What is 221, 000, 000, 000, 000, 000, 000, expressed in scientific notation

Answers

Answer 1

Answer:

Answer:

2.21 × 10^17

stepbystepexplanation:

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Identify which equations have one solution, infinitely many solutions, or no solution. No

Answers

Answer: all of them have one solutions

Step-by-step explanation:

A farm stand wants to sell fruit to local grocery stores in packages withbaskets of apples, worth $10 apiece, and baskets of peaches, worth $13
apiece. The owner wants each package to include 50 baskets total, and he
wants to sell each package for $566. How many baskets of apples and how
many baskets of peaches should he put in each package?
A. 10 apples, 13 peaches
B. 13 apples, 10 peaches
C. 28 apples, 22 peaches
D. 22 apples, 28 peaches

Answers

Answer:

28 apples and 22 peaches

Step-by-step explanation:

Select a discrete probability distribution and present a real-life application of that distribution. Interpret the expected value and the standard deviation of your selected distribution within the context of the real-life example that you have selected, and describe how these values can be used by enterprise decision-makers.

Answers

Answer:

If a new product wants to be tested by a company and decides to show 50 samples of this product to 50 selected customers. The company estimates that the probability that the customer buys the product is 0.67, the objective is to determine approximately how many people expect to buy the product.

Let X the random variable of interest "Number of people that will buy a selected product", on this case we now that:

$X \sim Binom(n=50, p=0.67)$

The expected value is given by this formula:

$E(X) = np=50*0.67=33.50$

And the standard deviation for the random variable is given by:

$sd(X)=√(np(1-p))=√(50*0.67*(1-0.67))=3.32$

So then they can conclude that for each group of 50 people they expect that about 33-34 peoploe will buy the product with a standard deviation of 3.32.

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Solution to the problem

Let X the random variable of interest "Number of people that will buy a selected product", on this case we now that:

$X \sim Binom(n=50, p=0.67)$

The expected value is given by this formula:

$E(X) = np=50*0.67=33.50$

And the standard deviation for the random variable is given by:

$sd(X)=√(np(1-p))=√(50*0.67*(1-0.67))=3.32$

So then they can conclude that for each group of 50 people they expect that about 33-34 peoploe will buy the product with a standard deviation of 3.32.

A plane leaves the airport in galisteo and flies 170 km at 68 degrees east of north; then it changes direction to fly 230 km at 36 degrees south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

Answers

Answer:

4.68° south east 317.36 km

Step-by-step explanation:

We can find the angle between the two distances (vectors) because according to the diagram, we can draw two right triangles between them.

The complement of the 36 degree angle is 54 (90-36=54), and the complement of the 68 angle is 22, (90-68=22) the sum of 22 and 54 is 76. So the angle between the two distances is 76.

Then we apply the cosine law

$b^(2) =a^(2) +c^(2) -2*a*c*cosB\n \nb^(2) =230^(2) +170^(2) -2*230*170*cos(76)\n\nb=\sqrt{230^(2) +170^(2) -2*230*170*cos(76)} \n\nb=317.36 km$

then we apply the sin law

$(sin(C))/(c) =(sin(B))/(b) \n\nsin(C)=c*(sin(B))/(b)\n\nsin(C)=170*(sin(76))/(317.36)\n\nsin(C)=0.52\n\narcsin(0.52)=C=31.32\n\n$

and because in any triangle, the sum of the inside angles is equal to 180

$180=76+31.32+68+y\n\ny=180-76-31.32-68\n\ny=4.68^(o)$

180= 76+C+(68+Y)

y=180-76-C-68

So the emergency plane has to travel 317.36 km, 4.68° southeast.

A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this store in week t after its release is R=f(t)=350 ln tR=f(t)=350lnt with t>1. Find f(5), f'(5), and the relative rate of change f'/f at t=5. Interpret your answers in terms of revenue.

Answers

Solution :

It is given that :

$f'(t) = (350 \ln t)'$

$=350(\ln t)'$

$=(350)/(t)$

So, $f(5)=350 \ln (5) \approx 563$

$f'(5) = (350)/(5)$

$=70$

The relative change is then,

$(f'(5))/(f(5))=(70)/(350\ \ln(5))$

$=(1)/(5\ \ln(5))$

$\approx 0.12$

$=12\%$

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ σ = 10 milligrams. Juan repeats the measurement 4 times and records the mean x x of his 4 measurements.

Answers

Final answer:

Juan is applying basic statistical principles in a chemistry laboratory by reviewing the standard deviation of the lab measurements and repeating his measurements multiple times to find a more accurate mean. The more Juan repeats his measurements, the closer he gets to a normal distribution or an accurate mean as per the central limit theorem.

Explanation:

In this chemistry laboratory scenario, you're dealing with a situation in statistics known as repeated measurements. Essentially, you are considering the standard deviation of the lab measurements, which is a typical measure of the dispersion of a set of values. The standard deviation is denoted by σ, and it is given as 10 milligrams.

When Juan repeats the measurement 4 times and records the mean of his measurements, he's using another common measure of central tendency, the arithmetic mean.

According to the central limit theorem in statistics, the distribution of the mean of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution. In this case, as Juan repeats his measurements, the mean of these measurements is likely to be more accurate (closer to the true value) than a single measurement.

Learn more about Standard Deviation and Mean here:

brainly.com/question/37170642

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Final answer:

The standard deviation a measure of dispersion in a data set, lower values indicating data points closer to the mean of the data set, and higher values indicating a wide range of the data points. The scenario discusses the calculation of standard deviation for repeated measurements, with the standard error calculated as the original standard deviation divided by the square root of the number of measurements.

Explanation:

The subject matter of the question pertains to statistical concepts, primarily the standard deviation. In statistics, the standard deviation is a measure of the amount of variation or dispersion in a data set. A low standard deviation indicates that the data points tend to be close to the mean of the data set, while a high standard deviation indicates that the data points are spread out over a wider range.

In the scenario provided, Juan makes a measurement in a chemistry lab and the standard deviation of the students' lab measurements is 10mg. He repeats the measurement 4 times and records the mean of his 4 measurements. When you repeat a measurement multiple times and take the mean, the standard deviation of the mean tends to be smaller than the standard deviation of the individual measurements. In statistical terms, the standard deviation of the mean, also known as the standard error, is given by the original standard deviation σ divided by the square root of the number of measurements n. In this case, n is 4, so the standard error would be σ/√n = 10mg/√4 = 5mg.