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3 years ago

7

A room contains 55 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the num

ber of rows.

2 answers:

miss Akunina [59]3 years ago

7 0

Answer:

i believe its 27

Step-by-step explanation:25 times two= 50 27 times two= 54 +one more is 55. so it is 27

uysha [10]3 years ago

4 0

Answer:

<h2>11 rows.</h2>

Step-by-step explanation:

Givens

The room contains 55 chairs arranged in rows.
The number of rows is one more than twice the number of chairs.

We know that the total number of chairs must be the product between the number of chairs per row and the total number of rows, which can be expressed as

$c \times r = 55$

Where $c$ represents the number of chairs per row and $r$ representes the number of rows.

The second given statment defined a second equation

$r=2c+1$

Now, we can substitute the second equation into the first one, and solve

$c \times r = 55\\c (2c+1)=55\\2c^{2}+c-55=0$

Which can be factored by multiplying the expression by 2, and solve has a perfect trinomial

$2(2c^{2}+c-55)=0\\2^{2}c^{2}+2c- 110=0\\(2c)^{2}+2c-110=0$

So, we need to find two number which product is 110 and is 1. If you think this through, those numbers are 11 and 10, because 11*10=110 and 11-10=1.

The factors are

$\frac{(2c+11)(2c-10)}{2} =0$ , we have to divide by the number we multiplied before, then we simplify this number with the second factor

$(2c+11)(c-5)=0$

Where the positive solution is the only one that can be part of the answer because it doesn't make sense if we say -3 chairs. So,

$c-5=0\\c=5$

This means there are 5 chairs per row.

Then, we use this value to find the other one.

$c \times r=55\\5 \times r=55\\r=\frac{55}{5}\\ r=11$

Therefore, there are 11 rows and 5 chairs per row.

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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

kenny6666 [7]

Given:

The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation

$y=-29x^2+1388x-10040$

To find:

The maximum amount of profit the company can make, to the nearest dollar.

Solution:

If a quadratic equation is $f(x)=ax^2+bx+c$ , then the vertex is

$Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)$

If a>0, then vertex is the minimum point and if a<0, then the vertex is the maximum point.

We have,

$y=-29x^2+1388x-10040$

Here, $a=-29,b=1388, c=-10040$ . Clearly, a<0. So, the vertex is the point of maxima.

$-\dfrac{b}{2a}=-\dfrac{1388}{2(-29)}$

$-\dfrac{b}{2a}=-\dfrac{1388}{-58}$

$-\dfrac{b}{2a}\approx 23.931$

Putting x=23.931 in the given equation, we get

$y=-29(23.931)^2+1388(23.931)-10040$

$y=-16608.09+33216.228-10040$

$y=6568.138$

The vertex is at (23.931,6568.138).

Therefore, the maximum profit is $6568.138 when x=23.931.

5 0

3 years ago

Which number is an integer? 1, 0.5, 3/2

aksik [14]

An integer is any whole number (not fractions) that can be either negative or positive.

1 is the only integer because 0.5 and 3/2 are not whole numbers and are fractions, while 1 is a whole number.

7 0

3 years ago

An Account grows at an annual interest rate, it grows by a factor of x=1 + r each year. The function A(x)=800x^4 + 350x^3 + 500x

Marina86 [1]

Answer:

Applying the formula, it is found that the total amount in the account will be of $2,431.3. I THINK

Step-by-step explanation:

IM NOT SURE!

7 0

2 years ago

Read 2 more answers

National Ave gas prices

Musya8 [376]

Question: What equation models the data?
For this question I used a software to calculate the equation. When plotted, we can notice that the points form a parabolic function therefore we needed quadratic regression for this one. The quadratic equation is in the form of $y=A+Bx+Cx^{2}$ where y represents the gas prices, x is the year, and A, B, and C are coefficients. I have found A, B, and C using the software and the equation for the data is:

$y=-0.092+0.587x-0.026x^{2}$

Question: What are the domain and range of the equation?
To find the range of the equation, we just transform the quadratic equation into the form $y=a(x-h)^{2}+k$ . The value for k would be the maximum element in our range, and for the sake of the problem, let's assume that we don't have negative prices.

$y=-0.092+0.587x-0.026x^{2}$
$y+0.092=0.587x-0.026x^{2}$
$y+0.092=-0.026(x^{2}-22.577x)$
$y+0.092-0.026(127.442)=-0.026(x^{2}-22.577x+127.442)$
$y-3.221=-0.026(x-11.289)^{2}$
$y=-0.026(x-11.289)^{2}+3.221$

We can see that 3.221 is the maximum value of the range while zero is the minimum. Thus, we can express the range as { $y|0 \leq y \leq 3.221$ }

For the domain, the number of years can extend infinitely but it will also depend if we want to consider the years where the price will be negative. Thus, let's just find the year when the price would be zero.

$0=-0.026(x-11.289)^{2}+3.221$
$-3.221=-0.026(x-11.289)^{2}$
$123.885=(x-11.289)^{2}$
$+-11.130=x-11.289$

$x=0.159$
$x=22.419$

Anywhere before and after the range of the x values above would result to a negative price therefore we can restrict the domain to those values. However, since x represents the year, we would need to round up the first value and round down the larger value.

Domain: { $x|01 \leq x \leq 22$ }

Question: Do you think your equation is a good fit for the data?
To know whether our equation is a good fit or not, we just look at the value of the correlation coefficient r. We can calculate this manually but in this case I just used a software. According to the software, the value for r is 0.661. This is almost close to a strong correlation which is 0.7 thus we can say that this equation is a good fit.

Question: Is there a trend in the data?
There might be a trend, but it won't be a simple linear one. Since the data initially rose before continuously decreasing, our data would best be described by a quadratic trend. The quadratic trend would be the parabolic equation we just used to model the data.

Question: Does there seem to be a positive correlation, a negative correlation, or neither?
Neither. A positive or negative correlation only applies when we are talking about linear trends, where it's either one variable increases as the other one also increases or the variable decreases as the other one increases. In our case, the price rose and fall as the years increase so there is neither a positive nor a negative correlation.

Question: How much do you expect gas to cost in 2020?
We can answer this question by using the equation that we used to model the data. For this question, we would just need to substitute 20 for x since we want to know the price in 2020 (we have only used the last two digits of the year for the equation) while the answer to this would be the expected price.

$y=-0.092+0.587(20)-0.026(20)^{2}$
$y=-0.092+11.740-10.400$
$y=1.248$

The expected price in 2020 would be 1.248 units.

4 0

3 years ago

The price of tickets for the dance was 1 ticket for $6 or 2 tickets for $8 she looked inside the cash box and found $200 and tic

Aleks04 [339]

We can say that exchanging one couple's ticket for an individual's ticket would increase the money in the cash box from 200 to 202 and it would result in an even number of couples tickets sold.

<u>Step-by-step explanation:</u>

Let the number of tickets sold to the individuals = s

Let the number of tickets sold to the couples = c

According to the question,

s + c = 46 ( Equation 1)

Since each individual's ticket is $6, the total amount of money made by selling tickets to individuals is 6s.

Similarly, since each ticket sold to couples is $8, the total amount of money made by selling tickets to couples is 8c.

So,

6 s + 8 c = 200 ( Equation 2)

On solving both the equations, we get

c = 38 and s = 8

Therefore, 8 tickets were sold to individuals and 38 tickets were sold to the couples.

5 0

3 years ago