Using the Fundamental Counting Theorem, it is found that there are 1000 possible numbers that Lina could pick.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
In this problem:
- The number is more than 5000, hence the first digit can be 5, 6, 7, 8 or 9, hence .
- The second digit is prime, that is, 2, 3, 5 or 7, hence .
- For the third digit, there are no restrictions, hence .
- The number is odd, hence the fourth digit can be 1, 3, 5, 7 or 9, hence .
Hence the number of combinations is given by:
N = 5 x 4 x 10 x 5 = 1000
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
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Answer:
[1, 1]
Step-by-step explanation:
Translation → [-1, 3] moves down to [-1, 1]
Now, a <em>90°-clockwise rotation </em>is the exact same as a <em>270</em><em>°</em><em>-</em><em>counterclockwise</em><em> </em><em>rotation,</em><em> </em>and according to the <em>270°-counterclockwise </em><em>rotation</em><em> </em>[<em>90°-clockwise rotation</em>] rule, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:
<u>Extended Rotation Rules</u>
- 270°-clockwise rotation [90°-counterclockwise rotation] >> (<em>x</em><em>,</em><em> </em><em>y</em>)<em> </em>→<em> </em>(<em>-</em><em>y</em><em>,</em><em> x</em>)
- 270°-counterclockwise rotation [90°-clockwise rotation] >> (<em>x</em><em>,</em><em> </em><em>y</em>) → (<em>y</em><em>,</em><em> </em><em>-</em><em>x</em>)
- 180°-rotation >> (<em>x, y</em>) → (<em>-</em><em>x</em><em>,</em><em> </em>-y)
Then, you perform your rotation:
270°-counterclockwise rotation [90°-clockwise rotation] → [-1, 1] moves to [1, 1]
I am joyous to assist you anytime.
That is 77 to the power of twelve which is 77x77x77x77x77x77x77x77x77x77x77x77.
Answer:43439888521963583647921
I^15 = -i
i^32 = 1
i^99 = -i
i^22 = -1
9514 1404 393
Answer:
45 meters
Step-by-step explanation:
The equation is given in vertex form:
h(t) = a(t -b)^2 +c
where (b, c) is the vertex (maximum).
The values of the parameters are ...
a = -5, b = 3, c = 45
Then the maximum height is (time, height) = (3, 45).
The maximum height of the ball is 45 meters.