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podryga [215]
3 years ago
11

Consider the following case and determine whether there is sufficient information to solve the triangle using the low of sines.

Two angles and the side included between them are known.
A. There is insufficient information because to use the law of sines, one side and the angle opposite it must be known.
B. There is sufficient information because if two angles and a side included between them are known, the third angle and the remaining two sides can be determined using the law of sines.
C. There is insufficient information because to use the law of sines, two angles and a side opposite one of them must be known.
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Mathematics
1 answer:
In-s [12.5K]3 years ago
7 0

Answer:

D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

Step-by-step explanation:

A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.

If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.

For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;

a/sinA = b/sinB = c/sinC

Any two can be equated to get any unknown sides and angles.

Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.

<C = 180°-(<A+<B)

Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

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A simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute
Katyanochek1 [597]

Answer:

Step-by-step explanation:

Given that:

sample size n = 36

standard deviation = 10.1

level of significance ∝ = 0.10

The null hypothesis and the alternative hypothesis can be computed as follows:

H_0 : \sigma = 10

H_1 : \sigma \neq 10

The test statistics can be computed as follows:

X^2 = \dfrac{(n -1)s^2 }{\sigma ^2}

X^2 = \dfrac{(36 -1)10.1^2 }{10^2}

X^2 = \dfrac{(35)102.01 }{100}

X^2 = \dfrac{3570.35 }{100}

X^2 =35.704

degree of freedom = n - 1 = 36 - 1 = 35

Since this test is two tailed .

The P -value can be determined by using the EXCEL FUNCTION ( = 2 × CHIDIST(35.7035, 35)

P - value = 2 × 0.435163515

P - value = 0.8703      ( to four decimal places)

Decision Rule : To reject the null hypothesis if  P - value is less than the 0.10

Conclusion: We fail to reject null hypothesis ( accept null hypothesis) since p-value is greater than 0.10 and we conclude that there is sufficient claim that the normal range of pulse rates of adults given as 60 to 100 beats per minute resulted to a standard deviation of 10 beats per minute.

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4 years ago
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Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.

Tina sends 12 text messages each day in June

June has 30 days, so in June, Tina sent 12*30 = 360 text messages.

Package A:

First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.

She sends 360 messages, with:

The first 100 costing 3p.

The next 100 costing 2p.

The final 360 - 200 = 160 costing 1p.

She pays:

100*3 + 100*2 + 160*1 = 660

Package B:

2p for each message, 360 messages, so:

360*2p = 720p.

Which package is better?

Package A costs less, thus, it offers her the better value for money in 30 days.

Another example of a problem in which a person has to choose between two packages is given in brainly.com/question/10693932

6 0
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