0.001 in Standard form

Find the missing side or angle round to the nearest tenth b=15 a=30 c=29 A=[?]°

pogonyaev

Answer:

71.6056

Step-by-step explanation:

c² = a² + b² - 2abcosC°

29² = 30² + 15² - 2(30)(15)cosC°

841 = 900 + 225 - 900cosC°

-59 = 225 - 900cosC°

-284 = -900cosC°

71/225 = cosC°

cos⁻¹(71/225) = C°

C° = 71.6056

6 0

3 years ago

(4.1.4) Let X and Y be Bernoulli random variables. Let Z = X + Y. a. Show that if X and Y cannot both be equal to 1, then Z is a

Fynjy0 [20]

Step-by-step explanation:

Given that,

a)

X ~ Bernoulli $(p_x)$ and Y ~ Bernoulli $(y_x)$

X + Y = Z

The possible value for Z are Z = 0 when X = 0 and Y = 0

and Z = 1 when X = 0 and Y = 1 or when X = 1 and Y = 0

If X and Y can not be both equal to 1 , then the probability mass function of the random variable Z takes on the value of 0 for any value of Z other than 0 and 1,

Therefore Z is a Bernoulli random variable

b)

If X and Y can not be both equal to 1

then,

$p_z = P(X=1$ or $Y=1)\\$

$p_z = P(X=1)+P(Y=1)-P(=1$ and $Y =1)$

$p_z = P(x=1)+P(Y=1)\\\\p_z=p_x+p_y$

c)

If both X = 1 and Y = 1 then Z = 2

The possible values of the random variable Z are 0, 1 and 2.

since a Bernoulli variable should be take on only values 0 and 1 the random variable Z does not have Bernoulli distribution

7 0

3 years ago

Can someone please explain the steps to solve these questions.

Amiraneli [1.4K]

Alright! So to solve these questions, you need to find out the difference. You can use ratios to solve this. For example, question #25:

A class had 30 pupils at the beginning of this school term, but now has 5 more pupils. What is the percent of increase?

The question is basically asking how much 5 is in ratio to 30. So just divide 5 (the given amount) by 30 (the total amount). The answer is 0.16, or 16%

3 0

2 years ago

The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees°

Schach [20]

Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples can be 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$