Find four consecutive integers whose sum is 114.

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 5; B: the numbers add to 2

labwork [276]

Answer:

Part 1

A = {5}

B = {(1,1)}

C = {(2,1), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2)}

D = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,6), (4,1), (4,2), (4,3), (4,5), (4,6), (5,1), (5,2), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

Part 2

35

Step-by-step explanation:

Part 1

We use brakets for indicate that the elements belong to a event.

In each event, the first member of each parentheses belong to dice red and the second belong to green dice.

We consider in each event all elements that accomplish the condition.

Part 2

When we combinate pair with the two dice obtain 36 pairs (6*6, six possible results in the red dice and six possible results in the green dice), now we look for all of them that do not add 2.

(1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

4 0

3 years ago

Please help, I'm stuck on this question

vesna_86 [32]

Answer: Option C

$a> 0$

Step-by-step explanation:

The graph shows a radical function of the form $f(x)=a(x+k)^{\frac{1}{n}}+c$

Where n is a positive number.

For this type of function, if the coefficient $a> 0$ then then when x tends to $\infty$ f(x) tends to $\infty$ and when x tends to $-\infty$ then f(x) tends to $-\infty$ .

Notice in the graph that as x increases then f(x) also increases and as x decreases f(x) also decreases.

This indicates that the coefficient $a> 0$

5 0

3 years ago

"is it appropriate to use the normal approximation for the sampling distribution of"

Katyanochek1 [597]

Answer: Normal approximation can be used for discrete sampling distributions, such as Binomial distribution and Poisson distribution if certain conditions are met.

Step-by-step explanation: We will give conditions under which the Binomial and Poisson distribitions, which are discrete, can be approximated by the Normal distribution. This procedure is called normal approximation.

1. Binomial distribution: Let the sampling distribution be the binomial distribution $B(n,p)$ , where $n$ is the number of trials and $p$ is the probability of success. It can be approximated by the Normal distribution with the mean of $np$ and the variance of $np(1-p)$ , denoted by $N(np,np(1-p))$ if the following condition is met:

$n>9\left(\frac{1-p}{p}\right)\text{ and } n>9\left(\frac{p}{1-p}\right)$

2. Poisson distribution: Let the sampling distribution be the Poisson distribution $P(\lambda)$ where $\lambda$ is its mean. It can be approximated by the Normal distribution with the mean $\lambda$ and the variance $\lambda$ , denoted by $N(\lambda,\lambda)$ when $\lambda$ is large enough, say $\lambda>1000$ (however, different sources may give different lower value for $\lambda$ but the greater it is, the better the approximation).