Answer:
In a rhombus, the diagonals bisect at right angles. That means half the diagonals form a right angle triangle then we can try the Pythagorean theorem. so -
one side of triangle = 6/2 =3 (half of the diagonal)
other side = 8/2 = 4
a^2 + b^2 = c2
3 ^2 + 4^2 = c^2
9+16 = c^2
c^2=25
c = = 5
the hypothenus forms one side of the rhombus and here the hypothenus is 5, so the lenght of a side is 5 !
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus .
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
.
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
,
where
For this confidence interval:
Hence the width of the 90% confidence interval is
.
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
.
