Determine The Angle Between The Planes √3x+2-5 = 0 And 2x+2-√3z +10=0,

Answers

Answer 1

The values in the formula for the cosine of the angle between the planes:

[tex]\frac{{2\sqrt 3 }}{{3\sqrt 3 }} = \frac{2}{3}\][/tex]

The angle between the planes is: 48.19 degrees.

The angle between the planes, √3x + 2 − 5 = 0 and

2x + 2 − √3z + 10 = 0

can be determined using the formula:

[tex]\[\cos \theta =n_1.n_2[/tex]

where [tex]\[\cos \theta \][/tex] is the angle between the planes and [tex]n_1[/tex] and [tex]n_2[/tex]

are the normal vectors to the planes.

The normal vectors can be written as:

[tex]\[{n_1} = \left\langle {\sqrt 3 ,0,0} \right\rangle \]and \[{n_2} = \left\langle {2,0, - \sqrt 3 } \right\rangle \][/tex]

The dot product of the normal vectors can be calculated as:

[tex]\[{n_1}.{n_2} = \left\langle {\sqrt 3 ,0,0} \right\rangle .\left\langle {2,0, - \sqrt 3 } \right\rangle \\= \sqrt 3 \times 2 + 0 + 0 = 2\sqrt 3 \][/tex]

Magnitude of [tex]\[{n_1}\][/tex] can be calculated as:

[tex]\[\left\| {{n_1}} \right\| = \sqrt {{{\left( {\sqrt 3 } \right)}^2} + {{(0)}^2} + {{(0)}^2}} \\= \sqrt 3 \][/tex]

Magnitude of [tex]\[{n_2}\][/tex]

can be calculated as:

[tex]\[\left\| {{n_2}} \right\| = \sqrt {{{\left( 2 \right)}^2} + {{(0)}^2} + {{\left( { - \sqrt 3 } \right)}^2}} = 3\][/tex]

Now, we can plug the values in the formula for the cosine of the angle between the planes:

[tex]\[\cos \theta =n_1.n_2\\ = \frac{{2\sqrt 3 }}{{3\sqrt 3 }} = \frac{2}{3}\][/tex]

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Related Questions


How many bit strings of length 8 can you have if each string has
only two zeros that are never together

Answers

There are 28 different bit strings of length 8 that satisfy the condition of having two zeros that are never together.

To count the number of bit strings of length 8 with two zeros that are never together, we can use the concept of combinations.

First, let's consider the possible positions for the two zeros. The zeros cannot be adjacent to each other, which means they must be placed in non-adjacent positions in the string.

Since there are 8 positions in the string, we can choose 2 positions for the zeros in C(8, 2) ways. This gives us the number of ways to select the positions for the zeros.

Once we have chosen the positions for the zeros, the remaining 6 positions must be filled with ones. There is only one way to do this, as all the remaining positions will be filled with ones.

Therefore, the total number of bit strings of length 8 with two zeros that are never together is equal to C(8, 2) = 28.

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What is the volume of the can below? Use Pi = 3.14 and round your answer to the nearest tenth. A cylinder with height 96 millimeters and diameter of 66 millimeters.

Answers

Answer

328,268.2 mm cubed is correct!

Step-by-step explanation:

If you use the formula V=πr²h with these steps:

1. Calculate the area of the base (which is a circle)

2. use the equation πr² where r is the radius of the circle.

3. Then, multiply the area of the base by the height of the cylinder

4. The volume is found!

Answer:

328,268.2 cubic millimeters

Step-by-step explanation:

I did it on edge

Expand x(4 --3.4y) show FULL work

Answers

Answer:

4x - 3.4xy

Step-by-step explanation:

x(4 - 3.4y)

4x - 3.4xy

PLEASE HELP ME OUT! QUICK POINTS FOR YOU!

All information needed can be found in the image below
Thank you in advance.

Answers

Answer:

circle area = 50.24 units²

Step-by-step explanation:

circle area = πr² = 3.14(4²) = 3.14(16) = 50.24 units²

I really need help with this

Answers

Answer:add 11 on both sides sorry

Answer: subtract 11 from both sides

Step-by-step explanation: this was an assigned assignment for me two days ago

What percent of a day does this child spend doing homework? (Round to the nearest whole percent)

Answers

Answer:

Step-by-step explanation:

Look at the graph, look at homework and then look at the number right outside of it.

Please answer correctly! I will mark you as Brainliest!

Answers

Answer:

I have actually done this before, I got it right and I chose C!

hope this helps. love u guys!

Answer:

The 4th answer choice

Explain:

195 divided by 3 is 65. Then the diameter of 307 needs to be divided by 2 to get the radius. Now take the radius and square it to get 23562.25. Now times 3.14. Lastly, multiply by the 65 to get 4809055.225. Hope that helps! :)

Does the residual plot show that the line of best fit is appropriate for the data?

Answers

The correct statement regarding the residual plot in this problem, and whether the line of best fit is a good fit, is given as follows:

Yes, the points have no pattern.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, hence it is defined by the subtraction operation as follows:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, and no pattern between the residuals.

As there is no pattern between the residuals in this problem, the line is in fact a good fit and the first option is the correct option.

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8 divided by 618 ..............

Answers

Answer:

0.0129449838188

0.01294498

that’s your answer

if T= 101+102+103+...+199 find T

Answers

...............................................

PLEASEEEE HELP ‼️‼️1️⃣

Answers

Answer:

8/7

Step-by-step explanation:

12*2=24.

7*3=21

24/21 is divisible by 3

=8/7

Caught error while evaluating the code in this question: syntax error, unexpected" Let S be the universal set, where: Let sets A and B be subsets of S, where: LIST the elements in the set (AUB) [(AUB)]={ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.

Answers

The solution to the problem is `{5, 10, 15, 20, 25, 30}`.

The error message "syntax error, unexpected" is a common message you might encounter when there is a syntax error in your code.

This error message often points to an unexpected symbol or typo in your code. For instance, in the context of a code snippet like this, such an error message could be prompted due to an invalid command or misspelling, or a misused symbol or expression.

Also, another likely cause could be an incorrect use of a function or a non-existent variable or keyword. Hence, to solve the error message, you might need to double-check your code and fix any errors that could cause such an issue. Now, let's answer the question that follows: Given the universal set, S, as;`S = {5, 10, 15, 20, 25, 30}` and the subsets A and B as; A = {5, 10, 15, 20} B = {15, 20, 25, 30}.

To list the elements in the set (AUB) we need to find the union of A and B. The union of two sets A and B is a set of all the elements that are either in A or in B or in both. That is, `AUB = {x: x ∈ A or x ∈ B}`

Therefore, the union of sets A and B is the set `AUB = {5, 10, 15, 20, 25, 30}`

Thus, the list of elements in the set (AUB) is:`{5, 10, 15, 20, 25, 30}` Hence, the solution to the problem is `{5, 10, 15, 20, 25, 30}`.

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11 Megan has $500 in her savings account. The interest rate is 7%, which is not compounded. How much money in dollars) will she have in her account after 5 years? Write the correct
answer.

Answers

Answer:

701

Step-by-step explanation:

At the end of 5 years, your savings will have grown to $701.

You will have earned in $201 in interest.

answer.

use a reference angle to write sec290 (where the angle is measured in degrees) in terms of the secant of a positive acute angle. do not include the degree symbol in your answer.

Answers

sec 290° = 1/cos 110°= -2.9238.

To find the value of sec 290° using a reference angle, we first need to determine the reference angle for 290°.

The reference angle is the acute angle formed between the terminal side of the given angle (290°) and the x-axis. To find the reference angle, we subtract the nearest multiple of 180° from the given angle:

Reference angle = 290° - 180° = 110°

Now, we can express sec 290° in terms of the secant of the reference angle (110°). The secant function is defined as the reciprocal of the cosine function:

sec(x) = 1/cos(x)

Therefore, sec 290° can be written as:

sec 290° = 1/cos 110° = -2.9238.

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Sam just purchased a new car. After his employee discount and the sale that the dealership applied to the original
price, Sam paid $13,734.60. If Sam's employee discount was applied to the original price after the dealer discount,
then determine the original price of the vehicle given that the employee discount was 8% and the dealership
discount was 25%. Round your answer to the nearest cent.
a $20,375.21
c. $19,250.13
b. $18,350.33
d. $19,905.22

Answers

Answer:

D 19,905

Step-by-step explanation:

19,905.22×25%=4976.31

19905.22-4976.31=14,928.91

14928.91×8%=1194.31

14928.91-1194.31=13734.6

Let W = {a + 2x + bx^2 ∈ P2 : a, b ∈ R} with the standard operations in P2. Which of the following statements is true?
A. W is not a subspace of P2 because 0 € W.
The above is true
B. W is a subspace of P2.
The above is true
C. None of the mentioned
D. 1+xEW

Answers

A subspace must satisfy three conditions: closure under addition, closure under scalar multiplication, and containing the zero vector. Therefore, the correct statement is B. W is a subspace of P2.

In order to determine whether statement A or B is true, we need to check the subspace criteria.

Let's analyze the statements:

A. W is not a subspace of P2 because 0 € W.

If 0 € W, then W does not contain the zero vector. However, the zero vector is the polynomial 0 + 2(0)x + (0)x^2 = 0, which is an element of W. Thus, statement A is false.

B. W is a subspace of P2.

For W to be a subspace, it needs to satisfy all three subspace criteria. Let's check each criterion:

Closure under addition: Let's take two arbitrary polynomials in W: a + 2x + bx^2 and c + 2x + dx^2. Their sum is (a + c) + 2x + (b + d)x^2, which is also a polynomial in W. Therefore, W is closed under addition.Closure under scalar multiplication: Let's take an arbitrary polynomial in W: a + 2x + bx^2. If we multiply it by a scalar, say k, we get k(a + 2x + bx^2) = ka + 2kx + bkx^2, which is still a polynomial in W. Hence, W is closed under scalar multiplication.Contains the zero vector: The zero vector is the polynomial 0 + 2(0)x + (0)x^2 = 0, which is an element of W. Therefore, W contains the zero vector.

Since W satisfies all three subspace criteria, statement B is true.

Therefore, the correct statement is B. W is a subspace of P2.

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Marissa has a yard service to help people in her neighborhood. She earns $15 for each lawn she mows, $10 for each yard she weeds, and $5 for each yard she rakes. This month Marissa spent $3 on flyers to send out to neighbors, she purchased a new blower for $26, and paid her brother $18 for helping her mow lawns. If Marissa mowed 4 lawns and raked 8 yards, how much money did she make in profit? 1. 53 2. 100 3. 36 4. 71

Answers

Answer:

100-47=53 so 53$ profit

Step-by-step explanation:

help me please, i’m confused. thanks!

Answers

Answer:

Step-by-step explanation:

The answer is x=9/5. Hope this helps!

factor 5a2 – 30a 40. question 17 options: a) 5(a – 2)(a 4) b) 5(a – 2)(a – 4) c) (5a – 5)(a – 8) d) (a – 20)(a – 2)

Answers

The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)

The following procedures can be used by us while factoring polynomials:

Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.

Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.

Eliminate any factors that are frequent.

In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).

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A bag contains white, blue and red ping-pong balls in the ratio 8 : 3 : 2. There are 10 balls. If 10 white and 10 blue balls are removed from the bag, the new ratio is ?

Answers

Answer:

the new ratio of white, red and blue balls is 6:2:1

Step-by-step explanation:

The computation of the new ratio is shown below:

If you have 10 red balls, so the blue balls is in proportion of 3:2 that means 15 would be the blue balls. In addition to this, the while balls is in proportion 8:2 = 4:1 so there is a 40 white balls

Now if 10 white and 10 blue balls would be eliminated

So there is 30 white, 10 red, 5 blue bals

Also

30 = 5 × 6

And,

10 = 5 × 2

so the new ratio of white, red and blue balls is 6:2:1

Over a 5-year period, a company reported annual profits of $8 million, $3 million, $2 million, and $9 million. In the fifth year, it reported a loss of $7 million. What was the mean annual profit?


Answers

Given

Annual profits of four years $8 million, $3 million, $2 million, and $9 million.

In the fifth year, it reported a loss of $7 million.

To find:

The mean annual profit.

Solution:

Formula for mean is:

[tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

Annual profits are $8 million, $3 million, $2 million, $9 million and -$7 million. Here negative sign represent loss.

So, the mean annual profit is:

[tex]\text{Mean}=\dfrac{8+3+2+9+(-7)}{5}[/tex]

[tex]\text{Mean}=\dfrac{22-7}{5}[/tex]

[tex]\text{Mean}=\dfrac{15}{5}[/tex]

[tex]\text{Mean}=3[/tex]

Therefore, the  mean annual profit is $3 million.

Find the radius of a cone with a volume of 196 x 3.14 mm and a height of 12 mm.

Answers

Answer:

r=7 my

answer needs to be 20 characters long

What is the surface area of this prism?
5 yd
5 yd
11 yd
6 yd

Answers

Is (A) because of u multiple all the triangle sides u will get 5 yd so (a) the answer

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Answers

Answer:

12 inches

Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

3456 = 2x³

x³ = 3456/2

x³ = 1728

Cube root both sides

Cube root(x³) = cube root (1728 cubic Inches)

x = 12 inches

Therefore, the height is 12 inches

Width, Height and Length of rectangular prism are 12, 12 and 24 inch respectively.

Assume;

Width of rectangular prism = a

Height of rectangular prism = a

Length of rectangular prism = 2a

We know that;

Volume of the rectangular prism = (l)(b)(h)

Volume of the rectangular prism = (2a)(a)(a)

3,456 = 2a³

a³ = 1,728

a = 12 inch

So,

Width of rectangular prism = 12 inch

Height of rectangular prism = 12 inch

Length of rectangular prism = 2(12)

Length of rectangular prism = 24 inch

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A math teacher is trying to analyze her test grades. She surveys the students to find out how many minutes they studied. She then makes a scatterplot of time studying and test grades.


What is the domain?

A) the students' grades on their tests

B) the number of students in the class

C) the different courses the teacher teaches

D) the number of minutes the students studied

Answers

In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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What is the value of t? need an answer asap

Answers

Answer:

im pretty sure its 69

Step-by-step explanation:

im not joking im pretty sure both angles are 69 because of the triangle formula

A firm's marginal revenue and marginal cost functions are given by MR = R'(x) = 205 -0.5x2 and MC = C'(x) = 85 +0.7x2. Fixed costs are 10. a) Write down an expression for total revenue and deduce the corresponding demand function. Write down an expression for the total cost function. c) Determine the maximum profit.

Answers

a) The expression for total revenue is:

[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]

The demand function is:

[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]

b) The expression for the total cost function is:

[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]

c)The maximum profit, is 1079.56

How to write an expression for total revenue and deduce the corresponding demand function?

a) Total revenue is the integral of marginal revenue. Thus, expression for total revenue is:

[tex]R(x) = \int MR(x) dx = \int (205 -0.5x^2) dx = 205x - 0.25x^3[/tex]

The demand function is the inverse of the total revenue function:

[tex]x = R^{-1}(R) = \frac{205}{0.25R + 1}[/tex]

b) Total cost is the integral of marginal cost:

[tex]C(x) = \int MC(x) dx = \int (85 +0.7x^2) dx = 85x + 0.21x^3 + 10[/tex]

c) Profit is total revenue minus total cost:

P(x) = R(x) - C(x) = 205x - 0.25x³ - (85x + 0.21x³ + 10) = 120x - 0.46x³ - 10

To find the maximum profit, we need to find the point where marginal profit is zero. Marginal profit is the derivative of profit:

P'(x) = 120 - 1.38x² = 0

Solve for x:

120 - 1.38x² = 0

1.38x²  = 120

x² = 120/1.38

x = √(120/1.38)

x = 9.33

We find that the maximum profit is achieved when x = 9.33. Thus, the maximum profit:

P(9.33) = 120(9.33) - 0.46(9.33)³ = 1079.56

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A researcher would like to estimate the mean amount of money the typical American spends on lottery tickets in a month. The researcher would like to estimate the mean with 99% confidence. Which sample size options would yield the smallest margin of error?

Answers

Based on the formula, we can say that the margin of error will be reduced if the sample size is increased.

To obtain the smallest margin of error with 99% confidence, a sample size of 1689 would be needed.

A margin of error refers to the degree of error that may arise due to chance when attempting to estimate a population parameter such as a mean. It is calculated as the product of a critical value, a standard deviation, and a confidence interval, then divided by the square root of the sample size.

N is the sample size, which refers to the number of items included in the sample from the population. A larger sample size would be beneficial since it lowers the margin of error. When the sample size rises, the standard error of the mean decreases, implying that we are more confident in our estimate of the population mean. A smaller margin of error is desirable since it results in a more precise estimate of the population parameter.

The formula for the margin of error is given by:

Margin of Error = (Critical Value) (Standard Deviation) / sqrt(N).

To obtain the smallest margin of error with 99% confidence, a sample size of 1689 would be needed. The formula for the sample size calculation for this scenario is:

N = [(Zα/2)σ / E]²

Where, Zα/2 = 2.58, σ is the standard deviation, and E is the margin of error.

Using Zα/2 = 2.58 for a 99% confidence interval and the smallest possible margin of error to obtain a sample size for which the margin of error is minimized, we have:

N = [(Zα/2)σ / E]² = [(2.58)σ / E]²

Since the goal is to minimize the margin of error, we use the smallest possible value for E:1.

Therefore, N = [(2.58)σ / 1]²2.

Solving for N:

N = 6.6564σ²

To obtain the smallest margin of error with 99% confidence, we must solve for the smallest possible value of N that satisfies the above equation. We obtain:

N = 6.6564σ²

We don't have any information about the standard deviation, σ, in the given question, so we can't solve for N.

However, based on the formula, we can say that the margin of error will be reduced if the sample size is increased.

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a grating that has 3200 slits per cm produces a third-order fringe at a 24.0 ∘ angle.

Answers

To solve this problem, we can use the grating equation:

m * λ = d * sin(θ)

Where:

m is the order of the fringe

λ is the wavelength of light

d is the slit spacing (distance between adjacent slits)

θ is the angle of the fringe

In this case, we're given:

m = 3 (third-order fringe)

θ = 24.0°

We need to calculate the slit spacing (d) using the information that the grating has 3200 slits per cm. First, we convert the number of slits per cm to the slit spacing in meters:

slits per cm = 3200

slits per m = 3200 * 100 = 320,000

Now we can calculate the slit spacing (d):

d = 1 / (slits per m)

d = 1 / 320,000

Now, let's substitute the given values into the grating equation and solve for λ (wavelength):

m * λ = d * sin(θ)

3 * λ = (1 / 320,000) * sin(24.0°)

λ = (1 / (3 * 320,000)) * sin(24.0°)

Using a calculator, we can calculate the value of λ:

λ ≈ 5.79 × 10^(-7) meters or 579 nm

Therefore, the wavelength of light for which the grating with 3200 slits per cm produces a third-order fringe at a 24.0° angle is approximately 579 nm.

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Which is the correct stem-and-leaf plot for the data set?
16, 15, 47, 41, 40, 39, 16, 37

Answers

Answer:

the first plotting was correct.

Step-by-step explanation:

the values will be arranged in an ascending order from their roots which are the first digit

Other Questions
Rewrite each of the following as a base-ten numeral. a. 3 106 +9.104 + 8 b. 5.104 + 6 . Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a three-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible promotion options are playing free gigs, making a demo CD, hiring an agent, handing out fliers, and creating a Web site. Each free gig costs them $250 for travel and equipment but generates about three paying gigs. A high-quality studio demo CD should help the band book 20 gigs but will cost $1,000. A demo CD made on home recording equipment will cost $400 but may result in only ten bookings. A good agent will get the band 17 gigs but will charge $1,500. The band can create a Web site for $450 and would expect to generate six gigs from this exposure. They also estimate that they may book one gig for every 500 fliers they hand out, which would cost $0.08 each. They don't want to play more than six free gigs or send out more than 2,500 fliers, and can only produce one high-quality demo CD, produce one home demo CD, hire one agent, and make one website. Develop and solve an integer optimization model to find the best promotion strategy to maximize their profit. Which are independent clauses? Check all that apply.1. They decided to take a long walk2. We were able to arrive on schedule3. He was unsure how to proceed What is ""Acceptance""? Who has the legal power to accept an offer? Can a terminated offer be accepted? Which of the following concerning the auditor's report on internal control over financial reporting correct? Multiple Choice The auditor needs to state management's assessment of internal control over please me with an essay on these three securities. VERYURGENT1. Ideanomics.com2. Amazon3. MGIC investment corporation what type of marriage pattern, exchange, and residence pattern are practiced by the masai? a company has a pension liability of $410,000,000 that it must pay in 26 in years. if it can earn an annual interest rate of 3.7 percent, how much must it deposit today to fund this liability?a. 130,545,018.79b. $140,677,021.20c. $153,729,577.72d. $64,278,729.02e. $159,417,572.09 In this chapter, we briefly discussed 3 methods (other than hiding the name, etc.) of inference control. . The query set size control: don't return an answer if the set size is too small; N-respondent, k% dominance rule: don't return an answer if = k% of the population/data; - Randomization: add a small amount of random noise to the data. I. (1 pt) What is the advantage of using "randomization" compared to using "query set size control" or "N-respondent, k% dominance rule"? II. (1 pt) What is the disadvantage of using "randomization" compared to using "query set size control" or "N-respondent, k% dominance rule"? III. (1 pt) Outline an attack on a system using "query set size control". That is, outline a way of getting some information (such as average) of a small set A. IV. (1 pt) Outline an attack on a system using "N-respondent, k% dominance rule". That is, outline a way of getting some information (such as average) of a set A(with size < N) that contributes the majority (>k%) of data (let's say, set B). V. (1 pt) Outline an attack on a system using "randomization". That is, outline a way of "recovering" the original data that does not include the random noise. Current Attempt in Progress The Vice President for Sales and Marketing at Waterways Corporation is planning for production needs to meet sales demand in the coming year. He is also trying to determine how the company's profits might be increased in the coming year. This problem asks you to use cost-volume-profit concepts to help Waterways understand contribution margins of some of its products and decide whether to mass-produce any of them. Waterways markets a simple water control and timer that it mass-produces. Last year, the company sold 755,000 units at an average selling price of $5.00 per unit. The variable costs were $2,265,000, and the fixed costs were $1,026,800. (51) Waterways is thinking of mass-producing one of its special-order sprinklers. To do so would increase variable costs for all sprinklers by an average of $0.70 per unit. The company also estimates that this change could increase the overall number of sprinklers sold by 10%, and the average sales price would increase $0.20 per unit. Waterways currently sells 496,000 sprinkler units at an average selling price of $28.80. The manufacturing costs are $8,039,000 variable and $2,100,879 fixed. Selling and administrative costs are $2,674,600 variable and $793,460 fixed. If Waterways begins mass-producing its special-order sprinklers, how would this affect the company? (Round ratio to 2 decimal places, eg, 5.25% and Net income to O decimal places, eg. 2,520.) Current New Effect Contribution margin ratio % % Decrease by Net income $ ta $ Increase by $ e Textbook and Media As discussed in the lesson, the development of project networks is simplified using Project software. Create a table with a list of five project management software programs available on the market today (Microsoft Project and ProjectLibre are two examples). List two benefits and two drawbacks for each program. Awate and has height 8 meters and radius 2 meters. If the tank is filled to a te te the integral that determines how much work is required to pump the tappe above the top of the tank? Use p to represent the density of water and gegant Do not evaluate the integral. a voltaic cell consists of an mn/mn2 half-cell and a cd/cd2 half-cell. calculate [mn2 ] when [cd2 ] = 1.207 m and ecell = 0.848 v. how does the discussion of evolution (in pinker) inform your understanding of the conflict beween egoism and altruism an investment has an installed cost of $574,380. the cash flows over the four-year life of the investment are projected to be $216,700, $259,300, $214,600, and $167,410, respectively. if the discount rate is zero, what is the npv? if the discount rate is infinite, what is the npv? at what discount rate is the npv just equal to zero? the slope of the line is below -3. Which of the following is the point slope form if the line? What is science?Use your course text or other scholarly sources to define and discuss the key conceptsthat make up life, physical and earth sciences.Why should elementary students learn these three branches of science?Include a citation from a scholarly source and scripture in your initial thread A cable hangs between two poles 12 yards apart. The cable forms a catenary that can be modeled by the equation y=12cosh( 12x)7 between x=6 and x=6. Find the total arc length of the catenary. Round your answer to four decimal places. Arc Length yards Question Help: Message instructor Organizations should be sure to link incentives to performance outcomes.a. Trueb. False A permanent magnet is moved toward and away from a solenoid with a frequency of 60 Hz. The ends of the solenoid are connected in series with a light bulb. Which one of the following statements concerning an induced current, if any, in the loop is true?