what is f(x)=8x^2+4x written in vertex form

To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, calculate the cumulative probability for each scenario and subtract them from 1. The resulting probability is approximately 0.8413.

To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, we need to calculate the cumulative probability for each scenario and then subtract them from 1.

Step 1: Calculate the z-scores for both values using the formula:

z = (x - mean) / standard deviation

For 90.3 millimeters:

z = (90.3 - 90.2) / 0.1 = 1

For 89.7 millimeters:

z = (89.7 - 90.2) / 0.1 = -5

Step 2: Use a standard normal distribution table or a calculator to find the cumulative probability for each z-score.

For a z-score of 1, the cumulative probability is approximately 0.8413.

For a z-score of -5, the cumulative probability is approximately 0.0000003.

Step 3: Subtract the cumulative probability for the shorter length from 1 and add the cumulative probability for the longer length.

Probability = (1 - 0.0000003) + 0.8413 = 0.8413

Therefore, the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters is approximately 0.8413.

Answer:

The probability that exactly 2 of the next four customers order turkey entries is 6 * 0.0393359 = 0.2360

Step-by-step explanation:

There are a total of 8+12+10 = 30 entries, 8 of them being turkey. Lets compute the probability that the first 2 customers order turkey entries and the remaining 2 do not.

For the first customer, he has 8 turkey entries out of 30, so the probability for him to pick a turkey entry is 8/30. For the second one there will be 29 entries left, 7 of them being turkey. So the probability that he picks a turkey entry is 7/29. The third one has 28 entries left, 6 of them which are turkey and 22 that are not. The probability that he picks a non turkey entry is 22/28. And for the last one, the probability that he picks a non turkey entry is 21/27. So the probability of this specific event is

8/30*7/29*22/28*21/27 = 0.0393359

Any other event based on a permutation of this event will have equal probability (we are just swapping the order of the numerators when we permute). The total number of permutations is 6, and since each permutation has equal probability, then the probability that exactly 2 of the next four customers order turkey entries is 6 * 0.0393359 = 0.2360

Answer:

No, it depend on reflective surface

Step-by-step explanation:

concave, convex, if plane mirror angle between the two mirrors, the parallel will produced infinity images

Answer:

[tex]z=\frac{0.333 -0.3}{\sqrt{\frac{0.3(1-0.3)}{195}}}=1.01[/tex]  

[tex]p_v =P(z>1.01)=0.156[/tex]  

So the p value obtained was a very low value and using the significance level asumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of women who complain of nausea between the 24th and 28th week of pregnancy is not significantly higher than 0.3 or 30%

Step-by-step explanation:

Data given and notation

n=195 represent the random sample taken

X=65 represent the women who complain of nausea between the 24th and 28th week of pregnancy

[tex]\hat p=\frac{65}{195}=0.333[/tex] estimated proportion of women who complain of nausea between the 24th and 28th week of pregnancy

[tex]p_o=0.3[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportion is higher than 0.3.:  

Null hypothesis:[tex]p\leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.333 -0.3}{\sqrt{\frac{0.3(1-0.3)}{195}}}=1.01[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>1.01)=0.156[/tex]  

So the p value obtained was a very low value and using the significance level asumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of women who complain of nausea between the 24th and 28th week of pregnancy is not significantly higher than 0.3 or 30%

To find the p-value for testing the hypothesis that the incidence rate of nausea for the erythromycin group is greater than for a typical pregnant woman, we can use the binomial probability formula.

To find the p-value for testing the hypothesis that the incidence rate of nausea for the erythromycin group is greater than for a typical pregnant woman, we can use the binomial probability formula.

The formula is:

P(X ≥ k) = 1 - P(X < k)

where X is the number of women in the erythromycin group who complain of nausea, and k is the number of complaints of nausea in the control group. In this case, X = 65 and k = 0, because the question specifies that there are no complaints of nausea in a typical pregnant woman. By plugging these values into the formula, we can calculate the p-value.

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Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]\mu = 98.6, \sigma = 0.6, n = 36, s = \frac{0.6}{\sqrt{36}} = 0.1[/tex]

If 36 adults are randomly​ selected, find the probability that their mean body temperature is greater than 98.4degrees° F.

This is 1 subtracted by the pvalue of Z when X = 98.4. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{98.4 - 98.6}{0.1}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

1 - 0.0228 = 0.9772

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Answer:

31

Step-by-step explanation:

116 - 27 -27 = 62 / 2 = 31

Answer:

The length is 31 in

Step-by-step explanation:

Perimeter = 2(Length + width)

say p = perimeter, l = length and w = width

perimeter = 166, w = 27

166 = 2(l  + 27)

116 = 2l + 2×27

2l + 54 = 116

2l = 116 - 54

2l = 62

l = 62/2

l = 31 in

say

Answer:

Step-by-step explanation:

The first two answers could not possibly be correct.

"Skewed to the right" implies that the mean is larger than the median.  This is the correct answer.

The mean is much larger than the median is the statement that would indicate that a data set is skewed to the right. This can be obtained by understanding the characteristics of a data set skewed to the right, that is positively skewed.

⇒Characteristics of a positively skewness

Hence the mean is much larger than the median is the statement that would indicate that a data set is skewed to the right. Therefore option 3 is correct.

Learn more about skewness here:

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Answer:

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

Based on the defnitions above we can conclude that the best answer for this case is:

B. rejecting the null hypothesis when it is true.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

Based on the defnitions above we can conclude that the best answer for this case is:

B. rejecting the null hypothesis when it is true.

Answer:

Step-by-step explanation:

You can find your answer in attached documents.

The student's question involves calculating compensating variation, equivalent variation, and change in consumer surplus due to a price increase in one of two goods, given a quasilinear utility function. These calculations require the application of microeconomic principles related to utility functions, indifference curves, and consumer choices, but cannot be completed without specific mathematical expressions and functions provided in the coursework.

The question relates to a consumer's preference relation and utility maximization in the context of an increase in the price of one of the goods. The compensating variation, equivalent variation, and change in consumer surplus are economic measures used to quantify the impacts of price changes on consumer welfare. These concepts involve understanding indifference curves, marginal rates of substitution, and consumer budget constraints.

Computing the compensating and equivalent variations requires setting up and solving expenditure function problems before and after the price change, whereas the change in consumer surplus can be represented graphically and calculated as the area under the demand curve and above the price level. Unfortunately, without specific details or mathematical expressions for utility maximization and budget constraints, which are typically provided in academic coursework, it is not possible to provide explicit calculations for these measures.

Understanding the utility function's form and how it translates into demand can help derive these economic measures. For instance, the quasilinear utility function is notable for its constant elasticity of demand and specific responses to income and price changes which can be used to predict consumer behavior and welfare changes.

Answer:

Probability of receiving the signal incorrectly is ".05792"

Step-by-step explanation:

Since it is mentioned here that the majority decoding is used so it implies that if the message is decoded as zero if there have been minimum of 3 Zeros in the messgae.

As we can see that there have been 5 bits, so the incorrection will occur only if there have been atleast 3 incorrect bits. Here we are asked to find out the probability of receiveing the signal incorrectly so i will take incorrectly transmiited bit as "Success".

The binomial distribution gives the probability of exactly m successes in n trials where the probability of  each individual trial succeeding is p.

With this method, we get the following pattern,

Binomial at (m=3, n=5, p=0.2) for probability of incorrection due to exactly 3 fails,

Binomial at (m=4, n=5, p=0.2) for probability of incorrection due to exactly 4 fails,

Binomial at (m=5 ,n=5, p=0.2) for probability of incorrection due to exactly 5 fails.

hence the probability "P" of receiving the signal incorrectly will be,

           P=(⁵₃) p³ (1 − p)⁵⁻³   +     (⁵₄) p⁴(1 − p)⁴⁻³      +      (⁵₅) p³(1 − p)³⁻³

whereas,

(⁵₃)= 5! / (5-3)! = 10

(⁵₄)= 5! / (5-4)! = 5

(⁵₅)= 5! / (5-5)! = 1

Putting these values in above equation we get,

P= 10 (0.2)³(1-0.2)²  + 5(0.2)⁴(1-0.2)¹  + (0.2)⁵

P=.05792

So the probablility "P" of receiving the signal incorrectly becomes ".05792"

Answer:

Correct option: As the sample size decreases, the margin of error increases.

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

The margin of error in this confidence interval is:

[tex]\\ MOE=z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

The sample size n is inversely related to the margin of error.

An inverse relationship implies that when one increases the other decreases and vice versa.

In case of MOE also, when n is increased the MOE decreases and when n is decreased the MOE increases.

Compute the new margin of error for n = 125 as follows:

[tex]\\ MOE=z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }=1.96\times \sqrt{\frac{0.40(1-0.40)}{125} }=0.086[/tex]

*Use z-table for the critical value.

For n = 125 the MOE is 0.086.

And for n = 275 the MOE was 0.058.

Thus, as the sample size decreases, the margin of error increases.

Answer:

D.The events are disjoint. They cannot occur at the same time.

Step-by-step explanation:

Event A = randomly selecting a french horn from the instrument assembly line and getting one that is free of defects

Event B = randomly selecting a french horn from the instrument assembly line and getting one with a dented bell

The two Events are disjoint because they cannot happens at the same time. It is either a french horn is free of defects or it has defects.

Disjoint event is when two event cannot occur at the same time.

The statement 'All insects have six legs' is converted to 'If x is an insect, then x has six legs' using the principle of Universal Generalization.

The process used here is known as Universal Generalization. This principle allows us to infer that something is true for all objects in a particular domain, provided it has been proved to be true for an arbitrary object in that domain. In this case, the statement 'All insects have six legs' has been converted into a formal logical statement using 'x' as the arbitrary object in the domain of all animals. By stating 'If x is an insect, then x has six legs' and using ∀x (denoting 'for all x'), we are using Universal Generalization to indicate this is true for all members of the domain.

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Answer:

$1.9006

Step-by-step explanation:

The expected value out of an event with value v and the probability p of that event to happen is the product of the value v and the probability p itself.

Therefore, the expected value of winning $215000 with probability of 0.00000884 bottle purchase is

E = pv = 215000 * 0.00000884 = $1.9006

The expected value, multiplied by the chance of winning the Lamborghini, is approximately $1.9004. This value means that if you could repeat this contest over and over, on average, you would gain about $1.90 per bottle purchased.

The subject of this question is about the expected value in probability. In the given scenario, when a Pepsi or Mountain Dew bottle is purchased, there's a probability of .00000884 of winning a Lamborghini sports car worth $215,000.

The expected value is calculated as the product of the value of the prize and the probability of winning it. Therefore, the expected value for this case would be (215000*.00000884) which equals to $1.9004, rounded to 4 decimal places. However, in the previous calculation, there was an error, resulting in a negative value which should not be the case in this context.

Expected value offers a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence. It is widely used in Probability Theory and Statistics.

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Answer:

Her speed on the mountain route was 52 miles per hour.

She travelled 12 miles per hour faster on the highway route.

Step-by-step explanation:

Speed is given by distance ÷ time taken

On the mountain,

distance = 312 miles

time = 6 hours

speed = 312 ÷ 6 = 52 miles per hour

On the highway,

distance = 320 miles

time = hours

speed = 320 ÷ 5 = 64 miles per hour

This is greater than the mountain route speed by 64 - 52 = 12 miles per hour.

Answer:

Speed at mountain route = 52 miles/hour

Speed at highway route = 64 miles/hour

Difference in speed = 12 miles/hour

Difference in speed = 18.75 % greater than mountain route

Step-by-step explanation:

As we know the speed is given by

Speed = Distance/time

Albuquerque to New Mexico using mountain route:

Speed = 312/6

Speed = 52 miles/hour

Albuquerque to New Mexico using highway route:

Speed = 320/5

Speed = 64 miles/hour

Difference in speed:

difference = 64 - 52 = 12 miles/hours

difference = 12/64*100 = 18.75 %

Therefore, Nella's speed at the highway route was 12 miles/hour greater than her speed at the mountain route.

Nella's speed at the highway route was 18.75 % greater than the speed at mountain route.

Answer:

x = 1   ,or   x = -7

Obviously, the true answer is not in the options given.

Step-by-step explanation:

x² + 6x - 6 = 10

The above equation can not be factorized, hence the use of Almighty Formula.

x = [-b +- √b² - 4ac] / 2a

Where a = 1, b = 6, c = -6

x = [-6 +- √6² - (4*1*-6)] / 2*1

x = [-6 +- √36 - (-24)] / 2

x = [-6 +- √36 + 24] / 2

x = [-6 +- √60] / 2

x = [-6 +- 7.75] / 2

x = [-6 + 7.75] / 2   ,or   x = [-6 - 7.75] / 2

x = 1.75/2   ,or   x = -13.75/2

x = 0.875   ,or   x = -6.875

Approximately

x = 1   ,or   x = -7

Answer:D

Step-by-step explanation:

Final answer:

BJ must deposit approximately $41,191.39 today to reach their goal of $50,000 at the end of Year 5, considering a 4.5% interest rate.

Explanation:

To find out how much BJ must deposit today to reach their goal of $50,000 at the end of Year 5, we can use the concept of compound interest. The formula to calculate the future value of a lump sum deposit is:

Future Value = Principal Amount x (1 + Interest Rate)^Number of Periods

In this case, BJ wants to find out the principal amount, which is the deposit they need to make today. We have the future value ($50,000), the interest rate (4.5%), and the number of periods (5).

Let's substitute the values into the formula and solve for the principal amount:

$50,000 = Principal Amount x (1 + 0.045)^5

Simplifying the equation:

$50,000 = Principal Amount x 1.21550625

Dividing both sides by 1.21550625:

Principal Amount = $41,191.39

Therefore, BJ must deposit approximately $41,191.39 today to reach their goal.

Answer:

95.4% of family vehicles is between 1 and 3 years old.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 2

Standard Deviation, σ = 6 months = 0.5 year

We are given that the distribution of age of cars is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(family vehicles is between 1 and 3 years old)

[tex]P(1 \leq x \leq 3)\\\\ = P(\displaystyle\frac{1 - 2}{0.5} \leq z \leq \displaystyle\frac{3-2}{0.5}) = P(-2 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2)\\= 0.977 -0.023 = 0.954= 95.4\%[/tex]

[tex]P(1 \leq x \leq 3) = 95.4%[/tex]

95.4% of family vehicles is between 1 and 3 years old.

Final answer:

Approximately 95.4% of family vehicles are between 1 and 3 years old based on the normal distribution with a mean of 2 years and a standard deviation of 6 months.

Explanation:

To determine the percentage of family vehicles that are between 1 and 3 years old when the age is normally distributed with a mean of 2 years and a standard deviation of 6 months, we can use the properties of the normal distribution.

First, convert the years to a z-score, which is the number of standard deviations away from the mean a data point is. The formula to calculate a z-score is: z = (X - μ) / σ

Where X is the value, μ is the mean, and σ is the standard deviation.

For 1 year: z = (1 - 2) / 0.5 = -2

For 3 years: z = (3 - 2) / 0.5 = 2

By looking up these z-scores on a z-table or using a calculator with a normal distribution function, we find that roughly 95.4% of the data falls between z-scores of -2 and 2. Therefore, approximately 95.4% of family vehicles are between 1 and 3 years old.

Answer:

economic order quantity is 258 cases per purchase

Step-by-step explanation:

The economic or quantity (EOQ) is the ideal order quantity that should be purchased in order to minimize costs.

Q = √(2DS / H)

D = 50 cases x 52 weeks = 2,600 cases per year

S = $350 per purchase order

H = $110 x 25% = $27.50

Q = √[(2 x 2,600 x 350) / 27.50] = √(1,820,000 / 27.5) = √66,181.82 = 257.26 cases ≈ 258 cases

Final answer:

The economic order quantity is 258 cases per purchase

Explanation:

The question pertains to the economic order quantity (EOQ) model in business operations and supply chain management, specifically in the context of a wholesaler dealing with inventory of sparkling wines.

The economic or quantity (EOQ) is the ideal order quantity that should be purchased in order to minimize costs.

[tex]Q = \sqrt{(2DS / H)[/tex]

Where,

D = annual demand in units

S = order cost per purchase order

H = holding cost per unit, per year

D = 50 cases x 52 weeks = 2,600 cases per year

S = $350 per purchase order

H = $110 x 25% = $27.50

Q = [tex]\sqrt{[(2 x 2,600 x 350) / 27.50][/tex]

[tex]= \sqrt{(1,820,000 / 27.5)[/tex]

= [tex]\sqrt{66,181.82[/tex]

= 257.26 cases

= 258 cases

Answer:

The number of complete award announcements possible are 19,554,575,040.

Step-by-step explanation:

Combination is the number of ways to select k items from n distinct items when the order of selection does not matters.

Whereas permutation is the number of ways to select k item from n items when order of selection matters.

The number of people entering this year is 22.

The number of ways to select 5 people for Grand Prize is, [tex]{22\choose 5}=\frac{22!}{5!(22-5)!} =26334[/tex].

The remaining number of people is, 22 - 5 = 17.

It is provided that the other 5 are selected according to an order.

The number of ways to select other 5 winners is,

[tex]^{17}P_{5}=\frac{17!}{(17-5)!} =742560[/tex]

The total number of ways to select 10 winners of 22 is:

Total number of ways = 26334 × 742560 = 19,554,575,040.

the length of the diagonal of the blue tablecloth is five times the length of the diagonal of the red tablecloth. So , Aaron is not correct .

Step-by-step explanation:

Here we have , The red tablecloth has a diagonal of V 10 feet. The blue tablecloth has a diagonal  V 50 feet .  Aaron says that the length of the diagonal of the blue tablecloth is three  times the length of the diagonal of the red tablecloth. Let's find out what Aaron says is correct or not :

Length of red tablecloth = 10 feet = p feet

Length of blue tablecloth = 50 feet

⇒ Length of blue tablecloth = 50 feet

⇒ Length of blue tablecloth = 5(10) feet

⇒ Length of blue tablecloth = 5p feet

That means the length of the diagonal of the blue tablecloth is five times the length of the diagonal of the red tablecloth. So , Aaron is not correct .

Aaron's claim that the length of the diagonal of the blue tablecloth is three times that of the red one is incorrect because the square root of 50 is not equal to three times the square root of 10.

No, Aaron is not correct. The length of the diagonal of the blue tablecloth is not three times the length of the diagonal of the red tablecloth. This is because the square root of 50 (√50) is not equal to three times the square root of 10 (3 * √10). In reality, the square root of 50 is approximately 7.07 and three times the square root of 10 is approximately 9.49.

Indeed:√50 ≈ 7.07 and 3 * √10 ≈ 9.49. These are not the same, hence Aaron's claim is incorrect.

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Answer:C

Step-by-step explanation:

Argument against the person, abusive as the US government should completely eradicate dictatorship and also curb the incident of abusive things from the dictatorship.

Answer:

This is No Fallacy ( A )

Step-by-step explanation:

This is a no Fallacy statement because it embodies the truth in its argument against dictatorship and its evil deeds/effects on the society that is been ruled by a dictator.

while a fallacy is an argument that is based on invalid reasoning or unjust reasoning while creating an argument in other to win a judgement.in most cases Fallacious argument deceive the audience into believing that the argument is true and passing blind judgement on the subject matter , but with the argument found in the question every part of the argument is a valid reason for the U.S to eradicate dictatorship.

Answer:

The probability that the result is positive is P=0.04475=4.475%.

Step-by-step explanation:

We have the events:

D: disease present

ND: disease not present

P: test positive

F: test false

Then, the information we have is:

P(D)=0.005

P(P | D)=0.99

P(P | ND)=0.04

The total amount of positive test are the sum of the positive when the disease is present and the false positives (positive tests when the disease is not present).

[tex]P(P)=P(P | D)*P(D)+P(P | ND)*(1-P(D))\\\\P(P)=0.99*0.005+0.04*0.995\\\\P(P)=0.00495+0.0398=0.04475[/tex]

The probability that the result is positive is P=0.04475.

Final answer:

The overall probability of a diagnostic test delivering a positive result, given its sensitivity and false positive rate, alongside the prevalence of the disease in the population, is calculated to be 4.475%.

Explanation:

The question revolves around calculating the probability that a diagnostic test for a given disease is positive. Given that the disease is present in 0.5% of the population, the test has a 99% sensitivity (true positive rate) and a 4% false positive rate (when the disease is not present, the test incorrectly indicates disease 4% of the time).

Steps to Calculate the Probability of a Positive Test Result

This calculation shows that the overall probability of getting a positive test result, regardless of actually having the disease, is 4.475%.

Answer:

The PMF of B is given by

P(B=0) = 0.7

P(B=1) = 0.16

P(B=2) = 0.08

P(B=3) = 0.04

P(B=4) = 0.02

Step-by-step explanation:

Let x denote P(B=1), we know that

P(B=0) = 1-0.3 = 0.7

P(B=1) = x

P(B=2) = x/2

P(B=3) = x/4

P(B=4) = x/8

Also, the probabilities should sum 1, thus

0.7+x+x/2+x/4+x/8 = 1

15x/8 = 0.3

x = 0.16

As a result, the PMF of B is given by

P(B=0) = 0.7

P(B=1) = 0.16

P(B=2) = 0.08

P(B=3) = 0.04

P(B=4) = 0.02

Based on given conditions, the probability of a single (B=1) is 0.160, a double (B=2) is 0.080, a triple (B=3) is 0.040, and a home run (B=4) is 0.020. The probability of player making an out (B=0) is 0.700.

Let's denote the probability of a home run as p. Then, the probability of a triple would be 2p, the double would be 4p, and the single would be 8p, all because of the twice-as-likely condition. As these are all the situations in which the player can get a hit, their sum should equal the player's batting average, i.e., 0.300.

So, 8p + 4p + 2p + p = 0.300. Solving this equation, we get that p = 0.020.

Therefore, using the same notations, the PMF of B (probability mass function) would be as follows: P(B=0) = 0.700, P(B=1) = 0.160, P(B=2) = 0.080, P(B=3) = 0.040, and P(B=4) = 0.020.

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Answer:

Moving average MSE =1.235

Exponential smoothing MSE =3.555

forecast for next month =(83+84+83)/3=83.33

Step-by-step explanation:

a)

Select your answer - Plot (iii)

What type of pattern exists in the data? -Horizontal Pattern

b)

for Moving Average MSE =1.235

for Exponential smoothing MSE =3.555

Moving Average is better

c)

forecast for next month =(83+84+83)/3=83.33

It can be deduced from the graph that the type of pattern that exists in the data is a horizontal pattern.

From the complete question, when comparing the three-month moving average forecast with an exponential smoothing forecast, the forecast for moving average is 1.235 while that of exponential smoothing is 3.555. Therefore, moving average is better.

In conclusion, the forecast for next month will be:

= (83 + 84 + 83)/3

= 83.33

Learn more about graphs on:

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Answer:

DE = 3 units

Step-by-step explanation:

The image is attached.

There are 2 secant lines in the circle. We can use secant theorem to solve this easily.

It states that "if 2 secants are drawn to a circle from an outside point, then product of 1 secant and its "outside" part is equal to product of other secant and its "outside" part.

From the figure, we can say:

AX * BX = EX * DX

We let the length to find , DE, be "x".

Thus, we can write:

[tex]AX * BX = EX * DX\\(7+2)(2)=(x+3)(3)[/tex]

Now, we solve this for x:

[tex](7+2)(2)=(x+3)(3)\\(9)(2)=(3)(x+3)\\18=3x+9\\3x=18-9\\3x=9\\x=3[/tex]

Thus,

DE = 3 units

Answer:

the answer is b 3 units

Step-by-step explanation:

Answer:

sigma formulas are executed by using for loop to sum all the values.

public class H4_Q3{

public static void main(String[] args)

{

//Part a

double[] values = {100000000.6, 99999999.8, 100000002.8, 99999998.5, 100000001.3};

int n = values.length;

//Part b;

double sum = 0;

double sample_average = 0;

double sample_variance = 0;

int i = 0;

for(i = 0; i < n; i++)

{

sum = sum + values[i];

}

sample_average = sum/n;

for(i = 0; i < n; i++)

{

sample_variance = sample_variance + (Math.sqrt(values[i]) - sample_average);

}

System.out.println("Sample variance (Part b formula): "+sample_variance);

//Part c

double sum_squared = 0;

double sum_values = sample_average;

for(i = 0; i < n; i++)

{

sum_squared = sum_squared + Math.sqrt(values[i]);

}

sum_squared = sum_squared/n;

sample_variance = (sum_squared - Math.sqrt(sum_values)) * (n/ (n - 1));

System.out.println("Sample variance (Part c formula): "+sample_variance);

//Part d

sample_variance = 0;

double[] M = new double[n];

double[] S = new double[n];

M[0] = values[0];

S[0] = 0;

i = 1;

while(i < n)

{

M[i] = M[i-1] + ((values[i] - M[i-1])/i+1);

S[i] = S[i-1] + (values[i] - M[i-1]) * (values[i] - M[i]);

i++;

}

System.out.println("Sample variance (Part d formula): "+S[n-1]/n);

}

}

Answer:

b. 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit

c. $41,800

d. 1,200 units of aluminium is left over

Step-by-step explanation:

a. Let:

x= Number of racing bikes,

y= Number of touring bikes and

z = Number of mountain bikes

Constraints are;

17x+19y+34z<=64600

9x+21y+12z<=24000

x>=0

y>=0

z>=0

b. Maximize P = 8x+12y+22z

Subject to;

17x+19y+34z<=64600

9x+21y+12z<=24000

with x>=0 ; y>=0 ; z>=0

applying simplex method (see attachment);

z=1900 ; x=0; y=0; P=41,800 ; s₁=0 ; s₂=1200

b.  The manufacturer are to make 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit

c. Maximum profit is $41,800

d. no steel is leftover while 1,200 units of aluminium is left over.  

a. The Linear Programming problem is set up as follows:

Objective function:

Maximize profit: [tex]P = 8x + 12y + 22z \)[/tex]

Constraints:

1. Steel constraint: [tex]\( 17x + 19y + 34z \leq 64,600 \)[/tex]

2. Aluminum constraint: [tex]\( 9x + 21y + 12z \leq 24,000 \)[/tex]

3. Non-negativity constraints: [tex]\( x, y, z \geq 0 \)[/tex]

b. To maximise profit, the company should produce 1000 racing bikes, 2800 touring bikes, and 1400 mountain bikes.

c. The maximum possible profit is $97,600.

d. There are 600 units of steel leftover and no units of aluminium leftover.

Let's set up and solve a linear programming problem for the given scenario.

a. Set up the Linear Programming Problem

Let x be the number of racing bikes, y be the number of touring bikes, and z be the number of mountain bikes.

Objective Function (Profit): Maximise P = 8x + 12y + 22z

Constraints:

b. Solution to Maximise Profit

Using the constraints and the objective function, we use a method such as the Simplex method or graphical method to find the optimal solution. Performing these calculations, we get:

x = 1,000 racing bikes

y = 0 touring bikes

z = 600 mountain bikes

c. Maximum Possible Profit

Substituting the values into the profit function:

P = 8(1,000) + 12(0) + 22(600) = $20,200

d. Leftover Steel and Aluminum

Steel used: 17(1,000) + 19(0) + 34(600) = 37,400 units

Steel leftover: 64,600 - 37,400 = 27,200 units

Aluminum used: 9(1,000) + 21(0) + 12(600) = 16,200 units

Aluminum leftover: 24,000 - 16,200 = 7,800 units

Hence, a. The Linear Programming problem is set up as follows:

Objective function:

Maximize profit: [tex]P = 8x + 12y + 22z \)[/tex]

Constraints:

1. Steel constraint: [tex]\( 17x + 19y + 34z \leq 64,600 \)[/tex]

2. Aluminum constraint: [tex]\( 9x + 21y + 12z \leq 24,000 \)[/tex]

3. Non-negativity constraints: [tex]\( x, y, z \geq 0 \)[/tex]

b. To maximise profit, the company should produce 1000 racing bikes, 2800 touring bikes, and 1400 mountain bikes.

c. The maximum possible profit is $97,600.

d. There are 600 units of steel leftover and no units of aluminium leftover.

Answer:

The value of the test statistic is 1.667

Step-by-step explanation:

We are given that the sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. For this a random sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200.

We have to determine whether or not the advertising campaigns have been effective in increasing sales.

Let, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $8,000 {means that the advertising campaigns have not been effective in increasing sales}

Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > $8,000 {means that the advertising campaigns have been effective in increasing sales}

The test statistics that will be used here is One sample z-test statistics;

             T.S. = [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, Xbar = sample mean = $8,250

                [tex]\sigma[/tex]  = population standard deviation = $1,200

                 n = sample size = 64

So, test statistics = [tex]\frac{8,250-8,000}{\frac{1,200}{\sqrt{64} } }[/tex]

                            = 1.667

Therefore, the value of test statistics is 1.667 .

Answer:

Step-by-step explanation:

Hello!

You have the variable

X: Area that can be painted with a can of spray paint (feet²)

The variable has a normal distribution with mean μ= 25 feet² and standard deviation δ= 3 feet²

since the variable has a normal distribution, you have to convert it to standard normal distribution to be able to use the tabulated accumulated probabilities.

a.

P(X>27)

First step is to standardize the value of X using Z= (X-μ)/ δ ~N(0;1)

P(Z>(27-25)/3)

P(Z>0.67)

Now that you have the corresponding Z value you can look for it in the table, but since tha table has probabilities of [tex]P(Z<Z_{\alpha })[/tex], you have to do the following conervertion:

P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143

b.

There was a sample of 20 cans taken and you need to calculate the probability of painting on average an area of 540 feet².

The sample mean has the same distribution as the variable it is ariginated from, but it's variability is affected by the sample size, so it has a normal distribution with parameners:

X[bar]~N(μ;δ²/n)

So the Z you have to use to standardize the value of the sample mean is Z=(X[bar]-μ)/(δ/√n)~N(0;1)

To paint 540 feet² using 20 cans you have to paint around 540/20= 27 feet² per can.

c.

P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999

d.

No. If the distribution is skewed and not normal, you cannot use the normal distribution to calculate the probabilities. You could use the central limit theorem to approximate the sampling distribution to normal if the sample size was 30 or grater but this is not the case.

I hope it helps!