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devlian
14 days ago
9

You are hiking and trying to determine how far away the nearest cabin is, which happens to be due north from your current positi

on. Your friend walks 220 yards due west from your position and takes a bearing on the cabin of N 21.2°E. How far are you from the cabin
Mathematics
1 answer:
PIT_PIT [3.9K]14 days ago
6 0

Answer:

The cabin is located 567 yards away.

Step-by-step solution:

The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.

Apply the tangent function:

Opposite side length: 220 yards

Adjacent side length: x (distance to cabin)

tan(21.2°) = opposite / adjacent

tan(21.2°) = 220 yards / x

Multiply both sides by x:

x × tan(21.2°) = 220 yards

Isolate x:

x = 220 yards / tan(21.2°)

x = 220 / 0.388

x = 567 yards

Hence, the cabin is 567 yards away.

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Terrence finished a word search in 3/4 the time it took Frank. Charlotte finshed the word search in 2/3 the time it took Terrenc
Zina [3914]

Answer: Charlotte completed the word search in 16 minutes.

Step-by-step explanation:

Frank took 32 minutes to finish the word search.

Terrence completed the word search in three-quarters of the time Frank used, which is:

3/4 × 32 = 24 minutes.

Charlotte finished it in two-thirds the time Terrence took, leading to:

2/3 × 24 = 16 minutes for Charlotte.

6 0
2 days ago
Question 5 Six pairs of shoes cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks co
Zina [3914]
4 socks equal 1 pair of jeans
2 pairs of jeans equal 3 pairs of shoes
6 pairs of shoes equal 1 coat

Since 1 pair of jeans equals 4 socks, 2 jeans amount to 8 socks.
That means 8 socks correspond to 3 shoes.
If 3 shoes equal 8 socks, then 6 shoes would equal 16 socks.
Therefore, 16 socks are equivalent to 1 coat.
By this logic, 64 socks would translate to 64 divided by 16, which equals 4 coats.
8 0
14 days ago
According to the U.S. Census Bureau (2016), a substantial pay gap still exists. The average American man, with an advanced colle
Leona [4166]

Answer:

The earnings gap, over a career spanning 30 years, between men and women totals $1,200,150

Step-by-step explanation:

Calculated annually.

The typical male earns $90,761 each year.

The typical female earns $50,756 per annum.

Therefore, the annual difference is:

90,761 - 50,756 = 40,005

Across 30 years:

30*40,005 = 1,200,150

The earnings gap over a 30-year career, when comparing men and women, is $1,200,150

0 0
16 days ago
Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
lawyer [4008]

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = \frac{1750}{1000}

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

x = \frac{825,000}{1,000,000}

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

8 0
9 days ago
What are three different ways to make the number 15,638 with only hundreds, tens, and ones?
zzz [4022]
I think it’s 156 hundreds, 3 tens, and 8 ones.
3 0
17 days ago
Read 2 more answers
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