Solve the following one-step equations using inverse operations.
1 answer:
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Let
<span>A------> (−3, −11)
B------> (6, 4)
step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3
step 2
with m=5/3 and point B (6, 4) find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6
case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3
case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0
y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)
y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)
case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because
if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0
y=35x−6-------> y=-6
the y intercept is the point (0,-6)
y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)
they have the same y-intercept but the two lines are not perpendicular
see the attached figure
<span>A------> (−3, −11)
B------> (6, 4)
step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3
step 2
with m=5/3 and point B (6, 4) find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6
case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3
case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0
y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)
y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)
case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because
if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0
y=35x−6-------> y=-6
the y intercept is the point (0,-6)
y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)
they have the same y-intercept but the two lines are not perpendicular
see the attached figure
Answer: The ball hits the ground at 5 s
Step-by-step explanation:
The question seems incomplete and there is not enough data. However, we can work with the following function to understand this problem:
(1)
Where models the height of the ball in meters and
the time.
Now, let's find the time when the ball Sara kicked hits the ground (this is when
):
(2)
Rearranging the equation:
(3)
Dividing both sides of the equation by :
(4)
This quadratic equation can be written in the form , and can be solved with the following formula:
(5)
Where:
Substituting the known values:
(6)
Solving we have the following result:
This means the ball hit the ground 5 seconds after it was kicked by Sara.
Answer:
1. Mean square B= 5.32
2. Mean square E= 16.067
3. F= 0.33
4. p-value: 0.28
Step-by-step explanation:
Hello!
You have the information of 3 groups of people.
Group 1
n₁= 20
X[bar]₁= 3.2
S₁²= 14.3
Group 2
n₂= 20
X[bar]₂= 4.2
S₂²= 17.2
Group 3
n₃= 20
X[bar]₃= 7.6
S₃²= 16.7
1. To manually calculate the mean square between the groups you have to calculate the sum of square between conditions and divide it by the degrees of freedom.
Df B= k-1 = 3-1= 2
Sum Square B is:
∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= general mean is the mean that results of all the groups together.
General mean:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (3.2+4.2+7.6)/3 = 5
Sum Square B (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (3.2 - 5)² + (4.2 - 5)² + (7.6 - 5)²= 10.64
Mean square B= Sum Square B/Df B= 10.64/2= 5.32
2. The mean square error (MSE) is the estimation of the variance error (σ →
), you have to use the following formula:
Se²=<u> (n₁-1)S₁² + -(n₂-1)S₂² + (n₃-1)S₃²</u>
n₁+n₂+n₃-k
Se²=<u> 19*14.3 + 19*17.2 + 19*16.7 </u>= <u> 915.8 </u> = 16.067
20+20+20-3 57
DfE= N-k = 60-3= 57
3. To calculate the value of the statistic you have to divide the MSB by MSE
4. P(F ≤ F) = P(F
≤ 0.33) = 0.28
I hope you have a SUPER day!