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You bought 8 movie tickets for $x each. You spent a<br> total of $42 at the movies.

charle [14.2K]

8 divided by 42 = 5.25 which means you spent $5.25 on each ticket

3 0

2 years ago

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

One of the tables shows a proportional relationship. Graph the line representing the proportional relationship from this table i

Mkey [24]

Answer:

Table C

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Find the value of the constant of proportionality in each table

Table A

For $x=-2, y=-4$ ------> $k=-4/-2=2$

For $x=-1, y=-3$ ------> $k=-3/-1=3$

This table has different values of k

therefore

the table A does not represent a proportional relationship

Table B

For $x=-2, y=-4$ ------> $k=-4/-2=2$

For $x=-1, y=-2$ ------> $k=-2/-1=2$

For $x=1, y=3$ ------> $k=3/1=3$

This table has different values of k

therefore

the table B does not represent a proportional relationship

Table C

For $x=-2, y=-4$ ------> $k=-4/-2=2$

For $x=-1, y=-2$ ------> $k=-2/-1=2$

For $x=1, y=2$ ------> $k=2/1=2$

For $x=2, y=4$ ------> $k=4/2=2$

This table has the same value of k

therefore

the table C represent a proportional relationship

Table D

For $x=-2, y=-4$ ------> $k=-4/-2=2$

For $x=-1, y=-2$ ------> $k=-2/-1=2$

For $x=1, y=2$ ------> $k=2/1=2$

For $x=2, y=6$ ------> $k=6/2=3$

This table has different values of k

therefore

the table D does not represent a proportional relationship

3 0

3 years ago

Read 2 more answers

exercise alone. Two methods of collecting data have been proposed. Method I: Recruit volunteers who are willing to participate.

aniked [119]

Answer:

I) If method I is used, population of generalization will include all those people who may have varying exercising habits or routines. They may or may not have a regular excersing habit. In his case sample is taken from a more diverse population

II) Population of generalization will include people who will have similar excersing routines and habits if method II is used since sample is choosen from a specific population

Step-by-step explanation:

past excercising habits may affect the change in intensity to a targeted excersise in different manner. So in method I a greater diversity is included and result of excersing with or without a trainer will account for greater number of variables than method II.

5 0

3 years ago

Please help if you want brianleist!! :) uhm don't mind update- NO LINkS child..<br> Ty!

GrogVix [38]

12 since there are 12 x’s:)

3 0

3 years ago

Read 2 more answers