Answer:
Step-by-step explanation:
The base of the pyramid we need to study is a hexagon.
Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.
Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")
Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.
We know the area of a triangle is the product of its base times its height, divided by 2: 
We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures 
, so replacing this value in the formula above for the area of one of the triangles:
Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):
Area of hexagon = 
which is the last option given in the list.
Answer:
Slope: 
y-intercept: 
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
The slope can be found with the following formula:
In this case you can say that:
Knowing this values you can substitute them into the formula and then evaluate, in order to find the slope. This is:
By definition, the line intersects the y-axis when the value of "x" is 0.
Notice in the table that when 
, 
Therefore, the y-intercept is:
Answer:
We conclude that the population mean is 24.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 24
Sample mean, 
= 22.8
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 8.3
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
We calculate the p-value with the help of standard z table.
P-value = 0.1498
Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.
Now, 
Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.
Answer:
a) 4,096
b) 0.000244
Step-by-step explanation:
a)
By the Fundamental rule of counting, there are
4*4*4*4*4*4 = 4,096
ways of forming six-digit arrangements where each position has 4 possibilities (1 to 4)
b)
The probability of entering the correct code on the first try, assuming that the owner does not remember the code is
1/4096 = 0.000244
Answer:
x=6
Step-by-step explanation:
distribute 2 to x and 3..you get 2x -6 +1. add 6 and subtract one to cancel it out and bring it to the other side. 2x=12...simplify x=6
