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storchak
18 days ago
12

Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This mont

h, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532. How much does a chicken cost, and how much does a duck cost?
Mathematics
1 answer:
tester [12.3K]18 days ago
4 0
Let the price of a chicken be represented as x and the price of a duck as y. The equations established are 50x + 30y = 550 (1) and 44x + 36y = 532 (2). By manipulating (1) with a factor of 6, we have 300x + 180y = 3,300 (3). Applying a factor of 5 to (2) results in 220x + 180y = 2,660 (4). Then, by subtracting (4) from (3), we find that 80x = 640, leading to x = 8. Substituting the value of x back into (1), we find 50(8) + 30y = 550, which simplifies to 30y = 150, and ultimately y = 5. Therefore, the costs are $8 for a chicken and $5 for a duck.
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Two boats start their journey from the same point A and travel along directions AC and AD, as shown below: ABC is a right triang
Inessa [12570]

*Refer to the image attached below

Answer:

346.4 ft

Step-by-step Explanation:

The distance between the boats, CD = BD - BC

Using trigonometry, find the length of BD in triangle ∆ABD and also calculate the length of BC in triangle ABC.

Length of BD in triangle ABD:

Opposite side to <30° = 300 ft

Adjacent side = BD

tan(30) = \frac{300}{BD}

BD*tan(30) = 300

Divide both sides by tan(30)

\frac{BD*tan(30)}{tan(30)} = \frac{300}{tan(30)}

BD = 519.6 ft (rounded to nearest tenth)

Length of BC in triangle ABC:

Opposite side to <60° = 300 ft

Adjacent side = BC

tan(60) = \frac{300}{BC}

BC*tan(60) = 300

Divide both sides by tan(60)

\frac{BC*tan(60)}{tan(60)} = \frac{300}{tan(60)}

BC = 173.2 ft (rounded to nearest tenth)

The distance, CD, between the boats is calculated as BD - BC

= 519.6 - 173.2 = 346.4 ft

4 0
1 month ago
Read 2 more answers
Suppose that in a casino game the payout is a random variable X . If X is positive, you gain money, if negative, you lose.
AnnZ [12381]
The conditional probabilities for X equaling 1, 2, and 3 are 0.7333 (73.33%), 0.25 (25%), and 0.0167 (1.67%) respectively.
8 0
27 days ago
How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =
lawyer [12517]

The adjusted equation $g(x)=\frac{1}{x+4}-6$, indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is $f(x)=\frac{1}{x}$.

The transformed equation is $g(x)=\frac{1}{x+4}-6$.

Applying the function transformation rules, it's clear that the parent function $f(x)=\frac{1}{x}$ has been modified into the function $g(x)=\frac{1}{x+4}-6$.

According to the function transformation rules,

$f(x+b)$ indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

$f(x)-b$ indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation $g(x)=\frac{1}{x+4}-6$, shows the graph shifted 4 units to the left and 6 units downward.

6 0
1 month ago
Read 2 more answers
Finally, suppose m1→∞, while m2 remains finite. what value does the the magnitude of the tension approach?
AnnZ [12381]
The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.

For m₁: m₁*g - T = m₁*a

For m₂: T - m₂*g = m₂*a

Assuming a massless cord and pulley without friction, the accelerations are the same.

From the second equation: a = (T - m₂*g) / m₂

Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g

This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>
5 0
1 month ago
P=100a÷t solve for a
tester [12383]

a=1/100pt is the right solution. Initially, you need to multiply both sides of the equation by t, which results in ⇒ pt=100a. After that, inverting the equation gives ⇒100a=pt. Alternatively, dividing both sides of the equation by one hundred (100) also leads us to \frac{100a}{100}=\frac{pt}{100}. Ultimately, the final answer is a=1/100pt is the result. I hope this offers assistance! Thank you for asking your question, and enjoy your day. -Charlie

8 0
1 month ago
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