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3 years ago

7

The auditorium has five doors. Three doors are only entrances; one door is only an exit; and the fifth door can be used to eithe

r enter or exit. In how many different ways can someone enter then leave the auditorium

1 answer:

Neko [114]3 years ago

4 0

Answer:

8 different ways

Step-by-step explanation:

To find how many different ways can someone enter then leave the auditorium, we need to find how many ways can someone enter, how many ways can someone leave, and then multiply these possibilities:

Number of ways that someone can enter: 4 (3 doors are only entrance and 1 door is entrance and exit)

Number of ways that someone can leave: 2 (1 door is only exit and 1 door is entrance and exit)

So the number of different ways that someone can enter and leave the auditorium is 4*2 = 8

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8) Find the endpoint Cif M is the midpoint of segment CD and M (2, 4) and D (5,7)

Elenna [48]

Answer:

8. c. (-1, -1)

9. a. (-6, -1)

b. True

Step-by-step Explanation:

8. Given the midpoint M(2, 4), and one endpoint D(5, 7) of segment CD, the coordinate pair of the other endpoint C, can be calculated as follows:

let $D(5, 7) = (x_2, y_2)$

$C(?, ?) = (x_1, y_1)$

$M(2, 4) = (\frac{x_1 + 5}{2}, \frac{y_1 + 7}{2})$

Rewrite the equation to find the coordinates of C

$2 = \frac{x_1 + 5}{2}$ and $4 = \frac{y_1 + 7}{2}$

Solve for each:

$2 = \frac{x_1 + 5}{2}$

$2*2 = \frac{x_1 + 5}{2}*2$

$4 = x_1 + 5$

$4 - 5 = x_1 + 5 - 5$

$-1 = x_1$

$x_1 = -1$

$4 = \frac{y_1 + 7}{2}$

$4*2 = \frac{y_1 + 7}{2}*2$

$8 = y_1 + 7$

$8 - 7 = y_1 + 7 - 7$

$1 = y_1$

$y_1 = 1$

Coordinates of endpoint C is (-1, 1)

9. a.Given segment AB, with midpoint M(-4, -5), and endpoint A(-2, -9), find endpoint B as follows:

let $A(-2, -9) = (x_2, y_2)$

$B(?, ?) = (x_1, y_1)$

$M(-4, -5) = (\frac{x_1 + (-2)}{2}, \frac{y_1 + (-9)}{2})$

$-4 = \frac{x_1 - 2}{2}$ and $-5 = \frac{y_1 - 9}{2}$

Solve for each:

$-4 = \frac{x_1 - 2}{2}$

$-4*2 = \frac{x_1 - 2}{2}*2$

$-8 = x_1 - 2$

$-8 + 2 = x_1 - 2 + 2$

$-6 = x_1$

$x_1 = -6$

$-5 = \frac{y_1 - 9}{2}$

$-5*2 = \frac{y_1 - 9}{2}*2$

$-10 = y_1 - 9$

$-10 + 9 = y_1 - 9 + 9$

$-1 = y_1$

$y_1 = -1$

Coordinates of endpoint B is (-6, -1)

b. The midpoint of a segment, is the middle of the segment. It divides the segment into two equal parts. The answer is TRUE.

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4 years ago

$11.25 is what percent of $375?<br> PLS Help Me!!!

Ivahew [28]

11.25/375 = 0.03 which is 3%

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4 years ago

The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72

Brut [27]

Answer:

The maximum number of songs that the symphonic choir can record is 14

Step-by-step explanation:

Let

x ----> the number of songs of the symphonic choir

we know that

The number of songs of the jazz choir multiplied by its average time per song plus the the number of songs of the symphonic choir multiplied by its average time per song, must be less than or equal to 72 minutes

so

The inequality that represent this situation is

$3(7)+3.5(x)\leq 72$

solve for x

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subtract 21 both sides

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divide by 3.6 both sides

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therefore

The maximum number of songs that the symphonic choir can record is 14

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3 years ago

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Marta_Voda [28]

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Any two numbers that add to 4.

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What is 607/100 as a percent?

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6.07 = decimal form

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