Correct answer is D.
Find the value of x.
1 answer:
Answer: The answer is x = 6 units.
Step-by-step explanation: Please refer to the attached diagram
The diagram in the question shows two triangles placed on each other and for convenience sake has been labelled ABDCE. Triangle ABC is a right angled triangle, and so is triangle ADE. From the marks on the lines, we can infer that line AD is equal in measurement to line DB. Also line AE is equal in measurement to line EC.
Therefore we can see the similarity in both triangles, if AD and AE equals DB and EC, then it follows that DE equals BC.
Hence if AD = DB and
AE = EC, and
DE = BC
Then, x - 3 = ½x
(½x can also be expressed as x/2)
x - 3 = x/2
By cross multiplication we now have
2(x - 3) = x
2x - 6 = x
By collecting like terms we now have
2x - x = 6
x = 6
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Answer:
A. <u>Normal</u>
B. <u>30.1</u>, <u>32.9</u>
C. <u>95</u>, <u>5</u>
Step-by-step explanation:
A. The sampling distribution follows a <u>normal</u> distribution
Given that the sample size is large, we have that the sample distribution follows a normal distribution according to the central limit theorem
B. The 95% confidence interval is given as follows;
The number of residents in the study, n = 120 residents
The sample mean, = 31.5 pounds
The standard deviation, s = 7.8 pounds
The z-value for 95% confidence level, z = 1.96
Therefore, we get;
C.I. = 31.5 ± 1.96 × 7.8/√(120)
The 95% C.I. ≈ 30.1 ≤ ≤ 32.9
Therefore, we have that with 95% confidence, the population mean number of pounds per person per week is between <u>30.1</u> and <u>32.9</u>
C. Therefore, according to the central limit theorem, about <u>95</u> percent of the groups of 120 will contain the true population mean number of pounds of trash generated per person per week and about <u>5</u> percent will not contain the true population mean number of pounds of trash generated per person per week.