Jon teaches a fourth grade class at an elementary school where class sizes are always at least 20 students and at most 28. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately for Jon he discovers that doing so could only result in one straight line of desks. How many students does Jon have in his class

Answer:

Hence the expression [tex]$(x+8)(x+3)=x^{2}+11 x+24$[/tex].

Step-by-step explanation:

- The given expression is (x+8)(x+3).

- We have to multiply the given expression.

- Multiply the (x+8) by 3 , multiply the (x+8) by x then add like terms.

[tex]$$\begin{array}{r}x+8 \\\underline {\times \quad x+3} \\3 x+24 \\\underline {x^{2}+8 x+24} \\x^{2}+11 x+24\end{array}$$[/tex]

The equation regarding the algebraic information that represents the total earnings is y = 22x + 125.

From the information that's given, it can be seen that the expression is:

y = 22x + 125

She earned $555 after working for 15 hours. Therefore, the equation to represent the total earnings will be:

y = 22x + 125.

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The y-coordinate of point C may have a value of 5 or -1.

If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.

The given data in the problem is;

A coordinate plane contains the right triangle ABC.

AB = 6 units

Surface area, A= 9 square units

The AB symbol is located on the x-axis parallel line y=2.AB will thus be perpendicular to the x-axis.

As a result, AB will be parallel to the side that contains point C. (BC or AC). As a result, the triangle's area should be justified by the length of the side or leg containing point C, which is the point's y-coordinate.

The other triangle leg's length should be,

BC = AC = 9/3

BC = AC = 3

Therefore, the point C's y-coordinate can be,

2±3 = 5,-1

Hence, the y-coordinate of point C may have a value of 5 or -1.

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Answer:

The population in year 2014 is 41100.

Step-by-step explanation:

In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .

It is required to predict the population in 2014 .

To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .

Step 1 of 2

The population in 2008 was 28200 and in 2012 it was, 36800 .

The equation relating population and year is,

[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]

Step 2 of 2

The population in year 2014 can be determined by substituting 2014 for x,

[tex]$$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$$[/tex]

The surface area of the right cone is 602.88 inch².

Given,

        length of radius of the base is = 8 inches

                          the slant height is  =16 inches.

Now using formula ,

the surface area of right circular cone is a right circular cone = πr(r + l)

So,    r = 8 inches  l = 16 inches

put values in  the formula ,

             surface area of right circular cone = 3.14 × 8 ( 8 + 16 )

                                                                       = 3.14 × 8 × 24

                                                                       = 602.88 inch²

Therefore, the surface area of the right cone is 602.88 inch².

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The local maximum of the function f(x) is (0,64)

Given,

From the table we can notice that when ₋2<x<0, f(x) is increasing

And in case of when 0<x<3, f(x) is decreasing progressively.

we know that a local maximum is present on the graph of the function y=f(x) at the location where the graph shifts from increasing to decreasing. The tangent has zero slope at this location. And at the point when the graph shifts from declining to increasing, a local minimum is present.

Therefore, a local maximum also known as relative maximum, is a maximum that exists in a certain area and is not necessarily(but could be) a global maximum.

Hence f(0) is a local maximum of the ordered pair (0,64)

Hence we get the local maximum pair as (0,64)

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Answer:

it is 0,64

which is C for me but looks like A for you

Answer: 3

Step-by-step explanation:

test the numbers

Answer:

3

Step-by-step explanation:

first you divide the given number with 11 the remainder you get substract in order to get 0

The transportation problem is an example of a category of problems that can be modeled as c. Network flow problems.

A transportation problem is a special kind of alignment that aims to calculate the cost of transporting a particular product from a set of sources or origins (factories, manufacturing facilities, etc.) to a set of destinations (warehouses, businesses, etc.). It's a planning issue. Minimize.

The transport problem is one of the models of linear programming problems. Its main purpose is to handle situations where goods are shipped from multiple sources to different destinations and to minimize overall shipping costs.

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Answer: 14.79

Step-by-step explanation:

[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]

Lily present age now 17 years old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Here, Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

We have been given that Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel.

We want to find the present age of lily.

Since five years ago rachel was 6, we know that Lily was twice as old as Rachel makes lily 12 years old.

For five years ago so 12 + 5 = 17.

Therefore, Lily is now 17 years old.

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Answer:

See attached image

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please post a picture of the triangle and the choices.

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The equation of the line of best fit is y = 50x/3

The missing graph is added as an attachment

From the graph, we have the following points

(x, y) = (0,0) and (3,50)

The equation is then calculated as:

y = (y2 - y1)/(x2 - x1) * (x - x1) + y1

This gives

y = (50 -0)/(3- 0) * (x - 0) + 0

Evaluate

y = 50x/3

Hence, the equation of the line of best fit is y = 50x/3

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Answer:

4

Step-by-step explanation:

n and (n + 2)

Therefore,

n × (n + 2) = 8

n^2 + 2n = 8

n^2 +2n - 8 = 0

n^2 + 4n - 2n -8 = 0

n (n + 4) -2 ( n + 4)

(n - 2 ) ( n + 4)

Therefore,

n = -4 or + 2

But since n can't be negative, n = 2

substituting

(n+2) = 2+2 = 4

Therefore, the value of the greater integer is 4

Answer:

(-4,-3)

Step-by-step explanation:

Just check each vertex point and move them by instruction, write them down and do elimination and you'll find the answer

Answer:

3b^3

Step-by-step explanation:

I assume the 6 in the denominator should be b.

-60 / -20 = 3

b^8/b^5 = b^(8 - 5) = b^3

Answer: 3b^3

We conclude that f(x) is odd, so the correct option is A.

f(x) is an odd function if:

f(-x) = -f(x).

f(x) is an even function if:

f(x) = f(-x).

In this case, we know that the function f(x) has the points:

{ (-2, 8), (-1, -3.5), (0, 0), (1, 3.5), (2, -8)}

As you can see:

f(-2) = 8

f(2) = -8

Then:

f(-2) = -f(2)

Also:

f(-1) = -3.5

f(1) = 3.5

Then:

f(-1) = -f(1).

So we conclude that this is an odd function, and the correct option is A.

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The distribution value's skewness Pearson coefficient is 2.5.

Given that the median is 12 and the standard deviation is 6, the mean value is 17.

The difference between the mean and median is multiplied by three to determine Pearson's coefficient of skewness. By dividing the outcome by the standard deviation, A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

To determine Pearson's coefficient of skewness, use the following formula:

Skewness=(3(Mean-Median))÷standard deviation

Replace the values there with,

Skewness=(3(17-12))÷6

Skewness=(3×5)÷6

Skewness=5÷2

Skewness=2.5

Therefore, for a distribution with a mean of 17, a median of 12, and a standard deviation of 6, the value of the Pearson coefficient of skewness is 2.5.

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Hello and Good Morning/Afternoon:

To find the slope of something:

  ⇒ let's consider what the formula of the slope needs

               [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

      ⇒ needs any two points on the line (x₁,y₁) and (x₂,y₂)

Let's get the required information:

Let's solve:

  [tex]Slope = \frac{2-0}{5-0} =\frac{2}{5}[/tex]

Answer: 2/5

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Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as [tex]$y=\frac{1}{3} x-\frac{13}{3}$[/tex].

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 2&4 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$5 \&-1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$[/tex]

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

Substitute [tex]$-\frac{1}{3}$[/tex] for m,-1 for [tex]$x_{1}$[/tex], and 4 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,

[tex]y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$[/tex]

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation [tex]$y-4=\frac{1}{3} x-\frac{1}{3}$[/tex], and simplify as follows,

[tex]y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$[/tex]

This is the required linear equation.

Answer:

3 whole pizzas

Step-by-step explanation:

[tex]10 \times \frac{1}{4} = \frac{10}{4} = \frac{5}{2} = 2 \frac{1}{2} [/tex]

So 3 whole pizzas will need to be ordered.

Answer:

2 and a half pies

Step-by-step explanation:

ten sixth graders eat 1/4 each, therefore 4 kids eat 1 whole pie. similarly, 8 kids eat two whole pies, since two kids are remaining they eat 2/4 of a pie.

which can also be put in as 1/2. this means they eat half a pie. and that is how altogether it is 2 and a half pies.

hope this helps!

The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).

It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.

It follows therefore that, given the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).

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The correct answer is. Proportional.

2. ce

3. Segment Addition Postulate.

By the angle-angle similarity postulate, △YXZ∼△YZQ, and △YXZ∼△ZXQ.

The corresponding sides of two similar triangles are proportional.

Since similar triangles have proportional sides, therefore

[tex]\frac{a}{c}=\frac{f}{a}[/tex] and [tex]\frac{b}{c}=\frac{b}{e}[/tex]

Solving the equation for a² and b² gives

[tex]a^2=cf[/tex] and [tex]b^2=ce[/tex]

The value of a² is cf and the value b² is ce.

Adding these together gives

[tex]a^2+b^2=cf+ce[/tex]

Factoring out the common segment gives

[tex]a^2+b^2=c(f+e)[/tex]

From the given figure it is clear that

[tex]c=f+e[/tex]

        (Segment Addition Postulate)

Using the Segment Addition Postulate, we get

[tex]a^2+b^2=c(c)[/tex]

On simplification, we get

[tex]a^2+b^2=c^2[/tex]

Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.

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Answer:

1. Angle-Angle similarity Postulate  2.Proportional 3. C

Step-by-step explanation:

By the Angle-Angle similarity Postulate,  △YXZ~ △YZQ and  △YXZ~ △ZXQ. Since similar Triangles have Proportional sides, a/c= f/a and b/c= e/b. Solving the equation for a² and b² gives a² = cf and b² =ce. Adding these together gives a²+b²=cf+ce. Factoring out the common segment gives  a²+b²=c(f+e). Using the segment addition postulate gives a²+b²=c(c)

, which simplifies to a²+b²=c²     (Look at image for proof)

.  

Thus, the rate of change per gallon of gas is 60 miles per gallon.

A motorcycle consumes 5 gallons of gas for 300 miles and 7 gallons for 420 miles.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Now,

Rate of change = Difference B/w volume (i.e. in gallons)  /difference in miles
= 420-300/7-2
= 60 gallons/mile

Thus, The required rate of change per gallon of gas is 60 miles per gallon.

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Answer:

option B is correct.

Explanation:

[tex]\sf Equation : y-4\ =-\frac{2}{3}\left(x+3\right)[/tex]

[tex]\sf \rightarrow y\ =-\frac{2}{3}x-2 + 4[/tex]

[tex]\sf \rightarrow y\ =-\frac{2}{3}x + 2[/tex]

comparing it with slope intercept form "y = mx + b'' where m is slope and b is y-intercept.

Here slope: -2/3 and y-intercept: 2

This means the slope is decreasing and has crosses the y axis at (0, 2)

Answer:

Step-by-step explanation:

Answer: D

This result is true by De Moivre's theorem.

Answer:

c

Step-by-step explanation:

If Year 1 is the base year, then the inflation rate in Year 2 was 2.10 percent. The correct option is a.

Inflation rate is the rate at which the general level of prices for goods and services in an economy is increasing over a certain period of time, typically one year.

To calculate the inflation rate, we need to compare the price level in Year 2 to the price level in Year 1.

Using the data from Table 24-1, we can see that the price index in Year 2 is 102.1 and the price index in Year 1 is 100.0.

The inflation rate can be calculated using the following formula:

Inflation rate = (Price index in Year 2 - Price index in Year 1) / Price index in Year 1 * 100%

Plugging in the values, we get:

Inflation rate = (102.1 - 100.0) / 100.0 * 100%

Inflation rate = 2.1%

Therefore, the correct answer is (a) 2.10 percent.

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