The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the
circle having area equal to the sum of the areas of the two circles.
In: Math
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
In: Math

In: Math
Select whether a chisquare test for association is the most appropriate for the following scenarios: Most appropriate or Not appropriate
a) Emma wishes to know whether gender has any relation with whether one prefers wine, beer, or liqueur. She surveys a group of men and women and records the number of participants who prefer wine, the number who prefer beer and the number who prefer liqueur. (yes or no)
b) Danielle surveys a group of people on how often they eat dinner at restaurants and diners. The age and annual income of each participant are recorded. Danielle is interested in knowing whether these two factors are important in determining how often one goes out for dinner. (yes or no)
c) A study intends to determine whether the average annual interest rate has any relation with the number of households who go overseas on a holiday at least once a year. Heidi collects data on the average annual interest rate and the number of households that travelled overseas at least once in that year over 6 years. (yes or no)
d) It has been proposed that one's education level has a strong relation with one's income level. Barbara collects data from a large group of 38 yearold adults about their education level (primary and lower, secondary, tertiary and higher) and their income level (to the nearest $100). Barbara plans to test this data to see whether the mean income in each education level is the same across all three levels. (yes or no)
In: Math
An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.
y  
p(x, y) 
0  5  10  15  
x  0  0.03  0.06  0.02  0.10 
5  0.04  0.15  0.20  0.10  
10  0.01  0.15  0.13  0.01 
(a) Compute the covariance for X and Y. (Round your answer to two decimal places.)
Cov(X, Y) =
(b) Compute ρ for X and Y. (Round your answer to two decimal places.)
ρ =
In: Math
To obtain information on the corrosionresistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of x = 53.2 and a sample standard deviation of s = 4.8. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude? (Use a = 0.05.)
State the appropriate null and alternative hypotheses.
Calculate the test statistic and determine the Pvalue. (Round your test statistic to two decimal places and your pvalue to four decimal places.)
State the conclusion in the problem context.
Reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils.
Reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils.
Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils.
Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils.
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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y_{0} (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.409 for this random variable. (Round your answers to three decimal places.)
(a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?
exactly 3 intervals  .0684 
at most 3 intervals 
(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
In: Math
In: Math
The shear strength of each of ten test spot welds is determined, yielding the following data (psi).
389  405  409  367  358  415  376  375  367  362 
(a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.)
average  382.3 psi  
standard deviation  20.8 psi 
(b) Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [Hint: What is the 95th percentile in terms of μ and σ? Now use the invariance principle.] (Round your answer to two decimal places.)
(c) Suppose we decide to examine another test spot weld. Let X = shear strength of the weld. Use the given data to obtain the mle of P(X ≤ 400). [Hint:
P(X ≤ 400) = Φ((400 − μ)/σ).]
In: Math
The structure of the figure is supported by the pin A of diameter d=3/4" and a cable that passes through the pulley of negligible diameter D.
pulley of negligible diameter D and whose assembly is shown in the figure. For the CE bar it was necessary to construct it by joining two sections of plate with a welded joint in the form of a thorn.
herringbone welded joint, as shown in the detail. For this configuration, determine
a. The minimum area of the CE bar, if its allowable stress is σperm = 12 Ksi.
b. The minimum diameter of the pin E, if its allowable stress is τperm = 10 Ksi.
c. The shear stress produced in pin A.
d. If the thickness of the bar AE is t=5/8", calculate the crushing stress σb on the pin A.
e. The normal stress σ and shear stress τ of the weld bead.
In: Math
The table below gives beverage preferences for random samples of teens and adults.
teens  adults  total  
coffee  50  200  250 
tea  100  150  250 
soft drinks  200  200  400 
other  50  50  100 
400  600  1000 
a. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. With a .05 level of significance, the critical value for the test is?
(a. 1.645 b. 7.815 c. 14.067 d. 15.507)
b. The expected number of adults who prefer coffee is? (a. 0.25 b. 0.33 c. 150 d. 200)
c. The test statistic for this test of independence is? (a. 0 b. 8.4 c. 62.5 d. 82.5)
d. The conclusion of the test is that the:
(Age is independent of drink preference, Age is not independent of drink preference, test is inconclusive, None of these alternatives is correct.)
In: Math
A data set lists earthquake depths. The summary statistics are n=600, x̅=671 km, s=4.53 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, Pvalue, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
2. Determine the PValue.
In: Math
The formula used to compute a largesample confidence interval for p is
p̂ ± (z critical value)

What is the appropriate z critical value for each of the following confidence levels? (Round your answers to two decimal places.)
(a) 95%
(b) 90%
(c) 99%
(d) 80%
(e) 80%
In: Math
In: Math