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saveliy_v [14]
3 years ago
7

On each of five slips of paper, you wrote the words eggs, waffles, pancakes, fruit, and muffin. Every day, you choose one slip f

rom a jar to help you decide what to eat for breakfast. You always put the chosen slip back into the jar. What is the probability of choosing eggs?
Mathematics
2 answers:
AnnyKZ [126]3 years ago
7 0

Answer:

20%

Step-by-step explanation:

There are 5 choices and eggs are one of them. Which is 1/5 and equal to 20%

Luda [366]3 years ago
6 0
The answer is 1/5, or 0.2, because if you're always putting the slip back in, then there will always by 5 slips to choose from, therefore making the probability 1 out of 5. I hope this helps!
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the volume of a cylinder is given by the formula v=3.14r^2h, where r is the radius of the cylinder and h is the height. suppose
photoshop1234 [79]

we know that

The volume of a cylinder is given by the formula

V=3.14 r^{2} h

where

r is the radius of the cylinder

h is the height of the cylinder

in this problem

r=x+8\\h=2x+3

Substitute the values in the formula above

V=3.14*(x+8)^{2}*(2x+3)

V=3.14*(x^{2}+16x+64)*(2x+3) \\ V=3.14 *(2x^{3} +3x^{2} +32x^{2} +48x+128x+192)\\ V=3.14*(2x^{3} +35x^{2} +176x+192)

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<u>the answer is</u>

The volume of the can is equal to

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3 years ago
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y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence
sukhopar [10]

Let

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots

Differentiating twice gives

\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots

\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0

\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0

Then the coefficients in the power series solution are governed by the recurrence relation,

\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

k=0 \implies n=0 \implies a_0 = a_0

k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}

k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}

k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}

It should be easy enough to see that

a_{n=2k} = \dfrac{a_0}{(2k)!}

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

k = 0 \implies n=1 \implies a_1 = a_1

k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}

k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}

k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}

so that

a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}

So, the overall series solution is

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)

\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}

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3 years ago
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U^2(2u+3)+7(2u+3)

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vitfil [10]

Answer:

20

Step-by-step explanation:

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