 out of 15 questions right, or 120%out of 150%.
The following image is a graph of f(t)= a sin(bt+c)+d. Use the graph to determine the amplitude, period, phase shift, and vertical shift of the function.
Answer:
Step-by-step explanation:
b.)
amplitude: 4
period; 4pi
phase shift; pi/2
vertical shift: -3
Analyzing the graph shows that the parameters are in
b. amplitude: 4
period; 4π
phase shift; π/2
vertical shift: -3
What is amplitude?Amplitude: The amplitude of a periodic function is the measure of its maximum displacement from its average or equilibrium position.
Period: The period of a periodic function is the distance along the x-axis between one cycle of the function and the next identical cycle.
Vertical Shift: The vertical shift (or translation) of a function is a vertical displacement of the entire graph either upward or downward.
Phase Shift: The phase shift is a horizontal displacement or translation of a function.
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Help Me PLZZZZZZZ
Raoul's taxable income is $38,438. He is filling as head of household, and he has already paid $4428 in federal taxas.
What will he receive or pay after he figueres his taxas for the year?
Options:
A. He will receive a refund of $908
B. He will pay $908
C.He Will receive a Refund of $916
D.He will pay $916
Answer:
He will pay 916
Step-by-step explanation:
Find the Area of the circle
Answer: 530 cm^2
Step-by-step explanation:
A = 3.14 * r^2
A = 3.14 * 13 * 13
A = 3.14 * 169
A = 530 cm ^2
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
The wide would be 7.2 cm
Step-by-step explanation:
Let
x------> the wide of the proportional wall map
we know that
Using proportion
45/27=12/x
x=27*12/45
x=7.2 cm
Edward wants to have $50,000 in 10 years for college. What single deposit would he need to make now into
an account that pays 4.3% interest, compounded daily, to meet his goal?
Answer:
[tex]\$32,526.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$50,000\\ r=0.043\\n=365[/tex]
substitute in the formula above
[tex]\$50,000=P(1+\frac{0.043}{365})^{365*10}[/tex]
[tex]P=\$50,000/[(1+\frac{0.043}{365})^{3,650}]=\$32,526.28[/tex]