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4 years ago

15

The observation deck is about 20 m above sea level. From the observation deck, the angle of depression of the boat is 6 degrees.

How far is the boat from the lighthouse?

1 answer:

Leno4ka [110]4 years ago

7 0

θ\ 6 degrees
    \
\ so the θ= 180-90-6 =84 degrees so we need to find x
20m   \ tan (84)=x/20
  ____  \ x=20 tan(84)
x x=190.287

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Gre4nikov [31]

Answer:

Because z is higher than any given value in the chart we come to the conclusion To reject null hypothesis

Step-by-step explanation:

Sample proportion = p= 531/648 = 0.8194

This is the proportion of men that were hit by lightening

Null hypothesis: H0: p = 0.5

Alternate hypothesis: H1: p ≠ 0.5

Test statistics z = 0.8194-0.5/(√0.5x0.5/648)

= 0.8194-0.5/√0.0003858

= 0.3194/0.019642

= 16.26

Since the z > 1.96 (at 5% significance) we reject the null hypothesis.

Therefore in conclusion we say z is higher than given values in the chart so we reject null hypothesis.

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3 years ago

Of 1800 students enrolled in school 55% are girls. of the girls attending this school 30% take the bus to school

leonid [27]

55% of 1800 = 0.55(1800) = 990...so there are 990 girls in the school

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3 years ago

the odds of rolling a certain number on a single die is 1 chance in 6 rolls. in course of a game, someone rolled 3 fives. accord

Zina [86]

Answer:

18

Step-by-step explanation:

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S / F

Probability is the ratio of number of successes to number of all outcomes:

S / (S + F)

So the probability of rolling a 5 is 1/6. The odds of rolling a 5 is 1/5.

Furthermore, the word "must" is also incorrect. The player didn't <em>have</em> to roll 18 times. They could have rolled three times and gotten a 5 each time. Or they could have rolled 100 times. 18 is simply the most <em>likely </em>number of rolls needed to get three 5's.

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3 years ago

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ehidna [41]

From the recursive rule, you can tell the initial value is 3 and the common ratio is 12. The explicit rule is always
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3 years ago

(c). It is well known that the rate of flow can be found by measuring the volume of blood that flows past a point in a given tim

aleksklad [387]

(i) Given that

$V(R) = \displaystyle \int_0^R 2\pi K(R^2r-r^3) \, dr$

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$V(0.30) = \displaystyle \int_0^{0.30} 2\pi \left(0.30-3.33r^2\right)r \, dr \approx \boxed{0.0425}$

and this is a volume so it must be reported with units of cm³.

In Mathematica, you can first define the velocity function with

v[r_] := 0.30 - 3.33r^2

and additionally define the volume function with

V[R_] := Integrate[2 Pi v[r] r, {r, 0, R}]

Then get the desired volume by running V[0.30].

(ii) In full, the volume function is

$\displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

Compute the integral:

$V(R) = \displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

$V(R) = \displaystyle 2\pi K \int_0^R (R^2r-r^3) \, dr$

$V(R) = \displaystyle 2\pi K \left(\frac12 R^2r^2 - \frac14 r^4\right)\bigg_0^R$

$V(R) = \displaystyle 2\pi K \left(\frac{R^4}2- \frac{R^4}4\right)$

$V(R) = \displaystyle \boxed{\frac{\pi KR^4}2}$

In M, redefine the velocity function as

v[r_] := k*(R^2 - r^2)

(you can't use capital K because it's reserved for a built-in function)

Then run

Integrate[2 Pi v[r] r, {r, 0, R}]

This may take a little longer to compute than expected because M tries to generate a result to cover all cases (it doesn't automatically know that R is a real number, for instance). You can make it run faster by including the Assumptions option, as with

Integrate[2 Pi v[r] r, {r, 0, R}, Assumptions -> R > 0]

which ensures that R is positive, and moreover a real number.

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3 years ago