What is the remainder obtained by dividing x7 x5 1 by the generator polynomial x3 1?

We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour

To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.

So the solution would be:

4485/3=1495
Then multiply this by 4.

1495 multiplied by 4 is equal to 5980 square feet.

So Richard can apply fertilizer to 5980 square feet in 1 hour.

We know that the formula for area is simply:

area = l w

where l is length and w is width

yard dimensions: l = 13x – 4, w = 5x

Ayard = (13x – 4) 5x = 65x^2 – 20x

shed dimensions: l = 2x + 4, w = 2x

Ashed = (2x + 4) 2x = 4x^2 + 8x

Therefore the area to mow is:

Amow = Ayard – Ashed

Amow = 65x^2 – 20x – (4x^2 + 8x)

Amow = 65x^2 – 20x – 4x^2 – 8x

Amow = 61x^2 – 28x

The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.

Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.

Thus, we have proved that the quotient of any two rational numbers is a rational number.

Answer: The area of the cover = 56 square inches.

Step-by-step explanation:

We know that the shape of a tablet is rectangle.

Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.

The area of rectangle is given by :-

[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]

Therefore, the area of the protective cover is 56 square inches.

1 mile = 1.6 kilometers

 multiply 40 mph by 1.6 = 64

car's rate = 64 kilometers per hour

multiply kilometers per hour by 4 = 256

 car will travel 256 kilometers in 4 hours

354,738 rounded to the nearest thousand is 355,000.

In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.

354,738 ≈ 355,000.

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Answer:

The value of the 7 in 507,264 is 10 times the value of the 7 in number 2

Step-by-step explanation:

Given Number : 507,264

To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .

Starting from the left ,

4 is in ones place

6 is in tens place

2 is in hundreds place

7 is in thousands place

0 is in ten thousands place

5 is in lakhs place

Here, 7 is in thousands place

7000 = 10 x 700

2 is in hundreds place

200 = 2 × 100

Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in  number 2 .

A circle is an object which has the lowest surface area to volume ratio. So in this case, the shape should be like that of a circle but we cannot have a circle here because we want to form a 6 sided box. So the next thing closer to circle is a square. Hence the shape should be a square:

Answer:

square

To minimize surface area for a given volume of 1/2 cubic meter, the box should be shaped as a cube with each side measuring approximately 0.7937 meters. This cube shape offers the smallest surface area for the given volume.

To minimize the surface area of a six-sided rectangular box with a volume of 1/2 cubic meter, it is best to make the box in the shape of a cube. This shape has the smallest surface area for a given volume. To find the dimensions of the box, let's denote the side of the cube as 's'. We know that volume V of a cube is given by V = s³. So, if the volume is 1/2 cubic meter, we have:

s³ = 1/2

s = ∛(1/2) ≈ 0.7937 meters

Each side of the cube should be approximately 0.7937 meters to achieve the minimal surface area. The surface area SA of the cube can be calculated as:

SA = 6s²

SA = 6 × (0.7937)² ≈ 3.770 meters²

Thus, a cube with sides of about 0.7937 meters will have the minimal surface area for a volume of 1/2 cubic meter.

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n-8=75

n is the number

so number minus 8 equals 75

Answer:

11.5 cm²/s

Step-by-step explanation:

We must solve two problems to answer this question:

For the first problem, we have ...

... 9 = 5t +4√t

... 9 -5t = 4√t . . . . . subtract 5t

... 81 -90t +25t² = 16t . . . . square both sides

... 25t² -106t +81 = 0 . . . subtract 16t

... (t -1)(25t -81) = 0 . . . . factor

... t = 1 or 3.24 . . . . . . t=3.24 is an extraneous solution

_____

For the second problem, we have area (a(t)) is ...

... a(t) = length×height = (5t +4√t)(√t) = 5t^(3/2) +4t

Then the derivative is ...

... a'(t) = (3/2)(5√t) +4

and

... a'(1) = (3/2)(5√1) +4 = 11.5 . . . . . cm²/s

_____

Comment on the attachment

A graphing calculator can help solve both problems. It can help find the time at which length is 9 cm by solving ... length-9 = 0. (The nice thing here is that there is no extraneous solution.) It can compute the derivative of a function, too.

a) P(X >= 6) = 0.0160

b) P(X > 10) ≈ 6.88 x 10^-6

c) P(X = 0) ≈ 0.1339

d) P(X < 5) ≈ 0.9482

a. Probability of six or more pages with errors:

This is the sum of probabilities for 6, 7, 8, ..., 200 errors:

P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.

P(X >= 6) ≈ 0.0160

b. Probability of more than 10 pages with errors:

Similar to part (a), but calculating from 11 errors onwards:

P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]

P(X > 10) ≈ 6.88 x 10^-6 (very small probability)

c. Probability of none of the pages containing errors:

P(X = 0) = (0.99)^200 ≈ 0.1339

d. Probability of fewer than five pages containing errors:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

P(X < 5) ≈ 0.9482

Answer:

Shifted 2 units left and 4 units up

Step-by-step explanation:

Given are two triangles

ABC is having vertices as (4,6) (7,6) and (5,9)

The transformed image A'B'C' has vertices as

(2,10) (5,10) (3,13)

On comparing the vertices corresponding we find a certain pattern.

X coordinate is reduced by 2 and y coordinate is increased by 4.

This implies the transformation is

Shifted 2 units left and 4 units up

To check for symmetry on the x axis, replace y with –y

-y^2 –x(-y) =2

 Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis

 Now do the same for y axis by replacing x with –x

 Again using product rule the equations are not identical, so it is not symmetric about the y axis

 To check the origin,

 Replace both x & y with –x  & -y

Again using product rule, the equations are not identical so it is not symmetric about the origin

To check for symmetry, replace x with -x and y with -y in the equation. Upon doing that for y^2 -xy =2, we find it lacks x-axis, y-axis, and origin symmetry.

To determine whether a function has x-axis symmetry, y-axis symmetry, or origin symmetry, we have to replace x with -x and y with -y and see whether we get the same function.

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