What is a rule for the height<br> as an algebraic expression?

a charitable organization in Lanberry is hosting a black tie benefit. Yesterday, the organization sold 55 regular tickets and 49

jenyasd209 [6]

Answer:

regular: $67
VIP: $122

Step-by-step explanation:

Let r and v represent the costs of a regular and VIP ticket, respectively. The two sales can be represented by ...

55r +49v = 9663

79r +84v = 15541

We can subtract 7 times the second equation from 12 times the first to eliminate the v terms.

12(55r +49v) -7(79r +84v) = 12(9663) -7(15541)

660r +588v -553r -588v = 115,956 -108,787 . . . . . eliminate parentheses

107r = 7169 . . . . . . . simplify

r = 67 . . . . . . . . . . . divide by 107

Using this value in the first equation, we have ...

55(67) +49v = 9663

v = 5978/49 . . . . . . . . . subtract 3685, divide by 49

v = 122

A regular ticket costs $67; a VIP ticket costs $122.

_____

<em>Additional comment</em>

When using "elimination" to solve a system of equations, you're looking for coefficients of the same variable that are related by small factors. Preferably, one coefficient is the same as, or a small multiple of, the other. Here, 55 and 79 (the coefficients of x) are not related by an integer, or a couple of small integers. On the other hand, the y-coefficients 49 and 84 have a common factor of 7, and are in the ratio 7:12, a pair of small numbers. This is why we chose to eliminate the y-variable.

The x-variable could be eliminated using 55 and -79 as multipliers of the equations. This results in larger numbers, and more chance for error. (Errors tend to creep in when computing or copying large numbers.)

Of course, any of several machine methods could be used to solve these equations, including graphing and matrix-solving functions. Here, we tried to honor the requirement to solve by elimination.

7 0

3 years ago

What are the mean absolute deviation and population standard deviation of this data set? Round to the nearest tenth if necessary

tekilochka [14]

Answer:

For a data set of N elements:

{x₁, x₂, ..., xₙ}

The mean is:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

The mean absolute deviation is:

$MAD = \frac{|x_1 - M| + ... + |x_n - M|}{N}$

And the population standard deviation is:

$PSD = \frac{\sqrt{|x_1 - M|^2 + ... + |x_n - M|^2} }{\sqrt{N}}$

In this case, our set has 5 elements, and the set is:

{2, 4, 6, 9, 14}

The mean of this set is:

$M = \frac{2 + 4 + 6 + 9 + 14}{5} = 7$

The mean absolute deviation is:

$MAD = \frac{|2 - 7| + |4 - 7| + |6 - 7|+ |9 - 7| + |14 - 7| }{5} = 3.6$

And the population standard deviation is:

$PSD = \sqrt{\frac{|2 - 7|^2 + |4 - 7|^2 + |6 - 7|^2+ |9 - 7|^2 + |14 - 7|^2 }{5}} = 4.2$

6 0

3 years ago

Find the midpoint of the line segment that has endpoints at (10,8) (-3,-10)

dem82 [27]

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

$(x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Plug in the coordinates given:

$(\frac{10-3}{2}, \frac{8-10}{2})$

Simplify:

$(\frac{7}{2}, \frac{-2}{2})$

Therefore, the coordinates of the mid-point are:

(3.5, -1).

7 0

3 years ago

-6=-8+<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bp%7D%7B11%7D%20" id="TexFormula1" title=" \frac{p}{11} " alt=" \frac{p}

vekshin1

P=22 rewrite the question as -8+p/11=-6 then move all terms not containing p to the right side p/11=2 multiply both sides of the given equation by 11, the reciprocal, 11*p/11=11*2

8 0

3 years ago

Which graph shows a line with a slope of 3/2

madreJ [45]

Graph C shows the line of slope

4 0

3 years ago

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What is a rule for the height as an algebraic expression?