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Bumek [7]
3 years ago
6

A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?

Please Explain how you got the answer if you can. I'd like to understand this question more.
Mathematics
1 answer:
Bezzdna [24]3 years ago
3 0
The <span>Pythagorean theorem</span> is what is most useful here, and a calculator; for the following...
Imagine forming a triangle by creating that last leg between the starting position and the ending position; the length of that side will be our missing variable "y".

600<span>² + 800</span>²= y<span>²

The sum of the two (600</span><span>² & 800</span>²) must then be square rooted to find the length

y² = 1,000,000 and the square root of y<span>²= 1,000 (YOUR ANSWER) "y"</span>
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What is the justification for each step taken from line 2 to line 3?
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2x was subtracted from both sides.

A. Subtraction Property of Equality
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3 years ago
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In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.
Irina-Kira [14]
Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

c^{2} = a^{2} + b^{2} - 2abcosC

Rearranging this equation, we can find the value ∠C as shown below.

\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}
C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})

We can apply the same reasoning for finding the value of ∠B as shown.

B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})
C \approx 37.19

B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})
B \approx 53.13

Answer: ∠C = 37.19° and ∠B = 53.13°

7 0
3 years ago
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In a​ study, 36​% of adults questioned reported that their health was excellent. A researcher wishes to study the health of peop
steposvetlana [31]

Answer:

0.3907

Step-by-step explanation:

We are given that 36​% of adults questioned reported that their health was excellent.

Probability of good health = 0.36

Among 11 adults randomly selected from this​ area, only 3 reported that their health was excellent.

Now we are supposed to find the probability that when 11 adults are randomly​ selected, 3 or fewer are in excellent health.

i.e. P(x\leq 3)=P(x=1)+{P(x=2)+P(x=3)

Formula :P(x=r)=^nC_r p^r q ^ {n-r}

p is the probability of success i.e. p = 0.36

q = probability of failure = 1- 0.36 = 0.64

n = 11

So, P(x\leq 3)=P(x=1)+{P(x=2)+P(x=3)

P(x\leq 3)=^{11}C_1 (0.36)^1 (0.64)^{11-1}+^{11}C_2 (0.36)^2 (0.64)^{11-2}+^{11}C_3 (0.36)^3 (0.64)^{11-3}

P(x\leq 3)=\frac{11!}{1!(11-1)!} (0.36)^1 (0.64)^{11-1}+\frac{11!}{2!(11-2)!}  (0.36)^2 (0.64)^{11-2}+\frac{11!}{3!(11-3)!} (0.36)^3 (0.64)^{11-3}

P(x\leq 3)=0.390748

Hence  the probability that when 11 adults are randomly​ selected, 3 or fewer are in excellent health is 0.3907

5 0
3 years ago
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iVinArrow [24]
Here I hope this helps you out

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It takes at least 12 hours for the newer machine to make 10,000 cans
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