General Idea:
The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.
Applying the concept:
Angles PBC and BAD are congruent by the <u>Corresponding Angle Theorem</u>.
Angles ABC and BAT are congruent by the <u>Alternate Interior angle Theorem</u>.
Answer: The 95% confidence interval for the mean of x is (94.08, 101.92) .
Step-by-step explanation:
We are given that ,
A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12.
i.e. 
Also, it is given that , Sample mean 
having sample size : n= 36
For 95% confidence ,
Significance level : 
By using the z-value table , the two-tailed critical value for 95% Confidence interval :
We know that the confidence interval for unknown population mean
is given by :-
, where 
= Sample mean
= Population standard deviation
= Critical z-value.
Substitute all the given values, then the required confidence interval will be :
Therefore, the 95% confidence interval for the mean of x is (94.08, 101.92) .
Answer:
I think it is -5+root-7/2 & -5-root-7/2
Step-by-step explanation:
Answer:
<h3>b. y=arcsinx</h3>
Step-by-step explanation:
Given the function y = sinx
The equation of its inverse can be gotten by first taking the arcsin of both sides as shown
arcsiny = arcsin(sinx)
The arcsin will cancel out the sin function at the right hand side to have;
arcsiny = x
x = arcsiny
Replacing the variable 'y' with x and 'x' in y in the resulting equation we have;
y = arcsinx
This gives the required inverse.
For simplicity’s sake:
D = dogs, C = cats, R = rabbits
Since the dogs and the cats are the same number, we can say C = D.
R = 1/4D
2D + 1/4D = 36
Combine like terms and get the same denominator
9/4D = 36
9D = 144
D = 16
Now we know that D is 16, so C must be 16 as well. That leaves us with 32 cages.
36 - 32 = 4 rabbit cages. To double check this, 1/4 of 16 does equal 4.
Final answer: 16 D, 16 C, 4 R
