Answer:
Step-by-step explanation:
Given: The radius of circle O is r, and the radius of circle X is r'.
To prove: Circle O is similar to circle X.
Proof: Move the center of the smaller circle onto the center of the largest circle. Translate the circle X by the vector XA onto circle O. The circles now have the same center.
A dilation is needed to increase the size of circle X to coincide with the circle O. A value which when multiplied by r' will create r.
The scale factor x to increase X:
⇒
A translation followed by a dilation with scale factor will map one circle to the other, thus proving the given both circles similar.
Therefore, circle O is similar to circle X.
Step-by-step explanation:
Answer:
There is not sufficient evidence to support the claim.
Step-by-step explanation:
The claim to be tested is:
The mean respiration rate (in breaths per minute) of students in a large statistics class is less than 32.
To test this claim the hypothesis can be defined as follows:
<em>H₀</em>: The mean respiration rate of students is 32, i.e. <em>μ</em> = 32.
<em>Hₐ</em>: The mean respiration rate of students is less than 32, i.e. <em>μ</em> < 32.
The sample mean respiration rate of students is 31.3.
According to the claim the sample mean is less than 32.
The sample mean value is not unusual if the claim is true, and the sample mean value is also not unusual if the claim is false.
Thus, there is not sufficient evidence to support the claim.
Answer:
(2√5)/5
Explanation:
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION
From the question we can deduced that the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance, we can say that the y-coordinate, is twice of the horizontal, then let call the horizontal "y", the vertical would be 2y.
from the attachment the question on the unit circle is interpreted using a figure,then, hypotenuse was first calculated
Answer:
225.78 grams
Step-by-step explanation:
To solve this question, we would be using the formula
P(t) = Po × 2^t/n
Where P(t) = Remaining amount after r hours
Po = Initial amount
t = Time
In the question,
Where P(t) = Remaining amount after r hours = unknown
Po = Initial amount = 537
t = Time = 10 days
P(t) = 537 × 2^(10/)
P(t) = 225.78 grams
Therefore, the amount of iodine-131 left after 10 days = 225.78 grams
1/3 + 2/9 equals 3/9
3/9 is then simplified to 1/3 :)
