Answer:
√2:1
Step-by-step explanation:
First we need to know that the length of the side of the square is equal to the diameter of the inscribed circle i.e
L = di
Given the area of the square to be 9in², we can get the length of the square.
Area of a square = L²
L is the length of the square.
9 = L²
L = √9
L = 3in
Hence the length of one side of the square is 3in
This means that the diameter of the inscribed circle di is also 3in.
Circumference of a circle = π×diameter of the circle(di)
Circumference of inscribed circle = π×3
= 3π in
For the circumscribed circumscribed circle, diameter of the outer circle will be equivalent to the diagonal of the square.
To get the diagonal d0, we will apply the Pythagoras theorem.
d0² = L²+L²
d0² = 3²+3²
d0² = 9+9
d0² = 18
d0 = √18
d0 = √9×√2
d0 = 3√2 in
Hence the diameter of the circumscribed circle (d0) is 3√2 in
Circumference of the circumscribed circle = πd0
= π(3√2)
= 3√2 π in
Hence, ratio of the circumference of the circumscribed circle to the one of the inscribed will be 3√2 π/3π = √2:1
Make the internet a fraction and then multiply them
Since ABC is equilateral, all 3 sides have equal length. side AC is 8 units since side BC is 8 units.
Line BD is placed in the middle, making D the midpoint of side AC.
knowing this information we can determine that the length of DC is 4 units (half of AC)
since triangle BDC is a right triangle, we can use the side lengths in the pythagorean theorem to find the length of BD
a²+b²=c² where a & b = legs of triangle , and c= hypotenuse (longest side)
we are given the hypotenuse and found one leg so we can plug our values into the equation to find the third
4² + b²= 8²
16 + b² = 64
b² = 48
b = 
b= 4√3 or about 6.928 units
hope this helped
Answer:
Type of drink given to each group
Step-by-step explanation:
Answer:
When we compare the significance level 
we see that 
so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the average age of the evening students is significantly different from 21, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a two sided test the p value would be:
Conclusion
When we compare the significance level we see that so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.
