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Alex777 [14]
2 years ago
10

Lara is setting up a convention room. She is expecting 240 attendees and can comfortably fit chairs in rows of 16. How many rows

does she need to set up?
Mathematics
1 answer:
madam [21]2 years ago
8 0

Answer:

Hello, lets break it down.

Step-by-step explanation:

Expecting 240 attendees.

Can fit

16 chairs into a row so

240 divided by 16 is 15 that means she needs to set up 15 rows.

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How many solutions does the equation 3x − 7 = 4 + 6 + 4x have
Sunny_sXe [5.5K]

Answer:

The given equation 3x − 7 = 4 + 6 + 4x has one solution.

Step-by-step explanation:

Given : Equation 3x − 7 = 4 + 6 + 4x

We have to find the number of solutions of the given equation.

Consider the given equation 3x − 7 = 4 + 6 + 4x

Simplify, we have,

3x − 7 = 10 + 4x

Now subtract 3x both side, we hvae,

-7 = 10 + 4x - 3x

Simplify, we have,

- 7 = 10 + x

Subtract 10 both side, we have,

-7 - 10 = x

x = - 17

Thus, The given equation 3x − 7 = 4 + 6 + 4x has one solution.

8 0
3 years ago
Read 2 more answers
A 1.50 liter sample of dry air in a cylinder exerts a pressure of 3.00 atmospheres at a temperature of 25oC. Without change in t
cricket20 [7]
The answer is 4.5 l

To calculate this, we will use the Boyle's law using constant k, pressure P, and volume V:

 PV = k

We can forget temperature since it is constant.

We have:

P1V1 = k

P2V2 = k

So, P1V1 = P2V2

P1 = 3 atm

V1 = 1.5 l

P2 = 1 atm

V2 = ?

_____

P1V1 = P2V2

3 atm * 1.5 l = 1 atm * V2

4.5 atm/l = 1 atm * V2

V2 = 4.5 atm l / 1 atm

V2 = 4.5 l

5 0
3 years ago
Read 2 more answers
The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac
olya-2409 [2.1K]

Answer:

a) \frac{74}{10025}

b) \frac{3x-2}{x(8x+1)}

c) \frac{-24x^2+32x-2}{(8x^2+x)^2}

Step-by-step explanation:

For total cost function c(x), average cost is given by \frac{c(x)}{x} i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., \left ( \frac{c(x)}{x} \right )'

Given:c(x)=\frac{3x-2}{8x+1}

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

a)

At x = 50 units,

\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}

b)

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

c)

Marginal average cost:

Differentiate average cost with respect to x

Take f=3x-2\,,\,g=8x^2+x

using quotient rule, \left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}

Therefore,

\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}

3 0
3 years ago
The question is the screenshot
tiny-mole [99]

Answer:

Tasha is wrong because she can do more than six bags so she is wrong. Since she has a lot of stuff so she can more than six bags

Step-by-step explanation:

7 0
3 years ago
The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacen
kompoz [17]

Answer:

\fbox{\begin{minipage}{4em}36 ways\end{minipage}}

Step-by-step explanation:

<em>Step 1: Re-state the problem in an easier way to set up a permutation problem</em>

"The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven"

The series above can be represented again, in form of:

7a + 1, 7b - 1, 7c + 1, 7d - 1, 7e + 1, 7f - 1

with a, b, c, d, e, f are non-negative integers.

=> 3 numbers are multiply of 7 plus 1

=> 3 numbers are multiple of 7 minus 1

<em>Step 2: Perform the counting:</em>

For the 1st number, there are 6 ways to select

To satisfy that each pair of numbers creates a multiple of 7, then:

For the 2nd number, there are 3 ways left to select

For the 3rd number, there are 2 ways left to select

For the 4rd number, there are 2 ways left to select

For the 5th number, there are 1 way left to select

For the 6th number, there are 1 way left to select

=> In total, the number of possible ways to select:

N = 6 x 3 x 2 x 2 x 1 x 1 = 72

However, these numbers are located around a circle, each option is counted twice.

=> The final number of possible ways:

N = 72/2 = 36

Hope this helps!

:)

3 0
3 years ago
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