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never [62]
2 years ago
14

Someone please help me with this one quick

Mathematics
1 answer:
astraxan [27]2 years ago
4 0

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

<u>Let us first find angle C:</u>

<em>Sum of all angles in a triangle = 180°</em>

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

<u>To find the length of AC:</u>

<em>Using sine formula:</em>

$\frac{b}{\sin B } =\frac{c}{\sin C}

Substitute the given values in the formula.

$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }

Multiply by sin 89° on both sides.

$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ

$b=\frac{14}{0.8746 } \times0.9998

b=16

The length of AC is 16 km.

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Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time.
kenny6666 [7]

Answer:

No, the on-time rate of 74% is not correct.

Solution:

As per the question:

Sample size, n = 60

The proportion of the population, P' = 74% = 0.74

q' = 1 - 0.74 = 0.26

We need to find the probability that out of 60 trains, 38 or lesser trains arrive on time.

Now,

The proportion of the given sample, p = \frac{38}{60} = 0.634

Therefore, the probability is given by:

P(p\leq 0.634) = [\frac{p - P'}{\sqrt{\frac{P'q'}{n}}}]\leq [\frac{0.634 - 0.74}{\sqrt{\frac{0.74\times 0.26}{60}}}]

P(p\leq 0.634) = P[z\leq -1.87188]

P(p\leq 0.634) = P[z\leq -1.87] = 0.0298

Therefore, Probability of the 38 or lesser trains out of 60 trains to be on time is 0.0298 or 2.98 %

Thus the on-time rate of 74% is incorrect.

6 0
2 years ago
The scale of a map is 1 cm: 77 km.
laiz [17]

\bf \stackrel{map}{1~cm}\qquad :\qquad \stackrel{actual}{77~km}\qquad \cfrac{map}{actual}=\cfrac{1}{77}~\hfill \cfrac{\stackrel{map}{3}}{\underset{actual}{a}}=\cfrac{1}{77}\implies 231=a

4 0
2 years ago
the measure of the angles of a triangle are in the extended ratio 3 : 5 : 7 what is the measure of the smallest angle?
julia-pushkina [17]
3:5:7:15
?:?:?:180
by using cross multiplication 3×180÷15=36
the measure of the smallest angle is 36°
6 0
2 years ago
Read 2 more answers
Can someone please help me
Sloan [31]
X= 55 degrees           ...........
5 0
3 years ago
Ten points per answer plz hurry this is a timed quiz
4vir4ik [10]

Answer:

the solution is given by s=9 because it makes the value of 3s+12 equal to 21

Step-by-step explanation:

5 0
3 years ago
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