What is p(4,4) on two consecutive rolls of a number cube

1 answer:

6 0

The probability of rolling 1 number, a four, on a 6-sided number cube, is 1/6.
On the second roll, the probability of rolling 1 number, a four, is again 1/6 (remember theoretical probability for one event does not consider previous rolls).
But the probability of rolling a four on 2 on consecutive rolls will be the probability of the first event times the probability of the second event. Think of it as rolling a four on the first time <em>and</em> the second time, and whenever there is "and" you need to multiply the probabilities. The probability of rolling a four on two consecutive rolls is
(1/6)*(1/6) = 1/36.

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The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh

konstantin123 [22]

Answer:

33 copies were paperback and 12 were hardcover.

Step-by-step explanation:

Let h represent the number of hardcover copies and p represent the number of paperback copies.

We know that the total number of copies was 45; this gives us the equation

h+p = 45

We know that each hardcover copy is 7 ounces; this gives us the expression 7h.

We also know that each paperback copy is 5 ounces; this gives us the expression 5p.

We know that the total weight was 249 ounces; this gives us the equation

7h+5p = 249

Together we have the system

$\left \{ {{h+p=45} \atop {7h+5p=249}} \right.$

We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

$\left \{ {{5(h+p=45)} \atop {7h+5p=249}} \right. \\\\\left \{ {{5h+5p=225} \atop {7h+5p=249}} \right.$