20.03.2023

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-7 – 3x = 1x + 4(2 + x)

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24.06.2023, solved by verified expert
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x = -15/8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

-7 - 3x = 1x + 4(2 + x)

Step 2: Solve for x

Distribute 4:                                                                                                    -7 - 3x = x + 8 + 4xCombine like terms:                                                                                       -7 - 3x = 5x + 8[Addition Property of Equality] Add 3x on both sides:                                -7 = 8x + 8[Subtraction Property of Equality] Subtract 8 on both sides:                      -15 = 8x[Division Property of Equality] Divide 8 on both sides:                               -15/8 = xRewrite/Rearrange:                                                                                        x = -15/8
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Mathematics
Step-by-step answer
P Answered by PhD

x = -15/8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

-7 - 3x = 1x + 4(2 + x)

Step 2: Solve for x

Distribute 4:                                                                                                    -7 - 3x = x + 8 + 4xCombine like terms:                                                                                       -7 - 3x = 5x + 8[Addition Property of Equality] Add 3x on both sides:                                -7 = 8x + 8[Subtraction Property of Equality] Subtract 8 on both sides:                      -15 = 8x[Division Property of Equality] Divide 8 on both sides:                               -15/8 = xRewrite/Rearrange:                                                                                        x = -15/8
Mathematics
Step-by-step answer
P Answered by Master

There is no sufficient evidence to conclude that population mean number of times that adults go out for dinner each week is less than 1.5

Step-by-step explanation:

From the question we are told that

   The  population mean is  less than  1.5

   The sample size is  n  =  7

   The sample data is   2, 0, 1, 5, 0, 2, and 3

Generally the sample mean is mathematically represented as  

     \=  x =  \frac{ \sum x_i }{ n }

=>  \=  x =  \frac{ 2 +  0 +  1 +  5 +  0 +  2 +   3 }{ 7 }

=>  \=  x =  1.857

Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{\sum (x_i - \= x)^2}{n} }

=>   \sigma  =  \sqrt{\frac{ (2 -   1.857)^2 +  (0 -   1.857)^2 +\cdots  (3 -   1.857)^2}{7} }

=>   \sigma  =  1.773

The null hypothesis is  H_o :  \mu  =  1.5

The alternative hypothesis is H_a  :  \mu  < 1.5

Generally the test statistics is mathematically represented as

     z  =  \frac{\= x  -  \mu }{ \frac{\sigma }{\sqrt{n} } }

=>   z  =  \frac{\= x  - 1.857 }{ \frac{1.773 }{\sqrt{7} } }  

=>z =  0.53

Generally the p-value is mathematically represented as

      p-value  =  P(z  < 0.53 )

From the z-table  

        P(z  <  0.53 ) =  0.70194

So

       p-value  =  0.70194

From the values obtained we see that p-value    0.05  

Here there is no sufficient evidence to conclude that population mean number of times that adults go out for dinner each week is less than 1.5

StudenGPT
Step-by-step answer
P Answered by Studen AI
1. Illustrating \(8-5=3\) using different models: a. Take-away model: Start with 8 objects. Take away 5 objects. Count the remaining objects, which is 3. b. Missing addend model: Start with a whole group of objects, but the total is unknown. Add 5 objects to this group to make 8 objects in total. The missing addend is 3. c. Comparison model: Compare 8 objects to 5 objects. Notice that there are 3 more objects in the first group than in the second group. d. Number line model: Represent a number line with a starting point at zero. Move 8 units to the right to represent the starting value. Then move 5 units to the left to show subtracting 5. The final position is at 3 units on the number line. 2. Word problems corresponding to different subtraction models: a. Take-away model word problem: Sarah had 8 apples. She ate 5 apples. How many apples does she have left? b. Number line model word problem: John is on a number line at the position 8. He moves 5 units to the left. What position is John at now? 3. a. The fact family \(6+5=11\) has four members. To find the other three, we can use the same numbers but perform different operations: - Subtraction: \(11-6=5\) - Subtraction with the numbers switched: \(11-5=6\) - Subtraction with the numbers switched and subtracting a different number: \(5-11=-6\) b. Drawing number line models to illustrate the number facts: 1st number line model: Starting at 0, move 6 units to the right to reach 6. Then move 5 units to the right to reach 11. 2nd number line model: Starting at 11, move 6 units to the left to reach 5. Then move 5 units to the left to reach 0. 3rd number line model: Starting at 11, move 5 units to the left to reach 6. Then move 6 units to the left to reach 0. 4th number line model: Starting at 0, move 5 units to the right to reach 5. Then move 11 units to the right to reach 16. 4. To perform the operation \(a-b\) within the set of whole numbers: \(a\) must be greater than or equal to \(b\) in order to avoid negative results. If \(a\) is less than \(b\), the operation cannot be performed within the set of whole numbers. 5. Rewriting subtraction problems as equivalent addition problems: a. \(9-7=x\) can be rewritten as \(x+7=9\). b. \(x-6=3\) can be rewritten as \(x=3+6\). c. \(9-x=2\) can be rewritten as \(x=9-2\). Please note that it's important to double-check the work at each step to ensure accuracy.
English
Step-by-step answer
P Answered by PhD

B.  

Explanation:

I can see how this might be confusing as predicament would also work, but emergency is the better fit in this sentence.  

English
Step-by-step answer
P Answered by Specialist

Well, Humanity's early fire-starting tools may have been dangerous because in the text is says, "It could be lighted only by hard rubbing, and it sputtered and threw fire in all directions." This is dangerous because it would spew fire in all directions and if you think about it, the fire would hit something and then that thing would catch on fire. Lets say you were using the match inside your house. When you strike the match, a spark flies onto the wood floor and your house goes up in flames and you are stuck inside the house with no exit or escape. This may or may not happen, but because of the fire not being contained, there was a chance that you would be harmed.

hope this helped

English
Step-by-step answer
P Answered by PhD

Incomplete question. Here's the full text:

By S. E. Forman

1911

THE MATCH

There never was a time when the world was without fire, but there was a time when men did not know how to kindle fire; and after they learned how to kindle one, it was a long, long time before they learned how to kindle one easily. In these days we can kindle a fire without any trouble because we can easily get a match; but we must remember that the match is one of the most wonderful things in the world, and that it took men thousands of years to learn how to make one. Let us learn the history of this familiar little object, the match.

Fire was first given to man by nature itself. When a forest is set on fire by cinders from a neighboring volcano, or when a tree is set ablaze by a thunderbolt, we may say that nature strikes a match. In the early history of the world, nature had to kindle all the fires, for man by his own effort was unable to produce a spark. The first method, then, of getting fire for use was to light sticks of wood at a flame kindled by nature—by a volcano, perhaps, or by a stroke of lightning. These firebrands were carried to the home and used in kindling the fires there. The fire secured in this way was carefully guarded and was kept burning as long as possible. But the flame, however faithfully watched, would sometimes be extinguished. A sudden gust of wind or a sudden shower would put it out. Then a new firebrand would have to be secured, and this often meant a long journey and a deal of trouble.

In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate of potash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggist had discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemical because it is made by mixing certain chemicals together and rubbing them. Although Walker's match did not require the bottle of acid, nevertheless it was not a good one. It could be lighted only by hard rubbing, and it sputtered and threw fire in all directions. In a few years, however, phosphorus was substituted on the tip for antimony, and the change worked wonders. The match could now be lighted with very little rubbing, and it was no longer necessary to have sandpaper upon which to rub it. It would ignite when rubbed on any dry surface, and there was no longer any sputtering. This was the phosphorus match, the match with which we are so familiar.

How does the author convince readers that the match was "the most wonderful thing in the world"? Please respond in three to five complete sentences, using evidence from the text to support your answer.

Explanation:

We note the author's intriguing statement at the outset when he said "that it took men thousands of years to learn how to make" a match.

Also, he further highlighted how problematic it was to depend on nature when he said "in the early history of the world, nature had to kindle all the fires, for man by his own effort was unable to produce a spark".

To express the problems further, the author also says that they would have to guard the fire but the fire would still go out sometimes and then they would have to go on long and difficult journeys.

English
Step-by-step answer
P Answered by PhD

Incomplete question. Here's the full text:

By S. E. Forman

1911

THE MATCH

There never was a time when the world was without fire, but there was a time when men did not know how to kindle fire; and after they learned how to kindle one, it was a long, long time before they learned how to kindle one easily. In these days we can kindle a fire without any trouble because we can easily get a match; but we must remember that the match is one of the most wonderful things in the world, and that it took men thousands of years to learn how to make one. Let us learn the history of this familiar little object, the match.

Fire was first given to man by nature itself. When a forest is set on fire by cinders from a neighboring volcano, or when a tree is set ablaze by a thunderbolt, we may say that nature strikes a match. In the early history of the world, nature had to kindle all the fires, for man by his own effort was unable to produce a spark. The first method, then, of getting fire for use was to light sticks of wood at a flame kindled by nature—by a volcano, perhaps, or by a stroke of lightning. These firebrands were carried to the home and used in kindling the fires there. The fire secured in this way was carefully guarded and was kept burning as long as possible. But the flame, however faithfully watched, would sometimes be extinguished. A sudden gust of wind or a sudden shower would put it out. Then a new firebrand would have to be secured, and this often meant a long journey and a deal of trouble.

In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate of potash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggist had discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemical because it is made by mixing certain chemicals together and rubbing them. Although Walker's match did not require the bottle of acid, nevertheless it was not a good one. It could be lighted only by hard rubbing, and it sputtered and threw fire in all directions. In a few years, however, phosphorus was substituted on the tip for antimony, and the change worked wonders. The match could now be lighted with very little rubbing, and it was no longer necessary to have sandpaper upon which to rub it. It would ignite when rubbed on any dry surface, and there was no longer any sputtering. This was the phosphorus match, the match with which we are so familiar.

How does the author convince readers that the match was "the most wonderful thing in the world"? Please respond in three to five complete sentences, using evidence from the text to support your answer.

Explanation:

We note the author's intriguing statement at the outset when he said "that it took men thousands of years to learn how to make" a match.

Also, he further highlighted how problematic it was to depend on nature when he said "in the early history of the world, nature had to kindle all the fires, for man by his own effort was unable to produce a spark".

To express the problems further, the author also says that they would have to guard the fire but the fire would still go out sometimes and then they would have to go on long and difficult journeys.

English
Step-by-step answer
P Answered by Specialist

Well, Humanity's early fire-starting tools may have been dangerous because in the text is says, "It could be lighted only by hard rubbing, and it sputtered and threw fire in all directions." This is dangerous because it would spew fire in all directions and if you think about it, the fire would hit something and then that thing would catch on fire. Lets say you were using the match inside your house. When you strike the match, a spark flies onto the wood floor and your house goes up in flames and you are stuck inside the house with no exit or escape. This may or may not happen, but because of the fire not being contained, there was a chance that you would be harmed.

hope this helped

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