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inysia [295]
3 years ago
10

A pendulum hangs from a clock and swings over its base.

Mathematics
1 answer:
seraphim [82]3 years ago
5 0

Answer:

4.2

Step-by-step explanation:

Given the distance between the pendulum and the base of the

clock, f(x), over the horizontal distance, x, modeled by

the function shown.

f(x) = 0.25x² – 2x + 10

In order to get the minimum distance between the pendulum and the base of the clock, first, we need to find the turning point of the function.

At turning point, d{f(x)}/dx = 0

d{f(x)}/dx = 0.5x-2 = 0

0.5x = 2

x = 2/0.5

x = 4

Then we will substitute x = 4 into the function as shown;

f(4) = 0.25(4)²-2(0.4)+10

f(4) = 4-9.8+10

f(4) = 4.2

The minimum distance between the pendulum and the base of the clock is 4.2

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The length of a rectangle is 2 meters less than 2 times the width. The perimeter is 20 meters. Find the width.
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2 years ago
20. Based on student records, 25% of the students at a large high school have a
Elenna [48]

Answer:

(E) 0.71

Step-by-step explanation:

Let's call A the event that a student has GPA of 3.5 or better, A' the event that a student has GPA lower than 3.5, B the event that a student is enrolled in at least one AP class and B' the event that a student is not taking any AP class.

So, the  probability that the student has a GPA lower than 3.5 and is not taking any AP  classes is calculated as:

P(A'∩B') = 1 - P(A∪B)

it means that the students that have a GPA lower than 3.5 and are not taking any AP  classes are the complement of the students that have a GPA of 3.5 of better or are enrolled in at least one AP class.

Therefore, P(A∪B) is equal to:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where the probability P(A) that a student has GPA of 3.5 or better is 0.25, the probability P(B) that a student is enrolled in at least one AP class is 0.16 and the probability P(A∩B) that a student has a GPA of 3.5 or better and is enrolled  in at least one AP class is 0.12

So, P(A∪B) is equal to:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.25 + 0.16 - 0.12

P(A∪B) = 0.29

Finally, P(A'∩B') is equal to:

P(A'∩B') = 1 - P(A∪B)

P(A'∩B') = 1 - 0.29

P(A'∩B') = 0.71

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3 years ago
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Answer:

Associative property: The addition or multiplication of a several numbers is the same regardless of how the numbers are grouped. The associative property will always involve 3 or more numbers. The parenthesis groups the terms that are considered one unit.

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