We know for the problem that the performer earned $120 at a performance where 8 people attend. We also know that he u<span>ses 43% of the money earned to pay the costs involved in putting on each performance, so we need to find the 43% of $120. To do that, we are going to divide 43% by 100%, and then multiply it by $120:
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Now we know that the performer uses $51.6 of $120 to pay the costs involved in putting on each performance. The only thing left to find his profits is subtract $51.6 from $120:

We can conclude that the performer makes a profit of $68.4 when 8 people attend his performance.
Step-by-step explanation:
Remember SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
The side adjacent to W is 4. The side opposite of W is 3. The hypotenuse is 5.
Therefore:
Sine = 3 / 5
Cosine = 4 / 5
Tangent = 3 / 4
Answer:
Step-by-step explanation:
The volume of a sphere is

We are told our volume is 500pi/3, so we fill that in and solve for r:

Start by multiplying both sides by 3 over 4 pi:

Simplifying gives us

Take the cubed root of both sides to get that
r = 5
Answer:
The cost of 1 doll = $ 7.5
and The Cost of 1 toy train = $ 5
Step-by-step explanation:
Let the price of 1 doll = $ x
The price of 1 toy train = $ y
Now, according to the question:
6 x + 2 y = $ 55
and 4 x + 7 y = $ 65
Solving the given system of equation,
From (1), we get


or, solving for y , we get
110y - 4y + 21 y = 195
or, 17 y = 85
⇒ y= 85/17 = 5
This implies : 6 x + 2 (5) =55
or, 6x = 55 - 10 = 45
or, x = 45/ 6 = 15/2
Hence, the cost of 1 doll = x = $ 7.5
and the Cost of 1 toy train = y = $ 5
Answer:
y = (4/7)x² - (24/7)(x)
Step-by-step explanation:
4 = a(-1)² + b(-1)
4 = a - b
0 = a(6)² + b(6)
36a + 6b = 0
b = -6a
4 = a - (-6a)
7a = 4
a = 4/7
b = -24/7
y = (4/7)x² - (24/7)(x)