Consider an x distribution with standard deviation o = 34.
(a) If specifications for a research project require the standard error of the corresponding distribution to be 2, how
large does the sample size need to be?
B) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?

Answers

Answer 1

Part (a)

The standard error (SE) formula is

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

where n is the sample size. We're given SE = 2 and sigma = 34, so,

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]

So we need a sample size of n = 289 to have an SE value of 2.

Answer: 289

========================================================

Part (b)

We'll use SE = 1 this time

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

Answer:  1156

Related Questions

I need to know what goes in those two boxes and why I would really appreciate it if someone help me with this question

Answers

Answer:

below

Step-by-step explanation:

the is the procedure above

A , B, C , D probability

Answers

Answer:

your laptop is nice really

Sam can mow a lawn in 40 minutes. Melissa can mow the same lawn in 80 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?

Answers

Answer:

It will take them both 24 minutes to mow the lawn if they are working together.

Step-by-step explanation:

Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:

1/40 + 1/60 = 1 / X

3X + 2X = 120

X = 120/5

X = 24

Thus, it will take them both 24 minutes to mow the lawn if they are working together.

4x - 2 - 1 = 2 hep plz

Answers

Answer would be 11/4

4x - 2 - 1 = 2
4x - 2 = 2 + 1
4x - 2 = 3
4x - 2 = 9
4x = 9 + 2
4x = 11
x = 11/4

what is the image of ( 4, -8 ) after a dilation by a scale factor of 1/4 centered at the origin ?

Answers

what we know?:

* scale factor of 1/4

* the point (4, -8)

all we have to do is put 4/4 (because we are dilating by 1/4)

4/4= 1

same for the other one: -8/4= -2

FINAL ANSWER: (1, -2)

What are the x-intercepts of the graph of the function f(x) = x2 + 5x - 36?
O (-4,0) and (9, 0)
O (4,0) and (-9,0)
O (-3,0) and (12, 0)
O (3,0) and (-12, 0)​

Answers

Answer: (3,0) and (-12,0)

Step-by-step explanation:

The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).

Option B is the correct answer.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the 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,

To find the x-intercepts of the function f(x) = x^2 + 5x - 36,

we need to set y = f(x) to 0 and solve for x.

So, we have:

x² + 5x - 36 = 0

We can factor the left side of the equation:

(x + 9)(x - 4) = 0

Using the zero product property, we get:

x + 9 = 0 or x - 4 = 0

Solving for x, we get:

x = -9 or x = 4

Therefore,

The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

how you could find the shortest distance from A(6, 5) to the line y = 5x – 10?

Answers

Answer:

The distance between two points (a, b) and (c, d) is given by:

[tex]d = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

So the distance between the point (6, 5) and the line y = 5x - 10 can be thought as the distance between the point (6, 5) and the point (x, 5x - 10)

Where:

(x, 5x - 10) denotes all the points in the line y = 5x – 10

That distance is given by:

[tex]d = \sqrt{(x - 6)^2 + (5x - 10 - 5)^2} = \sqrt{(x - 6)^2 + (5x - 15)^2}[/tex]

Now we want to minimize this.

Because the distance is a positive quantity, we can try to minimize d^2 insted, so we have:

[tex]d^2 = (\sqrt{(x - 6)^2 + (5x - 15)^2})^2 = (x - 6)^2 + (5x - 15)^2}\\\\d^2 = x^2 - 2*x*6 + 36 + 25*x^2 - 2*15*x + (-15)^2\\\\d^2 = 26*x^2 - 42*x + 261[/tex]

Notice that this is a quadratic equation with a positive leading coefficient, which means that the arms of the graph will open upwards, then the minimum will be at the vertex of the parabola.

Remember that for a parabola:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/2a

Then for our parabola:

d^2 = 26*x^2 - 42*x + 261

The vertex is at:

x = -(-42)/(2*26) = 0.808

Then we just need to evaluate the distance equation in that value of x to get the shortest distance:

[tex]d = \sqrt{(0.808 - 6)^2 + (5*0.808 - 15)^2} = 12.129[/tex]

The shortest distance between the point A and the line is 12.129 units.

The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares?

Answers

Answer:

A square is 4 even sides.

the circumference around the square area is 1600 meters. This means that each side is 400 meters.

Square meters is the area of the square.

400 x 400 = 160000 m^2

To get to Hectares, you divide the squared measurement by 10,000.

Answer:

160000m^2 = 16ha

Step-by-step explanation:

Bit of a nit pick first the word is perimeter not circumference circumference only applies to circles. 1600/4=400 (divide by 4 because a square has 4 sides) 400^2=160000 (A=L*H the length and height are the same so you square it) 160000/10000=16 (1 hectare = 10000m^2), Hope this helps. :)

Find the area of a rectangle whose length is 14cm and breadth is 6cm

Answers

Answer:

Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.

 

Traza 1

Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.

 

Traza 2

Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.

 

Traza 3

La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.

 

Traza 4

La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.

 

Traza 5

Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.

 

Traza 6

La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.

 

Traza 7

Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.

 

Traza 8

La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.

 

Traza 9

La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.

 

Traza 10

Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?

 

Traza 11

Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.

 

Traza 12

La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

 

Traza 13

La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

 

Traza 14

La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.

 

Traza 15

El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.

 

Traza 16

El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.

 

Traza 17

Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.

 

Traza 18

Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?

 

Traza 19

Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.

 

Traza 20

Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.

 

Traza 21

La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.

 

Traza 22

Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.

 

Traza 23

En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.

 

Traza 24

Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.

 

Traza 25

Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.

 

Traza 26

Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.

 

Traza 27

Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.

 

Traza 28

Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.

 

Traza 29

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

 

Traza 30

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

 

Traza 31

Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.

 

Traza 32

Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.

 

Traza 33

Step-by-step explanation:

Answer:

A= 84cm

Step-by-step explanation:

length x width= area

plug in the given information.

14cm x 6cm = A

A=84

with a length of 14cm and a width of 6cm multiply them for an area of 84cm.

Explain why a + b = d.
B
lbº


A
С C

Answers

CC ib sh


Answer :




Amen w


• The difference between a polynomial or rational equation and polynomial or rational inequality

Answers

Answer:

An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.

Find the value of x from the given equation.
x3 = 125/512
518
Sla
516
815

Answers

Answer:

x = 5/8

Step-by-step explanation:

x^3 = 125/512

Take the cube root of each side

x^3 ^1/3 = (125/512)^ 1/3

We know (a/b) ^1/3 = a^ 1/3  / b^1/3

x = (125) ^1/3 / (512)^ 1/3

x = 5/8

One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.
A. 21°; 69°
B. 26°; 64°
C. 31°; 59°
D. 23°; 67°

Answers

Answer:

A. 21°, 69°

Step-by-step explanation:

If you work by process of elimination all you have to do is take 27 away from the bigger degree of the two and see if it is 2x as much as the smaller degree.

Ex.

1. 69°-27°= 42°, which is 2x as many as 21°.

Question 5 of 25
Find the common ratio for this geometric sequence.
0.7, 2.1, 6.3, 18.9,...
O A. 1.4
O B. 3
O C.-3
D. 0.33
SUBMIT

Answers

Answer:

3

Step-by-step explanation:

common ratio

2.1/0.7=3

6.3/2.1=3

18.9/6.3=3

therefore common ratio is equal to 3

Does this graph represent a function?

Answers

Answer:

I think it's a function

Step-by-step explanation:

as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.

Answer:

yes

Step-by-step explanation:

it's a cubic function having maximum and minimum turning points

it has a point of inflation, y - intercept and x-intercept

find the coefficient of the third term of (x+2)^5

Answers

Answer:

40

Step-by-step explanation:

(x+2)^5 use binomial theorem :

(a+b)^n = (n choose 0)*a^n*b^0 + (n choose 1)*a^(n-1)*b^1 + (n choose 2)*a^(n-2)*b^2) + ... + (n choose (n-1)*a^1*b^(n-1) + ( n choose n)*a^0*b^n

this seems like a lot but to break it down, notice how the exponent on 'a' decreases as the exponent on 'b' gets bigger.

also, the 'choose' formula is :

(n choose r ) = n!/ (n-r)!r!

now plug in your values

(x+2)^5 =

(5 choose 0)*x^5*2^0 + (5choose 1)*x^4*2^1 + (5 choose 2)*x^3*x^2 + (5 choose 3)*x^2*2^3 + (5 choose 4)*x^1*2^4 + (5 choose 5)*x^0*x^5

we only need the third term so we will solve for this :

(5 choose 2)*x^3*x^2

5 choose 2 = 5!/ (5-2)!2! = 5!/ 3!2! = 10

x^3 * 2^2 = 4x^3

10*4x^3 = 40x^3

Please helpppppp
ASAPpppppp

Answers

It should be B I’m pretty sure

Find the missing side. Round your answer to the nearest tenth

Answers

Answer:

x = 24.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Sin theta = opp / hypotenuse

sin 75 = 24 /x

x sin 75 = 24

x = 24/ sin 75

x=24.84662

Rounding to the nearest tenth

x = 24.8

I think the missing side is 24.8

state the hundred thousands place for 7,832,906,215

Answers

Answer:

Step-by-step explanation:

6 is the thousands place

0 (right next to it) is the 10 thousands place

9 is the hundred thousands place. There is only 1 nine present so the answer is unique.

a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years

Answers

beiausbehahahsusu shausis heished

he solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)

Answers

Answer:

The Answer Is Point B (2,0)

Step-by-step explanation:

Does anyone know how to take the fuzzy stuff off

Answers

Answer:

???

Step-by-step explanation:

I need the answers to this

Answers

Angle for C and B is 20
Angle for F and E is 85


Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12
h
slower than the other. If they meet in 3 hours, what is the rate of each bus?
km
Rate of the slower bus:

Rate of the faster bus:

Answers

Answer:

102 km/hr

90 km/hr

Step-by-step explanation:

Given that :

Total distance = 576

Time taken = 3 hours

Bus A :

Speed = x

Bus B :

Speed = x - 12

Recall :

Distance = speed * time

Hence,

Distance covered by A + Distance covered by B = total distance covered

(x * 3) + ((x - 12) * 3) = 576

3x + 3x - 36 = 576

6x = 576 + 36

6x = 612

x = 612 / 6

x = 102

Speed of faster bus, x = 102 km/h

Speed of slower bus, x - 12 = (102 - 12) = 90 km/hr

100 mice eat 100 cakes. If each big mouse eats 3 cakes, and 3 baby mice eat 1 cake, how many big mice and baby mice are there?

Answers

1 big mouse = 3 cakes
3 baby mice = 1 cake
1 baby mouse = 1/3 cake
Suppose x = the amount of big mice
y=the amount of baby mice
100 mice —> x+y=100
100 cakes —> 3x+1/3 y=100
Then solve it like how you solve linear equation with 2 variables
3x+3y=300
3x+1/3 y=100
——————— -
8/3 y=200
y=75
x+75=100
x=25
Hence,there are total of 25 big mice and 75 baby mouse

Tolong bantuin pakai cara ​

Answers

Answer:

1364

Step-by-step explanation:

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364

a1+a2 = a3, a2+a3=a4 etcetera..

1+3 =4

3+4 =7

4+7=11

.

.

a13+a14 = a15

521+843 = 1364

so, 1364 is the answer

Test for exactness. If exact, solve it directly. Otherwise, use integrating factors to solve it. Solve the IVP (if given). 2xy + (x^2) y' = 0
sin(x) cos(y) + cos(x) sin(y) y' = 0
(x^2) + (y^2) - 2xyy' = 0
e^(2x).(2 cos(y) - sin(y) y') = 0, where y(0) = 0​

Answers

• 2xy + x ² y' = 0

This DE is exact, since

∂(2xy)/∂y = 2x

∂(x ²)/∂x = 2x

are the same. Then there is a solution of the form f(x, y) = C such that

f/∂x = 2xy   ==>   f(x, y) = x ² y + g(y)

f/∂y = x ² = x ² + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x ² y = C

• sin(x) cos(y) + cos(x) sin(y) y' = 0

is also exact because

∂(sin(x) cos(y))/∂y = -sin(x) sin(y)

∂(cos(x) sin(y))/∂x = -sin(x) sin(y)

Then

f/∂x = sin(x) cos(y)   ==>   f(x, y) = -cos(x) cos(y) + g(y)

f/∂y = cos(x) sin(y) = cos(x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = -cos(x) cos(y) = C

• x ² + y ² - 2xyy' = 0

is not exact:

∂(x ² + y ²)/∂x = 2x

∂(-2xy)/∂y = -2x

So we look for an integrating factor µ(x, y) such that

µ (x ² + y ²) - 2µxyy' = 0

becomes exact, which would require that these be equal:

∂(µ (x ² + y ²))/∂y = (x ² + y ²) ∂µ/∂y + 2µy

∂(-2µxy)/∂x = -2xyµ/∂x - 2µy

Observe that if µ(x, y) = µ(x), then ∂µ/∂y = 0 and ∂µ/∂x = dµ/dx, so we would have

2µy = -2xy dµ/dx - 2µy

==>   -2xy dµ/dx = 4µy

==>   dµ/µ = -2/x dx

Integrating both sides gives

∫ dµ/µ = ∫ -2/x dx   ==>   ln|µ| = -2 ln|x|   ==>   µ = 1/x ²

So in the modified DE, we have

(1 + y ²/x ²) - 2y/x y' = 0

which is now exact and ready to solve, since

∂(1 + y ²/x ²)/∂y = 2y/x ²

∂(-2y/x)/∂x = 2y/x ²

We get

f/∂x = 1 + y ²/x ²   ==>   f(x, y) = x - y ²/x + g(y)

f/∂y = -2y/x = -2y/x + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x - y ²/x = C

• exp(2x) (2 cos(y) - sin(y) y' ) = 0

is exact, since

∂(2 exp(2x) cos(y))/∂y = -2 exp(2x) sin(y)

∂(-exp(2x) sin(y))/∂x = -2 exp(2x) sin(y)

Then

f/∂x = 2 exp(2x) cos(y)   ==>   f(x, y) = exp(2x) cos(y) + g(y)

f/∂y = -exp(2x) sin(y) = -exp(2x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = exp(2x) cos(y) = C

Given that y = 0 when x = 0, we find that

C = exp(0) cos(0) = 1

so that the particular solution is

exp(2x) cos(y) = 1

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?

Answers

Answer:

[tex]\displaystyle 64[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Rule [Variable Direct Substitution Exponential]:                                         [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]

Step 2: Solve

Rewrite [Limit Property - Multiplied Constant]:                                           [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:       [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer: C. 64

Step-by-step explanation:

Edge 100%

Find all the zeros of f(x).
f(x) = 2x3 + 7x2 - 28x + 12
Arrange your answers from smallest to largest. If
there is a double root, list it twice.

Plz help!

Answers

Answer:

The zeroes are -6, 1/2 and 2.

Step-by-step explanation:

f(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one guess for a zero is x = 2.

So substituting x = 2:

f(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient

       2x3  - 4x2

                 11x2 - 28x

                 11x2 - 22x

                          - 6x + 12

                           -6x + 12

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

Now we solve

2x2 + 11x - 6 = 0

(2x - 1)(x + 6) = 0

2x - 1 = 0 or x + 6 = 0, so:

x = 1/2,  x = -6.

Answer: -6, 1/2, 2.

Step-by-step explanation:

{(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one

guess for a zero is x=2.

So substituting x=2:

{(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <

Quotient

A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 10 yd3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

Answers

Answer:

The dimensions are:

l = 2*1.96 = 3.92 yd

h = 5/(1.96)² = 1.30 yd

w = 1.96 yd

Step-by-step explanation:

The volume is given by:

[tex]V=l*w*h[/tex]

Where:

l is the longw the wide h the height

We know that l = 2w, so we have:

[tex]V=2w^{2}*h[/tex]

[tex]10=2w^{2}*h[/tex]

[tex]5=w^{2}*h[/tex] (2)

Now, the surface of this parallelepiped is:

[tex]S=2wh+2lh+lw[/tex]

Using l = 2w:

[tex]S=2wh+4wh+2w^{2}[/tex]

Using (2) we obtain the surface equation in terms of w.

[tex]S=2w\frac{5}{w^{2}}+4w\frac{5}{w^{2}}+2w^{2}[/tex]    

[tex]S=2\frac{5}{w}+4\frac{5}{w}+2w^{2}[/tex]

We need to take the derivative with respect to w to minimize the surface area.

[tex]S=2\frac{5}{w}+4\frac{5}{w}+2w^{2}[/tex]  

[tex]S=\frac{30}{w}+2w^{2}[/tex]

[tex]\frac{dS}{dw}=-\frac{30}{w^{2}}+4w[/tex]

Now, let's equal it to zero.

[tex]0=-\frac{30}{w^{2}}+4w[/tex]  

[tex]\frac{30}{w^{2}}=4w[/tex]              

[tex]w^{3}=\frac{30}{4}[/tex]          

[tex]w=1.96\: yd[/tex]  

So, l = 2*1.96 = 3.92 yd and h = 5/(1.96)² = 1.30 yd

Therefore, the dimensions are:

l = 2*1.96 = 3.92 yd

h = 5/(1.96)² = 1.30 yd

w = 1.96 yd

I hope it helps you!

Other Questions
please tell this question answer I dont know Use the figure to find u. Which statement best summarizes the relationship between investments andproductivity?A. Companies improve their productivity using money frominvestments.B. Companies decide on their level of productivity based on theirinvestments.C. Companies use investments to avoid having to improveproductivityD. Companies with low levels of productivity have no need forinvestment.SUBNE Jeff has 20 coins. 2/5 of them are quarters. How many quarters does he have? How many coins are not quarters? you are pedaling forward on your bike. which of the following would decrease your acceleration?A. A decrease in your massB. A increase in your applied forceC. An increase in your massD. An increase in your speed In a poll, adults in a region were asked about their online vs. in-store clothes shopping. One finding was that % of respondents never clothes-shop online. Find and interpret a % confidence interval for the proportion of all adults in the region who never clothes-shop online. A human resources office is working to implement an increase in starting salaries for newadministrative secretaries and faculty at a community college. An administrative secretarystarts at $28,000 and new faculty receive $40,000. The college would like to determine thepercentage increase to allocate to each group, given that the college will be hiring 8secretaries and 7 faculty in the upcoming academic year. The college has at most $5,000 toput towards raises. What should the percentage increase be for each group? Given: Line AC is parallel to DF, Line BE is perpendicular to DF, and angle AEB is congruent to angle CEB, prove angle BAE is congruent to angle BCE. Will give Brainliest if explained thoroughly. A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x 4)2 = 202. What is the value of x, the length of the screen? x = 16 x = 12 x = 12 x = 16 someone help me my browser is updated I don't know what to do someone help me please I'm trying to watch Crunchyroll. which of the folleing is a statistical question? a) how tall is steve?b)what are the heights of students in class?c)what is the formula for the volume of the cube?d) what is the address of the white house? Construct a dialogue between Einstein and the History teacher. Eid Mubarak!!Since it's Eid Al-Adha today, explain why Muslims sacrifice goats, sheeps, camels, or cows?Do not use go.ogle or else you will be reported InshAllah. May Allah guide us all, ameen. Assume that abc = pqr. Which of the following congruence statements are correct? Check all that apply Please help me I will give brainliestDirections: Rewrite each sentence replacing the D.O.N.(direct object noun) with a D.O.P. (direct object pronoun) - (Underline the direct object noun, then replace it with the appropriate pronoun)1. Los estudiantes estn comiendo muchos tacos.____________________________________ if ax^3+9x^2+4x-10 when divided by x-3 leaves the reminder 5,then a= Which sequence or sequences are correct and why? Translate You were able to fo it into Spanish by filling in the missing letters How did the Atlantic slave trade impact the Americas role in triangular trade? DeWitt Industries has adopted the following production budget for the first 4 months of 2017. Month Units Month Units January 10,440 March 5,190 February 8,240 April 4,120 Each unit requires 3 pounds of raw materials costing $2 per pound. On December 31, 2016, the ending raw materials inventory was 9,500 pounds. Management wants to have a raw materials inventory at the end of the month equal to 20% of next months production requirements. Prepare a direct materials purchases budget by month for the first quarter.