The third side must be >2 and < 18
To test if a triangle is acute, right or obtuse:
1) Square all 3 sides
2) Sum the squares of the 2 shortest sides
3) Compare this sum to side 3 squared
if sum > side 3 squared it is an acute triangle
if sum = side 3 squared it is a right triangle
if sum < side 3 squared it is an obtuse triangle
The shortest side 2 can be is "less than 2" so we'll say it is 2.00000001
three sides squared =
<span>
<span>
<span>
4.00000004
</span>
</span>
</span>
64
100
Summing the 2 shortest sides 4.00000004 + 64 = <span>68.00000004
</span><span>68.00000004 is less than 100 so it is an obtuse triangle no matter how long the third side is.
</span>
Answer: a. 1.981 < μ < 2.18
b. Yes.
Step-by-step explanation:
A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.
First, we calculate mean of the sample:
2.08
Now, we estimate standard deviation:
s = 0.1564
For t-score, we need to determine degree of freedom and 
:
df = 12 - 1
df = 11
= 1 - 0.95
α = 0.05
0.025
Then, t-score is
= 2.201
The interval will be
± 
2.08 ± 
2.08 ± 0.099
The 95% two-sided CI on the mean is 1.981 < μ < 2.18.
B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.
Http://www.americanrhetoric.com/speeches/mlkihaveadream.htm <span>"I Have a Dream" is a public speech delivered by American civil rights activist Martin Luther King, Jr. during the March on Washington for Jobs and Freedom on August 28, 1963, in which he calls for an end to racism in the United States and called for civil and economic rights. Delivered to over 250,000 civil rights supporters from the steps of the Lincoln Memorial in Washington, D.C., the speech was a defining moment of the American Civil Rights Movement.</span>
Answer:
z= 3.63
z for significance level = 0.05 is ± 1.645
Step-by-step explanation:
Here p = 42% = 0.42
n= 500
We formulate our null and alternative hypotheses as
H0: p= 0.42 against Ha : p> 0.42 One tailed test
From this we can find q which is equal to 1-p= 1-0.42 = 0.58
Taking p`= 0.5
Now using the z test
z= p`- p/ √p(1-p)/n
Putting the values
z= 0.5- 0.42/ √0.42*0.58/500
z= 0.5- 0.42/ 0.0220
z= 3.63
For one tailed test the value of z for significance level = 0.05 is ± 1.645
Since the calculated value does not fall in the critical region we reject our null hypothesis and accept the alternative hypothesis that more than 42% people owned cats.
