Determine whether the random variable is discrete or continuous.

1 answer:

Pie4 years ago

3 0

If we count a quantity, it's discrete.
If we measure a quantity, its continuous.
The number of people in a crowd is discrete. So are the # of game points scored.
Since every dimension of a house is a continuous random variable, the square footage is also.
See whether you can now identify which of the above choices is discrete and which is continuous.

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Approximate the sum of the convergent infinite series the least usingnumber of terms so that the error is less than .0001. What

____ [38]

Solution :

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ $a_n= \frac{(-1)^n}{n ! 2^n} \ \ \ \ \ a_{n+1}= \frac{(-1)^{n+1}}{(n+1) ! 2^{n+1}}$

Error = $|a_{n+1}|$

Error ≤ 0.0001

$|\frac{(-1)^{n+1}}{(n+1)!2^{n+1}}| \leq 0.0001$

$|\frac{1}{(n+1)!2^{n+1}}| \leq 10^{-4}$

$(n+1)! 2^{n+1} \geq 10000$

Now try, n ≥ 5

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = $\sum_{n=1 }^{5 } \frac{(-1)^n}{n ! 2^n}$ (with error 0.0001)

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = $\frac{-1}{1!2}+\frac{1}{2!2^2}-\frac{1}{3! 2^3}+\frac{1}{4! 2^4}-\frac{1}{5! 2^5}$

$\sum_{n=1 }^{\infty } \frac{(-1)^n}{n ! 2^n}$ = 0.6065104

3 0

3 years ago

. Karen is building a model of the Lincoln Memorial for her History class. She found online that the building measures 204 feet

nignag [31]

Answer:

3 square feet

Step-by-step explanation:

The area of the base can be calculated as

$A_{base}=\text{width}\cdot \text{length}.$

The building measures 204 feet long and 134 feet wide. Since the model has to be 1/100 of the original, then the width is $204\cdot \dfrac{1}{100}=2.04$ ft and the length is $134\cdot \dfrac{1}{100}=1.34$ ft.