A group of people are having a dinner that costs $160, which is to be shared equally. If two more persons join the group and share the same cost, each will pay $4 less. Find the original number of people in the group.

Answer:

16c² + 32c + 16

Step-by-step explanation:

(4c+4)² =

(4c+4)(4c+4) =

16c² + 16c + 16c + 16 =

16c² + 32c + 16

I think this is the answer you are looking for.

Hope this helped and have a good day

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]

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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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:

x = 10

Step-by-step explanation:

Interior angles of a triangle sum to 180°

Therefore, to find the value of x, sum the given angles, equal them to 180, then solve for x:

⇒ 6x + 8x + 4x = 180

⇒ (6 + 8 + 4)x = 180

⇒ 18x = 180

⇒ 18x ÷ 18 = 180 ÷ 18

⇒ x = 10

The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.

Since the tank is cylindrical in shape, its volume can be written as:

V = πr²d,

where V is its volume, r is the radius, and d is the depth.

The radius is constant, given r = 5ft.

Thus the volume can be shown as:

V = π(5)²d,

or, V = 25πd.

Differentiating this with respect to time, we get:

δV/δt = 25πδd/δt ... (i),

where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.

Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.

Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:

δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.

Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.

The question written correctly is:

"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"

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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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The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.

In the question, we are given that the size of the lily pad doubles itself every day.

If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.

This makes a geometric progression, with the first term as a, and the constant ratio as 2.

We are given that on the 30th day, the size of the lily pad, covers the entire pond.

The size on the 30th day can be shown as the 30th term of this geometric progression

Therefore, size of the  pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.

We are asked the day on which the pond is half covered.

The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.

The day can be calculated as follows:

a.2ⁿ⁻¹ = a.2²⁸,

or, 2ⁿ/2 = 2²⁸,

or, 2ⁿ = 2²⁹,

or, n = 29.

Thus, the lily pad covers half the pond on the 29th day.

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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

The severe limitation of using the internet for primary research is that a sample universe  composed solely of internet respondents represents a potential bias.

Given options 1)The data on the Internet are usually outdated.

2) The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately.

3) A sample universe composed solely of Internet respondents represents a potential bias.

4)Secondary data cannot be accessed on the Internet for conducting research.

5) Using the Internet for primary research is the most expensive way of conducting primary research.

We have to choose most appropriate option which shows the severe limitation of using internet for primary research.

The most appropriate option is option third which is that a sample universe composed solely of internet respondents a potential bias

There is biasness because on internet people gives their own opinion and reviews and don't think about reality. The data may have been collected for the research according to researcher's priority. The data may be outdated but it is of our choice whether we use that data or not because generally the date is given on the internet. We can also access secondary data on the internet. Using internet in research is not so expensive because some organisation provides study materials to researchers themselves.

Hence the limitation of using the internet for primary research is that a sample universe composed solely of internet respondents a potential. bias.

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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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The probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes is 66.66%.

It is given that the time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes.

That means that the number of possible minutes it will take will be 6, 7, 8 ,9, 10, 11, 12, 13, 14 That's a total of 9 separate minutes or intervals.

If it takes between 8 and 13 minutes, that is only  8 ,9, 10, 11, 12, 13 that's only 6 separate minutes or intervals.

The probability of it taking between 8 and 13 minutes is therefore [tex]\frac{6}{9} = \frac{2}{3}[/tex]

Or 0.6666666667 x 100 is 66.66%.

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Answer:

Step-by-step explanation:

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:

See attached image

Step-by-step explanation:

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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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)

.  

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

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!

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Answer: D

This result is true by De Moivre's theorem.

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250

The profit (P) is the result of subtracting costs from sales (S). Cost (Cp) is the sum of rent (C) and production cost (C'). Now we proceed to create and solve the expression:

P = S - C - C'

P = 500 · x - 275 · x - 2500

P = 225 · x - 2500

P = 225 · 30 - 2500

P = 4250

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250.

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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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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:

(f + g)(x) = x - 7

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= - 3x - 5 + 4x - 2 ← collect like terms

= x - 7

Answer:

137,131

Step-by-step explanation:

Answer:

  (c)  x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

Step-by-step explanation:

The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.

The last step shown in the derivation so far is ...

  [tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}[/tex]

The left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.

  [tex]\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}[/tex]

Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

[tex]\left(x+\frac{b}{2a} \right)^2[/tex]

So, taking the square root of both sides,

[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

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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