PART B
How can the stage manager use the constant of proportionality to find the
dimensions of any new props the director requires?

Answer:

whats the question

Step-by-step explanation:

The operating profit for September was $168,418.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Using the given information, we can calculate the following:

Total fixed cost per month.

= Instructor wages + Classroom supplies + Utilities + Campus rent + Insurance + Administrative expenses

= $2,970 + $310 + $1,230 + $4,900 + $2,400 + $4,000

= $15,810

Variable cost per course.

= Cost per course for utilities + Cost per student for administrative expenses

= $65 + $4 = $69

Variable cost per student

= Sales revenue per student - Total variable cost per student

= $890 - $69

= $821

Using the planned number of courses and students, we can calculate the expected revenue:

Expected revenue.

= Planned number of courses x Planned number of students x Sales revenue per student

= 4 x 62 x $890 = $221,120

Using the actual number of courses and students, we can calculate the actual revenue and costs:

Actual revenue

= Actual number of courses x Actual number of students x Sales revenue per student

= 4 x 52 x $890

= $184,640

Total variable cost

= (Variable cost per course x Actual number of courses) + (Variable cost per student x Actual number of students)

= ($69 x 4) + ($4 x 52)

= $412

Total cost

= Total fixed cost + Total variable cost

= $15,810 + $412

= $16,222

Operating profit

= Actual revenue - Total cost

= $184,640 - $16,222

= $168,418

Therefore,

The operating profit for September was $168,418.

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Answer:

Step-by-step explanation:

A. -1/3x

B. -x

c.-5/4x

Answer:

x=7

Step-by-step explanation:

these 2 triangle sides are equal to each other so just set them equal to find x

X+3=3x-11

-x.  -x

3=2x-11

+11. +11

14=2x

=2. =2

7=x

Hopes this helps please mark brainliest

The fraction of the voters polled voted for Eric Jackson is 50/13. A fraction is a portion of a whole or, more broadly, any number of equal parts.

Therefore,

The fraction of the voters polled voted for Eric Jackson is 50/13

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Answer:

7

Step-by-step explanation:

13x - 7 + 30 = 30 + 84

13x - 7 + 30 - 30 = 30 - 30 + 84

13x - 7 = 84

13x = 84 + 7

13x = 91

x = 91 / 13

x = 7

The equation used to find the length of each afternoon practice is given as follows:

4(h + 3) = 20.

The variables in this problem are defined as follows:

During the summer, the team practices 4 days per week, for a total of 20 hours each week, hence the equation is of:

4(x + h) = 20.

The number of hours practiced during the morning is of:

x = 3.

Hence the equation to solve for h is given as follows:

4(3 + h) = 20

Applying the commutative property:

4(h + 3) = 20.

Hence the second option is correct.

The problem is given by the image shown at the end of the answer.

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Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.

Which equation can you use to find h, the length of each afternoon practice in hours?

Summer swim practice is 4 days per week. Each day has 3 hours of morning practice and h hours of afternoon practice. So, the number of hours of practice each day is h+3. Weekly practice is a total of 20 hours. This equation represents the situation.

4 (h+3)

=

20

days of practice per week

hours of practice each day

total hours of practice each week

The equation 4(h+3)=20 can be used to find the length of each afternoon practice in hours. Solve the equation for h.

4(h+3)

= 20

h+3

= 5 Divide both sides by 4

h

= 2 Subtract 3 from both sides

Each afternoon practice is 2 hours.

Answer: 15 books

Step-by-step explanation:

Given that the weight of 6 books is 1.260 kg

⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg

Let the number of books that will weigh 3.150 kg be x

as we know that

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15

The number of books is 15

15 books will weigh 3.150 kg.

Given the weight of 6 books is 1.260 kg

⟹ weight of each book is  

1.260/6

=0.210 kg

Let x be the total number of books that weigh 3.150 kg.

as we are aware

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= 3.150/0.210

=15

So, the number of books is 15.

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For given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

In this question we have been given a function f(x) = 7/(x² - 5)

We need to evaluate f(a + 4)

Substitute x = a + 4 in given function.

f(a + 4)

= 7/((a + 4)² - 5)

=  7/(a² + 8x + 16 - 5)

=  7/(a² + 8x + 11)

Therefore, for given function  f(x) = 7/(x² - 5),

f(a + 4) = 7/(a² + 8x + 11)

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Answer:

t = 12

Step by step explanation:

(t + 6)(t - 8) = 72

t² - 8t + 6t - 48 = 0

t² - 2t - 120 = 0

(t + 10)(t - 12) = 0

t + 10 = 0 OR t - 12 = 0

t = -10 OR t = 12

(reject)

The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase

From the question, we have the following parameters that can be used in our computation:

Initial weight = 2500 pounds

New weight = 2525 pounds

The percentage increment is then calculated as

Percentage = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation

Percentage = (2525 - 2500)/2500 * 100%

Evaluate the difference

So, we have

Percentage = 25/2500 * 100%

Evaluate the quotient

So, we have

Percentage = 0.01 * 100%

Evaluate the product

So, we have

Percentage = 1%

Hence, the percent increase is 1% increase

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Lucas will be using the shipping box D as it is the box with the greatest volume of 27ft³

The volume of a rectangular box is calculated by multiplying its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.

volume of box A = 5ft × 3ft × 1ft

volume of box A = 15ft³

volume of box B = 4ft × 2ft × 3ft

volume of box B = 24ft³

volume of box C = 7ft × 1ft × 2ft

volume of box C = 14ft³

volume of box D = 3ft × 3ft × 3ft

volume of box D = 27ft³

Therefore, the shipping box with the largest volume is box D with 27ft³

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Answer:

Step-by-step explanation:

FEEL ME ITS D

ITS D

THE ONE WITH THE 333

The quadratic equation f(x) = - (x + 2)² + 17 represents the graph shown.

In this problem we have the definition of a quadratic equation in its vertex form, whose definition is explained below:

f(x) = a · (x - h)² + k

Where:

We need to determine the quadratic equation related to a graph shown.

First, determine the coordinates of the vertex:

(h, k) = (- 2, 17)

Second, find the vertex constant:

a = [f(x) - k] / (x - h)²

a = (13 - 17) / (0 + 2)²

a = - 4 / 4

a = - 1

Third, write the resulting function:

f(x) = - (x + 2)² + 17

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The equation that shows a proportional relationship between x and y is y=6x

The options represent the given parameters

As a general rule

A proportional relationship is represented as y = kx

Where k represents the constant of proportionality

So, we check the options for equations that has the same form as y = kx

We have

y = 6x

The above equation is a linear equation

In fact, it is a linear equation that shows a proportional relationship

Note that all linear equations have a constant rate of change

So, the proportional relationship is given as

y = 6x

Where the constant of proportion is 6

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Answer:

  336, 504

Step-by-step explanation:

You want the next two numbers in the sequence beginning 6, 24, 60, 120, 210, ....

When attempting to identify a sequence it is often useful to look at the differences between terms, then at the differences of those, and so on. If The differences at some level are constant, that level tells you the degree of the polynomial that will describe the sequence. If they have a common ratio, then the sequence will be based on an exponential function.

1st differences: 18, 36, 60, 90

2nd differences: 18, 24, 30

3rd differences: 6, 6 . . . . . . . . constant, indicating a cubic function

We can go to the trouble to write four equations in the four coefficients of the cubic describing this sequence, or we can let suitable technology find it for us. The attachment shows a graphing calculator solution for the coefficients. The 10^-14 value for the 'd' coefficient is effectively 0. This value is due to the inexact representation of numbers in the floating point arithmetic used by the calculator.

The equation of the n-th term a[n] is ...

  a[n] = n³ +3n² +2n

The next two terms are ...

  a[6] = 336

  a[7] = 540

__

Additional comment

The equations for the coefficients of y = ax³ +bx² +cx +d will use the given sequence values and x values of 1..4. Here they are:

  6 = a·1 +b·1 +c·1 +d

  24 = a·8 +b·4 +c·2 +d

  60 = a·27 +b·9 +c·3 +d

  120 = a·64 +b·16 +c·4 +d

The second attachment shows a calculator solution for these four equations. (a, b, c, d) = (1, 3, 2, 0)

The graph of the function g(x) = -2x - 3 is attached below.

Graph:

Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.

Given,

Here we have the function g(x) = -2x - 3

Now, we need to plot the graph of the function.

In order to plot the graph for the given function,

First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.

Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.

Then we get the value of the function as,

x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1

x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1

x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3

x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5

x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7

Now, we can get the table like the below

Now, we have to plot the graph through this table, then we get the graph like the following.

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Answer:

Just add the 3 sides together

Step-by-step explanation:

if a triangle has the side values of 3, 4, 6. Then you would simply add them together!

3+4+6=13

therefor that triangles perimeter is 13

hope this helps!

The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.

According to the question,

We have the following system of equations:

x+y = 3 .....(1)

4x-y = 7 ....(2)

Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.

We can solve these equations by adding as follows:

x-y+4x+y = 3+7

5x = 10

x = 10/5

x = 2

Now, we can put the value of x in equation 1 to find the value of y:

2+y = 3

y = 3-2

y = 1

Hence, the correct option is B.

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Answer:i think the answer is 2/4 or 3/2

Step-by-step explanation:

The hypothesis are given as follows:

H0: p = 0.301; H1: p ≠ 0.301.

a) The level of significance is of 0.05.

b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.

The test statistic is of: z = -2.09.

c) The p-value is of: 0.0366.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:

[tex]H_0: p = 0.301[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:

[tex]H_1: p \neq 0.301[/tex]

The test statistic is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

The parameters of the equation are listed as follows:

The values of these parameters for this test are:

[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]

Hence the value of the test statistic is of:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]

z = -2.09.

We have a two-tailed test, as we are testing if the proportion is different of a value.

Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.

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The point (-6,6) is in the solution region of the inequality and is plotted in given below graph.

Given,

Equation -> y > x - 3 +8

                    y > x + 5

Lets take a point A(-6,6)

Putting the value in equation,

6 > -6 + 5

6 > -1

which is true.

Hence, A(-6,6) lies in the region of the inequality.

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Answer: y=-2x-5

Check this in desmos

Answer:

answer,(2)x≥-1

Step-by-step explanation:

it was right

The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.

From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

The mean is 0.09 and the standard deviation is 0.012.

The probability will be:

= 1 - P[Z < (0.12 - 0.09/0.013)]

= 1 - P(Z < 2.5)

= 1 - 0.99379

= 0.0062

This shows the concept of solving probability regarding z values.

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Answer: 32

Step-by-step explanation:

If you multiply 2 1/5 by 35 you would get 70.4, .4 is equivalent to 2/5, so 70.4 = 70 2/5.

Answer:

The distance would be 13m.

Answer:

13 m

Step-by-step explanation:

this can be looked at like a triangle sorry for the bad drawing I’m in the car lol

But we know the base is 12m and the height of this triangle is 5 since the secon pole is 5m taller hence 14-9=5

So we use the Pythagorean theorem

a^2+b^2=c^2

12^2+5^2=c^2

144+25=c^2

169=c^2

Now find the square root of 169 to get the answer

13 m is the distance between the tops

Hopes this helps please mark brainliest

The correct option regarding which option represents a polynomial is given as follows:

b. ii only.

Polynomials are expressions that are given in the following format:

[tex]p(x) = a_nx^n + a_{n-1}x^{n - 1} + \cdots + a_1x + a_0[/tex]

In which n is the degree of the polynomial.

The exponents n have to be all whole numbers for the expression to represent a polynomial, meaning that they cannot be negative neither fractions or decimal values.

Thus the only expression that represents a polynomial is:

ii. 5x³ + 3x² + x + 2.

The reasons for the expressions that do not represent a polynomial are given as follows:

Hence the correct option is given by option b.

The problem is given by the image at the end of the answer.

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Answer:

z=-52/3

Step-by-step explanation:

1) 12 + -3/2 z= -14

2) -3/2 z = -26

3) z=-26(-2/3)

4) z= 52/3

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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The required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).

Range, it is the set of values that come out to an outcome for certain mathematical operations.

Here,
A graph of the function is shown,
and the graph of the function is defined from -∞ to ∞, so the domain of the function is (-∞, ∞).
Also, the function has a value of the y-axis from -3 to ∞, and the range of the function is (-3, ∞).

Thus, the required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).

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