A rectangular gift box has dimensions that can be represented as shown in the figure. The volume of the box is 56w cubic inches. Which of the following is not a dimension of the box?

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

Answer:

Solution given:

AB parallel BH parallel CH

1.

In triangle ∆AFD ,∆BGD ,∆CHD

<AFD=<BGD=<CHD

[being corresponding angle]

<DAF=<DBG=<DCH

[being corresponding angle]

<D is common for all.

So

∆AFD ~∆BGD ~∆CHD

[By A .A .A. axiom]

The graph is attached below:

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given:

x − 10 ≤ x ≤ 15

as, the given inequality we have to break the inequality is

x − 10 ≤ x and x ≤ 15

The graph to the inequality is attached below.

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2HD + 3S = $7 and 4HD + 2S = $10

Then cost of 1 HD is $2 and 1S is $1.

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Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

\(\rm y = 90 e^{-0.0678 * x}\\\)

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

\(\rm 45 = 90 e^{-0.0678 * x}\\\)

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

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Answer:

A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.

Step-by-step explanation:

ABCD: A(-4,-3), B(-3,-1), C(-2,-3), and D(-3,-4).

If we rotate ABCD counterclockwise by 90 degrees, we obtain the translation

\(R$otation of 90\º: (x,y)\rightarrow (-y,x)\)

This gives:

A''(3,-4), B''(1,-3), C''(3,-2), and D''(4,-3).

Next, we reflect A''B''C''D'' across the x-axis. (Note that the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.)

\(R$eflection accross the x-axis: (x,y)\rightarrow (x,-y)\)

This then gives us the coordinates

A'B'C'D': A'(3, 4), B'(1, 3), C'(3, 2), and D'(4, 3)

Answer:

A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.

Step-by-step explanation:

ABCD: A(-4,-3), B(-3,-1), C(-2,-3), and D(-3,-4).

If we rotate ABCD counterclockwise by 90 degrees, we obtain the translation

This gives:

A''(3,-4), B''(1,-3), C''(3,-2), and D''(4,-3).

Next, we reflect A''B''C''D'' across the x-axis. (Note that the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.)

This then gives us the coordinates

A'B'C'D': A'(3, 4), B'(1, 3), C'(3, 2), and D'(4, 3)

Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours

Step-by-step explanation:

Damien = X -21

Caitlyn = X

2X - 21 = 14

2X = 14 + 21

X = (14+21)/2

X = 7.5

The dotted folded image in option {A} can be used to make a triangular prism.

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Given is a triangular prism as shown in the image.

The dotted folded image in option {A} can be used to make a triangular prism.

Therefore, the dotted folded image in option {A} can be used to make a triangular prism.

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Answer:

11/17

Step-by-step explanation:

Answer:

vertex = (0, -4)

equation of the parabola:  \(y=3x^2-4\)

Step-by-step explanation:

Given:

Vertex form of a parabola:  \(y=a(x-h)^2+k\)

(where (h, k) is the vertex and \(a\) is some constant)

Substitute point (0, -4) into the equation:

\(\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}\)

Substitute point (-2, 8) and \(ah^2+k=-4\) into the equation:

\(\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}\)

Substitute point (1, -1) and \(ah^2+k=-4\) into the equation:

\(\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}\)

Equate to find h:

\(\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}\)

Substitute found value of h into one of the equations to find a:

\(\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}\)

Substitute found values of h and a to find k:

\(\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}\)

Therefore, the equation of the parabola in vertex form is:

\(\implies y=3(x-0)^2-4=3x^2-4\)

So the vertex of the parabola is (0, -4)

It can be solved through some shortcut tricks of parabola

It passes through (-2,8) and (1,-1)

The minimum equation of the parabola (as it's quadratic) for vertex at (0,0)

whatever our required parabola be it's translated from the above one

So

Let a be 0

So it has vertex as well as y inetrcept at (0,0)

For x=-2

For x=1

It wasn't negative but in translation it's negative so something is subtracted

Take a =2 and subtract (-2)² i.e 4 as it's minimal value of y=x² where x≠y

For

(-2,8)

No try a=3

Yes satisfied

Take (1,-1)

Verified

The required equation is

Answer:

Mark up percent is 17.2 and the new price is 60.8

Step-by-step explanation:

22% = 100/22 = 0.22

so 0.22 of 78 is 0.22 x 78

and you get 17.16

round it and you get 17.2 for the mark up

To find the new price simply subtract the original price to the markup

78-17.16=60.84

Answer: 584 yds

Step-by-step explanation:

3mi-3mi=0

1622-1038=584yds

Answer:

2251.86

Step-by-step explanation:

hope this works

The multiplication is gives 2400.

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.

Given number:

288.7 x 7.8

Now, rounding to 1 significant figure

288. 7 = 300

7.8 = 8

So, the multiplication is as follows:

=300* 8

= 2400

Hence, the multiplication is 2400.

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Answer:

100% = 65 Gallons; 70% = 45.5 Gallons

Step-by-step explanation:

The important piece of information here is that 13 gallons of water makes the container 1/5 of the way full, aka 20%.  If the question is simply, how many gallons will it hold, then we multiply 13 by 5 to get 100% at 65 gallons.  To get the amount held at 7/10, or 70%, we simply multiply 65 with 7/10 to get 45.5 gallons.

Cheers.

Answer:

europa can blow my almonds OwO

Step-by-step explanation:

Answer:

D. \(3x\sqrt{2x}\)

Step-by-step explanation:

The problem gives on the following equation:

\(\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}\)

Alongside the information that (\(x\geq0\)).

One must bear in mind that the operation (\(\sqrt\)) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

\(\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}\)

Now remove the duplicate factors from underneath the radical,

\(2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}\)

Simplify,

\(4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}\)

\(3x\sqrt{2x}\)

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

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

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

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

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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For given functions, The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

What is the definition of a function?

A function is a mathematical rule that gives each input value a distinct output value. A function is officially defined as a collection of ordered pairs (x, y) in which each input value x is coupled with exactly one output value y. The domain of the function refers to the input values, while the range refers to the output values. A graph, table, equation, or verbal explanation can all be used to depict a function. When the input value is x, the notation f(x) is commonly used to express the output value of a function f.

Now,

From given function f(x) and g(x)

For f(x) when x=0 then y=1 or y-intercept=1

for g(x), the y-intercept is 1 from equation y=4x+1

and slope of g(x)=4

and slope of f(x)=(11-1)/(2-0)

=10/5

=2

Hence,

           The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

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The other number in discuss which is related to 189 as described in the task content is; 297.

It follows from the task content that the LCM and HCF of the two numbers in discuss are given and hence, the second number is to be determined accordingly.

Since it follows from the concept of lowest common multiple, LCM and greatest common factor, HCF that the product of LCM and HCF is equivalent to the product of the two numbers in discuss.

Consequently, let, x = the other number

2079 × 27 = 189 × x

x = (2079 × 27)/189

x = 297.

Therefore, it follows from evaluation that the other number in discuss which is related to 189 as described in the task content is; 297.

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Answer:

0.14 i guess

Step-by-step explanation:

Step-by-step explanation:

nl the way home now so I'm gonna get

The volume of the solid rounded to the nearest whole number is approximately 262 cubic units.

If we rotate a semicircle about its diameter, we get a solid called a hemisphere. The volume of a hemisphere is given by the formula:

V = (2/3)πr³

where r is the radius of the hemisphere.

In this case, the diameter of the semicircle is given as 10, so the radius is half of that, i.e., r = 5. Substituting this value in the formula, we get:

V = (2/3)π(5)³

= (2/3)π(125)

= 250π/3

≈ 261.8

What is the area and volume of hemisphere?

The curved surface area of a hemisphere = 2r² square units. The total surface area of a hemisphere = 3r² square units. The volume of a hemisphere is determined by the formula (⅔)r cubic units.

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Answer:

A would be your answer if I'm not mistaken