Answer:
495 combinations of 4 students can be selected.
Step-by-step explanation:
The order of the students in the sample is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
How many combination of random samples of 4 students can be selected?
4 from a set of 12. So
495 combinations of 4 students can be selected.
• The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.
• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.
• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.
• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.
• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.
1. TRUE
2. False
3. TRUE
4. False
5. False
The simplified expressions are 2^-2 and 60^6
<h3>How to simplify the expressions?</h3>
<u>Expression (a)</u>
We have:
2^3 * 2^-5
Apply the product law of indices
2^3 * 2^-5 = 2^(3 - 5)
Evaluate the difference
2^3 * 2^-5 = 2^-2
<u>Expression (b)</u>
We have:
(60^2)^3
Apply the power law of indices
(60^2)^3 = 60^(2 * 3)
Evaluate the product
(60^2)^3 = 60^6
Hence, the simplified expressions are 2^-2 and 60^6
Read more about expressions at:
brainly.com/question/723406
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Put the first equation in slope-intercept form, or y = mx + b. Start by subtracting y from both sides.
2x - y = -10, subtract 2x from both sides.
-y = -10 - 2x
Divide both sides by negative one.
y = 10 + 2x
To find the slope when the equations are in slope-intercept form you look at the coefficient of x. The first equation has the slope of 2 (which we just found), and the second equation has the slope of -2.
Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.
