This is a good question!
The steps are like follows:
Form the confidence level (99%), we calculate the "alpha" value
alpha=1-(99/100)=0.01
Now, calculate the critical probability (p-start)
p*=1-(alpha/2)=1-(0.01/2)=0.995
z-score could be calculated from p*,,,
z-score=<span>2.57583
(http://www.socscistatistics.com/tests/ztest/zscorecalculator.aspx)
Now, calculate the Margin of Error:
</span>standard<span> deviation = s
number of adults = n
</span><span>
ME=(z*s)/(sqrt n)=(</span><span>2.57583*12)/(sqrt 250) = 1.955
The confidence interval = mean +or- ME
= 70+1.955</span> or 70-1.955
So that we can conclude that <span>the 99% confidence interval for the mean beats per minute is 68.045 and 71.955
</span>
I hope you got
the idea!
If you still need help, just let me know!
Answer:
Step-by-step explanation:
The standard form of a quadratic equation is 
The vertex form of a quadratic equation is 
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
In this case, our quadratic equation is 
. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
⇒ 
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is
⇒ 
⇒ 
⇒ 
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is:
a: 1
h: 3
k: -25
Hope this helps!
Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140.
may not know the answer that well but try this called symbolab. Hope that could help you
Answer:
The first thing you should do for this case is to draw the ordered pairs in the plane and join the points.
The area you are looking for is the area of a rectangle plus the area of a triangle.
Thus, the total area will be
At = (8) * (4.5) + (1/2) * (4) * (2.5) = 41
answer
the area of the city is 41 units^2
Step-by-step explanation:
41 square miles If you draw the outline of the city, you'll realize that if you draw a line from point B to point D, that you can subdivide the city into a triangle and a trapezoid. After performing the division, you can then calculate the area of both polygons and the add their areas together. So first, let's deal with the trapezoid ABDE. The area of a trapezoid is the average of the length of the parallel sides multiplied by the height. The parallel sides are AB and DE. So: ((18-10)+(14-10))*(9-4.5)/2 =(9 + 4)*(4.5)/2 = 12*4.5/2 = 27 Now for the area of triangle BCD. The area of a triangle is 0.5*b*h where b is the base and h the height. I'll use BC as the base and the distance from BC to D as the height. So: (9-2)*(18-14)/2 = 7*4/2 = 14 And now to add the areas. 27 + 14 = 41 So the area of the city is 41 square miles. Note: The subdivision used is not the only possible subdivision, just one of the easier ones. I could have divided the city area into 3 triangles ABE, BDE, and BCD and solved it that way instead. It was just a happy coincidence that AB and DE were parallel and as such I was able to use trapezoid ABDE instead of the two triangles ABE and BDE.
