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3 years ago

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Help mee A scout troop are hiking in a forest. Starting from their base, they walk 4.2km south followed by 7.1km west. They want

to walk the shortest distance back to their base. On what bearing should the scouts walk?

1 answer:

slega [8]3 years ago

4 0

Answer:

They should walk on a bearing of 59.4 degrees

Step-by-step explanation:

Given

$South = 4.2km$

$West = 7.1km$

Required

The bearing back to the base

The given question is illustrated with the attached image.

To do this, we simply calculate the measure of angle a using:

$\tan(a) = \frac{Opposite}{Adjacent}$

$\tan(a) = \frac{7.1}{4,2}$

$\tan(a) = 1.6905$

Take arctan of both sides

$a = \tan^{-1}(1.6905)$

$a = 59.4^o$

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If she deposited $600 and had $621.60 after four years, then she earned: $621.60 - $600 = $21.60 in four years. It means in one year she earned $21.60 ÷ 4 = $5.40. Now we have to find out how many percent of $600 is $5.40:

$5.40 = x% from $600
5.4 = x/100 * 600
5.4 = 600x/100 / * 100 (both sides)
540 = 600x / ÷ 600 (both sides)
x = 0.9

So the interest rate was 0.9% annually.

Now we have to find out how much is 0.9% from $1100:

$1100 * 0.9% =
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It means in one year she would earn $9.90. After 7 years she would earn $9.90 * 7 = $69.30, so she would have in her account:

$1100 + $69.30 = <u>$1169.30</u>

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3 years ago

1. Jill had the following scores on quizzes. 1 quiz: 1 3 quizzes: 2 4 quizzes: 3

Irina-Kira [14]

The mean score is 3.08.

There is 1 quiz with score 1, so 1 point; 3 quizzes with score 2 for 3*2 = 6 points; 4 quizzes with score 3 for 4*3 = 12 points; 4 quizzes with score 4 for 4*4 = 16 points; and 1 quiz with score 5 for 5 points.

This is a total of 1+6+12+16+5 = 40 points.

This is out of 1+3+4+4+1 = 13 quizzes.

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3 years ago

a small plane lands at a point 324 miles east and 92 miles north of the point at which it took off. Find the distance the plane

Setler79 [48]

Answer: 336.80 miles, $15.85^{\circ}$ North of east

Step-by-step explanation:

Given

Plane lands at a point 324 miles east and 92 miles north

Distance is given by using Pythagoras theorem

$\Rightarrow d=\sqrt{324^2+92^2}\\\\\Rightarrow d=\sqrt{113,440}\\\\\Rightarrow d=336.80\ \text{miles}$

Direction is given by using figure i.e.

$\Rightarrow \tan \theta=\dfrac{92}{324}\\\\\Rightarrow \tan \theta=0.2839\\\\\Rightarrow \theta=15.85^{\circ}$

Direction is $15.85^{\circ}$ North of east

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2 years ago

The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms. How lo

liberstina [14]

Answer:

16.34 hours

Step-by-step explanation:

According to the given information we can see that the case is of exponential growth

Hence, we will use the formula

$A=P(2)^\frac{t}{24}$

Here A =800 is the amount that is needed to reach

P is the initial amount that is 500

We have to find the time it will take to reach 800 that is we need to find t

On substituting the values in the formula we get

$800=500(2)^\frac{t}{24}$

On simplification we get

$\Rightarrow\frac{8}{5}=(2)^\frac{t}{24}$

Taking log on both sides we get

$\Rightarrow\log\frac{8}{5}=\log(2)^\frac{t}{24}$

using $\log\frac{m}{n}=\log m-\log n$

And $\log a^m=m\log a$

$\Rightarrow\log{8}-\log{5}=\frac{t}{24}\log2$

Now substituting values of log 8=0.903, log 5=0.698 and log 2=0.301 we get

$\Rightarrow 0.903-0.698=\frac{t}{24}0.301$

$\Rightarrow 0.205=\frac{t}{24}0.301$

$\Rightarrow \frac{0.205}{0.301}\cdot 24=t$

$\Rightarrow t=16.34$

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3 years ago

Read 2 more answers

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Leya [2.2K]

Answer:

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157.08

May be the answer is...... Thank you..... ✧༺♥༻✧

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2 years ago