Simplify the following expression:

(2-3y)+(6+8y)

(2-3y)+(6+8y)

vazelinahS
2021-10-20
Answered

Simplify the following expression:

(2-3y)+(6+8y)

(2-3y)+(6+8y)

You can still ask an expert for help

Jayden-James Duffy

Answered 2021-10-21
Author has **91** answers

The final answer:

asked 2021-02-23

Interpreting z-scores: Complete the following statements using your knowledge about z-scores.

a. If the data is weight, the z-score for someone who is overweight would be

-positive

-negative

-zero

b. If the data is IQ test scores, an individual with a negative z-score would have a

-high IQ

-low IQ

-average IQ

c. If the data is time spent watching TV, an individual with a z-score of zero would

-watch very little TV

-watch a lot of TV

-watch the average amount of TV

d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be

-positive

-negative

-zero

a. If the data is weight, the z-score for someone who is overweight would be

-positive

-negative

-zero

b. If the data is IQ test scores, an individual with a negative z-score would have a

-high IQ

-low IQ

-average IQ

c. If the data is time spent watching TV, an individual with a z-score of zero would

-watch very little TV

-watch a lot of TV

-watch the average amount of TV

d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be

-positive

-negative

-zero

asked 2022-04-10

Interpreting Normal Quantite Plots. In Exercises 5–8, examine the normal quantite plot and determine whether the sample data appear to be from a population with a normal distribution.

Dunkin’ Donuts Service Times The normal quantile plot represents service times during the dinner hours at Dunkin’ Donuts (from Data Set 25 “Fast Food” in Appendix B).

Dunkin’ Donuts Service Times The normal quantile plot represents service times during the dinner hours at Dunkin’ Donuts (from Data Set 25 “Fast Food” in Appendix B).

asked 2022-05-13

When we solve an equation, do we suppose that it is true and then work backward?

A couple of days ago I was reading Calculus by James Stewart and I read this:

Sometimes it is useful to imagine that your problem is solved and work backward, step by step, until you arrive at the given data. Then you might be able to reverse your steps and thereby construct a solution to the original problem. This procedure is commonly used in solving equations. For instance, in solving the equation 3x−5=7, we suppose that x is a number that satisfies 3x−5=7 and work backward. We add 5 to each side of the equation and then divide each side by 3 to get x=4. Since each of these steps can be reversed, we have solved the problem.

This sounded strange to me! I have always thought that when we solve an equation we don't suppose that the equation is already satisfied. I have always thought that when we solve an equation we use algbraic property of numbers to obtain a simpler equation that is equivalent to the starting equation. And since the equations are equivalent we don't need to suppose that the initial equation is true, because when the last one is true, is true also the first one.

In other words: if I have to solve 3x−5=7 I don't need to suppose that x is a number that satisys 3x−5=7, I simply ad 5 to bothe sides to obtain the equivalent equation 3x=12, then I divide both sides by 3 to obtain the equivalent equation x=4, when the last one is true, is true also the first one and vice versa, the last one is true when x is replaced by 4, so 4 is the solution.

And so this is my question: is it true that when we solve an equation we implicitly suppose that x satisfies the equation (and we need to do that) to apply algebraic properties that give us the equivalent and simplier equation? Do we need this logic assumption in solving equations?

Thanks.

EDIT

Let me try to explain in a better way why I don't understand the need to suppose that x satisfies the equation (i.e. that x makes true the equality). Excuse me for the lenght of this edit.

Let's say I want to solve in R the equation 3x−5=7.

I know that

∀a,b,c∈R,a+c=b+c↔a=b(P1)

and I know that

∀a,b,c∈R,(c≠0→(ac=bc↔a=b))(P2)

Property P1 says to me that:

if a+c=b+c is true, then a=b is true;

if a=b is true, then a+c=b+c is true;

if a+c=b+c is false, then a=b is false;

if a=b is false, then a+c=b+c is false;

and property P2 says to me that, if c≠0, then

if ac=bc is true, then a=b ia true;

if a=b is true, then ac=bc is true;

if ac=bc is false, then a=b is false;

if a=b is false, then ac=bc is false;

If I know all of this, then starting from 3x−5=7 I don't need to suppose that x makes true the equality, because:

I can say that 3x−5=7 is equivalent to 3x=12 because of P1 without supposing that 3x−5=7 is true, they have the same truth value for the same value of x;

from 3x=12, I can say that it is equivalent to x=4 because of P2 without supposing that 3x=12 is true, they have the same truth value for the same value of x;

now I can say that 3x−5=12 is equivalent to x=4 without supposing that 3x−5=12 is true, they have the same truth value for the same value of x;

in the end I have the solution, because when x=4 is true, also 3x−5=7, so 4 is the solution.

What am I doing wrong? Why do I need to suppose that x satisfy the equation?When we solve an equation, do we suppose that it is true and then work backward?

A couple of days ago I was reading Calculus by James Stewart and I read this:

Sometimes it is useful to imagine that your problem is solved and work backward, step by step, until you arrive at the given data. Then you might be able to reverse your steps and thereby construct a solution to the original problem. This procedure is commonly used in solving equations. For instance, in solving the equation 3x−5=7, we suppose that x is a number that satisfies 3x−5=7 and work backward. We add 5 to each side of the equation and then divide each side by 3 to get x=4. Since each of these steps can be reversed, we have solved the problem.

This sounded strange to me! I have always thought that when we solve an equation we don't suppose that the equation is already satisfied. I have always thought that when we solve an equation we use algbraic property of numbers to obtain a simpler equation that is equivalent to the starting equation. And since the equations are equivalent we don't need to suppose that the initial equation is true, because when the last one is true, is true also the first one.

In other words: if I have to solve 3x−5=7 I don't need to suppose that x is a number that satisys 3x−5=7, I simply ad 5 to bothe sides to obtain the equivalent equation 3x=12, then I divide both sides by 3 to obtain the equivalent equation x=4, when the last one is true, is true also the first one and vice versa, the last one is true when x is replaced by 4, so 4 is the solution.

And so this is my question: is it true that when we solve an equation we implicitly suppose that x satisfies the equation (and we need to do that) to apply algebraic properties that give us the equivalent and simplier equation? Do we need this logic assumption in solving equations?

Thanks.

EDIT

Let me try to explain in a better way why I don't understand the need to suppose that x satisfies the equation (i.e. that x makes true the equality). Excuse me for the lenght of this edit.

Let's say I want to solve in R the equation 3x−5=7.

I know that

∀a,b,c∈R,a+c=b+c↔a=b(P1)

and I know that

∀a,b,c∈R,(c≠0→(ac=bc↔a=b))(P2)

Property P1 says to me that:

if a+c=b+c is true, then a=b is true;

if a=b is true, then a+c=b+c is true;

if a+c=b+c is false, then a=b is false;

if a=b is false, then a+c=b+c is false;

and property P2 says to me that, if c≠0, then

if ac=bc is true, then a=b ia true;

if a=b is true, then ac=bc is true;

if ac=bc is false, then a=b is false;

if a=b is false, then ac=bc is false;

If I know all of this, then starting from 3x−5=7 I don't need to suppose that x makes true the equality, because:

I can say that 3x−5=7 is equivalent to 3x=12 because of P1 without supposing that 3x−5=7 is true, they have the same truth value for the same value of x;

from 3x=12, I can say that it is equivalent to x=4 because of P2 without supposing that 3x=12 is true, they have the same truth value for the same value of x;

now I can say that 3x−5=12 is equivalent to x=4 without supposing that 3x−5=12 is true, they have the same truth value for the same value of x;

in the end I have the solution, because when x=4 is true, also 3x−5=7, so 4 is the solution.

What am I doing wrong? Why do I need to suppose that x satisfy the equation?When we solve an equation, do we suppose that it is true and then work backward?

asked 2022-05-14

Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/l. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements are shown below. (Reference: EPA Wetland Case Studies.)

Reading 1 2 3 4 5 6 7 8 9 10 11 12

Inlet (mg/l) 59.1 25.7 70.5 71.0 37.6 43.5 13.1 24.2 16.7 49.1 67.6 31.7

Outlet (mg/l) 18.2 14.3 15.3 17.5 13.1 8.0 4.1 4.4 4.3 5.8 16.3 7.1

Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings.

(a) Rank-order the inlet readings using 1 as the largest data value. Also rank-order the outlet readings using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.

Reading Inlet

Rank x Oulet

Rank y d = x - y d2

1

2

3

4

5

6

7

8

9

10

11

12Σd2 =

Reading 1 2 3 4 5 6 7 8 9 10 11 12

Inlet (mg/l) 59.1 25.7 70.5 71.0 37.6 43.5 13.1 24.2 16.7 49.1 67.6 31.7

Outlet (mg/l) 18.2 14.3 15.3 17.5 13.1 8.0 4.1 4.4 4.3 5.8 16.3 7.1

Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings.

(a) Rank-order the inlet readings using 1 as the largest data value. Also rank-order the outlet readings using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.

Reading Inlet

Rank x Oulet

Rank y d = x - y d2

1

2

3

4

5

6

7

8

9

10

11

12Σd2 =

asked 2021-02-04

Basic facts and techniques of Boats and Streams of Quantitative Aptitude
Boats and Streams is a part of the Quantitative aptitude section. This is just a logical extension of motion in a straight line. One or two questions are asked from this chapter in almost every exam. Today I will tell you some important facts and terminologies which will help you to make better understanding about this topic.

asked 2021-12-16

Maria's Pizza sells one 16-inch cheese pizza or two 10-inch cheese pizzas for $9.99. Determine which size given more pizza.

asked 2021-09-10

Given two integers. What can you claim about them, when their quotient is:

1. Positive?

2. Negative?

3. =0?

1. Positive?

2. Negative?

3. =0?