What is the solution to the equation 5 (x minus 6) = 2 (x 3)? x =

a) The height of the rectangular shower stall is ( 3x - 2 )

b) The volume of the shower stall when x = 4 is 240 feet³

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

a)

Let the width of the rectangular shower stall be W = x

Let the length of the rectangular shower stall be L = ( x + 2 )

Let the height of the rectangular shower stall be H = H

Now , the equation will be

The volume of the rectangular shower stall is V = 3x³ + 4x² - 4x

And ,

Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

3x³ + 4x² - 4x = x ( x + 2 ) H

On simplifying the equation , we get

3x³ + 4x² - 4x = ( x² + 2x ) H

Dividing by ( x² + 2x ) on both sides of the equation , we get

H = ( 3x - 2 )

Therefore , the value of L is ( 3x - 2 )

On substituting the value for H in equation for volume of rectangular stall ,

Volume of rectangular shower stall = x ( x + 2 ) ( 3x - 2 )

Volume of rectangular shower stall = ( x² + 2x ) ( 3x - 2 )

Volume of rectangular shower stall = 3x³ + 4x² - 4x

Therefore , the height of the shower stall is ( 3x - 2 )

b)

The volume of rectangular shower stall = 3x³ + 4x² - 4x

when the value of x = 4

Substitute the value for x = 4 in the equation , we get

Volume of rectangular shower stall = 3x³ + 4x² - 4x

Volume of rectangular shower stall = 3 ( 4 )³ + 4 ( 4 )² - 4 ( 4 )

Volume of rectangular shower stall = 3 x 64 + 4 x 16 - 16

Volume of rectangular shower stall = 192 + 64 - 16

Volume of rectangular shower stall = 240 feet³

Therefore , the volume of the rectangular shower stall is 240 feet³

Hence , a) The height of the shower stall is ( 3x - 2 )

b) The volume of the shower stall when x = 4 is 240 feet³

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Answer:

I'm sorry I can't really help but I'll try. I'm only a middle schooler T^T.

Slope-intercept form with slope and y-intercept can be written as y = mx + b.

The slope-intercept form of a straight line is one of the most common ways to show the equation of a line. The slope-intercept formula can be used to derive the equation of a line when the y-intercept and slope of the straight line are known.

Consider a straight line with y-intercept "b" and slope "m." The slope-intercept form equation of a straight line is given by y = mx + b. For example, the equation of the line with a y-intercept = 5 and slope = -1 is written as y = -x+5.

When two points (x1, y1) and (x2, y2) are given, then the slope-intercept form is written as (y2 - y1)/(x2 - x1).

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In 4 months, the total cost of Yoga Studio A would equal that of Yoga Studio B

What is total ?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

The cost of Yoga Studio A at any given month can be represented as:

= Membership fee + (Monthly fee x Number of months)

Assuming number of months is x, the formula would be:

= 24 + (21.50 × x)

= 24 + 21.50x

Yoga Studio B would be:

= 41 + (17.25 × x)

= 41 + 17.25x

In order to find the month that these costs would be equal, equate both formulas:

24 + 21.50x = 41 + 17.25x

21.50x - 17.25x = 41 - 24

4.25x = 17

x = 17 / 4.25

x = 4 months

In conclusion, their costs would be the same in the 4th month.

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Unit Rate: 3

11 movie tickets: $33

Step-by-step explanation:

$24/8 = 3

The unit rate is 3

3 x 11 = $33

$33 for 11 movie tickets

Answer:

Answer =6/100

=3/50

hope it's help uhh

The total number of leaves the tree has is :

19 where  the degrees of the non-leaf vertices are 10, 7, 4, and 4.

Given:

a tree contains some number of leaves (degree 1 vertices) and four non-leaf vertices.

the degrees of the non-leaf vertices are 10, 7, 4, and 4.

how many leaves does the tree have = ?

The degree of the non leaf vertices are 10, 7, 4, 4

let the number of leaves be = k

So the tree has 4+k vertices.

and hence (4+k)-1 edge ⇒ 3+k

so ∑ deg(v) = 10+7+4+4+1k

                   = 25+k

and 2[E(T)] = ∑ deg(v)

2(3+k) = 25+k

6 + 2k = 25+k

2k-k = 25-6

k = 19

Hence the number of leaves the tree have is 19.

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Answer: 64 ounces

Step-by-step explanation:

Let's start with what we know:
1 pound = 16 ounces, so

4 pounds would equal

64 ounces!

Answer:

64 oz

Step-by-step explanation:

1lb =16oz so you multiply 16 by 4 and you get 64

410 milliliters of compound A needed to make 902ml of the drugs.

the link between two or more things in terms of quantity, amount, or size.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

We know the ratio of A to B is 7:4

let x = the multiplier

then

7x = amt of compound A

and

4x = amt of compound B

7x + 4x = 902

11x = 902

x = 902/11

x = 82 is the multiplier

therefore

5(82) = 410 milliliters of compound A needed

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The equation of the line passing through point P(4,-6) and perpendicular to the line y = -3 is x = 4.

A number that identifies the direction and steepness of a line is its slope or gradient. The slope of the straight line is written as y=mx+c where m is the slope and c is the y-intercept.

Given the equation of a line is y = -3 and point P(4,-6).

From the given equation, we can say that y is a horizontal line. The line perpendicular to this horizontal line will be a vertical line. The equation of the line perpendicular to y is of the form x = n where n is the x-coordinate of the point passing through this line.

Here, the x-coordinate is 4 from the point (4,-6). Then, the required line is x=4.

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The given statement is true, multicollinearity exists when a variable is correlated to other variables.

What is multicollinearity ?

Correlations between two or more independent variables in a multiple regression model can be referred to as multicollinearity. When a researcher or analyst tries to figure out how well each independent variable can be utilized to predict or comprehend the dependent variable in a statistical model, multicollinearity can result in skewed or misleading conclusions.

When two or more explanatory variables in a multiple regression model have strong linear relationships with one another but not with the dependent variable, this is referred to as multicollinearity.

Since a variable is multicollinear when it is correlated with other variables, the offered statement in the question is true.

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1) It is a conservative force, yes.

2) At (5m, 5m), the potential energy is 20 J.

1) If the work that a force performs when moving an item depends only on the object's initial and final positions and not on the path travelled, the force is said to be conservative.

Let's verify if this condition is met for the force in this problem:

- For moving from (0 m, 0 m) to (5 m, 5 m), the work done is 20 J (A)

Then we can go from (0 m, 0 m) to (5 m, 5 m) through a different path:

- from (0 m, 0 m) to (5 m, 0 m) (work done: 25 J)

- from (5 m, 0 m) to (5 m, 5 m) (work done: -5 J)

Total work done in the second path: 25 J + (-5 J) = 20 J --> same as (A)

We can also go from (0 m, 0 m) to (5 m, 5 m) through a different path:

- from (0 m, 0 m) to (0 m, 5 m) (work done: 35 J)

- from (0 m, 5 m) to (5 m, 5 m) (work done: -15 J)

Total work done in the third path: 35 J + (-15 J) = 20 J --> same as (A)

So, the force is conservative, since the work done does not depend on the path taken.

2) For a conservative force, the change in potential energy of the object moved by the force is equal to the work done by the force in moving the object from A to B.

Here have:

Point A: (0m, 0m)

Point B: (5m, 5m)

In this problem, the potential energy at the origin (point A) is zero, so,

[tex]W = U_{b} - U_{a}[/tex]

Also we know that the work done is W = 20 J

So, we find

[tex]U_{b} = W + U_{a}\\=20 + 0\\= 20J[/tex]

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Correct Question:

A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); -5 J from (5 m, 0 m) to (5 m, 5 m); -15 J from (0 m, 5 m) to (5 m, 5 m); and 20 J from (0 m, 0 m) to (5 m, 5 m).

Is this a conservative force?

If the zero of potential energy is at the origin, what is the potential energy at (5m, 5m)?

Answer:

x = -3.57

Step-by-step explanation:

First, subtract the answer and the other interger: -5.37 - (-1.8). Two negatives equal a negative. So, your answer would be -3.57

To double check, you would add -3.57 + (-1.8) [-+-=-] Equals, -5.37.

I hope this helped you!

x = - 3 / 4Y

y = - 117 + 4Y / 9

Steady state vector represent the long term market share of both groceries i.e WB and ZA. The long term market share of ZA is 0.727...

The steady-state behavior of a Markov chain is the long-term probability that the system is in each state. In other words, no matter how many transitions are applied to the system, it does not affect the state vector.

We have, WB and ZA are two competing grocery stores.

Probability that a customer who shops this week at WB will shop again here next week , p₁= 64% = 0.64

Probability(not shop again from WB) = 1-p₁

= 1 - 0.64 = 0.36

Probability that a customer who shops this week at ZA will shop again here next week , p₂ = 76% = 0.76

P(not shop again from ZA) = 1- p₂= 1 -0.76

= 0.24

Let market share of WB and ZA be "x" and "y" respectively, So, steady state vectors , s = [x y]

and x + y = 1 ---(*)

The Transition matrix, P=[1- p₁ p₁ ; 1-p₂ p₂]

P = [ 0.36 0.64 ; 0.24 0. 76 ]

we have to determine the value of x and y . So, we solve the following matrix equation, s[ I - P] = 0

matrix where I is identity matrix of 2×2

=> s([ 1 0 ; 0 1 ] - [0.36 0.64 ; 0.24 0. 76 ] ) = [0 0 ; 0 0 ]

=> s[1- 0.36 0- 64 ; 0 - 0.24 1 -0.76]

=[0 0 ; 0 0]

=> s[ 0.64 - 0.64 ; - 0.24 0.24] = [0 0;0 0]

=> [ x y] [0.64 -0.64 ; -0.24 0.24] = [0 0; 0 0]

Matrix multiplication,

=> [ 0.64x - 0.24y ; - 0.64x + 0.24y ]

= [ 0 0 ; 0 0]

equating the LHS and RHS

0.64x - 0.24y = 0 --(1)

- 0.64x + 0.24y = 0 --(2)

If we multiply equation (1) by -1 then we get equation(2). So, both equations are identical and we can collpase them in one equation for further calculation. Now, we have to equations

0.64x - 0.24y = 0 --(3)

x + y = 1

we can solve these equations either matrix method or substitution. We use here substitute

x = 1- y in equation (3) we get

0.64x - 0.24y = 0=> 0.64(1 - y) - 0.24 y = 0

=> 0.64 - 0.64y - 0.24 y = 0

=> 0.64 = 0.88y

=> y = 0.64/0.88 = 8/11 = 0.727

from equation (*) , x = 1 - 8/11 = 3/11 = 0.272

So, Market share of grocery ZA is y i.e 0.727.

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Mia's is the mother of the daughter of the mother of Mia's daughter.

What is athematic?

Athematic is a type of language that does not use inflectional morphology. This means that words do not change their form to indicate different aspects of meaning, such as tense, person, number, gender, case, and mood. Instead, the meaning of a sentence is conveyed through the use of different words and word order. Many languages, such as English, Chinese, and Japanese, are athematic. Additionally, some languages, such as Russian, have both athematic and inflectional forms.

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Complete Question:
_____ is the mother of the daughter of the mother of Mia's daughter.
A) Mia
B) Emely
C) Tena
D) Anna

Linear equation , quadratic equation and polynomial equation are the three types of equation.

1. Linear Equations: These equations have one or more variables and can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

2. Quadratic Equations: These equations have one variable and can be written in the form of ax^2 + bx + c = 0, where a, b and c are constants.

3. Polynomial Equations: These equations have one or more variables and can be written in the form of a polynomial, such as ax^n + bx^n-1 + ... + c = 0, where a, b, c, and n are constants.

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The graph increasing over the given entire interval: -3 < x < 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=2x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=2 and b=5.

A function can be classified as:

The question gives the entire interval where the function increases. Thus, from the graph is possible to see that the function increases when x is between –3 and 0 because the values of y increase with the increasing of x-values.

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Answer:

Those must-haves should include food, clothing, housing and insurance. And it also should include emergency and retirement savings, Luber said.

Step-by-step explanation:

hope this helped:)

brainliest for the brains:)

The equation the line perpendicular to the line given is y = -x/4+2

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, a line is perpendicular to y = 4x + 8 and passes through (−8, 4).

The equation of general line is; y = mx+c, where m is the slope.

We know that, two lines perpendicular to each other will have slope negative reciprocal of each other.

Therefore, the slope of the asked line is -1/4

Finding for c,

4 = -1/4x(-8)+c

c = 4-2

c = 2

Therefore, equation will be; y = -x/4 +2

Hence, The equation the line perpendicular to the line given is y = -x/4+2

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Answer:47

Step-by-step explanation:

Answer:

Your answer is 47, hope it helps.

The vertex of the absolute function g(x) = − |x + 3| − 4 will be at (-3, -4).

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as,

f(x) = | x - h| + k

The function is given below.

g(x) = − |x + 3| − 4

The vertex of the absolute function g(x) = − |x + 3| − 4 will be at (-3, -4).

The absolute function is drawn below.

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Answer: y=1/2x+3

Step-by-step explanation:

y-0=1/2(x+6) : point-slope

x-2y=-6 : standard

Answer:

Step-by-step explanation: Plug coordinates into y=ax+b

Simultaneous equations

0=-6a+b

7=8a+b

so 7=14a

a=0.5

Then b=3

So y=0.5x+3

Answer: No.

Step-by-step explanation: In order for a motion to be considered "rigid", it must undergo a transformation or rotation in which the distance between the vertices does not change. The distance between the vertices becomes larger in the image, meaning this is not a rigid motion.

Good luck!

385 Sample size is necessary is the 95% confidence Interval for p .

Sample Size:

Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population. Sampling is the process of selecting a subset of individuals from a population to estimate characteristics of the population as a whole. The number of entities within a subset of the population is selected for analysis

According to the Question:

The Necessary Sample Size is calculated as follows:

Necessary Sample Size =

(Z-score)² * Std Dev*(1-StdDev) / (margin of error)²

For example, given a 95% confidence level, 0.5 standard deviation, and a margin of error (confidence interval) of +/- 5%. Necessary Sample Size =

= (1.96)² x 0.5(0.5)) / (0.05)²

= (3.8416 x 0.25) / .0025

= 0.9604 / 0.0025

= 384.16

So in order to get 95% confidence level, with confidence interval of +/- 5%, and standard deviation of 0.5, I have to survey 385 samples.

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Answer:

Translation, then reflection. E

Step-by-step explanation:

E is correct because 1 and 2 have a reflection meanwhile number 3 has a translation.

Answer: They will each get 6 and there will be 1 left over.

Step-by-step explanation:

6*4 is 24. 25-24=1

The required value of PQ is 18.5 inches in the given triangle PQR.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

As per the given question, let's call the length of side PR (the hypotenuse). Since we know that PR = 37 inches and angle R = 30°, we can use the sine rule to write the following equation:

sin R = perpendicular/hypotenuse

sin R = PQ/PR

sin 30° = PQ/37  

1/2 = PQ/37  

PQ = 37/2

Apply the division operation, and we get

PQ = 18.5

Therefore, the required value of PQ is 18.5 inches.

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In a triangle PQR, right-angled at Q, PR = 37 inches and angle R =

30°. Find: PQ

If Anova is used in a research study using two therapy groups , then there will be 6 different sample means , the correct option is (d) .

In the question ,

it is given that ,

Anova is used in a research study using two therapy groups ,

for each group , scores will be taken

(i) before the therapy,

(ii) right after the therapy, and (iii) one year after the therapy.

that means ,

the number of therapies group = 2 and

the number of times the measurement is taken is = 3 .

So , the number of sample means is = 2 × 3 = 6 .

Therefore , there will be 6 different sample means .

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