A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a function

The expression simplifies using multiple properties of exponents, including the power of a product, properties of exponents for multiplication and division, the zero exponent property, and squaring.

The expression you're asking about applies multiple properties of exponents to simplify the given expression. To start, applying the power of a product property, it simplifies [tex](4*9)^5[/tex] to [tex]4^5*9^5[/tex]. Following that, the property of exponents for division is used to combine [tex]4^{-5[/tex] and [tex]4^5[/tex], leading to [tex]4^0[/tex], as well as [tex]9^5[/tex] and [tex]9^{-3[/tex], resulting in [tex]9^2[/tex]. The zero exponent property translates [tex]4^0[/tex]into 1. Lastly, the square of 9 gives the end result of 81.

In summary, these are the properties applied: power of a product, properties of exponents for multiplication and division, zero exponent property, and squaring.

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Final answer:

To determine the volume of a greenhouse, multiply its length, width, and height to find its volume in cubic feet, then convert to cubic yards using the conversion factor of 1 cubic yard being equivalent to 27 cubic feet. The volume for the given dimensions is approximately 129.63 cubic yards.

Explanation:

The volume of a structure, including a greenhouse, is calculated by multiplying its length by its width by its height. The first step is to calculate the volume in cubic feet, then convert cubic feet to cubic yards knowing that 1 cubic yard equals 27 cubic feet. Here's how to calculate the volume of the given greenhouse:

Therefore, the volume of the greenhouse is 129.63 cubic yards.

L=3W

2(3W+W)=32 feet

8W=32 feet

W=4 feet

L=3W

L=3* 4 feet

L=12 feet

The width is 4 feet, the length is 12 feet.

Answer:the answer is B No,set of side length does not satisfy triangle inequality theorem

Step-by-step explanation:

cross multiply:

21*9 = 189

7*q = 7q

so you have 189/7q

 divide 189 by 7 to get q

189 / 7 =27

q = 27

The ratio should be 3:4

Given that,

Based on the above information, the calculation is as follows:

= 6:8

= 3:4

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Answer:

The answer is A. Thanks

Step-by-step explanation:

Making 'h' the subject , the expression obtained is h = 3V/ πr²

Given the volume formula :

To make 'h' the subject

multiply both sides by 3

3V = πr²h

divide both sides by πr² in other to isolate 'h'

3V/ πr² = πr²h/πr²

h = 3V/ πr²

Therefore, making 'h' the subject , the expression obtained is :

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Answer:

c

Step-by-step explanation:

The marginal product of the second worker is b. 75 dumplings.

To find the marginal product of the second worker, we need to determine how many additional dumplings the second worker is able to produce compared to the first worker. The marginal product (MP) of a worker is calculated as follows

[tex]\[ MP = \text{Total production with two workers} - \text{Total production with one worker} \][/tex]

[tex]\[\]\[ \text{Total production with one worker} = 100 \text{ dumplings} \]\[ \text{Total production with two workers} = 175 \text{ dumplings} \][/tex]

[tex]\[\]\[ MP = 175 \text{ dumplings} - 100 \text{ dumplings} \]\[ MP = 75 \text{ dumplings} \][/tex]

Answer:  The required area of the given circle is [tex]400\pi~\textup{m^2}.[/tex]

Step-by-step explanation:  We are given that the diameter of a circle i 40 m.

We are to find the area of the circle in terms of pie.

We know that

the AREA of a circle with radius of length r units is given by

[tex]A=\p r^2.[/tex]

Since the diameter of the given circle is 40 m, so the length of the radius is given by

[tex]r=\dfrac{40}{2}=20~\textup{m}.[/tex]

Therefore, the AREA of the circle is given by

[tex]A=\pi r^2=\pi\times 20^2=400\pi~\textup{m}^2.[/tex]

Thus, the required area of the given circle is [tex]400\pi~\textup{m}^2.[/tex]

28π in^3

56/3π in^3

196/3π in^3

196π in^3

These are the numbers they meant to put and the answer is 196/3 in^3.

since angle 3 = 47, then angle 1 also = 47

this would mean that both angles 5 & 7 are also 47

so angle 5 = 47 degrees

It will take approximately 1.459 years for a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.

To find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly, we can use the formula A = P(1+rn)^(nt). Plug in the values: A = 2200 + 210 = 2410, P = 2200, r = 0.10 (10%), n = 12 (compounded monthly), and t = ?

2410 = 2200(1 + 0.10/12)^(12t). Divide both sides by 2200 to isolate the expression:

1.095 = (1 + 0.10/12)^(12t). Take the natural logarithm of both sides to remove the exponent:

ln(1.095) = 12t * ln(1 + 0.10/12). Solve for t:

t = ln(1.095) / (12 * ln(1 + 0.10/12)). Use a calculator to find the value of t, which is approximately 1.459 years when rounded to 3 decimal places.

Answer: 0.1

Step-by-step explanation: Okay. So, the weight of 10,000 samples is 1 pound. To find the weight of each sample, we can do 10/10,000, which would give us 0.001. Each sample weighs 0.001 pound. We can multiply that times 100 to find the weight of 100 samples. 0.001 * 100 = 0.1. The weight of 100 samples is 0.1 pound.

Answer : The number of views expected to be four weeks from now is, 42

Step-by-step explanation :

Formula for exponential growth is :

[tex]y=a(1+r)^x[/tex]

where,

y = exponential growth = ?

a = initial amount of growth = 20

r = growth rate = 20% = 0.20

x = number of time intervals that have passed = 4

Now put all the given values in the above formula, we get:

[tex]y=20\times (1+0.20)^4[/tex]

[tex]y=41.475\aaprox 42[/tex]

Thus, the number of views expected to be four weeks from now is, 42