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White raven [17]
4 years ago
6

A stack of one hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 3 8 38 inches. how thic

k is one card?
Mathematics
1 answer:
sp2606 [1]4 years ago
3 0

Total number of cards in the stack =180

Height of stack (all cards) = 38 inches

Now, we know that the thickness of 180 cards is 38 inches,

now the thickness of one card can be obtained by dividing the total thickness by the number of cards

Thickness of 1 card = Total thickness of all cards/ total number of cards

Thickness of 1 card = 38 inches/180 = 0.211111.....inches

Each card is 0.21 inch thick (rounded to two decimals)

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Answer:

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We have the function

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1. For f^-1:

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Switch x and y to get:

x=(y+6)^3

And solve for y

\begin{gathered} x^{\frac{1}{3}}=y+6 \\ x^{\frac{1}{3}}-6=y+6-6 \\ x^{\frac{1}{3}}-6=y \end{gathered}

And we have y = f^-1(x)

Answer blank 1:

f^{-1}(x)=x^{\frac{1}{3}}-6

2. For f o f^-1 (x):

(f\circ f^{-1})(x)=f(f^{-1}(x))

And solve

\begin{gathered} =f(x^{\frac{1}{3}}-6) \\ =(x^{\frac{1}{3}}-6+6)^3 \\ =(x^{\frac{1}{3}})^3 \\ =x \end{gathered}

answer blank 2

x^{\frac{1}{3}}-6

answer blank 3

x^{\frac{1}{3}}-6

answer blank 4

x^{\frac{1}{3}}

3. For f^-1 o f:

(f^{-1}\circ f)(x)=f^{-1}(f(x))

Solve

\begin{gathered} =f^{-1}((x+6)^3) \\ =\sqrt[3]{(x+6)^3}-6 \\ =x+6-6 \\ =x \end{gathered}

answer blank 5

(x+6)^3

answer blank 6

(x+6)^3

answer blank 7

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4 0
1 year ago
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This means they are congruent. Each triangle would have the same two side lengths making the hypotenuse the same.

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Answer:

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Step-by-step explanation:

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