Answer:
<h2>The distance from the pitcher's mound and to second base is 37.99 approximately.</h2>
Step-by-step explanation:
The diamond is a square, which in this case has 50 feet long each side, and from home to pitcher is 38 feet. Notice that home is a vertex of the square and the pitcher's mound is the intersection of the diagonals, where they cut half.
We can find the distance from the pitcher to first base using Pythagorean's Theorem, where 50 feet is the hypothenuse.
Therefore, the distance from the pitcher to first base is 32.5 feet, approximately.
Now, we can use again Pythagorean's Theorem to find the distance from pitcher to second base, where the hypothenuse is 50 feet.
Therefore, the distance from the pitcher's mound and to second base is 37.99 approximately.
<em>(this results make sense, because the diagonals of a square intersect at half, that means all bases have the same distance from pitcher's mound, so the second way to find the distance asked in the question is just using theory)</em>
If one serving takes 3/8 of a cup and she wants two servings, just multiply 3/8 by 2.
2 * (3/8) = 6/8 or 3/4 of a cup.
Answer:
The maximum revenue is $900, obtained with 30 people
Step-by-step explanation:
Naturally, the answer should be a number equal or higher than 20, because up to 20 persons, each one pays the same. Lets define a revenue function for x greater than or equal to 20.
f(x) = x*(40-(x-20)) = -x²+60x
Note that f multiplies the number of persons by how much would they pay (here, assuming that there are more than 20).
f is quadratic with negative main coefficient and its maximum value will be reached at the vertex.
The value of the x coordinate of the vertex is -b/2a = -60/-2 = 30
for x = 30, f(x) = 30*(40-(30-20))=30*30=900
So the maximum revenue is $900.
The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.
<h3>What is the nth term of an arithmetic series?</h3>
The nth term of an arithmetic sequence is calculated by the formula
aₙ = a + (n - 1) · d
Here the first term is 'a' and the common difference is 'd'.
<h3>Calculation:</h3>
The given sequence is an arithmetic sequence.
3, 7, 11, 15, 19, ....
So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.
Thus, the required 21st term in the sequence is
a₂₁ = 3 + (21 - 1) × 4
⇒ a₂₁ = 3 + 20 × 4
⇒ a₂₁ = 3 + 80
∴ a₂₁ = 83
So, the 21st term in the given arithmetic sequence is 83.
Learn more about the arithmetic sequence here:
brainly.com/question/6561461
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Answer:
20cm or A
Step-by-step explanation:
pythagorean theorem
25^2=15^2+b^2
625=225+b^2
b^2=400
b=20
