Emily wins 22000$. She has to pay 10% for charity and then she decides to buy a car for 10800$. She divides the rest of them bet
1 answer:
Answer:
$7 200
Step-by-step explanation:
Amount of money paid for charity = × $22 000
= $2 200
Remaining money left for children = $22 000 - $2 200 - $10 800
= $9000
Let the amount of money her son receives be x and the amount her daughter gets be 4x.
Son's $ + Daughter's $ = $9000
x + 4x = 9000
5x = 9000
Amount of money her daughter gets (4x) = × 9000
= $7 200
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Answer:
We have to prove that,
|P(A)| = , if |A| = n for n = 0, 1, 2, 3.
For n = 0,
A = {}
P(A) = { {} } = = 1
For n = 1,
A = { a } ( suppose )
P(A) = { {}, a } = = 2,
For n = 2,
A = { a, b }
P(A) = { {}, {a}, {b}, {a, b} = = 4,
For n = 3,
A = { a, b, c },
P(A) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} } = = 8
Thus, it is verified for n = 0, 1, 2, 3.
Now, suppose it is valid for a set B having k elements,
That is, |P(B)| =
Also, there is a set A,
Such that, A = B ∪ {x}
Since, after including the element x in set B,
The element x will be come with every element of set B in the power set of B,
i.e. P(A) = =
=
=
Hence, by the induction it has been proved,
|P(A)| = , if |A| = n, Where, n∈ N ( set of natural numbers )
Answer:
The apothem of the Pentagon is about <u>12.9</u> inches long. The area of a regular pentagon is equal to its perimeter times its apothem divided by <u>2</u>. Therefore, the perimeter of the Pentagon on the map is about <u>94.4</u> inches. So, each side is about <u>18.9</u> inches long on the map.
Step-by-step explanation:
We know that this pentagon is a regular polygon, meaning we can divide this pentagon into five equal triangles. In order to find the length of the apothem, we need to find half the measure of the central angle of those triangles. Dividing 360° by 5, we get 72°. Next, divide 72° by 2 to get half the measure of the central angle, which is 36°. Then, we do: cos(36°) = or taking cos(36°) and multiplying it with 16, which equals 12.94427.
The formula to find the area of this polygon is: <em>A</em> = . This means the area of the polygon equals the apothem times its perimeter divided by 2. Using this formula, we can replace the variable with what we already know to solve for the perimeter.
608.7 = ← Multiply both sides of the equation by its reciprocal
<em>p</em> = 608.7 × ← Calculate 608.7 ×
<em>p</em> = ≈ 94.73209
Because we know the perimeter is about 94.4 inches, we can divide that by 5 to find the length of the sides of the pentagon.
94.4 ÷ 5 = 18.88
Rounding 18.88 to the nearest tenths, is 18.9 inches.
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