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Mathematics

1 answer:

Bond [772]3 years ago

5 0

Answer:

The given two triangles are not congruent.

Step-by-step explanation:

See the diagram of the two triangles attached to this question.

The third angle of the second triangle is [180° - (31° + 124°)] = 180° - 155° = 25°.{Since the other two angles of the triangle are 31° and 124°}

Now, for the first triangle, the values of the adjacent angles of the side with length 6 are 45° and 31°, but for the second triangle, the values of the adjacent angles of the side with length 6 are 25° and 31°.

Therefore, two triangles do not satisfy the Angle=Side-Angle i.e. ASA criteria to become congruent.

So, the given two triangles are not congruent. (Answer)

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Based on the sample of 500 people, 42% owned cats. Calculate the test statistic. Round to two decimal places.

Tanzania [10]

Answer:

z= 3.63

z for significance level = 0.05 is ± 1.645

Step-by-step explanation:

Here p = 42% = 0.42

n= 500

We formulate our null and alternative hypotheses as

H0: p= 0.42 against Ha : p> 0.42 One tailed test

From this we can find q which is equal to 1-p= 1-0.42 = 0.58

Taking p`= 0.5

Now using the z test

z= p`- p/ √p(1-p)/n

Putting the values

z= 0.5- 0.42/ √0.42*0.58/500

z= 0.5- 0.42/ 0.0220

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Since the calculated value does not fall in the critical region we reject our null hypothesis and accept the alternative hypothesis that more than 42% people owned cats.

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