The angle formed by two tangles results in half of the difference of the two arcs.
That is to say
70 = .5(Major arc - minor arc)
Think of the major arc as the larger and the minor the smaller.
So therefore the difference in the two arcs = 140 (multiplying both sides of the above equation by 2.
140 = major arc - minor arc.
Another necessary idea is that the arc of a whole circle = 360 degrees, that is to say the major arc + minor arc = 360, giving us a second equation to solve.
Assuming x is the minor arc.
140 = major arc - x
360 = major arc + x
Use linear combination and add these equations to get
500 = 2*major arc
major arc = 250
minor arc or x = 110.
The answer is 110 degrees.
Answer:
C) 52 in^3
Step-by-step explanation:
The first is to determine the formula of the volume of the box, which would be the following:
V = height * length * width
Knowing that we have a rectangular piece we will determine the maximum volume, we will double a distance x (which will be the height) in the width and length of the piece, therefore as it is on both sides, the length and width are defined from the Following way:
length = 10 - 2 * x
width = 8 - 2 * x
height = x
Now we calculate the volume:
V = x * (10-2 * x) * (8-2 * x)
To determine the maximum volume we will give values to x in order to see how it behaves:
Let x = 2.5
V = (5) * (3) * (2.5) = 37.5
Let x = 2
V = (6) * (4) * (2) = 48
Let x = 1.5
V = (7) * (5) * (1.5) = 52.5
Let x = 1
V = (8) * (6) * (1) = 48
Let x = 0.5
V = (9) * (7) * (0.5) = 31.5
It can be seen that the greatest volume is obtained when the height is equal to 1.5 and its volume is 52.5 in ^ 3
Answer:
See explanation below
Step-by-step explanation:
It depends on what null hypothesis is under consideration.
One of the most common null hypothesis that are subject of study in a given statistical model is <em>the mean</em> predicted by the model.
In this case, the scientist probably observed that the mean of tusk lengths she obtained in a sample did not match the one predicted with the H-W equation.
So, she decided to perform a statistical study by collecting random samples and measuring the tusk lengths to determine a new possible mean and contrast it against the one predicted by the H-W equation.
<em>Let's call M the mean predicted by the H-W equation, and S the mean obtained by the scientist.
</em>
If M different of S and the p-value is 0.021, that means that <em>there is at most 2.1% of probability that the difference between M and S could be due to a random sampling error.
</em>
It should be kept in mind that the p-value does not represent the probability that the scientist is wrong.
Answer:
Step-by-step explanation:
we have a exponential function of the form
where
y is the population of bacteria
a is the initial value
r is the rate of growth
x is the number of hours
we have
a=3,000 bacteria
For x=2, y=3,300
substitute
Apply square root both sides
substitute in the equation
<u><em>Predict how many bacteria will be present after 16 hours</em></u>
For x=16 hours
substitute
Answer:
∠CBD = 50°
Step-by-step explanation:
Step 1:
x + 130° = 180° Supplementary ∠'s
Step 2:
x = 180° - 130° Subtract 130° on both sides
Answer:
∠CBD = 50°
Hope This Helps :)
