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3 years ago

6

i have 3 sides one of my angles measures 15 degree. another measures 60 degree what kind of a triangle am I? scalene? isosceles?

equilateral?

1 answer:

Sergio039 [100]3 years ago

7 0

Answer:

isosceles

Step-by-step explanation:

it is always uneven remember

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The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean

Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 591}{42}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{50}} = 5.94$

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{5.94}$

$Z = 1.515$

$Z = 1.515$ has a pvalue of 0.9351

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{100}} = 4.2$

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{4.2}$

$Z = 2.14$

$Z = 2.14$ has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0

3 years ago

Delilah does 184 jumping jacks in 44 minutes. She does her jumping jacks at a constant rate. How many jumping jacks can Delilah

MariettaO [177]

Answer:

4

Step-by-step explanation:

if you divide 184 by 44 you get a decimal but you cant have 1/10 of a jumping jack so you get just the whole number

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4 years ago

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A fair four-sided die has two faces numbered 0 and two faces numbered 2. Another fair four-sided die has its faces numbered 0, 1

Mandarinka [93]

The two dice have PMFs

$P(X=x)=\begin{cases}\dfrac12&\text{for }x\in\{0,2\}\\\\0&\text{otherwise}\end{cases}$

$P(Y=y)=\begin{cases}\dfrac14&\text{for }y\in\{0,1,4,5\}\\\\0&\text{otherwise}\end{cases}$

The sum of the two rolls can take on 8 different values:

$W=\begin{cases}0&\text{if }x=0,y=0\\1&\text{if }x=0,y=1\\2&\text{if }x=2,y=0\\3&\text{if }x=2,y=1\\4&\text{if }x=0,y=4\\5&\text{if }x=0,y=5\\6&\text{if }x=2,y=4\\7&\text{if }x=2,y=5\end{cases}$

The outcome of either roll is independent of the other, so that

$P(X=x\text{ and }Y=y)=P(X=x)P(Y=y)$

a. Then PMF of $W$ is

$P(W=w)=\begin{cases}\dfrac12\cdot\dfrac14=\dfrac18&\text{for }w\in\{0,1,2,3,4,5,6,7\}\\\\0&\text{otherwise}\end{cases}$

b. The histogram is nothing special, same as the discrete uniform distribution over the interval [0, 7].

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4 years ago

What is the slope of this line??

Darya [45]

Answer:

3/2

Step-by-step explanation:

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3 years ago

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A swimming pool's large drain will empty the pool in 3 hours while its smaller drain takes 6 hours. If both drains are opened, h

makkiz [27]

Answer:

2 hours

Step-by-step explanation:

6 divided by 3 is 2

Im pretty sure this is correct :)

8 0

3 years ago

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