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ad-work [718]
3 years ago
6

A total of 762 people, consisting of parents, students, and teachers, attended the Community Fair. If 212 parents and 386 studen

ts were at the event, how many teachers attended?​
Mathematics
1 answer:
ikadub [295]3 years ago
7 0

Answer:

\boxed{\textsf{ The number of Teachers that attented is \textbf{ 164 } .}}

Step-by-step explanation:

Here it's given that a total of 762 people consisting of parents, students, and teachers, attended the Community Fair. There were 212 parents and 386 students at the fair .That is ,

<u>Number</u><u> </u><u>of</u><u> </u><u>stude</u><u>nts</u><u>:</u><u>-</u>

\sf\implies n(students) = 386

<u>Number</u><u> </u><u>of</u><u> </u><u>parents </u><u>:</u><u>-</u>

\sf\implies n(parents) = 212

<u>Number</u><u> </u><u>of </u><u>teachers</u><u> </u><u>:</u><u>-</u><u> </u>

\sf\implies n(teachers) = ?

Here the Number of teachers could be simply find out by subtracting the number of students and teachers from the total number of attendees .

\sf\implies n_{(teachers)}= n_{(total)}- n_{(students)}- n_{(parents)} \\\\\sf\implies n_{(teachers)}= 762 - 386 - 212 \\\\\sf\implies n_{(teachers)}= 762 - 598 \\\\\sf\implies\boxed{\pink{\frak{ n_{(teachers)}= 164 }}}

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mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}

For x, we will be using the Cosine Function:

\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}(16)Cosine(45^{\circ})\text{ =  x}(16)(\frac{1}{\sqrt[]{2}})\text{ = x}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = x}

Therefore, x = 8√2.

For y, we will be using the Sine Function.

\text{  Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}\text{ (16)Sine }(45^{\circ})\text{ =  y}\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = y}

Therefore, y = 8√2.

5 0
1 year ago
Suppose that you invest $400 in a bank account that has APR of 6% and it is compounded monthly (12 times a year)
Fed [463]
The answer would be $804.88
7 0
3 years ago
Diners frequently add a​ 15% tip when charging a meal to a credit card. What is the total amount charged if the cost of the​ mea
aksik [14]

Answer:

$40.25

Step-by-step explanation:

.15 x 35 = 5.25

35+ 5.25 = 40.25

Hope this helps!

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3 years ago
Is this done correctly or incorrectly??<br> PLEASE LET ME KNOW<br><br>PLZ HELP ASAP
Dimas [21]
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3 0
3 years ago
The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How m
densk [106]

Answer:

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Step-by-step explanation:

this is an arithmetic sequence :

an = an-1 + c

in our case

a1 = 10 (10 seats in the first row)

a2 = a1 + 1 = 10 + 1 = 11

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altogether this means the sum of the arithmetic sequence of a1 to a38.

the general sum of an arithmetic sequence from a1 to an is

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

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2 years ago
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