Two–thirds of the children in the fourth–grade class are girls. if there are 18 girls, what is the total number of children in the class?

Final answer:

The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.

Explanation:

The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:

"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."

To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:

This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:

Thus, the number we're looking for is 20.

Answer:- The quadrilateral must be a rhombus.

Explanation:-

Given :-For a craft project, two equilateral triangles are taped together to create a quadrilateral.

We know that an equilateral triangle is a triangle in which all the sides and angles are equal such that its each interior angle should be 60°.

If we join two equilateral triangle by to create a quadrilateral then the sides of the quadrilateral would be same as it was constructed by equilateral triangle.

Then the interior angle for the sides which are not joint will remain same as 60°.

But the interior angle for the vertex of quadrilateral which has formed by joining two triangles will become 60°+60°=120°.

Thus it is not a square , rectangle (no right angle )or trapezoid(quadrilateral have equal sides).

Therefore, the quadrilateral must be a rhombus.

Answer:

Acceleration, [tex]a=-2.14\ m/s^2[/tex]    

Step-by-step explanation:

Initial speed of the airplane, u = 245 m/s

Final speed of the airplane, v = 230 m/s

The pilot takes 7 seconds to slow down to this speed. Let a is the acceleration of the plane. The change in velocity per unit time is called the acceleration of an object. It can be calculated as :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{230\ m/s-245\ m/s}{7\ s}[/tex]

[tex]a=-2.14\ m/s^2[/tex]

So, the acceleration of the plane is [tex]-2.14\ m/s^2[/tex]. Hence, the correct option is (b).

the simplified expression is 25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12

To simplify the given expression, we first need to combine like terms. Like terms are those that have the same variables raised to the same powers. In this case, we have terms with x and y raised to different powers.

The expression is:

25xy^4 + 60xy^3 + 5xy^3 + 5xy + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2

Now, let's combine the like terms:

Combine the terms with xy^4: 25xy^4

Combine the terms with xy^3: 60xy^3 + 5xy^3 = 65xy^3

Combine the terms with xy^2: 12xy^2

Combine the terms with xy: 5xy + 5xy + 12xy = 22xy

Combine the terms with y^2: 5y^2 + 12

Combine the terms with y: 12y + 5y + 12y^2 = 18y + 12y^2

Combine the terms with y^3: 5y^3 + 5y^3 = 10y^3

Now, let's put all the combined like terms together:

25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12

This is the simplified expression.

The probable question maybe:

simplify the given expression [tex]\(25xy^4 + 60xy^3 + 5xy + 5xy^3 + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2\)[/tex]

You sold 36 tickets and your friend sold 22 tickets.

Let's represent the number of tickets you sell as x and the number of tickets your friend sells as y.

We know that you sell 14 more tickets than your friend, so we have the equation:

x = y + 14

We also know that together you and your friend sell 58 tickets, so the equation becomes:

x + y = 58

Now we can solve these two equations simultaneously to find the values of x and y.

(y + 14) + y = 58

2y + 14 = 58

2y = 44

y = 22

x = 22 + 14

x = 36

Therefore, you sold 36 tickets and your friend sold 22 tickets.

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The system of equations representing the problem is y = x + 14 and x + y = 58. Solving this system we get x = 22 (friend's sold tickets) and y = 36 (your sold tickets).

We'll use a system of linear equations to model this situation. Let's define x as the number of tickets your friend sells, and y as the number of tickets you sell. From the problem, we know two things:

1. You sell 14 more tickets than your friend: y = x + 14.

2. Together, you and your friend sell 58 tickets: x + y = 58.

To solve this system, we can substitute y in the second equation with x + 14 from the first equation. This gives us:

x + (x + 14) = 58.

Solving this we get x = 22 and substituting x into the first equation gives: y = 22 + 14 = 36.

So, your friend sold 22 tickets, and you sold 36 tickets.

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Answer:

The equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].

Step-by-step explanation:

We know that,

If in the equation of the parabola,

1. If x is squared, then the parabola opens upwards or downwards.

2. If y is squared, then the parabola opens towards left or right.

Since, we want the equation of the parabola which opens left or right.

So, we get that,

The variable 'y' is being squared in the equation of the given parabola (from 1).

Answer:

x = ay^2 + by + c

Step-by-step explanation:

it was correct for me

Answer:

The object would travel 7 meters.

Step-by-step explanation:

The distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

If applying 6 newtons of force to an object results in 42 joules of work

We know,

Work = Force x Distance

42 = 6xDistance

Distance = 7 meters

Thus, the distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.

Learn more about the distance here:

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An irrational number is something that cant be expressed as a ratio.  For ex:the square root of 2.  Hope this helps.

Answer: 1/4

Step-by-step explanation:

The volume of the wedge is 50π/3 - 25√3.

To find the volume of the wedge, we need to calculate the volume of the cylindrical segment between the two intersecting planes. The formula for the volume of a cylindrical segment is V = h((R^2θ)/2 - (R^2sinθ)/2), where h is the height of the segment, R is the radius of the cylinder, and θ is the angle of the intersection between the planes. In this case, h is 10 and θ is 30°, so the formula becomes V = 10((10^2 * π/6)/2 - (10^2 * sin(π/6))/2). Simplifying the equation gives V = 50π/3 - 25√3.

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Prince Edward Island in Canada has a population density that can range from less than 2 people to as many as 250 people per square mile. This is due to various factors including climate, farmland, and job opportunities.

The Canadian island with a population density that ranges from under 2 people to as many as 250 people per square mile is Prince Edward Island. This island is one of the three Maritime Provinces in Canada and is the smallest in both land area and population. But, when it comes to population density, it has a higher range than many other islands in Canada. This is due to its favorable climate, good farmland, and the job opportunities, mainly in farming and tourism, which attract a decent population.

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The most appropriate format for representing data depends on the intended audience, data type, and presentation purpose. Adherence to professional formatting guidelines is critical, and while figures can make data accessible, they should not duplicate table data. The effectiveness of formats such as complete sentences, tweets, Prezi, and visual figures varies based on the context.

When choosing the most appropriate format for representing data, several factors need to be considered such as the intended audience, the type of data, and the purpose of the data presentation. Complete sentences, Prezi presentations, 140 character tweets, and drawn pictures each have their own strengths in conveying information effectively and engagingly depending on these factors.

For professional or academic reports, complete sentences and structured paragraphs provide in-depth analysis and explanation. However, for social media platforms, 140 character tweets can quickly capture attention and convey key points. A Prezi can be highly engaging and visually appealing for presentations, making complex information accessible. Conversely, when displaying detailed findings, sometimes a well-illustrated figure or a clear table can speak volumes more efficiently.

Nonetheless, adhering to formatting guidelines is crucial in a professional context, as non-compliance could lead to the rejection of the report. It's also important to note that while figures are useful for making data accessible, they should not duplicate data presented in tables. When using figures, they must be clearly titled, referenced in the text, and situated conveniently in the report. If the figures are too dense, they can be relegated to an appendix.

In summary, there is no one-size-fits-all format for data presentation. Preference may vary depending on personal comfort with certain formats or the requirements of a specific assignment. Reflecting on the exercise of presenting information in various formats can elucidate which is most effective for your specific needs and audience.

The problem can be represented by two inequalities: one to ensure earning at least $50 per week (5x + 10y >= 50) and another to restrict working to no more than 10 hours per week (x + y <= 10), alongside x >= 0 and y >= 0 to indicate non-negative hours worked for each job.

To determine the system of inequalities to solve the problem, we need to define variables for the number of hours spent on each job. Let's use x to represent the number of hours working as a cashier at the grocery store, and y to represent the number of hours mowing lawns. The student earns $5 per hour at the grocery store and $10 per hour mowing lawns. They want to earn at least $50 per week and work no more than 10 hours in total.

From this information, we can establish the following inequalities:

5x + 10y >= 50 (To ensure earning at least $50 per week)

x + y = 10 (To ensure working no more than 10 hours per week)

Additionally, we include y >= 0 and x >= 0 to represent that the number of hours worked at either job cannot be negative.

Hii!

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[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

72

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

To find the next term in the arithmetic sequence, we should first find the common difference.

The common difference is the amount we add or subtract to obtain the next term. In the given sequence we add 7.

So, let's find the next term.

[tex]\twoheadrightarrow\sf65+7[/tex]

[tex]\bullet[/tex] Add 7

[tex]\twoheadrightarrow\sf72[/tex]

[tex]\bullet[/tex] Great job! We found the next term

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Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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Answer:

10.4 cm

Step-by-step explanation:

Looking at the triangle in the attached pic, we can see that the right, smaller triangle is a right triangle on which we can apply the pythagorean theorem to solve for the height, h.

Pythagorean theorem tells us [tex]c^2=a^2+b^2[/tex] where c is the hypotenuse (12 in our case) and a & b are the two legs (6 and h are the respective lengths).

So let's solve for h:

[tex]c^2=a^2+b^2\\12^2=6^2+h^2\\144=36+h^2\\144-35=h^2\\108=h^2\\h=\sqrt{108} \\h=10.4[/tex]