The probability will be found as follows:
z-score is given by:
z=(x-μ)/σ
where:
mean-μ=9.3
standard deviation-σ=1.1
but
σ/√n=1.1/√70=0.1315
thus the z-score will be:
z=(9.1-9.3)/0.1315
z=-1.5209
thus:
P(x<9.1)=P(z<-1.5209)=0.0643
The general form of the equation of a circle is,
x² + y² + Dx + Ey + F = 0, where D, E, F are constants.
The given equation is 7x² + 7y² − 28x + 42y − 35 = 0. So, to convert this equation into a general form we just need to get rid of the leading coefficient 7.
Hence, divide both sides of the equation by 7. So,
x² + y² − 4x + 6y − 5=0.
So, the general form of the equation is x² + y² − 4x + 6y − 5=0.
Notice that the denominator is a multiplied by 2 for each fraction.
1/1•2 = 1/2
1 /2•2 = 1/4
1/4•2 = 1/8
1/8•2 = 1/16
1/16•2 =1/32
The next size is 1/32.
4) You know slope-intercept form is y=mx+b. So using these two given points, you can find the slope!
(-8,5) (-3,10) [Use the y1-y2 over x1-x2 formula to solve for slope]
10 - 5 5
--------- = ----- = 1
-3-(-8) 5
Hurray! You got a slope of one. Now substitute this back into your original equation:
y=mx+b --> y=1x+b
Next, we find what our "b" is, or what our y-intercept is:
Using one of the previous points given, substitute them into the new equation:
[I used the point (-3, 10) ]
y=1x+b
10=1(-3)+b SUBSTITUTE
10=-3+b MULTIPLY
10=-3+b
+3 +3 ADD
----------
13=b SIMPLIFY
So, now we have our y-intercept. Use this and plug it into the equation:
y=1x+b --> y=1x+13
y=1x+13 is our final answer.
5) So for perpendicular lines, your slope will be the opposite reciprocal of the original slope. (Ex: Slope is 2, but perpendicular slope is -1/2)
We have the equation y= 3x-1, so find the reciprocal slope!
--> y=-1/3x-1
Good! Now we take our given point, (9, -4) and plug it into the new equation:
y=-1/3x-1
-4=-1/3(9)+b SUBSTITUTE and revert "-1" to "b", for we are trying to find the y- -4=-3+b intercept of our perpendicular equation.
+3 +3 ADD
--------
-1=b SIMPLIFY
So, our final answer is y=-1/3x+(-1)
6) I don't know, sorry! :(
Answer: I belive the answer is C
Step-by-step explanation: