What is the value of x?
2 answers:
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Answer:
Step-by-step explanation:
1. Area of base
The radius given is that of the circumcircle.
The general formula for the edge length a of a regular polygon is
a = 2Rsin(π/n)
So,
a = 2 × 5 × sin(π/5) = 10sin0.6283 = 10 × 0.5878 = 5.878 in
The general formula for the area of a regular polygon is
A = ¼na²cot(π/n)
So,
A = ¼ × 5 × 5.878²cot(π/5) = ¼ × 5 × 5.878² × 1.376 = 59.44 in²
2. Lateral area
The general formula for the lateral area L of regular prism is
L = nah
So,
L = 5 × 5.878 × 12 = 352.7 in²
3. Total area
Total surface area = lateral area + 2×base area
S = L + 2B = 352.7 + 2 × 59.44 = 471.6 in²
Answer:
d) The difference exists due to chance since the test statistic is small
Step-by-step explanation:
From the given information:
Population mean = 178 cm
the sample mean = 177.5 cm
the standard deviation = 2
the sample size = 25
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis:
Alternative hypothesis:
The t-test statistics is determined by using the formula:
Degree of freedom df = n- 1
Degree of freedom df = 25 - 1
Degree of freedom df = 24
At the level of significance ∝ = 0.05, the critical value = 2.064
Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance
Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small
Answer: 0.353
Step-by-step explanation:
We know that 42% of all the female students participate in 2 sports this season. (58% is the percent that did not)
This means that if we select a random student, there is a 0.42 probability that the student did participate in 2 sports this season.
Other thing that i will use is that, if we have a group of N objects, and we want to create a group of K objects out of the N, the number of combinations is:
Now, out of 5, we want to find the proability that, at least 3 of them, did participate in at least 2 sports this season.
The probability that all 5 of them participated, is equal to the product of the individual probabilities. (so N = 5, and K = 5)
P = (0.42^5)*1 = 0.013
Now, if only 4 of them did participate (N = 5, k = 4), the probability is equal to:
P = (0.42^4)*(0.58)*5!/4! = (0.42^4)*(0.58)*5 = 0.09
The probability for only 3 is: (N = 5 and K = 3)
P = (0.42^3)*(0.58^2)*5!/(3!*2!) = (0.42^3)*(0.58^2)*(5*4/2) = 0.25
Then the total probability is:
P = 0.013 + 0.09 + 0.25 = 0.353