A teacher is comparing the quarter grades between two of her classes. She takes a random sample of 8 students from each class an
1 answer:
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The price of a senior citizen ticket is $8 and the price of a student ticket is$ 10
Step-by-step explanation:
Let the cost of one seniors citizen ticket be x and student be y
First day:
10 seniors citizen tickets and 11 student for a total of $190.
10x + 11y = 190-----------------------------(1)
Second day:
$160 on the second day by selling 5 senior citizen tickets and 12 student tickets.
5x + 12y = 160---------------------------------(2)
Multiply eq(2) by 2
10x + 24y = 320----------------------------(3)
Subtract eq(1) from (3)
10x + 24y = 320
10x + 11y = 190
-----------------------------
0x + 13 y = 130
---------------------------
13y = 130
y = 10-------------------------------(4)
Substituting (4) in (2)
5x + 12(10) = 160
5x + 120 = 160
5x = 160-120
5x = 40
x = 8
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
