Answer:
Arc AB= 180 degrees
Arc BC= 15 degrees
Arc CA= 165 degrees
Step-by-step explanation:
In order to find the measure of each arc, start by recognizing that a circle equals 360 degrees, and the measure angle of the diameter of this circle is equal to half of 360 degrees, which is 180 degrees.
Since segment AB is the diameter of the circle, it will equal 180 degrees. Thus, causing arc AB equal to 180 degrees.
Next, arc BC equals 15 degrees because the measure of angle BOC is equal to the measure of arc BC.
Then, to find the measure of arc CA, use the diameter of the circle, which is segment AB. Segment AB is equal to 180 degrees, which makes arc AB equal to 180 degrees. Also known is the measure of arc BC, which is 15 degrees. To find the measure of arc CA, subtract the measure of arc BC from the measure of arc AB, and the answer will be 165 degrees.
This looks like 180 degrees - 15 degrees = 165 degrees.
To check if the arc measures are correct, add all the arc measures together. If they sum up to 360 degrees, then the measure of each arc is correct.
Answer:
h≈6.93 units
Step-by-step explanation:
To find the height of a cone with radius 2 units and volume of 29 cubic unit, we will follow the steps below;
first, write down the formula for finding the volume of a cone;
v=πr²
where v is the volume of the cone
r is the radius of the cone and
h is the height of the cone
From the question given, radius r = 2 units and volume v = 29 units³
π = 3.14
We can now proceed to insert the values into the formula and then solve for h
v=πr²
29 = 3.14 × 2² × 
29= 3.14 × 4 × 
29= 12.56 × 
29 =
Multiply both-side of the equation by 3
29 × 3 =
× 3
At the right-hand side of the equation 3 will cancel-out 3
87 = 12.56 h
Divide both-side of the equation by 12.56
87/12.56 = 12.56 h /12.56
At the right-hand side of the equation 12.56 will cancel-out 12.56 leaving us with just h while on the left-hand side of the equation 87 will be divided by 12.56
6.926756 = h
h = 6.926756
h≈ 6.93 to the nearest hundredth
h≈6.93 units
The area of a rhombus is half the product of its diagonals, so the missing diagonal is equal to (2*840)/40 = 42.
we also know that the 2 diagonals bisect the rhombus into 4 identical right triangles.
the legs of the right triangle are equal to half of the diagonals, which in this case are 20 and 21(40/2 & 42/2)
then we can use the Pythagorean theorem to solve for the side length, and get 29 :)
Answer:
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials?
2.45 standard deviations above the mean is Z = 2.45, so this probability is the p-value of Z = 2.45.
Looking at the z-table, Z = 2.45 has a p-value of 0.9929.
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Answer:
3.75=b
Step-by-step explanation: