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3 years ago

Help !!! Which formula can be used to describe the sequence

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

3 0

Answer:

f (x+1) = 2 f(x)

Step-by-step explanation:

If you write the sequence as improper fractions, you will obtain:

-8/3, -16/3, -32/3, -64/3, ....

so it can be seen that each term doubles prior term, and they are always negative

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When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 943 peas, with 717 of them hav

pshichka [43]

Using the normal approximation to the binomial distribution, it is found that:

a) 0.242 = 24.2% probability of getting 717 or more peas with red flowers.

b) Since Z < 2, 717 peas with red flowers is not significantly high.

c) Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

For each pea, there are only two possible outcomes. Either they have a red flower, or they do not. The probability of a pea having a red flower is independent of any other pea, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

Normal distribution:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

If Z > 2, the result is considered <u>significantly high</u>.

If $np \geq 10$ and $n(1-p) \geq 10$ , the binomial distribution can be approximated to the normal with:

$\mu = np$

$\sigma = \sqrt{np(1-p)}$

In this problem:

943 peas, thus, $n = 943$
3/4 probability of being red, thus $p = \frac{3}{4} = 0.75$ .

Applying the approximation:

$\mu = np = 943(0.75) = 707.25$

$\sigma = \sqrt{np(1-p)} = \sqrt{943(0.75)(0.25)} = 13.297$

Item a:

Using continuity correction, this probability is $P(X \geq 717 - 0.5) = P(X \geq 716.5)$ , which is <u>1 subtracted by the p-value of Z when X = 716.5</u>.

Then:

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

$Z = \frac{716.5 - 707.25}{13.297}$

$Z = 0.7$

$Z = 0.7$ has a p-value of 0.758.

1 - 0.758 = 0.242

0.242 = 24.2% probability of getting 717 or more peas with red flowers.

Item b:

Since Z < 2, 717 peas with red flowers is not significantly high.

Item c:

Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

A similar problem is given at brainly.com/question/25212369

6 0

3 years ago

Nts) in a certain population of voters, 72% of them plan to vote in favor of a new

Ganezh [65]

Answer:

Probability that 10 of them plan to vote against this piece of proposed legislation is 0.0701 or 7.01 %.

Step-by-step explanation:

Consider the event of voting against the piece as success, 'p'. So, voting in favor of the piece is failure and denoted by 'q'.

Given:

Sample size is, $n=25$

Probability of failure is, $q=72\%=0.72$

Therefore, probability of success is, $p=1-q=1-0.72=0.28$

Number of successes is, $x=10$

Now, from Bernoulli's distribution, probability of $x$ successes out of $n$ samples is given as:

$P(X=x)=_{n}^{x}\textrm{C}p^xq^{n-x}$

Here, $n=25,x=10,p=0.28,q=0.72$ . Therefore,

$P(X=10)=_{25}^{10}\textrm{C}(0.28)^{10}(0.72)^{25-10}\\P(X=10)=_{25}^{10}\textrm{C}(0.28)^{10}(0.72)^{15}\\P(X=10)=3.269\times 10^{6}\times 2.962\times 10^{-6}\times 7.244\times 10^{-3}\\P(X=10)=70.142\times 10^{-3}=0.0701=7.01\%$

Therefore, probability that 10 of them plan to vote against this piece of proposed legislation is 0.0701 or 7.01 %.

8 0

3 years ago

Moore's law says that the number of transistors in a dense integrated circuit increases by 41\%41%41, percent every year. In 197

stiv31 [10]

Answer:

In 1979 the amount of transistors in a chip was approximately 27865.

Step-by-step explanation:

Since the number of transistors in 1974 was 5000 per chip and it increases at a rate of 41% per year, the number of transistors in a chip per year can be modelled by the following expression:

chips(t) = 5000*(1.41)^(t - 1974)

Therefore in 1979, we have:

chips(1979) = 5000*(1.41)^(1979 - 1974)

chips(1979) = 5000*(1.41)^5

chips(1979) = 27865.4183

In 1979 the amount of transistors in a chip was approximately 27865.

8 0

3 years ago

The cost of a taxi ride is $5 plus $0.50 per mile write an algebraic expression that models the cost of a taxi of M miles. A-m(5

Alex787 [66]

The answer would be A or D

3 0

3 years ago

A maple tree in the backyard of a home has a height of 0.75 meters. How many times as tall (t) is a nearby hickory tree that is

anygoal [31]

Answer: 12

Step-by-step explanation:

Since we are informed that a maple tree in the backyard of a home has a height of 0.75 meters.

To know the jow many times tall (t) is a nearby hickory tree that is 9 meters tall, we've to divide the height of the hickory tree by the height of the maple tree. This will be:

= 9meters / 0.75meters

= 12

Therefore, the hickory tree is 12 times tall as the maple tree.

4 0

3 years ago