2.1, -2.1, 2 and 2 1/11, -2 from least to greatest show work

Three different equivalent expressions for 16x^8 are [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex].

Expressing [tex]\(16x^8\)[/tex] in three different equivalent forms:

1. Expanded Form:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex]

2. Factored Form:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex]

3. Exponential Form with a Common Base:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex]

These expressions show the flexibility in representing the original expression using different algebraic manipulations. The key is to recognize patterns, use properties of exponents, and factor out common terms.

Answer: [tex]\dfrac{7}{3}x-2[/tex]

Step-by-step explanation:

Let x be the width of the rectangle , then the length of the rectangle will be :_

Length = [tex]\dfrac{1}{6}x-1[/tex]

We know that the perimeter of a rectangle is given by :-

[tex]P=2(l+w)[/tex]

Substitute the value of length and width we get,

[tex]P=2(\dfrac{1}{6}x-1+x)[/tex]

Combine like terms, we get

[tex]P=2(\dfrac{1+6}{6}x-1)\\\\\Rightarrow\ P=2(\dfrac{7}{6}x-1)\\\\\Rightarrow\ P=2\times\dfrac{7}{6}x-2\times1\\\\\Rightarrow\ P=\dfrac{7}{3}x-2[/tex]

Hence, the expression represents the perimeter of the rectangle : [tex]\dfrac{7}{3}x-2[/tex]

Final answer:

The conditional pmf of x, the number of patterns tested until the correct m-bit password is found, given that the password has not been found after k tries, is uniformly distributed with 1/(2^m - k) for x = k+1, k+2, ..., 2^m.

Explanation:

The question deals with the topic of probability and specifically centers around the concept of a conditional probability mass function (pmf). Given that an m-bit password is systematically being guessed by a hacker and has not been found after k attempts, we need to find the conditional pmf of x, where x is the number of patterns tested until the password is found.

Since the password has not been guessed within the first k tries, the conditional probability is based on the remaining 2m - k possibilities. The distribution of x will be uniform because each subsequent attempt has an equal probability of being correct. The conditional pmf of x given that the password was not found after k tries is 1/(2m - k) for x = k+1, k+2, ..., 2m.

The value of 'w' using the given slope is [tex]\frac{9}{2}[/tex]

Given :

the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8

apply slope formula

[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values given in the points and make it equal to 1/8

[tex]slope =\frac{4-w}{-10+6}=\frac{1}{8} \\\frac{4-w}{-4}=\frac{1}{8}\\(4-w)(8)=-4(1)\\32-8w=-4\\-8w=-4-32\\-8=-36[/tex]

Divide both sides by -8

[tex]w=\frac{-36}{-8} =\frac{9}{2}[/tex]

The value of 'w' is [tex]\frac{9}{2}[/tex]

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The Boardman family's walking speed is 1.4 miles per hour, which is calculated by dividing the distance walked (2/5 mile) by the time it took (2/7 hour).

A unit rate defines how many units of the first type of quantity correspond to one unit of the second type of quantity. In this case, we need to find out how many miles they walk in one hour.

To calculate the unit rate, we divide the distance by the time. They walked 2/5 of a mile in 2/7 of an hour. Setting up the division, we have:
(2/5) miles / (2/7) hours = (2/5) × (7/2) miles per hour = 7/5 miles per hour

After simplifying, we get that the Boardman family's walking speed is 1.4 miles per hour.

Answer:

x.(-1/7,0)

y.(0,1/4)

Step-by-step explanation:

To solve the problem we must know about the volume and the surface area of cuboids.

The length of the aquarium is 4, and the width of the aquarium is 8.

Given to us

We know that the base of the aquarium should be a square, therefore, the length and the breadth of the aquarium will be the same.

Length x breadth x height = 256 ft³

Length x Length x height = 256 ft³

Length ² x height = 256 ft³

[tex]L^2\times H = 256\\\\H = \dfrac{256}{L^2}[/tex]

Surface Area of the Aquarium

= Area of the base + (4 x Area of the 4 sides)

[tex]= L^2 + 4(L\times H)[/tex]

Substituting the value of H,

[tex]= L^2 + 4L(\dfrac{256}{L^2})[/tex]

Let the surface area be a function of L, therefore,

[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})[/tex]

Differentiating the function to get the minimum,

[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})\\\\f(L) = L^2 + (\dfrac{1024}{L})\\\\f'(L) = 2L - (\dfrac{1024}{L^2})[/tex]

Equating against zero,

[tex]2L - (\dfrac{1024}{L^2}) = 0\\\\\dfrac{2L^3-1024}{L^2} = 0\\\\2L^3-1024 = 0\\\\L = 8[/tex]

Substituting the value of L,

[tex]H = \dfrac{256}{L^2}\\\\H = \dfrac{256}{8^2}\\\\H = 4[/tex]

But this way the area will be more, therefore, replace the value of L with 8,

L = 4

H = 8

Hence, the length of the aquarium is 4, and the width of the aquarium is 8.

Learn more about Volume of the cuboid:

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The translation of the statement '55 times what number is 1265?' into an equation is '55 * x = 1265', which, with 'dot' finding use as multiplication, matches with the provided option A) 55 dot x = 1265.

The question asks for the translation of the problem statement into an equation. The phrase '55 times what number is 1265?' implies multiplication. Specifically, 55 is being multiplied by an unknown number (which we can denote by 'x'), and the result of this multiplication is 1265. Therefore, the correct translation of this problem into an equation would be 55 * x = 1265 or in the provided options A) 55 dot x = 1265 where 'dot' indicates multiplication.

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To measure the approximately 4,000 km long Mississippi River with M&Ms, we will need about 400,000,000 M&Ms, as there are 100 cm in a meter and 1,000 m in a km.

The question involves estimating the length of the Mississippi River using the size of M&Ms as a unit of measurement. Since the river is about 4,000 kilometers long and the standard unit of length in the SI system is the meter, we need to convert kilometers to centimeters to match the size of an M&M, which is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Therefore, we have:

Now, since each M&M is 1 centimeter, the number of M&Ms needed to measure the length of the Mississippi River is equal to the total number of centimeters:

400,000,000 M&Ms would be required to measure the approximate length of the Mississippi River.

to find the height of the building multiply the distance ( 34 feet) by the tangent of the angle(74)

34 * tan(74) = 118.57 feet

the mean is the average

-7+23 -5 +4 = 15

15 / 4 = 3.75

 Answer is A

From the above equation putting the value of x. we get yhat and reducing it from actual value of y we will get residual

Therefore, as shown on the image below, 

The area of the square dance floor when each side is increased by one foot becomes 441 square feet. Since 441 is an integer, the new area is a rational number because it can be expressed as a fraction with a non-zero denominator.

The question pertains to the change in area of a square dance floor when each side of the square is increased by one foot. Given that the initial area is 400 square feet, we understand that the dimensions of the dance floor are 20 feet by 20 feet, since 20 * 20 = 400. If each side of the square increases by one foot, the new dimensions of the square will be 21 feet by 21 feet, resulting in a new area of 441 square feet.

To answer the question as to whether the new area is a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, with a denominator that is not zero. Given that 441 is an integer, and the area can be written as 441/1, the new area of the dance floor is indeed a rational number.