What is the answer for this

Answer:

Distribution is used from steps 1-2

They eliminate 2x by subtracting it on both sides (steps 3-4)

They eliminated 6 by subtracting it from both sides (steps 5-6)

(steps 3-6 is eliminating like-terms)

Thus this leaves the answer being x=-3

Step-by-step explanation:

Equation 3(x+2) = 2x+3 solved using distributive property and simplification, final solution is x = -3.

Let's identify the reason for each step in the solution to the equation 3(x+2) = 2x+3:

Distributive Property

The first step applies the Distributive Property,

which states that multiplying a number outside the parentheses by the terms inside the parentheses.

Here, we multiply 3 by (x+2),

3(x+2)

= 3 × x + 3 ×2

= 3x + 6

Combining Like Terms

In the second step, combine like terms on both sides of the equation.

On the left side, we have 3x, and on the right side, we have 2x.

We also have constants 6 on the left side and 3 on the right side.

3x + 6 = 2x + 3

Move Variables to One Side

To solve for 'x', we want all the terms with 'x' on one side of the equation.

Here,  move the term with 2x to the left side by subtracting 2x from both sides of the equation:

3x + 6 - 2x = 2x + 3 - 2x

Simplify

On the left side, the term 2x cancels out with the 2x on the right side, leaving us with:

x + 6 = 3

Move Constants to the Other Side

To isolate 'x', we need to get rid of the constant term on the left side.

Subtracting 6 from both sides of the equation:

x + 6 - 6 = 3 - 6

Simplify

On the left side, the +6 and -6 cancel out, leaving us with:

x = -3

Final Solution

After simplifying, find that the value of 'x' that satisfies the original equation is x = -3.

This means that if we replace 'x' with -3 in the equation, it will hold true:

3(-3 + 2) = 2(-3) + 3

-3 = -6 + 3

-3 = -3

And that's why the solution to the equation is x = -3.

Therefore, the reason required for solving the equation are distributive property and simplification which gives solution is x = -3

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Answer:

curtiss can buy 7 pounds of pistachios

Step-by-step explanation:

5 cappuccinos x $5 = 25, 32 - 25=7

The number of pounds of pistachios will be 7 pounds.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The cost of cappuccinos is $5.00 each. The cost of pistachios is $1.00 per pound. Assuming Curtiss has paid $32.00 and buys 5.00 cappuccinos.

Let 'x' be the number of pounds of pistachios. Then the correct option is given as,

1x + 5 × 5 = 32

x + 25 = 32

x = 32 - 25

x = 7 pounds

The number of pounds of pistachios will be 7 pounds.

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Check the picture below.

The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.

To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.

First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.

Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.

The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.

(3/10) * 100 = 0.3 * 100 = 30%

Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.

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Answer:

6418698

-3485835

2932863

Step-by-step explanation:

The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

\(3y - 12x = 18\\\\2y - 8x = 12\)

To do this, we can rearrange each equation to solve for y in terms of x:

\(3y = 12x + 18\\\\y =4x + 6\)

For the second equation.

\(2y = 8x + 12\\\\y = 4x + 6\)

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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Answer: 24 ft

Step-by-step explanation:

There were approximately 6056 no votes.

Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.

Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.

The total number of votes is given as 9854, so we can set up the following equation:

\(5x + 8x = 9854\)

Combining like terms, we have:

\(13x = 9854\)

To solve for x, we divide both sides of the equation by 13:

\(x = \frac{9854 }{13}\)

\(x \approx 757.23\)

Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.

Now, we can find the number of no votes by multiplying x by the ratio of no votes:

No votes \(= 8x\)

\(= 8 \times 757\)

\(= 6056\)

Therefore, there were approximately 6056 no votes.

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Answer:

The minimum sample size is  \(n =135\)

Step-by-step explanation:

From the question we are told that

   The confidence interval is \(( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)\)

    The margin of error is  \(E = 0.1\)

Generally the sample  proportion can be mathematically evaluated as

     \(\r p = \frac{ upper \ limit + lower \ limit }{2}\)

    \(\r p = \frac{ 0.51 + 0.44}{2}\)

    \(\r p = 0.475\)

Given that the confidence level is  98% then the level of significance can be mathematically evaluated as

         \(\alpha = 100 - 98\)

        \(\alpha = 2\%\)

        \(\alpha =0.02\)

Next we obtain the critical value of  \(\frac{\alpha }{2}\) from the normal distribution table  

   The value is

        \(Z_{\frac{\alpha }{2} } = 2.33\)

Generally the minimum sample size is evaluated as

      \(n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )\)

     \(n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )\)

     \(n =135\)

The Solution.

To find the slope of the line from the given graph:

First, we shall pick two coordinates in the graph, that is

This implies that

By formula, the slope is given as below:

substituting the values in the above formula, we get

So, the slope of the line is -3/2

b. From the graph, and from the slope being a negative value, it is clear that the line graph is Decreasing.

c. To estimate the vertical intercept is to find the y-intercept of the line.

Clearly from the graph, we can see that the vertical intercept is (0,2), that is, the point where the line cut the y-axis.

Therefore, the vertical intercept is (0,2).

Answer:

The answer is 5.20

Step-by-step explanation:

Since the tenth place is lower than 5 it stays the same

Answer:

38 minutes

Step-by-step explanation:

Yards covered in a minute = 4850/20 = 242.5

Time needed to cover 9215 yards = 9215/242.5 = 38 min

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

Step-by-step explanation:

With 200 people, it is estimated that they can perform 1000 tests.

To solve this problem, we can use the concept of direct proportionality. Let's analyze the given information:

In the laboratory, there are 150 people who perform 750 tests in 30 days. We can set up a proportion to determine the relationship between the number of people and the number of tests:

150 people = 750 tests

200 people = x tests

Using the concept of direct proportionality, we can set up the following equation:

150/750 = 200/x

To solve for x, we can cross-multiply:

150x = 750 * 200

150x = 150,000

x = 150,000/150

x = 1000

Therefore, with 200 people, it is estimated that they can perform 1000 tests.

It is important to note that this estimation assumes that the productivity and efficiency of the people in the laboratory remain constant. In reality, other factors such as work distribution, coordination, and resource availability can also affect the number of tests that can be performed. Additionally, this estimation does not consider any time constraints or limitations on the laboratory's capacity.

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Note the translated questions is:

150 people work in a laboratory and in 30 days a

perform 750 tests. How many tests can be done with 200 people?

Answer:

$90

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

  (b)  -4.5

Step-by-step explanation:

Choosing the correct answer here is not the same as knowing what the correct value is.

You know that √30 < √100 = 10, so the sum must be negative. That is, 10 subtracted from a positive number less than 10 will give a negative result.

You know that 25 < 30 < 36, so √25 < √30 <√36. That is, √30 will be between 5 and 6. If we say √30 ≈ 5.5, then the sum is ...

  -10 +√30 ≈ -10 +5.5 = -4.5

__

Additional comment

Of course, a calculator can tell you the value to the desired precision.

Answer:

x = 42

y = 21

Step-by-step explanation:

Since its a right triangle, we have:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

\(sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42\)

\(cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21\)

Answer:

mhm

Step-by-step explanation:mhm

Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

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20 characters

Step-by-step explanation:

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Answer:

the ground level is -2

Step-by-step explanation:

hope this helps

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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Answer:

Nina will finish first.

Step-by-step explanation:

Let's calculate how many pages each person reads in one day:

Then we divide the number of pages of each book by reading speed of the respective person:

Thus Nina will take the shortest time finishing her book.

Answer:

Step-by-step explanation:

the amswer is     nina  

Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)