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Readme [11.4K]
3 years ago
7

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 2000 seats. The students

left 33% of the seats in the theater vacant. How many 6th graders went on the trip?
Mathematics
1 answer:
puteri [66]3 years ago
7 0

Answer:

1340 students

Step-by-step explanation:

since the students left 33% of the seats open, that means they took up 67% of the seats.

67% is 0.67

0.67 * 2,000 = 1340

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Describe all the positive integers that would make [(1/2|4] less than (1/2)7
Zielflug [23.3K]

Answer:

The only positive integers would be anything less than 3. So 1 or 2 would work

Step-by-step explanation:

If something that is already being raised to a power, gets raised to another power, those powers add up. So if it were (\frac{1}{2} ^{2} )^{2}, the exponents would add which would make it (\frac{1}{2}^{4} ).

In the case of your question, if 'n' was 2 it would be to the power of 6 making it less than to the power of. 1 could also work

5 0
1 year ago
The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is soli
stiks02 [169]
The first line through points (-3, 0) and (-4, -1) is the orange line.

The second line, through (1, 1) and (2, -1) is the purple line.

Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.

Both lines are included, since they are solid lines.



The equation of the first line can be found as follows:

the slope is \frac{0-(-1)}{-3-(-4)}=\frac{1}{1}=1, thus, the equation is:
y-0=1(x-(-4))\\\\y=x+4


The equation of the second line can be found as follows:

the slope is \frac{1-(-1)}{1-2}= \frac{2}{-1}=-2, 

thus the equation of the second line is :


y-1=-2(x-1)\\\\y-1=-2x+2\\\\y=-2x+3


We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines, 

so we write the inequalities so that they do not hold for (0, 4)


line 1:

y≥x+4

4≥0+4=4 is true, so we change the sign and write : y≤x+4


similarly, line 2:

y≤-2x+3

4≤-2*0+3=3, which is not true, so we have the correct direction.


Note that since the lines were solid, we include the equality case:


Answer: 

the shaded region is the solution to the system of inequalities:

i) y≤x+4
ii) y≤-2x+3

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The 2 triangles are congruent

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