Binomial distribution will be used to know the probability that the total weight of the samples will exceed 530 pounds.
It is given that the rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds.
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
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The system of inequalities is:
v + h ≤ 8
v < 2
h ≥ 1.5
<h3>
Which system of equations represents this situation?</h3>
Let's define the variables:
- v = number of hours playing video games.
- h = number of hours spent on homework.
The maximum time that you can spend on both activities is 8 hours, then:
v + h ≤ 8
You want to spend less than 2 hours on video games, so:
v < 2
You want to spend at least, 1.5 hours on homework, so:
h ≥ 1.5
Then the system of inequalities is:
v + h ≤ 8
v < 2
h ≥ 1.5
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Answer: First of all, we will add the options.
A. Yes, because 3 inches falls above the maximum value of lengths in the sample.
B. Yes, because the regression equation is based on a random sample.
C. Yes, because the association between length and weight is positive.
D. No, because 3 inches falls above the maximum value of lengths in the sample.
E. No, because there may not be any 3-inch fish of this species in the pond.
The correct option is D.
Step-by-step explanation: It would not be appropriate to use the model to predict the weight of species that is 3 inches long because 3 inches falls above the maximum value of lengths in the sample.
As we can see from the question, the model only accounts for species that are within the range of 0.75 to 1.35 inches in length, and species smaller or larger than that length have not been taken into consideration. Therefore the model can not be used to predict the weights of fishes not with the range accounted for.
If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are
ways of picking the vowels, and
ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is
Keep in mind that this means words like TRIES and TIRES are treated as different.
Answer: 
Step-by-step explanation:
Given
Sample space is 
There are 8 element in sample space which indicates the outcome of tossing a coin three times
Probability of obtaining at least one head
