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3 years ago

celia made 3 1/2 cups of rice. A serving of rice is 2/3 cups. how many servings of rice did celia make?

Mathematics

1 answer:

Nonamiya [84]3 years ago

5 0

Answer:

E. 5 1/4

Step-by-step explanation:

Divide the total cups of rice(3 1/2) by a serving of rice (2/3)

This is my first answer!

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A function f is defined by f(x) = 1 + 6x + x2 + 6x3 + x4 + ⋯ that is, its coefficients are c2n = 1 and c2n + 1 = 6 for all n ≥ 0

Alenkinab [10]

From the odd-degree terms, take out one copy and rewrite the series as

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$1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)$

Then if |<em>x</em>| < 1, we can condense this to

$\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}$

Since the series we invoked here converge on -1 < <em>x</em> < 1, so does this one.

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3 years ago

The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x

grandymaker [24]

Solution :

Given :

$f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.$

1. Cumulative distribution function

$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$

$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx$

$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$

$=\frac{1}{450} \int_6^x (x^2-x) \ dx$

$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$

$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right]$

$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$

2. Mean $E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$

$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$

$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$

$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$

$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right)$

$=\frac{1}{450} [4608 - 252]$

= 17.2857

5 0

3 years ago