Answer:
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Step-by-step explanation:
Answer: point estimate = 3.88
Margin of error = 0.63
Step-by-step explanation:
Confidence interval is written in the form,
(Point estimate - margin of error, Point estimate + margin of error)
The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that
x - m = 3.25
x + m = 4.51
Adding both equations, it becomes
2x = 7.76
x = 7.76/2
x = 3.88
Substituting x = 3.88 into x + m = 4.51, it becomes
3.88 + m = 4.51
m = 4.51 - 3.88
m = 0.63
Answer:
The required equation is:

Explanation:
Let us assume that the hole is at y = 0m, with x as the time.
From the question we have (-1s, 8m) as the vertex (here x being the time variable is supposed to be in seconds and y being the distance variable is supposed to be in meters)
At x = 1s, the ball gets to the hole, therefore we have point (1s, 0m)
We know that the vertex of the parabola y = ax² + bx + c is at

therefore we have:

We then have the following equations:



From the 3rd equation we have
1 X 2a = b.
Therefore we have:


We can simplify both equations and get:


The first equation now becomes:


With a, we can find the values of c and b.


Then the equation is:

The goal is to find the area of a pentagon with side length 8.
We can find the area of a pentagon very easily by splitting it up into 10 congruent right triangles with the apothem as the height. The base of one of these triangles would be 4. The base angle would be 54 degrees, because it's half of the angle of a regular pentagon.
Using trig we find that the height of this triangle/apothem of the pentagon is equal to 4tan(54 degrees), which is about 5.506.
The area of a triangle is bh/2, so...4*5.506/2 = 11.011 in².
Times 10 triangles is 110.11 in².
Answer:
A. 2y^4 over x^2
Step-by-step explanation:
4x^4y^6 ÷ 7x^8y^2
First, you will find the GCF of the equation which is: 7x^4y^2 .
Then, you will divide both of the equation by the GCF which will become:
14x^4y^6 ÷ 7x^4y^2 = 2y^4
7x^8y^2 ÷ 7x^4y^2 = x^2
Hence, the final answer is 2y^4 over x^2