In the figure below, the segment that appears to be tangent to the circle is tangent to the circle. Which of the following is th
e length of the diameter of the circle to the nearest tenth of a unit?
A. 41.7
B. 26.7
C.16.0
D. 9.0
A. 41.7
B. 26.7
C.16.0
D. 9.0
1 answer:
Answer:
Step-by-step explanation:
Check attachment for diagram,
Since line AB is tangent to the circle then, <OAB is a right angle,
Then, we can apply Pythagoras theorem to the right angle triangle,
NOTE: from the centre of the circle to the tangent point at A is the radius of the circle,
And also, the total length of OB is
OB = r + 15
Then, applying Pythagorean theorem
OB² = OA² + AB²
(r+15)² = r² + 25²
(r+15)(r+15) = r² + 625
r² + 15r + 15r + 225 = r² + 625
Collect like terms
r² + 30r - r² = 625 - 225
30r = 400
Divide both sides by 30
r = 400 / 30
r = 13.33
So, the diameter of the circle is related to the radius by the relation
Diameter = 2 × radius
d = 2 × r
d = 2 × 13.33
d = 26.67
To the nearest tenth implies that to 1d•p
d ≈ 26.7
So, the diameter of the circle is 26.7
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Answer:
The simplified form is
Step-by-step explanation:
To simplify the expression given to use, we need to reduce the given expression in its simplest form. There should not be any possibility for the further cancelling out of the division terms, if any.
Now the expression that is given to us is:
Here we will simplify it, as follows:
So this is the required simplified form.
Answer:
Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.
Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.
Step-by-step explanation:
We are given the following hypothesis below;
Let p = <u><em>proportion of people who write with their left hand</em></u>
So, Null Hypothesis, : p = 0.22 {means that the proportion of people who write with their left hand is equal to 0.22}
Alternate Hypothesis, : p
0.22 {means that the proportion of people who write with their left hand is different from 0.22}
Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.
So, in our question; Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.
Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.
So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.