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Identify three pythagorean triples using the known triple 8, 15, 17. What does this mean?

ELEN [110]

Answer:

yes

Step-by-step explanation:

8² + 15² = 17²

64 + 225 = 289

289 = 289

8 0

2 years ago

The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to

WINSTONCH [101]

The answer to the above question can be explained as under -

We know that, the sum of angles of triangle is 180°.

So, vertex angle plus base angles are equal are equal to 180°.

Let the vertex angle be represented by "v" and base angles be represented by "b".

Thus, v + b + b = 180°

So, v + 2b = 180°

Next, the question says, the vertex angle is 20° less than the sum of base angles.

Thus, 2b - 20° = v

<u>Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v</u>

6 0

3 years ago

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older

Viktor [21]

Answer:

$p_v =P(t_{(63)}>2.5)=0.0075$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=45$ represent the mean height for the sample

$s=16$ represent the sample standard deviation for the sample

$n=64$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean age is higher than 40 years, the system of hypothesis would be:

Null hypothesis: $\mu \leq 40$

Alternative hypothesis: $\mu > 40$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{45-40}{\frac{16}{\sqrt{64}}}=2.5$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=64-1=63$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(63)}>2.5)=0.0075$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

6 0

3 years ago

Six workers can do 9 identical jobs in 3 days. How long will it take 4 workers to do 10 such jobs ???

Delicious77 [7]

6 workers-9 jobs in 3 days
In one day 6 workers can do 3 jobs
In one day 1 worker can do 0.5 job
4 workers can so 2 jobs in a day
So. They can do 10 jobs in 5 days

4 0

3 years ago

John Jogger purchased a three-year membership at a local fitness center at the beginning of the year. It cost him $395 per year.

balu736 [363]

1. We need to find how many times John Jogger went to the gym.

He goes 2x weekly for 13 weeks.

13 x 2 = 26 times in the first 3 months.

We still have another 9 months left. He goes twice monthly for each month.

9 x 2 = 18.

We add the total times he went to the gym for the first 3 months to the other 9 months in the year.

26 + 18 = 44 times in one year. If we repeat this for 3 years, you get 44 x 3 = 132 gym visits in three years.

The gym membership is $395 per year. For three years this is 395 x 3 = $1185.

He went to the gym 132 times for a total of $1185. To find the price per visit, divide the total price by the amount of times he went to the gym.

1185/132 = ~$8.98 per gym visit.

2. If 13 weeks = 3 months (1/4 of a year), then there are 52 weeks per year.

If he goes twice every week for 52 weeks, that's 52 x 2 = 104 times per year. If he kept this up for three years, that's 104 x 3 = 312 gym visits in three years.

At the price we found earlier of $1185 for a three-year membership, divide the price by the total number of visits to find the price per visit.

1185/312 = ~$3.80 per gym visit.

3 0

3 years ago

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