A shipping box has the dimensions shown. What is the volume of the box in cubic yards?
À yard
yard
yard
Not drawn to scale.
1
yo
16 Yd3
32 Yd3
20 Y3

Answer:

Option (B) 0.00076

Step-by-step explanation:

Surface area of a sphere = 4πr²

Volume of a sphere = 4π/3 (r³)

Surface area : Volume = 4πr² : 4π/3 (r³)

                                      = r² : 1/3 (r³)

                                      = 3 r² : r³

                                      = 3/r

                                      = 3/3960

                          (AFTER SIMPLIFICATION)

                                      = 0.00076

Hence the answer is option (B) 0.00076

Hope my answer help you ✌️

The correct option is B) 0.00076. The surface-area-to-volume ratio is 0.00076.

To find the approximate surface-area-to-volume ratio of the Earth with a radius of approximately 3,960 miles, we will use the following formulas:

Surface area (A) of a sphere: A = 4πr²
Volume (V) of a sphere: V = (4/3)πr³

Step 1: Calculate the surface area:
A = 4π(3,960)² ≈ 197,392,088 square miles

Step 2: Calculate the volume:
V = (4/3)π(3,960)³ ≈ 260,625,332,197 cubic miles

Step 3: Calculate the surface-area-to-volume ratio (A/V):
A/V ≈ 197,392,088 / 260,625,332,197 ≈ 0.000757

The best answer from the choices provided is B. 0.00076.

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Answer:

4x⁶(1+2x²)²

Step-by-step explanation:

Factor out the common term 2x³

Use Multiplication Distributive Property: (xy)^a=x^a y^a

Simplify 2² to 4

The use the power rule and you get 4x⁶(1+2x²)²

This is the solution to the given system of initial value problem. x(t) = 2e^t[1 2 1] + e^(2t)[1 1 2] + e^(-2t)[1 -5 2]

To solve the system of initial value problem (IVP) x' = Ax, where A is the given matrix and x(0) is the initial condition, we need to find the solution x(t) at any time t.

First, let's represent the given matrix A:

A = [3 -1 0]

[4 -2 0]

[4 -4 2]

To find the solution, we need to find the eigenvalues and eigenvectors of the matrix A.

Using the characteristic equation, we have:

|A - λI| = 0

where λ is the eigenvalue and I is the identity matrix.

Solving the determinant equation, we get:

(3 - λ)(-2 - λ)(2 - λ) + 4(-1)(4 - λ) - 4(4)(-2 - λ) = 0

Expanding and simplifying, we have:

(λ - 1)(λ - 2)(λ + 2) = 0

From this equation, we can see that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = -2.

Next, we find the eigenvectors associated with each eigenvalue.

For λ₁ = 1, we solve the equation (A - λ₁I)v₁ = 0, where v₁ is the eigenvector:

(2 - 1)v₁₁ - v₁₂ = 0

4v₁₁ - 2v₁₂ = 0

4v₁₁ - 4v₁₂ + 2v₁₃ = 0

Simplifying and solving the system of equations, we find v₁ = [1 2 1].

For λ₂ = 2, we solve the equation (A - λ₂I)v₂ = 0, where v₂ is the eigenvector:

v₂₁ - v₂₂ = 0

4v₂₁ - 4v₂₂ + 2v₂₃ = 0

4v₂₁ - 2v₂₂ = 0

Solving the system of equations, we find v₂ = [1 1 2].

For λ₃ = -2, we solve the equation (A - λ₃I)v₃ = 0, where v₃ is the eigenvector:

5v₃₁ + v₃₂ = 0

4v₃₁ - 2v₃₂ = 0

4v₃₁ - 4v₃₂ + 4v₃₃ = 0

Solving the system of equations, we find v₃ = [1 -5 2].

Now, we can write the general solution of the system as:

x(t) = c₁e^(λ₁t)v₁ + c₂e^(λ₂t)v₂ + c₃e^(λ₃t)v₃

where c₁, c₂, and c₃ are constants determined by the initial condition x(0).

Given the initial condition x(0) = [7 10 2], we can substitute this into the general solution and solve for the constants:

[7 10 2] = c₁v₁ + c₂v₂ + c₃v₃

Solving this system of equations, we find c₁ = 2, c₂ = 1, and c₃ = 1.

Finally, substituting the values of the constants and the eigenvectors into the general solution, we obtain the solution to the system of IVP:

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To answer this question, we'll use the exponential distribution and the concept of the probability density function (pdf). Let X be the time until failure of a single device, with a mean lifetime of 20 months. The exponential distribution has the following pdf:

f(x) = (1/μ) * e^(-x/μ),

where μ is the mean lifetime (20 months in this case).

Now, let's find the probability that the first failure occurs at w months among the 5 independent devices. For this, we need to calculate the probability that none of the other 4 devices fail before w months and that the first device fails at w months.

The probability that a single device does not fail before w months is given by the complementary cumulative distribution function (ccdf) of the exponential distribution:

P(X > w) = e^(-w/μ).

Since the devices are independent, the probability that all 4 devices do not fail before w months is:

P(All 4 devices survive > w) = (e^(-w/μ))^4.

Now, the probability that the first device fails at w months is given by the pdf of the exponential distribution:

P(X = w) = (1/μ) * e^(-w/μ).

Finally, we multiply the two probabilities to find the chance that the first failure occurs at w months:

P(First failure at w) = P(All 4 devices survive > w) * P(X = w)
= (e^(-w/μ))^4 * (1/μ) * e^(-w/μ)
= (1/20) * e^(-5w/20).

Thus, the chance that the first failure will occur at w months is given by the expression (1/20) * e^(-5w/20).

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9514 1404 393

Answer:

  -3 < b < 3

Step-by-step explanation:

The inequality is equivalent to two inequalities.

For b ≥ 0, this is ...

  b < 3

Together with the restriction that b ≥ 0, the solution to this is ...

  0 ≤ b < 3

__

For b ≤ 0, this is ...

  -b < 3

  b > -3 . . . . multiply by -1

Together with the restriction that b ≤ 0, the solution to this is ...

  -3 < b ≤ 0

__

The solution is the 'or' of these two solutions. They can be expressed as the single compound inequality ...

  -3 < b < 3

_____

Comment on absolute value inequalities

When the inequality is of the form ...

  |p| < q

It can be written as the equivalent compound inequality ...

  -q < p < q

as we showed above.

Answer:

Please check the explanation!

Step-by-step explanation:

Given the expression what Lizzet said was correct

\(6^3\times \:\:3^6=18^8\)

No, she is not right. Let me solve the expression

Let us solve the expression

\(6^3\times \:\:3^6\)

\(=\left(3\times \:2\right)^3\times \:3^6\)

\(\mathrm{Apply\:exponent\:rule}:\:\:\:\left(ab\right)^c=a^cb^c\)

\(=3^3\times \:2^3\times \:3^6\)          ∵  \(\left(3\times \:2\right)^3=3^3\times \:2^3\)

\(\mathrm{Apply\:exponent\:rule}:\:\:a^b\times \:\:a^c=a^{b+c}\)

\(=2^3\times \:3^{3+6}\)                 ∵  \(3^3\times \:3^6=\:3^{3+6}\)

\(=2^3\times \:3^9\)

Therefore, the correct expression will be:

\(6^3\times \:\:3^6=2^3\times \:\:3^9\)

which can be further simplified such as:

\(6^3\times \:\:3^6=2^3\times \:\:3^9\)

             \(=8\times \:19683\)

             \(=157464\)

The length of the third side can be in range of [1, 17].

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Given is that in triangle ABC, AB = 6 and BC = 11.

In a triangle, the sum of two sides of a triangle is always greater than the third side. This means -

AB + BC > AC

(6 + 11) > AC

AC < 17

Therefore, the length of the third side can be in range of [1, 17].

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The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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Answer:

hm? is there any picture that they gave you or no?

Step-by-step explanation:

Answer:

Could you please help me with the two most recent questions of mine on my page? I will give u brainliest and 20 points! :))) X

Step-by-step explanation:

Answer:

a: 0

b: 1,3

c: 2

Step-by-step explanation:

a: 4 is the y intercept meaning 0 is the number of seconds when the ball is 4 feet in the air

b: to easily find this, we can graph.

1st screenshot is for B.

We see that y=52 intersects twice with the graph, meaning the ball was at 52 feet twice. the times are 1 second and 3 seconds

a: we graph again, but with y=68 we see that it only intersects once. at x=2.

Answer:

the answer is c 95

Step-by-step explanation:

180-41-44=95

a  triangle has 180 degrees

Answer: I think A. 75

Step-by-step explanation: why not pick A……

Hope this helps^^

Answer: 0.15%

Step-by-step explanation: edmentum

Answer:

Step-by-step explanation:

the answer is 0.15

if QRST is indeed a quadrilateral, then, Check the picture below.

Answer:

-5

Step-by-step explanation:

[] Slope can be solved by using rise over run when we have two points on a graph.

-> Starting at (0, 4) we will count down 5 units down to (0, -1)

-> Then, we will count one unit to the right to our second point, (1, -1)

[] We counted down 5, so -5 in the numerator, and we counted one to the right, so +1 in the denominator.

-> \(\frac{-5}{1}\) which can be written as -5

[] Slope can also be calculated mathematically with change in y divided by change in x

-> \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

d = 72

Step-by-step explanation:

d + 13 + 95 = 180

(Angles are supplementary)

d + 108 = 180

d = 180 - 108

d = 72

Answer:

No solutions

Step-by-step explanation:

They have the same slope(5), meaning that they are parallel. since they are parallel they will never touch, thus there are no solutions

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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A function is even if the graphic is symmetric with respect to the y-axis.

You can symbolize an even function as -f(x)=f(x) for all values of x on the domain of the function f.

A)

The expression |y| indicates that its the absolute value of y. This means that y can be positive or negative.

This function is even.

B)

In this example x is expressed as an absolute value and can be either positive or negative:

This function is symetrical with respect to the y-axis, so it an even function.

C)

This function is not symetrical with respect to the y-axis

D)

This function is not symmetrial with respect to the y-axis

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer:

c = 10

Step-by-step explanation:

The pythagoras theorem :

a² + b² = c²

a = 6 and b = 8

6² + 8² = c²

36+64 = c²

100 = c²

c = √100

c= 10

Hope this helped and brainliest please

Answer:

23%

Step-by-step explanation:

Answer:

23 %

Step-by-step explanation:

The total money earned:

124+ 30+ 46 =200

Percent earned babysitting

money earned babysitting / total * 100%

46/200 * 100 = 23 %

If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

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Answer:          A.O.C                                                   U.S.C          

Wrote it: Benjamin Franklin                             James Madison

Ratified It: 13 colonies                                    the federalists

Delays:   the insistence of Maryland that     War

all states give up their western land

claims to the central government.

Type Gov. created: loose confederate        democratic republic

government

Type Cong. :Second Continental Congress      the Legislative Branch

Title Exe. : President for both columns

Power to National:                         enumerated powers

Powers to state:these included the “police powers” of health, education, and welfare.

Answer:

12

Step-by-step explanation:

With PEMDAS you could know to do parentheses FIRST

6 x (10 - 2^3)

6 x (2)

12

Answer:

your answer would be 12

Step-by-step explanation:

Incordding to math this dot is mutpcation

but next to it is is a bracket in math a bracket me you need to add or subtrack evrything  in it  then multpliy the answer with the the number in it

so we just need simplfy what in the bracket

so the equation is actaliy 6x2.Hence the answer is 12

Answer:

8

Step-by-step explanation:

count up from where s is (-7) to where v is (1) there are 8 numbers in between them. making that he length

Answer:

S= -7 to V= 1 so your answer is 8

Answer:

measurement of each interior angle of a regular hexagon is 120°

sum of the numbered angles is 720°

Step-by-step explanation:

m<1 = 120°

m<2 = 120°

m<3 = 120°

the sum of the all the numbered six interior angles of a regular hexagon = 720°

Answer:

2,700in

Step-by-step explanation: