A rectangular prism has the dimensions (x), (2x), and (3x+2). Find the volume of the prism.

Answer:

the question is supposed to be \(8 \sqrt 200 - 3\sqrt 162\\\)

i think the answer is \(53\sqrt 2\)

I'll update if its right or wrong

Step-by-step explanation:

The expression 8√200 − 3√162 in the simplified form will be 53√2.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 8√200 − 3√162

Simplify the expression, then we have

⇒ 8√200 − 3√162

⇒ 80√2 − 27√2

⇒ 53√2

The expression 8√200 − 3√162 in the simplified form will be 53√2.

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Deciles are 61.3 and 67.7

What are deciles?

Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.

Given:

Normal distribution =64.5 inches

Standard deviation=σ =2.5 inches

​

So, here the z- score for left decile= -1.28

and for right decile= +1.28

we know,

z= x-\(\mu\)/σ

x= zσ + \(\mu\)

x=-1.28*2.5 + 64.5

x= 61.3  and,

x= 1.28*2.5 + 64.5

x=67.7

hence, the deciles are 61.3 and 67.7

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There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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Answer:

25 -4x^8

Step-by-step explanation:

Im pretty sure its this! <3 Hope it helped.

Answer: =−4\(x^{8}\)+25

The 8 is an exponent

Step-by-step explanation:

(5−2x4)(5+2x)

=(5+−2)(5+2)

=(5)(5)+(5)(2\(x^{4}\))+(−2

=25+10\(x^{4}\)−10

=−4\(x^{8}\)+25

False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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Answer:

10 liters

Step-by-step explanation:

x=12% solution, y=16% solution

x+y=40

0.12x+0.16y=6 .   (12x+16x=600)

-12x-12y=-480

      12x+16x=600

+     -12x-12y=-480

-------------------------------

             4x=120

x=30

12% solution= 30 liters

16% solution= 10 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Let 12% brine solution be x.

Let 16% brine solutions be y.

12% brine solution was mixed with a 16% brine solution to produce 40L of the 15% solution.

This can be written as,

x + y = 40 ______(1)

0.12x + 0.16y = 0.15 x 40

0.12x + 0.16y = 6 _______(2)

We will solve for x and y.

From (1) we get,

x + y = 40

x = 40 - y _____(3)

Putting ( 3) in (2)

0.12 (40 - y) + 0.16y = 6

4.8 - 0.12y + 0.16y = 6

4.8 + 0.04y = 6

0.04y = 6 - 4.8

0.04y = 1.2

y = 1.2/0.04

y = 30

Putting in (3) we get,

x = 40 - 30 = 10

Thus,

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

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Given that, height of the right-angled triangle = 4m. Width of the right-angled triangle = 1m. Let's assume that the rectangular enclosure will be built at the base of the right-angled triangle. The area of the rectangular enclosure can be obtained using the formula, Area of rectangle = length × breadth. Length of the rectangle = height of the right-angled triangle = 4mLet the breadth of the rectangle be x, then the length is the width of the right-angled triangle + x = 1 + x Hence, the area of the rectangular enclosure is given by: Area = Length × Breadth= (1+x)×4= 4x + 4m²Now, the maximum area can be obtained by differentiating the above expression with respect to x and equating it to zero: dA/dx = 4 = 0x = -1. This is not a valid solution since we cannot have a negative breadth, hence we conclude that the area is maximum when the breadth of the rectangular enclosure is equal to the width of the right-angled triangle, i.e., when x = 1m. Thus, Area of the rectangular enclosure = Length × Breadth= (1+1)×4= 8 m². Hence, the largest the area of Gottfried’s enclosure can be is 8 m².

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The area A of a trapezoid is the height h times the average of the parallel bases a and b.  

A = (1/2)(a + b)h

Solving for a,

2A = (a+b)h

2A/h = a+b

a = 2A/h - b

We have A=59.64, b=4, h=8.4

a = 2(59.64)/8.4 - 4

a = 10.2 yards

Answer: 10.2

Answer:

11/8 or 1 3/8

Step-by-step explanation:

5+6=11

11 goes into 8 1 so you have

1  /8

then theres the remander 3 so you get

1 3/8

Answer:

825 people

Step-by-step explanation:

In the City where the election came up, 33% of the eligible voters voted

It is observed that there are 2500 eligible voters approximately.

The people who voted in 2012 is =

33/100 * 2500

=825 People

In 2012, the total number of people who voted in the city is 825 people

Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

Train 1: (from Chicago to Milwaukee)

speed: 14 meters per second

Train 2: ( same time 100 miles away, from Milwaukee to Chicago)

speed : 22 meters/second

Both trains are traveling in opposite directions 100 miles away:

Distance = speed x time

D1 = 14 t

D2= 22t

Since the total distance between the cities is 100 miles:

14t+22t= 100

Solving for t:

36t=100

Since 1 mile = 1609 meters

100 miles= 100 miles x 1609=160,900 meters

36t= 160,900

t= 160,000/36

t= 4,469.45 seconds

Since 1 hour = 3600 sec

4,469.45/3600 = 1.24 hours

The two trains will pass each other on parallel tracks after 1.24 hours

Answer:

- 5

Step-by-step explanation:

The equation of a line in slope - intercept form is

y = mx + c ( m is the slope (gradient) and c the t- intercept )

y = 3x - 8 ← is in slope- intercept form

with gradient m = 3 and y- intercept c = - 8 , thus

m + c = 3 + (- 8) = 3 - 8 = - 5

Answer:

For 1,000 bricks, the amount charged will be the same

Step-by-step explanation:

Let the number of bricks for which they charge the same amount be $x

Thus;

The total cost from the first company will

be;

250 + 0.2(x) = 250 + 0.2x

The second will charge;

400 + 0.05(x) = 400 + 0.05x

Since the amount charged will be equal at x bricks, we need to equate both;

400 + 0.05x = 250 + 0.2x

400-250 = 0.2x-0.05x

150 = 0.15x

x = 150/0.15

x = 1,000

If Point M lies on AB, AB = 24 , and BM = 13, then the length of AM is; 11 units

We are given the following parameters;

Length of line segment AB = 24

Length of line segment BM = 13

Now, we are told that M lies on the line segment AB and as such;

If BM = 13, then it means that;

AM + BM = AB

AM + 13 = 24

AM = 24 - 13

AM = 11 Units

We conclude that the length of AM is 11 units.

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The percentage increase of the value of Tessa's stock is 21%.

Using this formula

Percentage increase=Current stock worth-Old stock worth/Old stock worth

Where:

Current stock worth=$297.66

Old stock worth=$246.00

Let plug in the formula

Percentage increase=$297.66 - $246.00 / 246.00 × 100

Percentage increase=$51.66/ 246.00 × 100

Percentage increase=21%

Inconclusion the percentage increase of the value of Tessa's stock is 21%.

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The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.

What is binomial random variable ?

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success or failure.

Let X be a negative binomial random variable with parameters r and p, and let Y be a geometric random variable with parameter q. The sum Z = X + Y is also a random variable.

The cumulative distribution function (CDF) of Z is given by:

F_Z(z) = P(Z <= z) = P(X + Y <= z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)

This expression is a double sum and does not have a closed-form solution, but it can be computed numerically.

Alternatively, the probability mass function (PMF) of Z can be found by counting the number of ways that X and Y can take on their respective values, and summing up their joint probabilities:

f_Z(z) = P(Z = z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)

The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.

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The percentage change in productivity for this worker is -5.9%.

Productivity is the amount of goods and services produced by a worker in a given amount of time.

A worker produced 79 units of output in 38 hours. The previous week, the same worker produced 75 units in 34 hours.

Let's determine the productivity of the worker each week.

Step 1: Calculate productivity of the worker in the first week (week 1)

Productivity in week 1 = Total output produced / Number of hours worked

= 75 units / 34 hours

= 2.21 units per hour

Step 2: Calculate productivity of the worker in the second week (week 2)

Productivity in week 2 = Total output produced / Number of hours worked

= 79 units / 38 hours

= 2.08 units per hour

Step 3: Determine the percentage change in productivity

Percentage change = ((New value - Old value) / Old value) x 100%

Where,Old value = Productivity in week 1New value = Productivity in week 2

Substituting the values,Percentage change = ((2.08 - 2.21) / 2.21) x 100%

                                                                        = (-0.059) x 100%

                                                                        = -5.9%

Therefore, This employee's productivity has decreased by -5.9% as a whole.The negative sign indicates a decrease in productivity.

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Answer:

The midpoint is ( 2,-3.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates and divide by 2

( 4+0)/2 = 4/2=2

To find the y coordinate of the midpoint, add the y coordinates and divide by 2

( -1+-6)/2 = -7/2 =-3.5

The midpoint is ( 2,-3.5)

The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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The number of silver coins Lily initially had is 28.

A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.

Now according to the question;

Let 'x' be the share of silver coin of Lily.

Let 'y' be the share of silver coin of Nada.

Lily and Nada share silver coins in the ratio 7:3

Thus, x/y = 7/3

Cross-multiplying

3x = 7y (equation 1)

Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.

(x - 3)/(y + 3) = 5/3

cross multiplying;

3x - 9 = 5y + 15

Simplifying;

3x  = 5y + 24 (equation 2)

Comparing equation 1 and 2.

7y = 5y + 24

2y = 24

y = 12 (Nada's share)

Substitute the value of y in equation 1;

3x = 7y

3x = 7×12

x = 28

Therefore, the initial share if Lily was 28.

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In order to multiply two fractions, we can follow the steps below:

0. find the product between the two numerators; ,(3 * 7 = 21)

1. find the product between the two denominators; ,(10 * 2 = 20)

2. the product of the two fractions will be the result of step 1 (the numerator of the final result), divided by the result of step 2 (the denominator of the final result):

Therefore, the answer is:

Answer:

Step-by-step explanation:

Since λa + ub is parallel to ha + tb, we can write:

λa + ub = k(ha + tb)

where k is some constant. We can simplify this equation by expanding both sides:

λa + ub = kha + ktb

Rearranging the terms, we get:

λa - kha = ktb - ub

Factoring out a, we get:

a(λ - kh) = b(kt - u)

Since a and b are non-parallel, they are linearly independent, which means that a and b are not multiples of each other. This also means that the only way for the left side of the equation to be equal to 0 is if λ - kh = 0, or λ = kh. Similarly, the only way for the right side of the equation to be equal to 0 is if kt - u = 0, or u/t = k/h.

Therefore, we have shown that λ/h = u/t.

Answer:

The fast food restaurant has the higher unit price

Answer:

its 10.

Step-by-step explanation:

if WZ is 12 then YZ has to be 12 too

and for YZ to be 12, x must be 9

2(9)-9=12

so if x=9 then

9+1 = 10

therefore XY= 10 :>

It is proved that <QST + <TSV = 180° becasue of the linear pair.

Here we know that vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

The sum of linear pair is equal to 180 degree

<QSVX= 180°

<TSR= 180°

Therefore, <QST= 90°

<TSV= 90°

Thus, <QST + <TSV = 180°

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Answer:

A quadratic trinomial in x with coefficient of x^2 equal to 1 is a perfect-square trinomial if the constant term is the square of 1/2 the coefficient of x.

\( {x}^{2} + 15x + {( \frac{15}{2} )}^{2} \)

\( {x}^{2} + 15x + \frac{225}{4} \)

\( {(x + \frac{15}{2} )}^{2} \)

The inequality shown in the diagram is the one in option C.

-2 < x ≤ 7

On the number line we can see that our variable is x, the graph of the solution set of the inequality starts with an open circle at x = -2.

The open circle means that x = -2 is not a solution of the inequality, then we start with:

-2 < x

Then we can see a closed circle at x = 7, a closed cirlce means that the value is a solution, so x can be equal to 7, and the inequality is:

-2 < x ≤ 7

So the correct option is C.

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