Nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his destination. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. Which of these statements is correct?

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.

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

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.

if 2 were banded that means 18 out of 20 were not banded

 18 divided by 20 = 0.9

 so 90% were not banded

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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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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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) 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

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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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

n-8=75

n is the number

so number minus 8 equals 75

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.

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.