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Salsk061 [2.6K]
2 years ago
9

A forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward the windmill by the lake. The angle o

f depression to the fire is 3°, and the angle of depression to the windmill is 8°. To the nearest foot, how close is the fire to the windmill?
Mathematics
1 answer:
Hoochie [10]2 years ago
3 0
To get how close the windmill is to the fire we proceed as follows:
distance from watch tower to the fire will be:
tan θ= opposite/adjacent
opposite=140 ft
adjacent=x
θ=3°
hence
tan 3=140/x
x=140/tan 3
x=2,671.36 ft

the distance from watch tower to windmill will be:
tan θ=opposite/ adjacent
θ=8°
opposite=140 ft
adjacent=y
thus
tan 8=140/y
y=140/tan8
y=999.15 ft
the distance between fire and wind mill will be:
2,671.36-999.15
=1675.21~1675 ft (to the nearest ft)

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A customer's stock value seems to be rising exponentially. The equation for
Rasek [7]
<h2>Hello!</h2>

The answer is:

The correct option is A. 8.3.

<h2>Why?</h2>

To calculate the number of weeks that will pass, we need to use the given information.From the statement we know that we need to use the value of $600 substituting it as "y", and then, isolate "x", so, calculating we have:

log(y)=0.30x+0.296\\\\log(600)=0.30x+0.296\\\\2.78=0.30x+0.296\\\\2.78-0.296=0.30x\\\\x=\frac{2.78-0.296}{0.30}=8.28=8.3

Hence, the correct option is A. 8.3.

Have a nice day!

4 0
2 years ago
Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un
Nataly_w [17]

Answer: 0.1289

Step-by-step explanation:

Given : The proportion of all students at a large university are absent on Mondays. : p=0.15

Sample size : n=12

Mean : \mu=np=12\times0.15=1.8

Standard deviation = \sigma=\sqrt{np(1-p)}

\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369

Let x be a binomial variable.

Using the standard normal distribution table ,

P(x=4)=P(x\leq4)-P(x\leq3)              (1)

Z score fro normal distribution:-

z=\dfrac{x-\mu}{\sigma}

For x=4

z=\dfrac{4-1.8}{1.2369}\approx1.78

For x=3

z=\dfrac{3-1.8}{1.2369}\approx0.97

Then , from (1)

P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289    

Hence, the probability that four students are absent = 0.1289

3 0
2 years ago
How many ways are there to put 8 beads of different colors on the vertices of a cube, if rotations of the cube (but not reflecti
Delvig [45]
What is being requested, if I'm not mistaken, is the number of permutations for placing each of the 8 beads on the vertices of the cubes;
In this case, we have 8 different beads and 8 possible locations for each of them;
So the number of permutations is:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
6 0
2 years ago
Read 2 more answers
replace each star with a digit to make the problem true.Is there only one answer to each problem? ****-***=2
Semenov [28]

Answer: We have two solutions:

1000 - 998 = 2

1001 - 999 = 2

Step-by-step explanation:

So we have the problem:

****-*** = 2

where each star is a different digit, so in this case, we have a 4 digit number minus a 3 digit number, and the difference is 2.

we know that if we have a number like 99*, we can add a number between 1 and 9 and we will have a 4-digit as a result:

So we could write this as:

1000 - 998 = 2

now, if we add one to each number, the difference will be the same, and the number of digits in each number will remain equal:

1000 - 998 + 1 - 1 = 2

(1000 + 1) - (998 + 1) = 2

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now, there is a trivial case where we can find other solutions where the digits can be zero, like:

0004 - 0002 = 2

But this is trivial, so we can ignore this case.

Then we have two different solutions.

7 0
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S_A_V [24]

Answer:

L(w) = 8 mm + (2 mm/wk)(wk)

Step-by-step explanation:

L(w) = length of beard as a function of time in weeks

L(w) = 8 mm + (2 mm/wk)(wk)

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2 years ago
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