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musickatia [10]
3 years ago
5

A ship leaves port at 1:00 P.M. and travels S35°E at the rate of 27 mi/hr. Another ship leaves the same port at 1:30 P.M. and tr

avels S20°W at 18 mi/hr. Approximately how far apart are the ships at 3:00 P.M.? (Round your answer to the nearest mile.)

Mathematics
1 answer:
Len [333]3 years ago
8 0

To solve this problem you must apply the proccedure shown below:

1. You must apply the Law of Cosines, as you can see in the figure attached. Then:

- The first ship travels at 27 mi/hr in for two hours. Therefore, the side a is:

a=(27 mi/hr)(2 hr)=54mi

- The second ship travels at 18 mi/hr for 1.5 hours. Therefore, the side b is:

b=(18mi/hr)(1.5hr)=27mi

- Now, you can calculate c:

c=\sqrt{54^{2}+27^{2}-2(54)(27)Cos(55)}=44 mi

The answer is: 44 miles

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Gavin and Jack are practicing shots against their goalie. On their last 15 attempts, Gavin made 6 and Jack made 7. Based on this
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Answer:

\dfrac{14}{75}

Step-by-step explanation:

Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be  successful is

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Jack made 7 out of 15 shots, so the probability that Jack's next shot will be  successful is

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The probability that they both make their next shot successfully is

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Step-by-step explanation:

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2 years ago
A boat that costs $8550 decreases in value by 12% per year. How much will the boat be worth after 3 years?
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Find the equation of the line that passes through the following two points: (3, -7) and (7, 2)
Wittaler [7]

Answer:

y=\frac{9}{4}x-\frac{55}{4}

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \frac{y2-y1}{x2-x1}

Given points: (3, -7), (7, 2)

(3, -7) = (x1, y1)

(7, 2) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

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\frac{2-(-7)}{7-3}

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The slope is \frac{9}{4}.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (7, 2)) into the equation and solve for b:

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Now that we know the slope and the y-intercept, we can write the equation:

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