3, 8, 13, 18, 23, 28, 33, 38

Mathematics

1 answer:

algol [13]3 years ago

3 0

The given series is

$3,8,13,18,23,28,33,38,...$

Where the first term, a , is 3.

And the difference is constant, that is

$8-3=13-8=18-13=5$

So the constant difference, d is 3.

Since the difference is constant, so the given series is arthmetic.

And for explicit rule, we use the formula of nth term, which is

$a_{n}= a+(n-1)d$

Substituting the values of a and d, we will get

$a_{n} = 3+(n-1)5
\\
a_{n} = 3+5n-5
\\
a_{n} = 5n -2$

Recursive rule is used to tell us the relationship between previous and current term. And the required rule is

$a_{n} = a_{n-1} +5 , a_{1} = 3$

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Which Exponential function has a initial and child value of 2

fredd [130]

For an exponential function the y-intercept is the "initial value" (not the common ratio).

$y = 2 \times {1}^{x}$

will always be 2. if that's what you need

note that

${1}^{0} = 1$

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7 0

3 years ago

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth wh

nirvana33 [79]

Answer:

47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth

Step-by-step explanation:

For each individual, there are only two possible outcomes. Either they cover their mouth when sneezing, or they do not. The probability of an individual covering their mouth when sneezing is independent of other individuals. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

This means that $p = 0.267$