Describe and correct the error in using the diagram to find the value of x

The product of rational expression is \(\rm \dfrac{x}{x^2-2x}\).

Given that

The rational expression is

\(\rm \dfrac{1}{x} \times \dfrac{x}{x-2}\)

We have to determine

The product of rational expression.

According to the question

The product of rational expression is determined in the following steps given below.

The rational expression is

\(\rm \dfrac{1}{x} \times \dfrac{x}{x-2}\)

Then,

The product of the rational expression is,

\(\rm= \dfrac{1}{x} \times \dfrac{x}{x-2}\\\\= \dfrac{1\times x}{x\times x - x \times 2}\\\\= \dfrac{x}{x^2-2x}\)

Hence, the product of rational expression is \(\rm \dfrac{x}{x^2-2x}\).

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Step-by-step explanation:

since they are consecutive even numbers, one is bigger by 2 than the other number.

so,

x + (x + 2) = 214

2x + 2 = 214

x + 1 = 107

x = 106

so, the 2 numbers are 106 and 108.

Answer:

135 minutes.

Step-by-step explanation:

To find the rate for 1 hour, you would divide 1.5 hours. by 6 miles. You would get .25. So a quarter of an hour is how long it takes for 1 mile. Now multiply .25 by 9. You should get 2.25 hours. .25= 1/4 so 2.25 is 2 hours and 15 minutes. There are 60 minutes in an hour and there are 2 hours. 2 times 60 plus 15. 135 minutes.

I hope this helps!

Answer:

135 minutes

Step-by-step explanation:

so 6 miles in 1.5 hours

1.5 hours = 90 minutes

   need to find minutes for 9 miles

divide 90 minutes into half = 45

45= the extra 3 miles

then add 90 + 45 = 135

Answer: 1/4

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer:

65 are not shaded

Step-by-step explanation:

35 are shaded. in order to find how many are not shaded, you subtract that number by 100:

100 - 35 = 65

Answer:

300.94 sq.m

Step-by-step explanation:

A solid in the shape of cylinder with two hemisphere to each of its ends.

Finding, the Curved surface area of cylinder

Calculate the height of cylinder

Height of cylinder = 11 m

Now, we have

Height of cylinder = 11 m

Radius of cylinder = 7 / 2 = 3.5 m

Using Formula :-

Curved surface area of cylinder = 2× π × r × h

Substitute the values

Curved surface area of cylinder = 2π× 3.5m×11m.

Using the value of π = 3.14

Curved surface area of cylinder =2×3.14× 3.5m × 11 m.

multiply, we get.

Curved surface area of cylinder = 241.78 m².

Finding curved surface area of hemisphere

Using Formula

Curved surface area of hemisphere = 2 × π × r²

substitute the values into the formula

Curved surface area of hemisphere = 2 π × ( 3.5 )²

Evaluate the exponent

Curved surface area of hemisphere =2π×12.25m².

Using value of π = 3.14

Curved surface area of hemisphere = 2 × 3 14 × 12.25 m ²

multiply , we get

Curved surface area of hemisphere = 76.93 m².

Total area of capsules = Curved surface area of cylinder + 2 (Curved surface area of hemisphere)

Total surface area of capsules = 241.78 m²+ 2 × 76.93 m².

Total surface area = 241.78m² + 153.86m².

Subtract and finally we get

Total surface area = 395.64 m ²

Answer:

Step-by-step explanation:

The probability of Jack picking a yellow or white sock is 0.6 (60%).

The probability of Jack picking a blue sock is 4/14 (28.6%)

The probability of Jack picking a red sock is 3/14 (21.4%)

The probability of Jack picking a white sock is 2/14 (14.3%)

The probability of Jack picking a yellow sock is 1/14 (7.1%)

Therefore, the probability of Jack picking a yellow or white sock is 0.6 (60%)

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A region defined by a particular function is known as a functional region. It is characterized by a shared attribute or behavior that is influenced by the function.

This type of region is created based on the relationship between a specific geographic area and a particular activity, purpose, or function that occurs within that area.

Functional regions are typically delineated based on the patterns of interaction and interdependence among different locations. They are defined by the presence of a central point or node that serves as a focal point for the function or activity. The surrounding areas within the region are connected to this central point through various transportation, communication, or economic networks.

For example, a functional region can be defined by a transportation hub such as an airport or a seaport. The surrounding areas that are linked to this transportation hub by roads, railways, or shipping routes form the functional region. The function of the region, in this case, is the movement of people, goods, and services facilitated by the transportation hub.

In summary, a functional region is a type of region defined by a specific function or activity that occurs within a geographic area. It is characterized by a central point or node and the interconnectivity of surrounding areas based on the function or activity.

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In this case, we can see that 1/3 fits into 2 a total of 6 times. Therefore, 2 divided by 1/3 is equal to 6.

To find the result of 2 divided by 1/3, we can utilize the number line.

The number line provides a visual representation of numbers and their relative positions. To find the answer, we can think of dividing 2 by 1/3 as the same as asking "how many times does 1/3 fit into 2?"

Starting from 0 on the number line, we move along in increments of 1/3 until we reach 2. Counting the number of increments will give us the result of the division.

In this case, we can see that 1/3 fits into 2 a total of 6 times. Therefore, 2 divided by 1/3 is equal to 6.

Using the number line helps us visualize the concept of division and provides a clear understanding of how many times one quantity can fit into another. In this case, it allows us to see that 2 divided by 1/3 results in 6.

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A study of all the students at a small college showed a mean age of 20.4 and a standard deviation of 2.7 years.

(a) These numbers are statistics because they are based on a sample of students from a small college. They are not certain, but estimates.

(b) The mean age is labeled with the symbol x and the standard deviation with the symbol s. The sample size is not given, so we cannot use the symbol n to represent it.

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The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

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Answer:

i think its D if not its B I'm sorry if I'm wrong

Step-by-step explanation:

Answer:3(2z-10)=-12

We move all terms to the left:

3(2z-10)-(-12)=0

We add all the numbers together, and all the variables

3(2z-10)+12=0

We multiply parentheses

6z-30+12=0

We add all the numbers together, and all the variables

6z-18=0

We move all terms containing z to the left, all other terms to the right

6z=18

z=18/6

z=3

Step-by-step explanation:

The dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

To use systematic random sampling, we need to choose a starting point and a sampling interval. In this case, we are starting with the third dealer in the list, so we need to skip the first two dealers.

Let's assume that the dealers are numbered 1 to 100 in the list. Since we are starting with the third dealer, our starting point is dealer 3. We also need to choose a sampling interval of 5, since we want to select every fifth dealer.

To find out which dealers are included in the sample, we can use the following formula:

Sampled Dealers = Starting Point + (Sampling Interval * Number of Samples)

Using the formula, we can calculate the dealers that are included in the sample as follows:

Sampled Dealers = 3 + (5 * n)

where n is the number of samples.

If we want to select a sample of 20 dealers, we can substitute n = 1 to 20 into the formula to get the following list of dealers:

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98

Therefore, the dealers included in the sample are dealers 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, and 98.

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Answer:

choice 3) area = 1188 in²

Step-by-step explanation:

area = 36 x 33 = 1188 in ²

The tendency to overestimate the extent to which others would notice their unusual T-shirt in the given experiment best illustrates the phenomenon known as the spotlight effect.

The spotlight effect refers to the tendency for individuals to believe that they are being noticed and evaluated by others more than they actually are. It is the feeling of being in the "spotlight" and assuming that others are paying more attention to one's appearance, behavior, or actions than they truly are.

In the experiment, participants wearing a Barry Manilow T-shirt may have felt self-conscious or believed that the shirt was highly noticeable to others. However, the spotlight effect suggests that their perception of others' attention and evaluation is exaggerated. In reality, people are often less observant and less concerned with the details of others' appearances or actions than individuals tend to think.

The spotlight effect can stem from a variety of factors, including self-consciousness, social anxiety, and the desire for social acceptance. It can influence how individuals present themselves, make choices, and interpret social situations.

Understanding the spotlight effect can help individuals recognize that their own perceived flaws or unique attributes are often not as noticeable or significant to others as they might think. This awareness can alleviate self-consciousness and promote a more accurate understanding of social interactions.

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the answer is table d !! good luck :)

Mr. Jones bought approximately 13 pamphlets.

In this problem, we have two types of items: books and pamphlets. Books cost 50¢ and pamphlets cost 15¢ at the book sale.

Let's use variables to represent the quantities we don't know. Let's say Mr. Jones bought x books and y pamphlets.

We are given two pieces of information:
1. Mr. Jones spent $90 on his purchases.
2. He bought 15 more pamphlets than books.

Now, let's set up the equations based on the given information.

First, let's consider the cost equation. The total cost of the books and pamphlets should equal $90.

The cost of x books is 50¢ * x, and the cost of y pamphlets is 15¢ * y. So, the equation becomes:
50x + 15y = 90

Next, let's consider the second piece of information. Mr. Jones bought 15 more pamphlets than books, which means y = x + 15.

Now, we have a system of two equations:
50x + 15y = 90
y = x + 15

To solve this system, we can use substitution or elimination method. Let's use substitution:

Substitute the value of y from the second equation into the first equation:
50x + 15(x + 15) = 90

Simplify the equation:
50x + 15x + 225 = 90
65x + 225 = 90

Subtract 225 from both sides:
65x = 90 - 225
65x = -135

Divide both sides by 65:
x = -135 / 65
x ≈ -2.08

Since we cannot have a negative number of books, we know that x must be a positive whole number. So, let's round x to the nearest whole number:
x ≈ -2

Now, substitute this value of x back into the second equation to find y:
y = x + 15
y ≈ -2 + 15
y ≈ 13

Therefore, Mr. Jones bought approximately 13 pamphlets.

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Answer:

5 out of 7.

Step-by-step explanation:

There are seven days in one week. They are asking what is the probability of the person chosen not being born in a Tuesday or Wednesday. There are five other days, so there are five other options.

I hope I helped you!

Answer:

620 cm²

Step-by-step explanation:

First I'll describe the net. There are 3 rectangles and 2 triangles. The triangles are identical and 2 out 3 of the rectangles are the same.

So, we know that the two similar rectangles have measurements of 13cm x 10cm. So, that's 130 cm² for one such rectangle. Add the other one and we get 260 cm².

The bottom rectangle has dimensions of 10cm x 24 cm, or 240 cm². Add that to our previous total and we'll get 500 cm².

On to the triangles. Now, we know that 1. these are isosceles triangles, and 2. they have a height of 5 cm. We can pretend to cut them in half at their highest point, which would give us 4 triangles with height 5 and length 12. Now, if you put two identical triangles together, it's a four-sided shape, and you can just multiply length by width. Let's do that.

Now we have 2 rectangles, each with width 5 and length 12. Calculate the area for each, and now we have 2 rectangles with area 60 cm². Add them together....120cm².

Add that to our previous total, and we'll get 620 cm². That should be the surface area of your prism :D

Answer:

Five times the sum of two times a number plus seven all minus three

Step-by-step explanation:

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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Heuristics refers to rules of thumb that simplify the decision-making process. Heuristics are mental shortcuts that help individuals make decisions quickly, often relying on previous experience or intuition rather than a more systematic approach.

While heuristics can be useful, they can also lead to biases and errors in judgment if they are applied too broadly or without careful consideration. It is important to be aware of these heuristics and how they can affect decision-making processes, especially in complex or high-stakes situations where careful consideration is necessary.

The answer is C.

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Answer:

12.5

Step-by-step explanation:

Answer:

$12.50

Step-by-step explanation:

so u do revers math 4 x ?? = 50

so i took the time and found out 4 x 12= 48 but 4 x 13= 52 so i did the math and added .5 so i then times 4 x 12.5 witch ended up = 50 so every one got 12 dollars and 50 cents

The boy can have 9 dimes, 0 nickels, and 8 pennies.

We have,

a boy finds $1.05 in dimes, nickels, and pennies.

Let's assume that the boy has x number of dimes, y number of nickels, and z number of pennies.

We know that the total value of these coins is $1.05, and there are 17 coins in total.

Now, let's convert the values into cents.

We have 10 cents for each dime, 5 cents for each nickel, and 1 cent for each penny.

Therefore, the equation we can set up is:

10x + 5y + z = 105

(since $1.05 is equal to 105 cents)

We also know that the total number of coins is 17, so:

x + y + z = 17

Now, we have a system of equations.

Let's solve it using a method called substitution.

From the second equation, we can express z in terms of x and y:

z = 17 - x - y

Substituting this value of z into the first equation, we get:

10x + 5y + (17 - x - y) = 105

Simplifying this equation, we get:

9x + 4y = 88

Now we have a new equation to work with.

We can rearrange it to solve for x:

x = (88 - 4y) / 9

To find the possible values for x and y, we can try different values of y and calculate the corresponding values for x.

Since the number of coins cannot be negative, we can start by setting y to 0 and calculate x:

x = (88 - 4(0)) / 9

x = 88 / 9

x ≈ 9.78

Since the number of coins must be a whole number, we can round x down to the nearest whole number, which gives us x = 9.

Now, let's substitute this value of x back into our second equation:

9 + y + z = 17

Simplifying this equation, we get:

y + z = 8

We can now try different values of y and calculate the corresponding values of z that satisfy this equation.

Let's start with y = 0:

0 + z = 8

z = 8

So, one possible solution is x = 9, y = 0, and z = 8.

This means the boy can have 9 dimes, 0 nickels, and 8 pennies.

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After forming a system of equations according to the given information

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

Given that,

The boy finds a total of $1.05 in dimes, nickels, and pennies.

There are 17 coins in total.

Number of pennies  = 5

Let "d" represent the number of dimes.

Let "n" represent the number of nickels.

Let "p" represent the number of pennies = 5

We know that,

1 $ = 100 cent

1 cent = 0.01$

According to the given information:

The system of equations be:

0.10d + 0.05n + 0.01 x 5 = 1.05   ......(i)

d + n + 2 = 17 .....(ii)

Proceeding with equation (i):

After simplifying:

0.10d + 0.05n = 1

Multiply 10 both sides

10d + 5n = 10  ....(iii)

Proceeding with equation (i):

After simplifying:

d + n = 15  .

Multiply 5 on both sides,

5d + 5n = 75 ....(iv)

Subtract (iii) from (iv):

5d = 65

d = 13

So, there are 13 dimes.

Now substitute this value of d into (iv),

n = 2

So, there are 2 nickels.

Hence.

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

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The complete question is attached below:

A boy finds $1.05 in dimes, nickels, and pennies.

Dimes are 10 cents coins, Nickle is 5 cents coins and pennies are 1 cent coins. If there are 17 coins and the number of pennies is 5 in all.

How many coins of each type can he have?

8c to the power of 18

The equation\(−cos2x=1+sinx−cosx\) simplifies to 2cosθ=1.

To explain the simplification, we start with the given equation:

\(−cos2x = 1 + sinx − cosx\)

Using the double-angle identity for cosine, \(cos2x = 2cos^2(x) - 1\), we can substitute it into the equation:

\(−(2cos^2(x) - 1) = 1 + sinx − cosx\)

Expanding and rearranging the terms, we get:

\(-2cos^2(x) + 1 = 1 + sinx − cosx\)

Now, we cancel out the common terms:

\(-2cos^2(x) = sinx - cosx\)

Next, we divide the equation by -2:

\(cos^2(x) = (cosx - sinx)/2\)

Finally, we simplify the equation:

\(2cos^2(x) = cosx - sinx\)

Using the identity cos^2(x) = 1 - sin^2(x), we substitute it into the equation:

\(2(1 - sin^2(x)) = cosx - sinx\)

\(2 - 2sin^2(x) = cosx - sinx\)

Rearranging the terms, we obtain:

\(2cos^2(x) = 1\)

Hence, the equation simplifies to\(2cosθ = 1.\)

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The number of boxes that need to be purchased for the art project can be determined by the expression ceil((x × 5) / 24). This can be answered by the concept of ceiling function.

To determine the number of boxes of crayons needed for the art project, we can use the ceiling function to round up the division of the total number of crayons required by the number of crayons in each box.

Let's break down the problem step-by-step:

Each child in the first grade will be given five crayons for the art project.

We need to determine the number of boxes of crayons needed to provide enough crayons for all the children.

Crayons come in boxes of 24.

To calculate the number of boxes needed, we can divide the total number of crayons required by the number of crayons in each box. The total number of crayons required can be obtained by multiplying the number of children (x) by the number of crayons given to each child (5).

Total number of crayons required = x × 5

Now, to find the number of boxes needed, we divide the total number of crayons required by the number of crayons in each box (24), and round up the result using the ceiling function. This is because we need to ensure that we have enough whole boxes to provide the required number of crayons.

Number of boxes needed = ceil((x × 5) / 24)

Therefore, the number of boxes that need to be purchased for the art project can be determined by the expression ceil((x × 5) / 24).

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