Answer:
(4,3)
Step-by-step explanation:
Given
x^2+y^2=25
x-y^2=-5
In order to solve the equations, from equation 2 we get
-y^2= -5-x
y^2=5+x
Putting the value of y^2 in equation 1
x^2+5+x=25
x^2+5-25+x=0
x^2+x-20=0
x^2+5x-4x-20= 0
x(x+5)-4(x+5)=0
(x+5)(x-4)=0
So
x+5=0 x-4=0
x=-5 x=4
Now for x=-5
x^2+y^2=25
(-5)^2+y^2=25
25+y^2=25
y^2=25-25
y^2=0
so Y=0
And for x = 4
x^2+y^2=25
(4)^2+y^2=25
16+y^2=25
y^2=25-16
y^2=9
y= ±3
So the solution to the system of equations is
(-5,0) , (4,3), (4,-3)
The only solution that belongs to first quadrant is (4,3)
Answer:
The critical value for this hypothesis test is 6.571.
Step-by-step explanation:
In this case the professor wants to determine whether the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes.
Then the variance will be,
The hypothesis to determine whether the population variance is less than 25.0 minutes or not, is:
<em>H</em>₀: The population variance is not less than 25.0 minutes, i.e. <em>σ²</em> = 25.
<em>Hₐ</em>: The population variance is less than 25.0 minutes, i.e. <em>σ²</em> < 25.
The test statistics is:

The decision rule is:
If the calculated value of the test statistic is less than the critical value,
then the null hypothesis will be rejected.
Compute the critical value as follows:

*Use a chi-square table.
Thus, the critical value for this hypothesis test is 6.571.
If three points were A, B and C are collinear points and B is between A and C, then AB+BC=AC
Answer:
-G + 15 = - 2G + 23
- 15 -15
-G = -2G + 8
+2G +2G
S0, G = 8 is the answer
Step-by-step explanation:
Answer:
Ypu are correct. It is -30
Step-by-step explanation: