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Semmy [17]
3 years ago
15

A sailboat leaves port and sails 12 kilometers west and then 9 kilometers north. The sailboat is now kilometers from port

Mathematics
1 answer:
Luden [163]3 years ago
5 0

Answer:  The sailboat is at a distance of 15 km from the port.

Step-by-step explanation:  Given that a sail boat leaves port and sails 12 kilometers west and then 9 kilometers north.

We are to find the distance between the sailboat from the port in kilometers.

Since the directions west and north are at right-angles, we can visualize the movement of the sailboat in the form of a right-angled triangle as shown in the attached figure.

The sailboat moves leaves the port at P and reach O after sailing 12 km west. From point O, again it moves towards north 9 km and reach the point S.

PS = ?

Using the Pythagoras theorem, we have from right-angled triangle SOP,

PS^2=OS^2+OP^2=9^2+12^2=81+144=225\\\\\Rightarrow PS=15~\textup{km}.

Thus, the sailboat is at a distance of 15 km from the port.

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Anika [276]
60 divided by 0.4(40%)=150

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8 0
3 years ago
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Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam
tigry1 [53]

Answer:

P(A) = \frac{30}{100}

P(B) = \frac{77}{100}

P(A\ n\ B) = \frac{22}{100}

P(A\ u\ B) = \frac{85}{100}

Step-by-step explanation:

Given

See attachment for proper format of table

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

In this row:

Yes = 22 and No = 8

So, we have:

n(A) = Yes + No

n(A) = 22 + 8

n(A) = 30

P(A) is then calculated as:

P(A) = \frac{n(A)}{Sample}

P(A) = \frac{30}{100}

Solving (b): P(B)

Here, we only consider data in the Yes column.

In this column:

(1) = 22    (2) = 25 and (3) = 30

So, we have:

n(B) = (1) + (2) + (3)

n(B) = 22 + 25 + 30

n(B) = 77

P(B) is then calculated as:

P(B) = \frac{n(B)}{Sample}

P(B) = \frac{77}{100}

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

This cell is: [Supplier 1][Yes]

And it is represented with; n(A n B)

So, we have:

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

8 0
3 years ago
Given the slope of the line containing the points (7 , b) and (-2 , 5) is 4/9, find the value of b​
MAVERICK [17]

Answer: b=9

Step-by-step explanation: To find the slope we use: y2-y1/x2-x1

Which would then be: 5-b/-2-7= 5-b/-9

Then we have to find a number for b that would give us -4 as the numerator. That number would be 9

This would give us 4/9 which is the slope we already had.

6 0
3 years ago
Plz help need to find both answers
saul85 [17]

Answer:

I hope it helped u.

Step-by-step explanation:

7 0
3 years ago
Need Help! 10 points!
Dominik [7]
The answer is d because 4+8=12 and they are 4 units away from eachother:)
6 0
3 years ago
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