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shepuryov [24]
2 years ago
10

2 angles measure 40 degrees each, what does the third angle measure? what type of triangle is it?

Mathematics
1 answer:
zimovet [89]2 years ago
3 0

Answer:

Part a): 100 degrees

Part b): Isosceles Triangle

Step-by-step explanation:

Part a): Since the angle measures of all triangles add up to 180 degrees and since the other two angles are 40 degrees, which add up to 80, we can use subtraction to find the answer.

180 - 80 = 100

Part b): Since only two of the three angles in this triangle have the same measure, we can find that it is an isosceles triangle, with base angles measuring 40 degrees, and the vertex angle being 100 degrees.

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Answer: The p-value is 0.154.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis :

H_0:\mu=20

Alternate hypothesis :

H_1:\mu

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Sample mean = 18.5 hours

Sample standard deviation = 4.3 hours

Sample size n = 35

So, test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{18.5-20}{\dfrac{4.3}{\sqrt{35}}}\\\\z=\dfrac{-1.5}{0.726}\\\\z=-2.066

So, the  p value would be 0.154.

Hence, the p-value is 0.154.

4 0
3 years ago
A group of 15 people are going to run a race. The top 8 will advance to the finals. Determine if the situation is a permutation
LUCKY_DIMON [66]

For the given situation we have a total of 259,459,200 permutations.

<h3>How many permutations are?</h3>

First, how we know that it is a permutation?

Because the order matters, we aren't only selecting 8 out of the 15 people, but these 8 selected also have an order (is not the same thing to finish the race first than fourth, for example).

Then we need to find the number of permutations, to do it, we need to find the numbers of options for each of the 8 positions.

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Then the total number of permutations (product between the numbers of options) is:

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    2  -5  -18    45    0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.

Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")

3║2  -5  -18    45 
  ║     6     3   -45   
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Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors.  Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.

Final Answer: (x-1)(x-3)(x+3)(2x-5)




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