Evaluation of E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid z = 4 - x² - y² is [tex]\frac{128}{15} + \frac{8\pi}{3}[/tex]
Cylindrical coordinates are a set of three coordinates used to locate a point in the cylindrical coordinate system.
When the polar coordinates are extended to a three-dimensional plane, an additional z coordinate is added.
These three measurements combine to form cylindrical coordinates. The coordinates describe two distances and one angle.
According to the question,
We have to find the area under paraboloid
Given : E is a region that lies under paraboloid z = 4 - x² - y² and in the first octant.
The intersection of this paraboloid with the xy plane will give z = 0,
z = 4 - x² - y² , z = 0, that is a circle x² +y² = 4 with radius 2
Therefore , 0 ≤ z ≤ 4 - r²
Therefore, the region E in cylindrical coordinates is
[tex]E = ( r , \theta , z ) | 0 \leq \theta \geq \frac{\pi}{2} , 0 \leq 4 \geq , 0 \leq z \geq 4 - r^2[/tex]
f(x , y ,z ) = x + y + z
=> f(x , y ,z ) = rcosθ + rsinθ + z
=> f(x , y ,z ) = r(cosθ + sinθ) + z
Integration ,
[tex]{\int \int \int }\limits_E {z} \,dv[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r ( cos \theta + sin \theta) + z] r \, dzdrd\theta[/tex]
simlifying,
[tex]= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r^2 ( cos \theta + sin \theta) + rz] \, dzdrd\theta\\= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [r^2 ( cos \theta + sin \theta)z + r\frac{z^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [(4r^{2} - r^{4})( cos \theta + sin \theta) + \frac{r(4 - r^2)^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(\frac{4}{3} r^{3} - \frac{r^{5}}{5})( cos \theta + sin \theta) + \frac{(4 - r^2)^3}{12}]^{2}_{0} \, d\theta[/tex]
Putting the limit and solving,
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(cos \theta + sin\theta )\frac{64}{15} + \frac{16}{3} \theta ]\, d\theta[/tex]
=> [tex][(sin\theta - cos\theta )\frac{64}{15} + \frac{16}{3} \theta ]^\frac{\pi}{2} _0[/tex]
Evaluating the limits,
[tex]\int\int\int\limits_E {x + y +z } \,dV = \frac{128}{15} + \frac{8\pi}{3}[/tex]
To know more about Cylindrical coordinates here
https://brainly.com/question/17185505
#SPJ4
There are 4 classrooms for fifth grade and 4 classrooms for sixth grade at a school. Each classroom has 20 students. A teacher is planning a field trip for some fifth and sixth grade students at this school. The teachers knows the following information:
90% of fifth and sixth grade students have permission to go on the trip.
4 teachers are going on the trip.
The school requires 1 parent volunteer for every 8 students going on the trip.
Part A
How many parent volunteers are needed to go on the trip? Show your work or explain your answer.
Enter your answer and your work or explanation in the space provided.
Answer:Żeby obliczyć ilu rodziców wolontariuszy potrzeba, najpierw trzeba obliczyć ile uczniów będzie brało udział w wycieczce. W klasie piątej jest 20 uczniów, z czego 90% ma pozwolenie na wyjazd, czyli 20 x 0,9 = 18 uczniów z piątej klasy pojedzie na wycieczkę. W klasie szóstej jest też 20 uczniów, z czego 90% ma pozwolenie na wyjazd, czyli 20 x 0,9 = 18 uczniów z szóstej klasy pojedzie na wycieczkę. Razem będzie 18 + 18 = 36 uczniów.
Szkoła wymaga 1 rodzica wolontariusza na każdych 8 uczniów, więc na 36 uczniów potrzeba 36/8 = <<36/8=4.5>>4,5 rodziców wolontariuszy. Ponieważ rodzice wolontariuszy trzeba wybrać całymi osobami, to potrzeba ich 5.
Odpowiedź: Potrzeba 5 rodziców wolontariuszy.
Step-by-step explanation:
What is the area of ΔOPQ if
a=18 b=17.5 and c=13.5
Answer:
Problem
Solution
Solve for the missing components of the triangle.
A
=
69.62591065
B
=
65.69947977
C
=
44.67460956
a
=
18
b
=
17.5
State whether each linear relationship is also a proportional correct box. Explain why or why not. If it does, writ form y=p x
Proportional relationship?
YES___
No___
Why?
y = p x is Proportional relationship.
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
The answer depends on the equation given.
If the equation is in the form y=px, where p is a constant, then it is a proportional relationship. If the equation is in the form y=mx+b, where m and b are constants, then it is not a proportional relationship.To know more about proportional relationship check the given link
brainly.com/question/28777033
#SPJ4
24) Evaluate the expression with its given values.
x/4 + 3y; x = 12, y = 2
Answer:
9
Step-by-step explanation:
[tex]\frac{12}{4}+3(2) \\ \\ =3+6 \\ \\ =9[/tex]
Answer:
Answer is 9.
Step-by-step explanation:
If x is 12, then do 12 divided by 4, and you get 3. If y is 2, then di 3 times 2, which is 6. 3 plus 6 is 9.
The functions S(t) = 1.0841t + 17.392 models the amount of money, S, in billions of dollars, the United States government spent on science, space, and technology for the time period 1999-2009, where t is the number of years since 1999.
a. Write the constraints for the variable t using set-builder notation.
b. Determine the value of S(7)
c. Interpret the value of S(7) in context
d. Name the key feature that is found when solving S(t) = 0. Then, label the key feature on the graph of S(t) = 1.084t + 17.392.
e. determine if the value for S(t) = 0 is reasonable for the context. Explain why or why not.
Hello,
I hope you and your family are doing well!
a. The variable t represents the number of years since 1999, so the constraints for t can be written as t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
b. To find the value of S(7), we substitute t = 7 into the function: S(7) = 1.084(7) + 17.392 = 22.688.
c. In context, the value of S(7) represents the amount of money, in billions of dollars, that the US government spent on science, space, and technology 7 years after 1999.
d. The key feature that is found when solving S(t) = 0 is the y-intercept of the graph of S(t). The y-intercept is the point where the graph crosses the y-axis.
e. The value for S(t) = 0 is not reasonable for the context because it represents the amount of money spent on science, space, and technology in 1999, which would be a negative number of years after 1999.
-----
Please consider giving this 5 stars if you find it helpful.
Happy Holidays!
Solve the equation for x
(x-5)/10=5
x=____
Answer:
x = 55
Step-by-step explanation:
[tex]\frac{x-5}{10}[/tex] = 5 ( multiply both sides by 10 to clear the fraction )
x - 5 = 10 × 5 = 50 ( add 5 to both sides )
x = 55
The angle of rotation, (teta), is a(n) ____ angle used to rotate the xy-coordinate plane to a new x'y'-plane for graphing a rotated conic section. A. negative B. double C. acute D. obtuse
The correct option B. double; angle used to rotate the xy-coordinate plane to a new x'y'-plane for graphing a rotated conic section.
Explain the term rotated conic section?Any curve created by intersection of such a plane as well as a right circular cone is known in geometry as a conic section, sometimes known as a conic.
The intersection can be a circle, a ellipse, a hyperbola, or a parabola, depending on the angle the plane makes with the cone.A plane curve, lines, pair of intersection points, or point that connects to or encompasses the point where a plane as well as a cone with two nappes converge.The preceding classes' conics were all of the formula Ax² + Cy² + Dx + Ey + F = 0. These conics are all either vertical or horizontal. For conics that are neither horizontal nor vertical, the B word is needed. Conics take on the generic pattern Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.Thus, teta is a double angle that is used to rotate the x-y coordinate plane into a new x'y' plane in order to graph a rotated conic section.
To know more about the rotated conic section, here
https://brainly.com/question/27273866
#SPJ4
The first four numbers in a pattern are 4,3.6,3.2 and 2.8. What is the next three next numbers in the pattern
Answer:
2.4 and 2
Step-by-step explanation:
x-0.4
Answer:
2.4, 2, 1.6
Explanation:
The sequence is counting down by 0.4.
The ratio of Pablo's age to Richard's age is 6 : 7. The ratio of Pablo's age to Tristan's age is 5 : 4. Find the ratio of Pablo's age to Richard's age to Tristan's age.
Ages of Tristan, Richard, and Pablo are in the order 6:7:4.
Detailed explanation:
Pablo is six years younger than Richard, seven years older than Tristan, and five years younger than Richard.
We can multiply the ratios of Pablo's age to Richard's age and Pablo's age to Tristan's age to determine the ratio of Tristan's age to Richard's age before determining the ratio of Tristan's age to Pablo's age.
These ratios add up to 6/7 * 5/4 = 30/28.
Pablo's age to Richard's age is 6:7, thus we may multiply this ratio by the age of Richard by Tristan's age to determine the age of Pablo, Richard, and Tristan.
Thus, the ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.
To see similar problems based on ratio and propotion cick the link below
brainly.com/question/11362061
#SPJ1
Find the value of zα.
Z0.47
The critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
What is the critical value?A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries, or the level of statistical significance for a given test.
Given:
The critical value, α = 0.47
Calculate the critical probability by the formula given below,
[tex]Z_\alpha = 1 - ( \alpha / 2)[/tex]
[tex]Z_{0.47}[/tex] = 1 - (0.47 / 2)
[tex]Z_{0.47}[/tex] = 1 - 0.235
[tex]Z_{0.47}[/tex] = 0.765 = 0.77
Therefore, the critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
To know more about critical value:
https://brainly.com/question/14508634
#SPJ1
how do i solve this question
Answer: (x-2)(x-10)
Step-by-step explanation:
1. Factor out 3x by diving everything by it, this makes the monomial 3x(x^2-12x+20)
2. From here, you do your basic factoring and reach that the answer is (x-2)(x-10)
lmk if you need more details for explanation
Which table(s) can represent values of a function? Select all that apply. Responses Input (x) 5 8 −8 −3 2 Output (y) 12 17 10 5 2 Input x 5 8 negative 8 negative 3 2 Output y 12 17 10 5 2 , Input (x) 18 20 22 24 26 Output (y) −9 −9 −6 −3 0 Input x 18 20 22 24 26 Output y negative 9 negative 9 negative 6 negative 3 0 , Input (x) 24 32 45 12 32 Output (y) 11 12 35 14 35 Input x 24 32 45 12 32 Output y 11 12 35 14 35 , Input (x) −4 8 3 −12 0 Output (y) 13 13 13 13 13 Input x negative 4 8 3 negative 12 0 Output y 13 13 13 13 13 , Input (x) 25 30 30 25 20 Output (y) 6 −2 0 13 11
The tables that represent a function are:
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
Options A, B, and D are the correct answer.
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can have many-to-one but not one-to-many.
Now,
The tables are given as,
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
This is a function.
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
This is a function.
Input x 24 32 45 12 32
Output y 11 12 35 14 35
This is not a function because it has one-to-many.
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
This is a function.
Input x 25 30 30 25 20
Output y 6 −2 0 13 11
This is not a function because it has one-to-many.
Thus,
The tables that represent a function are:
Input x 5 8 −8 −3 2
Output y 12 17 10 5 2
Input x 18 20 22 24 26
Output y -9 -9 -6 -3 0
Input x −4 8 3 −12 0
Output y 13 13 13 13 13
Options A, B, and D are the correct answer.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
You bought 8 apples at the store. The total cost was $6.00.
Let c be the cost of one apple.
Write and solve an equation to find the cost of one apple.
Answer:
Step-by-step explanation:
to put into an equation:
8c=6.00
c=6.00/8
c=$0.75
The cost of one apple is $0.75
Find the slope of the line
Answer:
1/4 and -20
Step-by-step explanation:
"Slope" just means the change in y divided by the change in x. In the first graph, the slope is the change in depth divided by the change in hours.
Using the equation, slope = (y - y1)/(x - x1), you can plug in 2 points and solve. I see that the line goes through the points (4,1) and (8,2), so I'll use these. Make sure that (x,y) are from the same point and (x1,y1) are from the same point.
slope = (2 - 1)/(8 - 4)
slope = 1/4
You can do the same process for the second graph but you'll use different points. I see the points (2,80) and (4,40), so I'll use those.
slope = (40 - 80)/(4 - 2)
slope = -40/2
slope = -20
Function 2
y=x+4
Rate of Change: 3/4 Rate of Change:
Which has the greatest rate of change?
Answer:
function 2
Step-by-step explanation:
function 1 has a slope of 8/7 which is equal to 0.75 and function 2 has a slope of 1 so function 2 is greater than function 1.
Answer: <
Step-by-step explanation:
One number is less than another number if their difference is less than zero.
Since x=2y-4 - 0.75 = -0.75 which is less than zero, x=2y-4 is less than 0.75
Therefore, x=2y-4 is 0.75 less/lower than 0.75
Write a polynomial f(x) that satisfies the given conditions
The least polynomial with degree 3 is equal to f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7.
What is the least polynomial that contains a given set of roots?
In this problem we need to determine the least polynomial such that its degree is 3 and - i 2 and 8 / 7 are roots of the resulting expression. By quadratic formula, the roots - i 2 is along with its conjugate i 2 to obtain a quadratic equation with real coefficients. The factor form of the cubic polynomial is:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.And we must determine the standard form of the polynomial by means of algebra properties. This form is shown below:
f(x) = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients.
First, write the polynomial in factor form: (a = 1)
f(x) = (x - 8 / 7) · (x + i 2) · (x - i 2)
f(x) = (x - 8 / 7) · (x² + 4)
f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7
To learn more on least polynomials: https://brainly.com/question/25667747
#SPJ1
what percentage of 64 is 16
Answer:
25%
Step-by-step explanation:
help meeeeeeeeeee pleaseee
(a) The population of the state was 18.5 million in 2000. (b) The population of the state reaches 26.6 million by 2002
What do you mean by Population?A population is a distinct collection of people, whether that group consists of a nation or a population that shares a particular trait. A population is the people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people with something in common.
(a) The right response is 18.5
Given that
t = 0,
A = 18.5
(b) 2002.
Using the formula
18.5e 0.173 x t
Given,
A= 26.6
Then,
A = 18.5 x
[tex]e^{(0.1708t)} 26.6 = 18.5 x[/tex]
[tex]\frac{26.6}{18.5}= e^{(0.1708t)}[/tex]
[tex]1.437838 = e^{(0.1708t)}[/tex]
[tex]Ln \frac{1.437838}{0.1708}[/tex]
About
t = 2.126116
t =2
As a result, 2 represents the closest year when rounding down.
To learn more about the population visit here: https://brainly.com/question/25787521
#SPJ1
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Kyle plans to invest $7000, part at 6% simple interest and the rest at 7% simple interest. What is the most that he can
invest at 6% and still be guaranteed at least $440 in interest per year?
Answer:
$5000
Step-by-step explanation:
Let x represent the amount invested at 6% interest. Then 7000-x is the amount invested at 7% interest
6% interest = 6/100 = 0.06 in decimal
7% interest = 7/100 = 0.07
Interest earned from depositing x dollars at 6% = 0.06x
Interest earned from depositing 7000-x at 7% = 0.07(7000-x)
Total interest earned would be
0.06x + 0.07(7000-x)
Since this must be at least $440 we get the equation interest as
0.06x + 0.07(7000-x) = 440
Simplifying
0.06x + 0.07 x 7000 - 0.07x = 440
0.06x + 490 -0.07x = 440
-0.01x = 440 - 490
-0.01x = -50
Multiply both sides by -1
==> 0.01x = 50
==> x = 50/0.01 = 5000
So max amount that can be invested at 6% interest = $5000
Please help a lot of points!! Will put bainliest answer!
Answer:
I haven't got a real clue
Step-by-step explanation:
I did some learning about it, I may be wrong(most likely)
but I think it might be SAS.
The shape can be proven congruent.
if you can find an angle which I think is H and K then most likely SAS. If this is a test and is very important then don't listen to this I am most likely wrong
Select all the expressions which are equivalent to 910x − 2.
A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is known as an algebraic expression.
What is an Algebraic Expression?A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division.In most cases, something is said to be equivalent if two of them are the same. Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning. The two expressions, however, produce the identical outcome when the values are inserted into them.Example910x − 2
simplify | 910 x - 2
2 (455 x - 1).
To Learn more About Algebraic Expression, refer To:
https://brainly.com/question/4344214
#SPJ1
Billing charges for Microsoft 365 Commercial licensing. When a customer purchases a subscription and changes the amount during the subscription period, a full refund is credited then prorated for what was used. For example, if a customer purchased 2 subscriptions for the month of June at $15 each, the total charge for the month would be $30. If they decide to return one subscription 5 days later, the full $30 would be credited then a prorated charge for what was used would be applied. Credit $30 Charge $15 Charge $0.5 * 5 = $2.50 $15 / 30 = $0.5 p/day Total Charge $17.50 Total Credit $12.50 If a customer purchases 10 Microsoft 365 Business Premium licenses at $22 each per month, for a full year then 6 months later decides they only need 5 licenses for the remainder of the year, what would be the total charge and credit for the year?
The customer who purchases 10 Microsoft 365 Business Premium licenses at $22 each per month, for a full year, then 6 months later decides they only need 5 licenses for the remainder of the year, would pay a total charge of $1,980 with a credit of $660 for the year.
How are the total charge and credit computed?The total charge the customer will pay is based on the difference between the total charge for the year and the prorated charge of credit for non-usage.
The charge per month for Microsoft 365 = $22
The charge per month for 10 Microsoft 365 = $220 ($22 x 10)
The charge for 1 year for one Microsoft 365 = $264 (22 x 12)
The charge for 6 months for 10 Microsoft 365 = $1,320 ($220 x 6)
The charge for 12 months for 10 Microsoft 365 = $2,640 (220 x 12)
The prorated charge for 6 months for 5 Microsoft 365 returned = $660 ($2,640 x 5/10 x 6/12)
The initial total charge for the year = $2,640
The total credit for the year = $660
The total charge for the year = $1,980 ($2,640 - $660)
Thus, the customer will pay $1,980 after receiving a prorated credit for 5 returned licenses worth $660.
Learn more about the total charge and proration at https://brainly.com/question/16028802
#SPJ1
For the function f(x) = 5(x - 5)7, find f-¹(x).
Answer:
Step-by-step explanation:
Marta's family plans to sell their kitchen table and buy a new one. Marta originally wrote down the length of their old table as 1,602.5 centimeters. She realized she made a mistake and that the table has an actual length of 162.5 centimeters.
Which of the statements correctly compares the digits in the original measurement and the actual measurement?
A. The value of the digit 5 in the original measurement is 10 times the value of the digit 5 in the actual measurement.
B. Removing the digit 0 in the original measurement did not change the value of any digits in the actual measurement.
C. The value of the digit 1 in the actual measurement is 110 the value of the digit 1 in the original measurement.
D. The digit 6 has the same value in both the original measurement and the actual measurement.
The correct option is the value of the digit 1 in the actual measurement is 110 the value of the digit 1 in the original measurement. (option C)
What are the value of the digits in the measurement?Here is the place value of each of the digits in the wrong table length :
1 = thousand
6 = hundred
0 = tens
2 = units
5 = tenth
Here is the place value of each of the digits in the actual table length :
1 = hundred
6 = tens
2 = units
5 = tenth
5 has the same value in both the wrong length and the right length.
The value of 6 in the actual measurement is ten times that of the wrong measurement .
To learn more about measurement, please check: https://brainly.com/question/29405166
#SPJ1
A university has 25,000 students, of whom 10,000 are older than 25. The registrar draws a simple random sample of 400 students. a) Find the expected value and SE for the number of students in the sample who are older than 25. b) Find the expected value and SE for the percentage of students in the sample who are older than 25. c) The percentage of students in the sample who are older than 25 will be around _____, give or take _____ or so.
The expected value is 160 and SE for the number of students in the sample is 9.78
a)Given: students of which 25000 of which 10000 are older than 25 and 25000-10000=15000 are not older than 25.
we represent 400 students by drawing 400 tickets from a box that contains 15000 tickets labeled 0 and 10000 tickets labeled 1
Expected value and standard deviation of a box:
First, we determine the expected value of the box, which is the sum of all values on the tickets by the number of tickets.
[tex]expected value box=\frac{15000*0+10000*1}{25000}\\\\ =\frac{10000}{25000} =\frac{2}{5}[/tex]
expected value box=0.4
let us next determine the standard deviation using the shortcut formula:
SD=(big number-small number)*√fraction with small number*fraction with a small number.
[tex]SD=(1-0)*\sqrt{\frac{10000}{25000} *\frac{15000}{25000} \\\\SD=1*\sqrt{\frac{2}{5} *\frac{3}{5} } \\SD=1*\sqrt{\frac{6}{25} } =\frac{\sqrt{6} }{5}[/tex]
SD=0.4899.
Expected value sum=Number of draws*expected value box
=400*0.4
Expected value sum=160
standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
SE Sum=√number of draws*SD box
SE Sum=√400*0.4899
=20*0.4899
SE Sum=9.78
b)EXpected value and standard error:
The expected value of the percentage is the expected value of the sum divided by the number of draws.
Expected value percentage=Expected value sum/Number of draws*100%
160/400*100
=0.4*100%
Expected value percentage=400%
The standard error of the percentage is the standard error for the sum divided by the sample size:
SE%=SE for number/Number of draws*100%
=9.798/400*100%
=0.0245*100%
SE% =2.45%
To learn more about Expected value:
https://brainly.com/question/24316739
#SPJ4
Andrew Industries purchased $163,000 of raw materials on account during the month of March. The beginning Raw Materials Inventory balance was $21,600, and the materials used to complete jobs during the month were $139,200 of direct materials and $12,800 of indirect materials. What is the ending Raw Materials Inventory balance for March?
The ending Raw Materials Inventory balance for March is 31,800.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main Body:
We use the Inventory identity to solve for ending inventory
Beginning Inventory + Purchase = ending Inventory + used
20,800 +159,000 = ending inventory + used materials
used materials:
135,600 direct
12,400 indirect
148,000 total materials used
20,800 + 159,000 = Ending Inventory + 148,000
20,800 + 159,000 - 148,000 = Ending Inventory
Ending Inventory = 31,800
Hence the ending Raw Materials Inventory balance for March is 31,800.
To know more about arithmetic , visit:
https://brainly.com/question/24536701
#SPJ1
HELP THANK YOU SO MUCH
Answer:
x = 3
Step-by-step explanation:
Since ∠CAT = ∠DOG, ∠CAT = ∠DGO
Therefore AC = DO
8x - 6 = 3x + 9
8x - 3x = 9 + 6
5x = 15
x = 15/5
x = 3
Mrs. James is on a train traveling 42 m.p.h. As Mrs. James is looking out the window, a freight train traveling at 18 m.p.h. moving in the opposite direction meets and passes her. She noticed it took 8 seconds for the freight train to pass her. The freight train is ___ feet long.
The freight train is 88.88 feet long.
What is Speed- Distance Formula?Speed = Distance/Time
Distance = Speed X Time
Time = Distance / Speed
As the trains travel in opposite direction then
Relative speed = (42 + 18) = 60 Km/ hr
= 60 x 5/18 = 300/ 18
= 100/9 m/s
So, length of the freight train = 100/9 x 8
= 88.88 feet
Hence, The freight train is 88.88 feet long.
Learn more about speed- distance formula here:
https://brainly.com/question/26209051
#SPJ1
Music Company A charges a $ 15 membership fee and $ 0.75 each to download a song. Music Company B charges $ 0.90 each to
download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
____songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of
money? Justify your answer using mathematics.
(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.
(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
Let, Songs Downloaded be x
Total Charges of Company A = 15 + 0.75*x
Total Charges of Company B = 0.9*x
(i) Total Charges by Company A = Total Charges by Company B
15 + 0.75*x = 0.9*x
15 = 0.15*x
x = 100 songs
(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150
= 15 + 112.5 = $127.5
Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135
I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
To learn more about Linear Equation in One Varibale from the given link
brainly.com/question/85774
#SPJ4