Find all solutions to the following equations:
(a) √2x − 2 = √x + 1
(b) x4 − 5x2 + 6 = 0
(c) |3x − 7| < 5
(d) |ax + b| ≥ c

Explain step by step please

Suppose 4 is a right triangle with leg-lengths a and b and hypotenuse
c. Find the missing side:
(a) a = 3, b = 4, c =?
(b) a = 12, c = 13, b =?
(c) a = 6, c = 9, b =?
2

A certain type of tomato seed germinates 90% of the time. A gardener planted 25 seeds. a What is the probability that exactly 20 seeds germinate? b What is the probability that 20 or more seeds germinate? c What is the probability that 24 or fewer seeds germinate? d What is the expected number of seeds that germinate?

AM -vs- PM Height (Raw Data, Software Required):
It is widely accepted that people are a little taller in the morning than at night. Here we perform a test on how big the difference is. In a sample of 30 adults, the morning height and evening height are given in millimeters (mm) in the table below. Use this data to test the claim that, on average, people are more than 10 mm taller in the morning than at night. Test this claim at the 0.05 significance level.

What is an example of a study that uses block randomization?

Cognitive-based therapy (CBT) and family-based therapy (FBT) are two different treatments for anorexia. In an experimental study, forty-six anorexic teenage girls were randomly assigned to two groups. One group, consisting of n1 = 29 individuals, received CBT, and the other group, consisting of n2 = 17 individuals, received FBT. Weight of each individual is measured twice, once at the beginning and once at the end of the study period. The variable of interest is the weight change, i.e. weight after therapy minus weight before therapy. The data collected from the two samples are given below.

cognitive = c(1.7, 0.7, -0.1, -0.7, -3.5, 14.9, 3.5, 17.1,  -7.6, 1.6, 11.7, 6.1,

    1.1, -4.0, 20.9, -9.1, 2.1, -1.4, 1.4, -0.3, -3.7, -0.8, 2.4, 12.6, 1.9, 3.9,

    0.1, 15.4, -0.7)

family = c(11.4, 11.0,  5.5,  9.4, 13.6, -2.9, -0.1,  7.4,  21.5, -5.3, -3.8, 13.4,

    13.1,  9.0,  3.9,  5.7, 10.7)

Note that a positive weight change (weight gain) is generally good for anorexia patients. Let μ1 be the population mean weight change in the CBT group, and μ2 the population mean weight change in the FBT group. The goal is to conduct statistical inference on the difference μ1 − μ2

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4. Two-sample t-test relies on the assumption that the two samples are either large enough (n1 ≥ 30 and n2 ≥ 30) or coming from normal distributions. In the context of this problem, neither of the two samples is large enough.

(a) Check the normality assumption for both samples using the normal quantile-quantile plot. Re- member that you can do this in R using the qqnorm command.

(b) Suppose one thinks that the normality assumption does not hold for this data set, hence does not trust the results provided in the two-sample t-test. Suggest a different hypothesis testing procedure that does not rely on the normality assumption. (Note: You don’t have to carry out the test.

Data for the IFSAC Firefighter I examination test scores for two separate groups are found below. A random sample of firefighters is selected for each group. Group 1 attended the State Fire Academy for their training and Group 2 attended an in-house academy. The groups are only tested once after they have received the training. All participants have no prior experience in the fire service. Assume normality of the populations.

1.Verify that assumptions are met (briefly list and explain)

2.Construct the hypotheses (null and alternative)

3.Formulate decision rule (calculate the p-value or critical value)

4.Calculate the test statistic

5.Discuss your conclusion

Is there sufficient evidence that firefighters attending the in-house academy have higher test scores on average than firefighters attending the State Fire Academy at the α=.05 significance level?

Is there sufficient evidence that the mean scores on the IFSAC Firefighter I examination test differ between the two groups at the α=.05 significance level?

In a test of the effectiveness of garlic for lowering​ cholesterol,

45

subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes

​(beforeminus−​after)

in their levels of LDL cholesterol​ (in mg/dL) have a mean of

5.2

and a standard deviation of

15.8.

Construct a 95​%

confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol?

Each of the distributions below could be used to model the time spent studying for an exam. Take one random sample of size 25 from each of the distributions below. Then, take 1,000 resamples (i.e., sample with replacement) of size 25 from your sample. In each case (a,b,c), plot the empirical distribution of the sample mean, estimate the mean of the sample mean, and estimate the standard deviation of the sample mean. Compare the results to the theoretical results.

a. N(5, 1.52)

b. Unif(0,10)

c. Gamma(5,1)

1.

Counting the number of people who have been exposed to the Zika virus is an example of which of the following?

Continuous data

Discrete data

Quantitative data

Binary data

unanswered

2.Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What is the independent variable?

The type of bait

The weight of the fish

Corn

None of the above

3.

Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What type of variable is the dependent variable?

Continuous

Discrete

Qualitative

Binary

unanswered

4.

A study was conducted to determine if rats gain weight after experiencing different levels of exercise. Researchers used 24 rats, for three different levels of exercise, plus a control group. Rats were randomly assigned to each group until there were six rats per group. How many replications are there?

3

4

6

24

unanswered

5.

Which of the following are true when using the stratified sampling method? (Choose all that apply)

All subjects have and equally likely chance of being selected

Subjects are selected from each strata

Strata are usually created by convenience

All subjects are measured in the selected strata

unanswered

We flip a fair coin 20 times. Find the probability that we obtain between 8 and 17 heads, inclusively. Show work and please explain to someone that hardly understands statistics!

Use 6.89 days as a planning value for the population standard deviation. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 1.5 days (round up to the next whole number)? Assuming 90% confidence, what sample size would be required to obtain a margin of error of 2 days (round up to the next whole number)?

a) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.79 million dollars. Assuming a population standard deviation gross earnings of 0.47 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions).

Confidence interval: ( __________________ , __________________ ).

Please explain steps to find these answers on the TI 84 plus calculator:

A machine used to fill gallon sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The same mean of the cans is 127.9 ounces. Does the machine need to be reset? Explain your reasoning.

1. Use the diamond data:

Is there enough evidence in the data that population average price of diamond for color “E” is more than 1500.

Please solve using R please.

Thank you