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3 years ago

How do you find a nonzero rational number closed under division

1 answer:

6 0

For rational numbers to be closed under division, then any rational number divided by another rational number would have to be a rational number. This works for every rational number except when the second number is 0. Since division by 0 is undefined, dividing any rational number by the rational number zero will not give you a rational number. In order to make the rational numbers closed under division, you can choose any rational number you want except 0.

In other words, the set of rational numbers is not closed under division. The problem occurs only with division by zero. The set of rational numbers from which zero is removed is closed under division.

Every nonzero rational number is closed under division.

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The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street

vredina [299]

Answer:

Median = $80,000 ; Mean = $84,000 ; Q1 = 67,000 ; Q3 = 106,000

Step-by-step explanation:

Given the data :

108 83 106 73 53 85 80 63 67 75 124 55 93 118 77

Reorderd data :

53, 55, 63, 67, 73, 75, 77, 80, 83, 85, 93, 106, 108, 118, 124

The median salary:

1/2(n+1)th term

Sample size, n = 15

1/2 (15 + 1)th term

1/2(16)th term

8th term = 80

Median is $80,000

Median reported by Wall Street Journal approximately $85000

The obtained and reported values are close

The mean annual salary :

ΣX / n = 1260 / 15 = 84

Mean annual salary = $84,000

Mean is the average of all earnings combined, median is the mid value of he data.

First and third quartile :

Q1 = 1/4(n+1)th term

Q1 = 1/4(16)th term

Q1 = 4th term = 67

Third quartile:.

Q3 = 3/4(n+1)th term

Q3 = 3/4(16)th term

Q3 = 12th term = 106

3 0

3 years ago

An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $6750 and her st

pantera1 [17]

Answer:

3.5%

Step-by-step explanation:

1. calculate starting total

$6750 + 4210=10960$

starting amount = $10,960

2. calculate stock A2's value

decreased by 18%

to make the percentage usable in this equation we need to divide it by 100 to get it in decimal form. ⇒ $\frac{18}{100} = 0.18$

multiply stock A1 by perctage decimal to get the amount decreased

$6750(0.18)=1215$ ($1,215)

subtract stock A1 by decreased amount to get stock A2's value

$6750-1215=5535$

A2 = $5,535

3. calculate stock B2's value

increased by 20%

to make the percentage usable in this equation we need to divide it by 100 to get it in decimal form. ⇒ $\frac{20}{100} = 0.20$

multiply stock B1 by perctage decimal to get the amount increased

$4210(0.20)=842$ ($842)

add stock B1 with increased amount to get stock B2's value

$4210+842=5052$

B2 = $5,052

4. get new amount of account

$5052+5535=10587$

new amount = $10,587

5. find percentage decrease of starting amount to new amount

divide starting amount by the new amount

$\frac{10960}{10587} = 1.03523188816$

then subtract by 1

$1.03523188816-1 =0.03523188816$

multiply by 100 to convert to percentage form

$0.03523188816(100) =3.523188816$

and round to <u>nearest tenth</u>

answer is ≈ 3.5%

::: (\_(\ Hope

*: (=' :') this

•.. (,('')('') helped :)

4 0

2 years ago

Find dx/dt when y=2 and dy/dt=1, given that x^4=8y^5-240<br><br> dx/dt=

katrin2010 [14]

Answer:

The value of $\frac{dx}{dt}$ is $\frac{160}{x^3}$ .

Step-by-step explanation:

The given equation is

$x^4=8y^5-240$

We need to find the value of $\frac{dx}{dt}$ .

Differentiate with respect to t.

$4x^3\frac{dx}{dt}=8(5y^4)\frac{dy}{dt}-0$ $[\because \frac{d}{dx}x^n=nx^{n-1},\frac{d}{dx}C=0]$

$4x^3\frac{dx}{dt}=40y^4\frac{dy}{dt}$

It is given that y=2 and dy/dt=1, substitute these values in the above equation.

$4x^3\frac{dx}{dt}=40(2)^4(1)$

$4x^3\frac{dx}{dt}=40(16)(1)$

$4x^3\frac{dx}{dt}=640$

Divide both sides by 4x³.

$\frac{dx}{dt}=\frac{640}{4x^3}$

$\frac{dx}{dt}=\frac{160}{x^3}$

Therefore the value of $\frac{dx}{dt}$ is $\frac{160}{x^3}$ .

4 0

3 years ago

Explain what the virtual line test is and how it’s used ?

soldi70 [24.7K]

One-to-One Function Defined The horizontal line test is a method that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one unique x-value. One simple example of a one-to-one function (often called an injective function) is with the daily specials at a restaurant. Let's say the specials are as follows: Sunday - Meat Loaf Monday - Turkey Tuesday - Fried Chicken Wednesday - Steak Thursday - Pork Chops Friday - Salmon Saturday - Pot Roast This example represents a one-to-one function because, for every y-value (day of the week) there is only one unique x-value (dinner special). A non-example might be with these breakfast specials at the same restaurant: Sunday - Omelet Monday - Pancakes Tuesday - Scrambled Eggs Wednesday - Waffles Thursday - Scrambled Eggs Friday - French Toast Saturday - Eggs Benedict This is not an injective function because, for two days (Tuesday and Thursday), the special is the same -scrambled eggs. The Horizontal Line Test The horizontal line test is a method to determine if a function is a one-to-one function or not. It is used exclusively on functions that have been graphed on the coordinate plane. It is called the horizontal line test because the test is performed using a horizontal line, which is a line that runs from left to right on the coordinate plane. How It Works When you have the graph of a function, place a horizontal line across the graph. Sometimes it is easiest to use a thin ruler or piece of paper as the line and hold it up against the graph. Be sure to move it up and down along the y-axis to hit all points of the graph. It is possible that the horizontal line will touch the graph in one place in some areas but in two places in other areas. null null If the horizontal line only crosses the graph of the function in one place, then the function is one-to-one. This is because there is only one x-value for each y-value. null If the horizontal line crosses the graph in more than one place, it is not a one-to-one function, because there is more than one x-value for certain y-values.

5 0

3 years ago

Please help me! i’m so bad at this lol

Bezzdna [24]

Answer:

its 8

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers