the number of students in the art club is 3 more than twice the number of students in the drama clud.
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The question is incomplete. Here is the complete question.
To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?
A. The distance remains constant throughout the transformation.
B. The distance decreases at the start and increases after all motion stops.
C. The distance stays the same at the start but decreasesexactly when motion ends.
D. The distance increases at the start and then decreases as the rack gets further from the player.
Answer: A. The distance remains constant throughout the transformation.
Step-by-step explanation: In a <u>rigid</u> <u>motion</u>, all moving points in the plane are moving in way such tha:
1) relative distance between them stays the same and
2) relative position of the points stays the same
There are four types of rigid motions: translation, rotation, reflexion and glide reflection.
<u>Translation</u>: every point or object is moved by the same amount and in the same direction;
<u>Rotation</u>: the object rotates by the same amount around a fixed point;
<u>Reflexion</u>: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;
<u>Glide</u> <u>Reflection</u>: is a mirror reflection followed by a translation parallel to the mirror.
In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.
Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.
We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.
Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).
Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.
<h3>Confidence Interval Formula</h3>The formula for constructing a <u>confidence interval for means</u> is as follows:
We are given these variables:
Plug these values into the formula for the confidence interval:
In order to find t*, we can use this formula:
Calculating the z-score associated with "A" will give us t*.
So, let's plug in the confidence interval 95% (.95) into the formula:
Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:
Now, let's finish the confidence interval we created:
We can calculate the confidence interval, using this formula, to be:
We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.