George says that 4+ a +a+a+b+b=24ab
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<h3>Answer: 33.75 feet</h3>
In fraction form, this value is equal to 135/4
33.75 ft is equivalent to 33 ft, 9 inches.
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Explanation:
Refer to the diagram below.
The key point to start with is point H, which is the vertex of the parabola.
Recall that vertex form is
y = a(x-h)^2 + k
What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.
So,
y = a(x-h)^2 + k
y = a(x-60)^2 + 30 .... plug in vertex
45 = a(0-60)^2 + 30 .... plug in y intercept coordinates
45 = a(-60)^2 + 30
45 = a(3600) + 30
45 = 3600a + 30
45-30 = 3600a
3600a = 15
a = 15/3600
a = 1/240
This then means:
y = a(x-h)^2 + k
y = (1/240)(x-60)^2 + 30
This is the equation of our parabola. Plug in x = 30 to determine the height of point K
y = (1/240)(x-60)^2 + 30
y = (1/240)(30-60)^2 + 30
y = (1/240)(-30)^2 + 30
y = (1/240)(900) + 30
y = 15/4 + 30
y = 15/4 + 120/4
y = 135/4
y = 33.75
Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.
Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches
The expressions represent the total time of her trip in hours is.
Given that,
For the first 80 miles of her road trip, Lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip.
It represents Lina's speed during the first part of her trip.
We have to determine,
Which expressions represent the total time of her trip in hours?
According to the question,
Let the speed traveled during the first part of the trip be "s".
The formula for calculating the distance is expressed as:
For the first part of the journey:
Distance = 80 miles
Time =
And Speed = s
Substitute all the values in the formula,
For the second part of the trip;
Distance traveled = 50 miles
Speed = s + 10 (10miles/hour faster than the first part of the trip)
time =
Substitute all the values in the formula,
Therefore,
Adding both the time to represent the total time of her trip in hours,
Hence, The required expressions represent the total time of her trip in hours is.
For more details refer to the link given below.
Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it.
The confidence interval can be calculated using following formula:
Where
is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:
The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income:
The confidence interval can be calculated using following formula:
Where
We know that standard deviation is simply a square root of variance:
The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income: